Gender differences in the distribution of children’s physical activity

Markdown Document for the purposes of Analysing ICAD 2.0 data using GAMLSS to explore the relative distribution of physical activity between genders.

This document was last edited on 2023-04-12 using R version 4.2.3

Working directory shall be on the university server throughout - both for access and data security.

1 Prepping the workspace

1.1 Load required packages Loading required packages. Code to install the packages is muted as is only needed on 1st instance

rm(list = ls())
x <- c("quantreg","gamlss","tidyr",
       "gtsummary","broom","broom.mixed",
       "ggplot2","dplyr","forcats",
       "foreign","tableone","kableExtra","psych",
       "trackdown","sjPlot","broom.mixed",
       "geomtextpath","ggpp", "gmodels",
       "cowplot","knitr")
#lapply(x, install.packages, character.only = TRUE)
lapply(x, require, character.only = TRUE)
rm(x)

2 Preparing the Data

2.1 Load the necessary dataframes into the workspace These lines are hidden but the command sequence is as follows:

setwd("") #Specifying where the raw CSV is located
icad <- read.csv("")
setwd("") #Resetting to main file location for this project. I'm using 2 different locations to ensure I don't write over the orignial files

Set all variable names to lower for easier use

names(icad) <- tolower(names(icad))

Next I subset the dataframe to the necessary variables using the subset command

icad<-subset(icad,select=c("icad_id",...))

2.2 Recoding Variables

Throughout there seems to be 83 NAs in the sample - with this present across all demographic data. As such, I am expecting 83 NAs in each demographic variable.

Check study $icad_study is set as.factor

class(icad$icad_study)
icad$icad_study <- as.integer(icad$icad_study)

Check $icad_country is set as.factor and/or rename to country name

class(icad$icad_country)
icad$icad_country <- as.integer(icad$icad_country)
summary(icad$icad_country)#TO check spread and ensure that there are no NAs

#Recoding to country names for ease of comprehension
icad$country <- as.factor(ifelse(icad$icad_country==1,"uk",
                       ifelse(icad$icad_country=="2","switzerland",
                              ifelse(icad$icad_country=="4","usa",
                                     ifelse(icad$icad_country=="5","australia",
                                            ifelse(icad$icad_country=="6","denmark",
                                                   ifelse(icad$icad_country=="7","estonia",
                                                          ifelse(icad$icad_country=="8","norway",
                                                                 ifelse(icad$icad_country=="9","portugal",
                                                                        ifelse(icad$icad_country=="10","brazil",NA))))))))))

This leaves a sample of 20076 from 9 countries

	# of Individuals
australia	2655
brazil	457
denmark	1814
estonia	662
norway	398
portugal	1256
switzerland	532
uk	6935
usa	5284
NA’s	83

Though it won’t be used in any analysis, I’m recoding the study design so that it is easier to interpret. Additionally, I can check that in longitudinal and interventional studies that I have only the 1st wave.

icad$icad_studydesign <- as.factor(ifelse(icad$icad_studydesign==0,"cross-sectional",
                                ifelse(icad$icad_studydesign==1,"longitudinal",
                                       ifelse(icad$icad_studydesign==2,"interventional",NA))))
summary(icad$icad_studydesign)

	# of Individuals
cross-sectional	5946
interventional	532
longitudinal	13515
NA’s	83

Recode $icad_sex so missing = NA, and that it is read as.factor

summary(icad$icad_sex)

icad$icad_sex <- as.factor(ifelse(icad$icad_sex==0,"male",
                        ifelse(icad$icad_sex==1,"female",
                               ifelse(icad$icad_sex==999,NA,NA))))

	# of Individuals
female	10293
male	9689
NA’s	94

Recode $icad_age so that missing = NA, ensure all other values are within the suitable range for a child (0-18)

summary(icad$icad_age) # NA coding for $icad_age is `999`

icad$icad_age <- ifelse(icad$icad_age==999,NA,icad$icad_age)

Create an age category variable to make sense of GAMLSS

icad$age_cat <- ifelse(icad$icad_age<5,"pre-school",
                       ifelse(icad$icad_age>=5&icad$icad_age<12,"child",
                              ifelse(icad$icad_age>=12,"teenage",NA)))

Recode $icad_ethnicity# to a consistent binary, ensure that coding is read as.factor

table(icad$icad_ethnicity1)
table(icad$icad_ethnicity2)
table(icad$icad_ethnicity3)
table(icad$icad_ethnicity4)

icad$ethnicity <- as.factor(ifelse(icad$icad_ethnicity1==0,"white",
                         ifelse(icad$icad_ethnicity1==1,"other",
                                ifelse(icad$icad_ethnicity2==0,"white",
                                       ifelse(icad$icad_ethnicity2>=1 & icad$icad_ethnicity2 <= 6,"other",
                                              ifelse(icad$icad_ethnicity3==0,"white",
                                                     ifelse(icad$icad_ethnicity3>=1 & icad$icad_ethnicity2 <= 6,"other",
                                                            ifelse(icad$icad_ethnicity4==1,"other",
                                                                  ifelse(icad$icad_ethnicity4==0,"white",NA)))))))))

summary(icad$ethnicity)

	# of Individuals
other	4417
white	9838
NA’s	5821

Recode $icad_mothereducation# to consistent minimum/Binary, recode missing to NA, ensure it is read as an ordered factor (as.factor(,levels=c()))

table(icad$icad_mothereducation1)
table(icad$icad_mothereducation2)

icad$mothereducation <- as.factor(ifelse(icad$icad_mothereducation1==0,0,
                                        ifelse(icad$icad_mothereducation1==1,1,
                                               ifelse(icad$icad_mothereducation2==0,0,
                                                      ifelse(icad$icad_mothereducation1==1,1,
                                                             ifelse(icad$icad_mothereducation1==2,1,
                                                                    ifelse(icad$icad_mothereducation1==999,NA,
                                                                           ifelse(icad$icad_mothereducation2==999,NA,NA))))))))

summary(icad$mothereducation)

Table of Mother’s Education, 0 = Up to and inclusive of Compulsory Education, 1 = Beyond Compulsory School leaving Age

	# of Individuals
0	6736
1	9388
NA’s	3952

Recode $icad_fathereducation# to consistent minimum/Binary, recode missing to NA, ensure it is read as an ordered factor (as.factor(,levels=c()))

table(icad$icad_fathereducation1)
table(icad$icad_fathereducation2)

icad$fathereducation <- as.factor(ifelse(icad$icad_fathereducation1==0,0,
                                        ifelse(icad$icad_fathereducation1==1,1,
                                               ifelse(icad$icad_fathereducation2==0,0,
                                                      ifelse(icad$icad_fathereducation1==1,1,
                                                             ifelse(icad$icad_fathereducation1==2,1,
                                                                    ifelse(icad$icad_fathereducation1==999,NA,
                                                                           ifelse(icad$icad_fathereducation2==999,NA,NA))))))))

summary(icad$fathereducation)

Table of Father’s Education, 0 = Up to and inclusive of Compulsory Education, 1 = Beyond Compulsory School leaving Age

	# of Individuals
0	5152
1	8007
NA’s	6917

Creating a measure of whether a parent had education beyond school leaving age (1= At least one parent had beyond school leaving age education, 0 = Neither parent)

icad$parenteducation <- ifelse(icad$mothereducation==1|icad$fathereducation==1,1,0)
icad$parenteducation <- ifelse(icad$mothereducation==0 & is.na(icad$fathereducation),0,icad$parenteducation)
d <- summary(icad$parenteducation)
#kbl(d,col.names=c("# of Individuals"),caption = "Table of Parental Education, 0 = Up to and inclusive of #Compulsory Education, 1 = Beyond Compulsory School leaving Age") %>% 
#  kable_styling(bootstrap_options = c("hover", "condensed", "responsive", "striped"))
rm(d)

Recode $icad_height so that it is read as numeric and and missing is read as NA

class(icad$icad_height) #No need to change class as it is already being read as numeric

## [1] "numeric"

summary(icad$icad_height) #Max height is realistic (204cm) so no need to recode

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##    99.6   140.4   150.0   149.6   159.9   204.4     285

d<- summary(tibble(icad$icad_height))
kbl(d,col.names=c("Height Summary"),caption = "Table of Fsummary statistics for particpant heights") %>% 
  kable_styling(bootstrap_options = c("hover", "condensed", "responsive", "striped"),full_width = FALSE)

Table of Fsummary statistics for particpant heights

	Height Summary
	Min. : 99.6
	1st Qu.:140.4
	Median :150.0
	Mean :149.6
	3rd Qu.:159.9
	Max. :204.4
	NA’s :285

Recode $icad_weight so that it is read as numeric and and missing is read as NA

class(icad$icad_weight) #No need to change class as it is already being read as numeric

## [1] "numeric"

summary(icad$icad_weight) 

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   13.40   33.60   42.60   45.56   54.80  215.30     282

d<- summary(tibble(icad$icad_weight))
kbl(d,col.names=c("Weight Summary"),caption = "Table of summary statistics for particpant weights") %>% 
  kable_styling(bootstrap_options = c("hover", "condensed", "responsive", "striped"),full_width = FALSE)

Table of summary statistics for particpant weights

	Weight Summary
	Min. : 13.40
	1st Qu.: 33.60
	Median : 42.60
	Mean : 45.56
	3rd Qu.: 54.80
	Max. :215.30
	NA’s :282

From $height and $weight I’m creating a measure of body mass index ($bmi) using the formula of BMI = Weight(kg) / Height (m) ²

icad$bmi <- ifelse(is.na(icad$icad_height)|is.na(icad$icad_weight),NA,(icad$icad_weight/(icad$icad_height/100)^2))
d <- summary(tibble(icad$bmi))
kbl(d,col.names=c("BMI Summary"),caption = "Table of summary statistics for particpant BMIs") %>% 
  kable_styling(bootstrap_options = c("hover", "condensed", "responsive", "striped"),full_width = FALSE)

Table of summary statistics for particpant BMIs

	BMI Summary
	Min. : 9.614
	1st Qu.:16.638
	Median :18.695
	Mean :19.731
	3rd Qu.:21.629
	Max. :62.734
	NA’s :296

As the distribution of BMI changes with age I’m creating a z score of BMI grouped by age and gender. I’m using this instead of an unstandardised measure of BMI as ‘healthy’ BMI changes with age - i.e. and individual with a BMI of 20 at age 7 should not be interpreted in a similar way to an individual with a BMI of 20 at age 17

icad$age_rounded <- ceiling(icad$icad_age)

icad <- icad %>% 
  group_by(icad_sex, age_rounded) %>% 
  mutate(bmi_z = scale(bmi))

Create a measure of the season in which recording happened - factoring in north/south hemisphere divide

icad$headerstartmonth <- as.factor(icad$headerstartmonth)
icad$season <- as.factor(ifelse(icad$country=="australia"|icad$country=="brazil",ifelse(icad$headerstartmonth=="December"|icad$headerstartmonth=="January"|icad$headerstartmonth=="February","summer",ifelse(icad$headerstartmonth=="March"|icad$headerstartmonth=="April"|icad$headerstartmonth=="May","autumn",ifelse(icad$headerstartmonth=="June"|icad$headerstartmonth=="July"|icad$headerstartmonth=="August","winter",ifelse(icad$headerstartmonth=="September"|icad$headerstartmonth=="October"|icad$headerstartmonth=="November","spring",NA)))),ifelse(icad$country!="australia"|icad$country!="brazil",ifelse(icad$headerstartmonth=="December"|icad$headerstartmonth=="January"|icad$headerstartmonth=="February","winter",ifelse(icad$headerstartmonth=="March"|icad$headerstartmonth=="April"|icad$headerstartmonth=="May","spring",ifelse(icad$headerstartmonth=="June"|icad$headerstartmonth=="July"|icad$headerstartmonth=="August","summer",ifelse(icad$headerstartmonth=="September"|icad$headerstartmonth=="October"|icad$headerstartmonth=="November","autumn",NA)))))))

icad$season <- ordered(icad$season, levels = c("spring", "summer", "autumn","winter"))

d<- summary(icad$season)
kbl(d,caption = "Summary Table of Seasonality") %>% 
  kable_styling(bootstrap_options = c("hover", "condensed", "responsive", "striped"),full_width = FALSE)

Summary Table of Seasonality

	x
spring	5083
summer	2862
autumn	3014
winter	9034
NA’s	83

x <- CrossTable(icad$country, icad$season, digits = 2,expected = FALSE, prop.r = T, prop.c=F,prop.t=F,prop.chisq = F)

## 
##  
##    Cell Contents
## |-------------------------|
## |                       N |
## |           N / Row Total |
## |-------------------------|
## 
##  
## Total Observations in Table:  19993 
## 
##  
##              | icad$season 
## icad$country |    spring |    summer |    autumn |    winter | Row Total | 
## -------------|-----------|-----------|-----------|-----------|-----------|
##    australia |      1129 |       264 |       296 |       966 |      2655 | 
##              |      0.43 |      0.10 |      0.11 |      0.36 |      0.13 | 
## -------------|-----------|-----------|-----------|-----------|-----------|
##       brazil |       264 |       149 |         0 |        44 |       457 | 
##              |      0.58 |      0.33 |      0.00 |      0.10 |      0.02 | 
## -------------|-----------|-----------|-----------|-----------|-----------|
##      denmark |       648 |        18 |       534 |       614 |      1814 | 
##              |      0.36 |      0.01 |      0.29 |      0.34 |      0.09 | 
## -------------|-----------|-----------|-----------|-----------|-----------|
##      estonia |       251 |         5 |       251 |       155 |       662 | 
##              |      0.38 |      0.01 |      0.38 |      0.23 |      0.03 | 
## -------------|-----------|-----------|-----------|-----------|-----------|
##       norway |       201 |        32 |        67 |        98 |       398 | 
##              |      0.51 |      0.08 |      0.17 |      0.25 |      0.02 | 
## -------------|-----------|-----------|-----------|-----------|-----------|
##     portugal |       617 |       206 |         0 |       433 |      1256 | 
##              |      0.49 |      0.16 |      0.00 |      0.34 |      0.06 | 
## -------------|-----------|-----------|-----------|-----------|-----------|
##  switzerland |        40 |       267 |       225 |         0 |       532 | 
##              |      0.08 |      0.50 |      0.42 |      0.00 |      0.03 | 
## -------------|-----------|-----------|-----------|-----------|-----------|
##           uk |      1933 |      1921 |      1641 |      1440 |      6935 | 
##              |      0.28 |      0.28 |      0.24 |      0.21 |      0.35 | 
## -------------|-----------|-----------|-----------|-----------|-----------|
##          usa |         0 |         0 |         0 |      5284 |      5284 | 
##              |      0.00 |      0.00 |      0.00 |      1.00 |      0.26 | 
## -------------|-----------|-----------|-----------|-----------|-----------|
## Column Total |      5083 |      2862 |      3014 |      9034 |     19993 | 
## -------------|-----------|-----------|-----------|-----------|-----------|
## 
## 

kbl(x,caption = "Cross Table of Seasonality") %>% 
  kable_styling(bootstrap_options = c("hover", "condensed", "responsive", "striped"),full_width = FALSE)

Cross Table of Seasonality

spring summer autumn winter australia 1129 264 296 966 brazil 264 149 0 44 denmark 648 18 534 614 estonia 251 5 251 155 norway 201 32 67 98 portugal 617 206 0 433 switzerland 40 267 225 0 uk 1933 1921 1641 1440 usa 0 0 0 5284

spring summer autumn winter australia 0.4252354 0.0994350 0.1114878 0.3638418 brazil 0.5776805 0.3260394 0.0000000 0.0962801 denmark 0.3572216 0.0099228 0.2943771 0.3384785 estonia 0.3791541 0.0075529 0.3791541 0.2341390 norway 0.5050251 0.0804020 0.1683417 0.2462312 portugal 0.4912420 0.1640127 0.0000000 0.3447452 switzerland 0.0751880 0.5018797 0.4229323 0.0000000 uk 0.2787311 0.2770007 0.2366258 0.2076424 usa 0.0000000 0.0000000 0.0000000 1.0000000

spring summer autumn winter australia 0.2221129 0.0922432 0.0982084 0.1069294 brazil 0.0519378 0.0520615 0.0000000 0.0048705 denmark 0.1274838 0.0062893 0.1771732 0.0679655 estonia 0.0493803 0.0017470 0.0832780 0.0171574 norway 0.0395436 0.0111810 0.0222296 0.0108479 portugal 0.1213850 0.0719776 0.0000000 0.0479300 switzerland 0.0078694 0.0932914 0.0746516 0.0000000 uk 0.3802872 0.6712089 0.5444592 0.1593978 usa 0.0000000 0.0000000 0.0000000 0.5849015

spring summer autumn winter australia 0.0564698 0.0132046 0.0148052 0.0483169 brazil 0.0132046 0.0074526 0.0000000 0.0022008 denmark 0.0324113 0.0009003 0.0267093 0.0307107 estonia 0.0125544 0.0002501 0.0125544 0.0077527 norway 0.0100535 0.0016006 0.0033512 0.0049017 portugal 0.0308608 0.0103036 0.0000000 0.0216576 switzerland 0.0020007 0.0133547 0.0112539 0.0000000 uk 0.0966838 0.0960836 0.0820787 0.0720252 usa 0.0000000 0.0000000 0.0000000 0.2642925

2.2.1 Check for Missingness

icad_na_map <- subset(icad,select=c("icad_studydesign","country","ethnicity","mothereducation",
                                    "fathereducation","icad_height","icad_weight","icad_sex"))
d<- icad_na_map %>% 
  summarise_all(~sum(is.na(.)))

kable(d,caption = "Summary of missingness by demographic variable",col.names=c("Study Design","Country","Ethnicity", "Mother's Education","Father's Education","Height","Weight","Sex"))%>% 
  kable_styling(bootstrap_options = c("hover", "condensed", "responsive", "striped"))

Summary of missingness by demographic variable

Study Design	Country	Ethnicity	Mother’s Education	Father’s Education	Height	Weight	Sex
female	0	0	3013	1955	3512	104	104
male	0	0	2714	1906	3314	92	89
NA	83	83	94	91	91	89	89

rm(d)
rm(icad_na_map)

2.3 Cleaning Activity Data

Theres a large array of variables that constitute the activity measures, which could prove confusing - as such, select variables are going to be recoded and renamed to aid analysis later. No variable will be deleted.

2.3.1 Creating a count per minute (cpm) measure from time device is worn

icad$cpm_wear <- icad$wearctsvaldystotperminute

d <- summary(tibble(icad$cpm_wear))

kable(d,col.names=c("CPM Summary"),caption = "Counts Per Minute (cpm) summary") %>% 
  kable_styling(bootstrap_options = c("hover", "condensed", "responsive", "striped"))

2.3.2 Creating a measure of mean wear time so that only individuals for a whom their measure represents a significnat portion of the wakeful day are included.

icad$weartime <- icad$wearminvaldystotperday

2.3.3 Defining time in each threshold using Evenson cutoffs

Evenson cut-offs in counts per minute are

Evenson Cut-offs

Sedentary	Light	Moderate	Vigorous	MVPA
<101	101 - <2296	2296 - <4012	4012<=	2296<=

icad$sedentary_evenson <- icad$evenson_sedminvaldystotperday #Sedentary
icad$light_evenson <- icad$evenson_lpaminvaldystotperday #Light 
icad$moderate_evenson <- icad$evenson_mpaminvaldystotperday #Moderate
icad$vigorous_evenson <- icad$evenson_vpaminvaldystotperday #Vigorous
icad$mvpa_evenson <- icad$evenson_mvpaminvaldystotperday #MVPA

2.3.4 Defining time in each threshold using Pate cutoffs

Pate Cut-offs

Sedentary	Light	Moderate	Vigorous	MVPA
<800	800 - <1680	1680 - <3368	3368<=	1680<=

icad$sedentary_pate <- icad$pate_sedminvaldystotperday #Sedentary
icad$light_pate <- icad$pate_lpaminvaldystotperday #Light 
icad$moderate_pate <- icad$pate_mpaminvaldystotperday #Moderate
icad$vigorous_pate <- icad$pate_vpaminvaldystotperday #Vigorous
icad$mvpa_pate <- icad$pate_mvpaminvaldystotperday #MVPA

Create Back-up containing all individuals for whom there is physical activity data (For use in sensitivity analyses)

write.csv(icad,"icad_cleaned_full.csv")

2.3.5 Exploring missingness within the dataframe and remove individuals with incomplete data in key fields

icad_na_map <- subset(icad,select=c("cpm_wear","sedentary_evenson","light_evenson","moderate_evenson","vigorous_evenson",
                                    "sedentary_pate","light_pate","moderate_pate","vigorous_pate"))
d<- icad_na_map %>% 
  summarise_all(~sum(is.na(.)))

kable(d,caption = "Summary of missingness by Physical Activity variable") %>%
  kable_styling(bootstrap_options = c("hover", "condensed", "responsive", "striped"))
rm(d)
rm(icad_na_map)

A total of 657 individuals do not have physical activity data. The following lines briefly explore who make up this group.

icad_pa_na = icad[is.na(icad$cpm_wear),]
icad_pa_na_map <- subset(icad_pa_na,select = c("icad_sex","icad_age","ethnicity","icad_height","icad_weight","icad_study","country"))

Summary of missing Physical Activity by Sex

Sex	Freq
female	300
male	333

There is a relatively even spread in missingness between the sexes with ~300 cases for each sex

Summary of missingness by Physical Activity and Age

	Summary of Age
	Min. : 5.153
	1st Qu.:11.190
	Median :13.804
	Mean :12.992
	3rd Qu.:15.583
	Max. :18.417
	NA’s :27

Individuals across the available age span have missing data, with the mean sitting near to the middle - median is slightly positively shifted in this group

Summary of missingness by Physical Activity and Country

Country	Freq
australia	53
brazil	1
denmark	73
estonia	2
norway	6
portugal	26
switzerland	16
uk	200
usa	258

Individuals are missing from all available countries, though not in equal proportions to the initial sample size, the two largest studies are contributing the largest amount to this missing group.

2.3.6 Subsetting to complete cases

missing_pa <- subset(icad,is.na(icad$cpm_wear))
icad <- subset(icad[!is.na(icad$cpm_wear),])

This leaves a sample of 19419

2.3.6.1 Beyond missing data, some individuals have very high mean cpm

	Counts Per Minute
	Min. : 1.07
	1st Qu.: 413.95
	Median : 546.43
	Mean : 726.27
	3rd Qu.: 706.40
	Max. :304474.97

hist(icad$cpm_wear,bins=seq(0,305000,5000))#Most individuals have values under 5000

length(icad$cpm_wear[icad$cpm_wear>5000])#111 are above 5000 cpm. Testing 5000 as 4000 is approximately lower limit for vigorous
icad_high_cpm <- subset(icad,icad$cpm_wear>5000)

Of the individuals who had very high cpm’s - all had a reliability flag ==1, indicating that the data is viewed as ‘spurious’. We have therefore subset the sample to individuals who do no have $reliability ==1 . Those that do are grouped into a new dataframe for use later in exploring missingness. Additionally, those who have been marked as spurious $reliability == 3 have been excluded, due to issues seen in later visual analysis, as have those that have been excluded from analysis by the EYHS study (Those in Norway, Portugal, Estonia and Denmark) $marked_invalid_bystudyt==1

reliability_flag <- subset(icad,icad$reliability==1)
icad <- subset(icad,!icad$reliability==1)
icad <- subset(icad,!icad$reliability==3)
icad <- subset(icad,!icad$marked_invalid_bystudyt==1)
icad_reliability <- subset(icad,icad$reliability>=1|icad$marked_invalid_bystudyt==1)

2.4 Next, missingness in demographic variables are explored

Summary of missingness by demographic variable

Study Design	Country	Ethnicity	Mother’s Education	Father’s Education	Height	Weight	Sex
female	0	0	2847	1839	3314	93	93
male	0	0	2559	1745	3091	87	83
NA	55	55	63	60	60	58	58

The minimum model will need sex and country, so the sample is being restricted to individuals with both sex and country specified. As before, those that are being removed for having NA in either $icad_sex or $country are placed in a new dataframe for use later.

country_missing <- subset(icad,is.na(icad$country))
icad <- subset(icad[!is.na(icad$country),])
sex_missing <- subset(icad,is.na(icad$icad_sex))
icad <- subset(icad[!is.na(icad$icad_sex),])

2.4.1 Create long form for use later

From the remaining individuals, long form datasets are made where each row is an intensity threshold for each person. This is done twice with both evenson and pate cut-points. The later is then subset and joined back to the original so that at each row of intensity and individual has a volume of time as measured by Evenson and Pate thresholds

# This is done twice over, once for Evenson, Once for Pate
columns_to_gather <- c("sedentary","light","moderate","vigorous")
icad_long_evenson <- icad_evenson_rename %>% gather(intensity,evenson_time,columns_to_gather)
icad_long_pate <- gather(icad_pate_rename,intensity,pate_time,columns_to_gather)
remove(columns_to_gather)

icad_long_pate <- subset(icad_long_pate,select=c("icad_id","intensity","pate_time"))

icad_long <- merge(icad_long_evenson,icad_long_pate,by = c("icad_id","intensity"))

2.4.2 Creating a data frame of excluded individuals so that there composition can be explored

Returning to those excluded from the final data frame, each group is given a $reason for exclusion, then bound to the other excluded dataframes to create one large set

missing_pa$reason <- "missing pa"
reliability_flag$reason <- "reliability score"
sex_missing$reason <- "no sex"
country_missing$reason <- "no country"

bind1 <- rbind(missing_pa,reliability_flag)
bind2 <- rbind(country_missing,sex_missing)
excluded_in_cleaning <- rbind(bind1,bind2)

This dataframe includes a total of 885 individuals who will not form part of the final analysis.

2.4.3 All Data Frames are then saved for later use

#write.csv(icad,"icad_cleaned.csv")
#write.csv(icad_long,"icad_long.csv")
#write.csv(excluded_in_cleaning,"excluded_in_cleaning")

2.4.4 Exploring demographics of excluded individuals

To finish, the excluded individuals are summarised in the below table using the tableone package. This table is stratified (strata) by sex, with categorical variables specified (factorVars)

library(tableone)
vars <- c("icad_age",
          "icad_height",
          "icad_weight",
          "ethnicity",
          "country",
          "mothereducation",
          "fathereducation",
          "reason",
          "cpm_wear")
strata <- "icad_sex"
factorVars <- c("icad_sex",
                "ethnicity",
                "country",
                "mothereducation",
                "fathereducation",
                "reason")
d <- CreateTableOne(vars = vars,strata = strata,factorVars = factorVars,data=excluded_in_cleaning,test = FALSE,addOverall = TRUE)
kableone(d,caption = "Summary Table of Exlcuded Individuals")%>% 
  kable_styling(bootstrap_options = c("hover", "condensed", "responsive", "striped")) %>% 
  add_indent(c(7,8,9,10,11,12,13,14,15,19,20,21))

Summary Table of Exlcuded Individuals

	Overall	female	male
n	885	380	411
icad_age (mean (SD))	12.77 (3.30)	12.70 (3.33)	12.83 (3.29)
icad_height (mean (SD))	154.03 (18.25)	150.96 (16.36)	156.78 (19.48)
icad_weight (mean (SD))	50.83 (19.93)	49.38 (19.58)	52.17 (20.29)
ethnicity = white (%)	287 (57.7)	130 (56.0)	157 (59.2)
country (%)
australia	93 (11.6)	53 (13.9)	40 ( 9.7)
brazil	1 ( 0.1)	1 ( 0.3)	0 ( 0.0)
denmark	85 (10.6)	43 (11.3)	42 (10.2)
estonia	2 ( 0.2)	1 ( 0.3)	1 ( 0.2)
norway	11 ( 1.4)	2 ( 0.5)	3 ( 0.7)
portugal	32 ( 4.0)	15 ( 3.9)	17 ( 4.1)
switzerland	32 ( 4.0)	17 ( 4.5)	15 ( 3.6)
uk	236 (29.4)	99 (26.1)	132 (32.1)
usa	310 (38.7)	149 (39.2)	161 (39.2)
mothereducation = 1 (%)	280 (52.4)	146 (54.1)	131 (50.2)
fathereducation = 1 (%)	231 (57.3)	125 (62.8)	103 (51.2)
reason (%)
missing pa	657 (74.2)	300 (78.9)	333 (81.0)
no country	55 ( 6.2)	0 ( 0.0)	0 ( 0.0)
no sex	8 ( 0.9)	0 ( 0.0)	0 ( 0.0)
reliability score	165 (18.6)	80 (21.1)	78 (19.0)
cpm_wear (mean (SD))	13513.98 (24193.73)	21453.10 (15574.56)	16913.01 (35328.10)

3 Data Analysis

3.1 Load the dataframes from the datacleaning process

icad <- read.csv("icad_cleaned.csv")
#icad_long <- read.csv("icad_long.csv")

3.1.1 Create Backups

3.1.2 Subsetting to key variables to reduce total workspace size and aid comprehension, full versions are kept in the backup

icad <- subset(icad,select=c("icad_id",...))

3.1.3 Check missingness -either by dataframe or by variable

As most of the NAs from the key variables should have be cleaned out by now, this table should just show missingness from other key variables.
Following cleaning, missingness should be restricted to ethnicity, parents education, height and weight as those with incomplete sex or country were removed during the cleaning process.

Summary of missingness by demographic variable

Study Design	Country	Ethnicity	Mother’s Education	Father’s Education	Height	Weight	Gender
0	0	5406	3584	6405	180	176	0

Previous cleaning restricted the sample to complete activity data - as such no entries should be expected in this table.

Summary of missingness by Physical Activity variable

cpm_wear	sedentary_evenson	light_evenson	moderate_evenson	vigorous_evenson
0	0	0	0	0

3.2 Descriptive Analysis

3.2.1 Summary of covariates

As before with the excluded individual, this table is constructed using tableone package passed through kable. This table is stratified (strata) by sex, with categorical variables specified (factorVars). In this table all physical activity measures are dropped, as such, the table only summarises demographic and anthropometric variables.

3.2.2 Tableone Stratified by Gender

Table One summary of complete dataframe by demographic data, stratified by Gender

	Overall	female	male
n	18980	9804	9176
icad_age (mean (SD))	11.80 (2.71)	11.78 (2.70)	11.82 (2.72)
icad_height (mean (SD))	149.43 (15.35)	148.46 (13.95)	150.46 (16.66)
icad_weight (mean (SD))	45.33 (16.79)	44.87 (15.58)	45.82 (17.98)
ethnicity = white (%)	9408 (69.3)	4882 (70.2)	4526 (68.4)
mothereducation = 1 (%)	9004 (58.5)	4708 (59.1)	4296 (57.8)
fathereducation = 1 (%)	7677 (61.0)	3982 (61.4)	3695 (60.7)
country (%)
australia	2542 (13.4)	1332 (13.6)	1210 (13.2)
brazil	456 ( 2.4)	218 ( 2.2)	238 ( 2.6)
denmark	1636 ( 8.6)	902 ( 9.2)	734 ( 8.0)
estonia	659 ( 3.5)	366 ( 3.7)	293 ( 3.2)
norway	387 ( 2.0)	190 ( 1.9)	197 ( 2.1)
portugal	1184 ( 6.2)	595 ( 6.1)	589 ( 6.4)
switzerland	500 ( 2.6)	258 ( 2.6)	242 ( 2.6)
uk	6696 (35.3)	3492 (35.6)	3204 (34.9)
usa	4920 (25.9)	2451 (25.0)	2469 (26.9)

Ages between the two sexes are relatively balanced with a difference of 0.04. This tracks into height and weight with narrow differences (+2cm & +1kg) in favour of boys. girls were slightly more likely to report being of white ethnicity, but this should be caveated against a good amount of missingness in this variable. Similar levels of mothers and fathers education are seen between the sexes.

3.3 Descriptive and Visual Analysis of key physical activity variables

Descriptive analysis Process will be basic visual –> basic numeric –> Detailed visual –> detailed numeric

3.3.1 Reminder of cut-point definitions

3.3.1.1 Evenson

Evenson cut-offs in counts per minute are

Evenson Cut-Points

Sedentary	Light	Moderate	Vigorous	MVPA
<101	101 - <2296	2296 - <4012	4012<=	2296<=

3.3.1.2 Pate

Pate cut-offs in counts per minute are

Pate Cut-offs

Sedentary	Light	Moderate	Vigorous	MVPA
<800	800 - <1680	1680 - <3368	3368<=	1680<=

Evenson cut-offs for sedentary are lower, limits on light are wider, and moderate to vigorous starts at a higher threshold. As such, it should be expected that compared to Pate cut-offs, Evenson should return lower volumes of sedentary activity, greater volumes of light activity, and reduced volumes of moderate to vigorous activity.

---

3.3.2 Restricting to wakeful activity

In line with other studies (See article for details), individuals who recorded in excess of 16hrs/day of activity were removed from analyses exploring eith mean activity (cpm) or sedentary activity. In particular, this restriction notable constrains the sample collected in Brazil and Switzerland

Further, in later analysis using GAMLSS complete cases are required. As such, at this point the datasets are subsetted to individuals who have complete data for physical activity, gender, study, bmi (z-score) and parental education.

3.4 Each Intensity

3.4.1 Counts Per Minute (cpm)

3.4.1.1 Plot

Repeating this plot but doing so with $sex as the grouping variable.

Table One summary of complete dataframe by demographic data, stratified by Age

	Overall	female:5	male:5	female:6	male:6	female:7	male:7	female:8	male:8	female:9	male:9	female:10	male:10	female:11	male:11	female:12	male:12	female:13	male:13	female:14	male:14	female:15	male:15	female:16	male:16	female:17	male:17	female:18	male:18
n	15437	53	45	400	387	239	230	161	144	483	410	923	871	708	623	2918	2723	414	428	324	306	459	404	561	513	173	189	173	175
icad_height (mean (SD))	148.95 (15.45)	112.25 (5.05)	113.21 (5.57)	116.50 (5.53)	117.97 (5.52)	122.46 (6.21)	123.00 (5.97)	129.53 (6.43)	129.89 (6.10)	136.17 (6.26)	136.30 (6.36)	140.19 (7.03)	140.00 (6.65)	146.50 (7.37)	145.85 (6.52)	151.40 (7.12)	150.36 (7.26)	156.77 (6.90)	158.56 (9.34)	159.52 (6.82)	164.57 (8.72)	163.09 (6.74)	172.08 (8.18)	163.33 (6.47)	174.57 (7.44)	161.41 (6.86)	175.45 (7.68)	161.88 (6.38)	175.28 (7.80)
icad_weight (mean (SD))	44.98 (16.87)	20.90 (3.15)	21.25 (4.12)	22.42 (4.10)	23.16 (4.51)	25.44 (5.88)	25.52 (5.86)	30.44 (8.82)	30.18 (8.41)	32.59 (7.32)	33.11 (7.66)	36.11 (8.96)	35.34 (7.86)	42.35 (10.94)	41.01 (10.05)	45.03 (10.68)	43.43 (10.54)	53.45 (13.54)	52.88 (15.41)	58.97 (15.85)	58.73 (15.52)	57.64 (11.96)	65.15 (15.71)	59.83 (12.57)	68.88 (16.65)	66.19 (19.45)	76.56 (22.17)	66.17 (18.08)	77.79 (20.96)
cpm_wear (mean (SD))	576.93 (234.91)	757.29 (192.49)	883.98 (292.12)	737.32 (186.74)	854.19 (221.14)	639.83 (196.56)	760.38 (236.24)	641.89 (243.23)	731.22 (205.30)	596.45 (197.57)	738.14 (299.12)	593.34 (213.36)	708.79 (269.98)	563.57 (182.93)	685.63 (227.55)	538.63 (186.45)	646.53 (198.37)	388.51 (163.02)	491.97 (208.97)	367.14 (172.62)	487.53 (196.86)	384.27 (148.05)	484.83 (191.93)	378.82 (154.52)	494.64 (210.11)	334.02 (126.91)	449.36 (204.98)	308.68 (110.31)	433.62 (189.05)
mvpa_evenson (mean (SD))	52.46 (29.84)	57.68 (21.23)	75.62 (30.87)	56.07 (20.60)	75.29 (27.44)	52.02 (22.06)	74.47 (31.61)	49.12 (30.23)	65.86 (28.96)	47.26 (25.34)	70.29 (36.53)	48.80 (27.20)	69.61 (37.37)	48.53 (21.47)	70.60 (29.97)	45.51 (21.01)	65.95 (29.03)	33.40 (21.25)	51.16 (28.27)	29.41 (21.15)	47.93 (27.39)	31.71 (21.89)	46.05 (27.68)	31.25 (21.96)	48.68 (30.40)	22.39 (18.50)	40.18 (28.26)	18.26 (13.75)	37.42 (25.04)
sedentary_evenson (mean (SD))	383.04 (133.92)	239.84 (77.16)	232.56 (72.70)	256.46 (93.55)	246.63 (89.17)	361.44 (164.81)	345.49 (172.05)	319.29 (90.38)	312.53 (105.31)	326.83 (91.61)	317.42 (98.70)	343.47 (106.01)	330.32 (108.96)	392.66 (149.07)	374.89 (138.72)	367.38 (82.33)	355.12 (88.78)	529.68 (177.93)	523.50 (199.53)	513.98 (157.26)	492.46 (175.84)	468.80 (108.80)	441.76 (110.88)	478.18 (113.38)	445.03 (116.10)	474.34 (121.18)	465.05 (139.94)	480.90 (121.79)	470.45 (142.49)
light_evenson (mean (SD))	363.35 (78.69)	388.34 (58.67)	401.01 (67.89)	407.42 (60.57)	403.56 (60.86)	433.40 (73.32)	426.69 (79.82)	408.40 (68.92)	407.18 (69.31)	407.11 (75.22)	404.05 (75.42)	396.57 (75.93)	393.26 (78.17)	380.02 (62.32)	371.50 (70.14)	360.68 (61.34)	363.30 (63.18)	337.95 (75.39)	354.85 (82.75)	318.38 (72.14)	343.62 (84.63)	308.80 (78.50)	313.59 (83.48)	296.05 (75.45)	310.56 (89.82)	302.47 (73.71)	314.19 (88.50)	295.26 (82.46)	316.37 (95.28)

Plot is muted at 1500 cpm to show more detail of centre of distribution Both genders appear to have positively skewed cpm values. Boys appear to have a slightly higher peak at ~600cpm, with girls peak at ~500cpm and boys seem to have a wider distribution.

3.4.1.2 Table

Counts Per Minute, Summarised by Gender

Gender	Count	Mean	Std Dev	Median	Skew
female	7368	532.75	200.37	508.59	0.76
male	6749	649.85	236.11	628.38	0.48

Supporting the visual inspection, boys are recording ~100cpm more on average. The measure of skew is marginally higher in boys (4.5 vs 4.3), combined with a higher standard deviation. Both genders seem to have some outliers, but the aforementioned individual with a cpm value is a girl, thus likely underlying the high kurtosis and skew score seen for girls.

Further - The difference between the genders seems to be stable across ages - highest values are observed for the youngest individuals in the study, with a near continuous decline throughout the sample until exit at age 18

3.4.1.3 Unadjusted

3.4.1.3.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = cpm_wear ~ icad_sex, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = gamlss_cpm_adjusted,      trace = FALSE) 
## 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.278044   0.004381 1432.88   <2e-16 ***
## icad_sexmale 0.198700   0.006225   31.92   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  5.300110   0.008238  643.39   <2e-16 ***
## icad_sexmale 0.164107   0.011914   13.77   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  14117 
## Degrees of Freedom for the fit:  4
##       Residual Deg. of Freedom:  14113 
##                       at cycle:  2 
##  
## Global Deviance:     191920.7 
##             AIC:     191928.7 
##             SBC:     191958.9 
## ******************************************************************

The Mu coefficient presents the percentage difference between the two genders. Here boys cpm is 19% greater than girls, which supports the difference observed in the glm run previously Male Estimate = 111.00, Intercept = 530.40. These values can also be obtained by exponentiating the estimate from the model exp(6.273633) = 530.400828 with a male value of 631.1881238. The standard deviations predicted from this model are 198.0425685 for girls and 231.5745421.

Then a model that allows the skew to vary

“Second, a more complex distribution which enables skewness to be investigated: the Box-Cox Cole and Green (BCCG). Here location is the median, scale is the generalised coefficient of variation (CoV), which is calculated in the normal case as SD/mean, and shape is skewness as defined by the Box-Cox power required to transform the outcome distribution to normality. The transformation requires the outcome to be on the positive line, so zero or negative values are excluded. BCCG is effectively NO with added skewness, though parameterised differently. A Box-Cox power of 1 indicates that the distribution is normal, 0 is log-normal and –1 inverse normal, so a smaller (i.e. more negative) power corresponds to more right skewness.” Bann, Wright and Cole, 2022

3.4.1.3.2 GAMLSS - Median + SE + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = cpm_wear ~ icad_sex, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = gamlss_cpm_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.240465   0.004734 1318.18   <2e-16 ***
## icad_sexmale 0.213240   0.006741   31.63   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  -0.958422   0.008648 -110.820   <2e-16 ***
## icad_sexmale -0.028929   0.012763   -2.267   0.0234 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.47886    0.02088  22.938  < 2e-16 ***
## icad_sexmale  0.19021    0.03038   6.262 3.91e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  14117 
## Degrees of Freedom for the fit:  6
##       Residual Deg. of Freedom:  14111 
##                       at cycle:  6 
##  
## Global Deviance:     191150.5 
##             AIC:     191162.5 
##             SBC:     191207.8 
## ******************************************************************

Including skewness, boys appear to have a significantly greater median volume of activity (Mu) that is 20.1% greater, a non-significantly reduced standard deviation (sigma) that is 1.5% lower with a skewness (nu) that is significantly lower than that of girls. The Nu being higher for boys indicates that the sample was less skewed than girls. Exponentiating these values gives an estimated median of 511.3861602 for girls and 614.2233601 for boys. And a coefficient of variance of 0.38092 for girls and 0.3751197 for boys

3.4.1.4 Adjusted

Based on the created DAG - the minimal adjustment for Gender involves SES (parental education),county and BMI. As GAMLSS requires complete cases, only those with complete data for these variables can be included. This reduced subset shall be re-run in an unadjusted model later as a sensitivity analysis to ensure that the composition of the sample is changing the associations between demographics and activity profiles.

3.4.1.4.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = cpm_wear ~ icad_sex + country + bmi_z +  
##     parenteducation, sigma.formula = ~icad_sex, family = NO(mu.link = log),  
##     data = gamlss_cpm_adjusted, trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         6.498478   0.008053 806.930  < 2e-16 ***
## icad_sexmale        0.197836   0.005823  33.978  < 2e-16 ***
## countrydenmark     -0.281159   0.011749 -23.931  < 2e-16 ***
## countryestonia     -0.140625   0.014886  -9.447  < 2e-16 ***
## countrynorway      -0.028139   0.016589  -1.696   0.0899 .  
## countryportugal    -0.232977   0.015968 -14.591  < 2e-16 ***
## countryswitzerland  0.014505   0.026869   0.540   0.5893    
## countryuk          -0.194465   0.007982 -24.364  < 2e-16 ***
## countryusa         -0.329512   0.008798 -37.453  < 2e-16 ***
## bmi_z              -0.032700   0.003148 -10.389  < 2e-16 ***
## parenteducation    -0.033727   0.007025  -4.801  1.6e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   5.23611    0.00825  634.71   <2e-16 ***
## icad_sexmale  0.17190    0.01195   14.38   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  14117 
## Degrees of Freedom for the fit:  13
##       Residual Deg. of Freedom:  14104 
##                       at cycle:  3 
##  
## Global Deviance:     190219.1 
##             AIC:     190245.1 
##             SBC:     190343.3 
## ******************************************************************

3.4.1.4.2 GAMLSS - Median + SE + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = cpm_wear ~ icad_sex + country + bmi_z +  
##     parenteducation, sigma.formula = ~icad_sex, nu.formula = ~icad_sex,  
##     family = BCCGo, data = gamlss_cpm_adjusted, trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         6.447650   0.009232 698.386  < 2e-16 ***
## icad_sexmale        0.211822   0.006377  33.219  < 2e-16 ***
## countrydenmark     -0.240026   0.012011 -19.984  < 2e-16 ***
## countryestonia     -0.120071   0.016154  -7.433 1.12e-13 ***
## countrynorway       0.008349   0.019983   0.418    0.676    
## countryportugal    -0.209686   0.016348 -12.826  < 2e-16 ***
## countryswitzerland  0.009379   0.032621   0.288    0.774    
## countryuk          -0.193477   0.008897 -21.746  < 2e-16 ***
## countryusa         -0.302745   0.009291 -32.584  < 2e-16 ***
## bmi_z              -0.035966   0.002918 -12.324  < 2e-16 ***
## parenteducation    -0.031816   0.007119  -4.469 7.92e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  -1.014385   0.008603 -117.912   <2e-16 ***
## icad_sexmale -0.016283   0.012685   -1.284    0.199    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.48069    0.02119  22.688  < 2e-16 ***
## icad_sexmale  0.17201    0.02979   5.773 7.94e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  14117 
## Degrees of Freedom for the fit:  15
##       Residual Deg. of Freedom:  14102 
##                       at cycle:  6 
##  
## Global Deviance:     189654.2 
##             AIC:     189684.2 
##             SBC:     189797.5 
## ******************************************************************

3.4.2 Summarizing MVPA

3.4.2.1 Plot

Plot is muted at 200 min/day to show more detail of centre of distribution

For both cut-offs, boys appear to have a higher average volume than girls. Both seem to have uni-modal distributions with a slight positive skew but there appears to be a greater variation amongst boys. By Evenson cut-offs girls seem to have an average volume of around 35 min/day while boys have an average volume around 50 min/day.

3.4.2.2 Table

MVPA, Summarised by Country

Gender	Count	Mean	Std Dev	Median	Skew
female	9804	43.52	24.18	40.27	0.90
male	9176	61.96	32.17	58.41	0.71

The numeric analysis largely supports the visual inspection. For both cut-offs boys recorded greater volumes than girls. With Evenson cut-offs girls recorded a mean of 43 min/day. Boys attained 61 min/day and 92 min/day respectively. By both thresholds, the mean boy was attaining health recommendations. The deviation and standard error was larger for boys but the skew and kurtosis lower.

3.4.2.3 Unadjusted

GAMLSS cannot pass zero’s. As such, any zero entries were recoded to 0.001 before analysis to ensure the maximum possible sample size.

3.4.2.3.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = mvpa_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = gamlss_mvpa_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.760828   0.006219  604.73   <2e-16 ***
## icad_sexmale 0.376413   0.008596   43.79   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.174164   0.007907  401.45   <2e-16 ***
## icad_sexmale 0.294981   0.011380   25.92   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  15461 
## Degrees of Freedom for the fit:  4
##       Residual Deg. of Freedom:  15457 
##                       at cycle:  2 
##  
## Global Deviance:     146430.8 
##             AIC:     146438.8 
##             SBC:     146469.4 
## ******************************************************************

3.4.2.3.2 GAMLSS - Median + SE + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = mvpa_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = gamlss_mvpa_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.683213   0.007067  521.15   <2e-16 ***
## icad_sexmale 0.397669   0.009754   40.77   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.51797    0.00923 -56.118  < 2e-16 ***
## icad_sexmale -0.08151    0.01346  -6.057 1.42e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.55651    0.01498   37.15  < 2e-16 ***
## icad_sexmale  0.08483    0.02299    3.69 0.000225 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  15461 
## Degrees of Freedom for the fit:  6
##       Residual Deg. of Freedom:  15455 
##                       at cycle:  7 
##  
## Global Deviance:     144507.2 
##             AIC:     144519.2 
##             SBC:     144565.1 
## ******************************************************************

3.4.2.4 Adjusted

3.4.2.4.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = mvpa_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = gamlss_mvpa_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         3.970836   0.011377 349.015  < 2e-16 ***
## icad_sexmale        0.377056   0.007940  47.486  < 2e-16 ***
## countrybrazil      -0.543652   0.034006 -15.987  < 2e-16 ***
## countrydenmark     -0.278249   0.016876 -16.488  < 2e-16 ***
## countryestonia     -0.022732   0.019499  -1.166 0.243702    
## countrynorway       0.082151   0.021582   3.806 0.000142 ***
## countryportugal    -0.194682   0.022027  -8.838  < 2e-16 ***
## countryswitzerland  0.160758   0.020226   7.948 2.03e-15 ***
## countryuk          -0.112929   0.011175 -10.105  < 2e-16 ***
## countryusa         -0.400654   0.012932 -30.980  < 2e-16 ***
## bmi_z              -0.060719   0.004546 -13.358  < 2e-16 ***
## parenteducation    -0.048520   0.009693  -5.006 5.63e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.107347   0.007921  392.28   <2e-16 ***
## icad_sexmale 0.302535   0.011424   26.48   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  15461 
## Degrees of Freedom for the fit:  14
##       Residual Deg. of Freedom:  15447 
##                       at cycle:  3 
##  
## Global Deviance:     144477.4 
##             AIC:     144505.4 
##             SBC:     144612.5 
## ******************************************************************

3.4.2.4.2 GAMLSS - Median + SE + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = mvpa_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = gamlss_mvpa_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         3.855878   0.013101 294.310  < 2e-16 ***
## icad_sexmale        0.404855   0.009260  43.721  < 2e-16 ***
## countrybrazil      -0.472598   0.026347 -17.937  < 2e-16 ***
## countrydenmark     -0.193033   0.016952 -11.387  < 2e-16 ***
## countryestonia      0.032435   0.023145   1.401    0.161    
## countrynorway       0.147903   0.028204   5.244 1.59e-07 ***
## countryportugal    -0.134544   0.023226  -5.793 7.05e-09 ***
## countryswitzerland  0.154800   0.027008   5.732 1.01e-08 ***
## countryuk          -0.098445   0.012510  -7.869 3.80e-15 ***
## countryusa         -0.332993   0.012968 -25.678  < 2e-16 ***
## bmi_z              -0.065924   0.004053 -16.266  < 2e-16 ***
## parenteducation    -0.051777   0.009808  -5.279 1.31e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.566080   0.008995 -62.932  < 2e-16 ***
## icad_sexmale -0.077346   0.013114  -5.898 3.76e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.53742    0.01358  39.561  < 2e-16 ***
## icad_sexmale  0.08215    0.02046   4.014 5.99e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  15461 
## Degrees of Freedom for the fit:  16
##       Residual Deg. of Freedom:  15445 
##                       at cycle:  7 
##  
## Global Deviance:     142912.9 
##             AIC:     142944.9 
##             SBC:     143067.3 
## ******************************************************************

3.4.3 Summarizing Sedentary

3.4.3.1 Plot

Both Genders seem to have relatively similar distributions peaking at ~350 min/day with Evenson. In both cases, girls seem to score marginally higher than boys, with a roughly normal distribution that has a slight positive skew.

3.4.3.2 Table

Sedentary as defined by Evenson Cut-offs, Summarised by Country

Gender	Count	Mean	Std Dev	Median	Skew
female	7368	365.96	99.38	359.85	0.40
male	6749	347.87	98.10	342.20	0.41

3.4.3.3 Unadjusted

3.4.3.3.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  
## gamlss(formula = sedentary_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = gamlss_cpm_adjusted,      trace = FALSE) 
## 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   5.902535   0.003163 1865.84   <2e-16 ***
## icad_sexmale -0.050716   0.004668  -10.87   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   4.598903   0.008238 558.270   <2e-16 ***
## icad_sexmale -0.012961   0.011914  -1.088    0.277    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  14117 
## Degrees of Freedom for the fit:  4
##       Residual Deg. of Freedom:  14113 
##                       at cycle:  2 
##  
## Global Deviance:     169732.8 
##             AIC:     169740.8 
##             SBC:     169771 
## ******************************************************************

3.4.3.3.2 GAMLSS - Median + SE + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  
## gamlss(formula = sedentary_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = gamlss_cpm_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   5.885431   0.003445 1708.57   <2e-16 ***
## icad_sexmale -0.051712   0.005087  -10.17   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  -1.289477   0.008535 -151.085  < 2e-16 ***
## icad_sexmale  0.039069   0.012370    3.158  0.00159 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.545539   0.032651  16.708   <2e-16 ***
## icad_sexmale 0.009641   0.046277   0.208    0.835    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  14117 
## Degrees of Freedom for the fit:  6
##       Residual Deg. of Freedom:  14111 
##                       at cycle:  6 
##  
## Global Deviance:     169367.5 
##             AIC:     169379.5 
##             SBC:     169424.8 
## ******************************************************************

3.4.3.4 Adjusted

3.4.3.4.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = sedentary_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = gamlss_cpm_adjusted,      trace = FALSE) 
## 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         5.703042   0.007811 730.092  < 2e-16 ***
## icad_sexmale       -0.050725   0.004427 -11.457  < 2e-16 ***
## countrydenmark      0.252459   0.009220  27.381  < 2e-16 ***
## countryestonia      0.134324   0.013132  10.229  < 2e-16 ***
## countrynorway       0.092957   0.016582   5.606 2.11e-08 ***
## countryportugal     0.204719   0.012875  15.901  < 2e-16 ***
## countryswitzerland  0.069962   0.027871   2.510   0.0121 *  
## countryuk           0.167309   0.007670  21.814  < 2e-16 ***
## countryusa          0.255200   0.007661  33.313  < 2e-16 ***
## bmi_z               0.004810   0.002179   2.207   0.0273 *  
## parenteducation     0.034849   0.005462   6.380 1.83e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   4.550548   0.008247 551.769   <2e-16 ***
## icad_sexmale -0.015924   0.011943  -1.333    0.182    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  14117 
## Degrees of Freedom for the fit:  13
##       Residual Deg. of Freedom:  14104 
##                       at cycle:  3 
##  
## Global Deviance:     168327.5 
##             AIC:     168353.5 
##             SBC:     168451.8 
## ******************************************************************

3.4.3.4.2 GAMLSS - Median + SE + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = sedentary_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = gamlss_cpm_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         5.697820   0.006902 825.585  < 2e-16 ***
## icad_sexmale       -0.052179   0.004788 -10.898  < 2e-16 ***
## countrydenmark      0.264840   0.008747  30.277  < 2e-16 ***
## countryestonia      0.145698   0.011981  12.161  < 2e-16 ***
## countrynorway       0.099970   0.014681   6.809 1.02e-11 ***
## countryportugal     0.206639   0.012045  17.155  < 2e-16 ***
## countryswitzerland  0.077223   0.024527   3.148  0.00164 ** 
## countryuk           0.150295   0.006673  22.522  < 2e-16 ***
## countryusa          0.257439   0.006766  38.049  < 2e-16 ***
## bmi_z               0.005057   0.002182   2.318  0.02045 *  
## parenteducation     0.032901   0.005264   6.250 4.22e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  -1.349447   0.008699 -155.121   <2e-16 ***
## icad_sexmale  0.036710   0.012608    2.912   0.0036 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.699742   0.035697  19.602   <2e-16 ***
## icad_sexmale 0.007186   0.049064   0.146    0.884    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  14117 
## Degrees of Freedom for the fit:  15
##       Residual Deg. of Freedom:  14102 
##                       at cycle:  6 
##  
## Global Deviance:     167808.2 
##             AIC:     167838.2 
##             SBC:     167951.5 
## ******************************************************************

3.4.4 Summarizing Light

3.4.4.1 Plot

3.4.4.2 Table

Light as defined by Evenson Cut-offs, Summarised by Country

Gender	Count	Mean	Std Dev	Median	Skew
female	7998	361.93	77.74	363.83	-0.21
male	7463	364.90	79.60	367.33	-0.25

3.4.4.3 Unadjusted

3.4.4.3.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = light_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = gamlss_comp_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  5.891452   0.002402 2453.071   <2e-16 ***
## icad_sexmale 0.008176   0.003485    2.346    0.019 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.353333   0.007907 550.589   <2e-16 ***
## icad_sexmale 0.023645   0.011380   2.078   0.0378 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  15461 
## Degrees of Freedom for the fit:  4
##       Residual Deg. of Freedom:  15457 
##                       at cycle:  2 
##  
## Global Deviance:     178843.1 
##             AIC:     178851.1 
##             SBC:     178881.7 
## ******************************************************************

3.4.4.3.2 GAMLSS - Median + SE + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = light_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = gamlss_comp_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  5.898334   0.002514 2346.03   <2e-16 ***
## icad_sexmale 0.009022   0.003624    2.49   0.0128 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  -1.557878   0.008793 -177.177   <2e-16 ***
## icad_sexmale  0.011396   0.012678    0.899    0.369    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1.29554    0.03950  32.796   <2e-16 ***
## icad_sexmale  0.02646    0.05459   0.485    0.628    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  15461 
## Degrees of Freedom for the fit:  6
##       Residual Deg. of Freedom:  15455 
##                       at cycle:  7 
##  
## Global Deviance:     178695.3 
##             AIC:     178707.3 
##             SBC:     178753.2 
## ******************************************************************

3.4.4.4 Adjusted

3.4.4.4.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = light_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = gamlss_comp_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)         5.937936   0.005189 1144.308  < 2e-16 ***
## icad_sexmale        0.008840   0.003384    2.612 0.009008 ** 
## countrybrazil      -0.057188   0.010974   -5.211 1.90e-07 ***
## countrydenmark     -0.063513   0.007039   -9.023  < 2e-16 ***
## countryestonia      0.058741   0.008924    6.583 4.77e-11 ***
## countrynorway       0.027801   0.011097    2.505 0.012247 *  
## countryportugal    -0.027994   0.009504   -2.946 0.003229 ** 
## countryswitzerland  0.167727   0.009754   17.196  < 2e-16 ***
## countryuk          -0.041383   0.005225   -7.921 2.52e-15 ***
## countryusa         -0.082493   0.005352  -15.413  < 2e-16 ***
## bmi_z              -0.003279   0.001746   -1.878 0.060431 .  
## parenteducation    -0.014754   0.004110   -3.590 0.000332 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   4.31992    0.00792 545.473  < 2e-16 ***
## icad_sexmale  0.03260    0.01142   2.855  0.00431 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  15461 
## Degrees of Freedom for the fit:  14
##       Residual Deg. of Freedom:  15447 
##                       at cycle:  3 
##  
## Global Deviance:     177943.7 
##             AIC:     177971.7 
##             SBC:     178078.8 
## ******************************************************************

3.4.4.4.2 GAMLSS - Median + SE + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = light_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = gamlss_comp_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)         5.921807   0.004936 1199.805  < 2e-16 ***
## icad_sexmale        0.008670   0.003527    2.458   0.0140 *  
## countrybrazil      -0.019160   0.010075   -1.902   0.0572 .  
## countrydenmark     -0.002740   0.006486   -0.422   0.6727    
## countryestonia      0.082196   0.008783    9.358  < 2e-16 ***
## countrynorway       0.051185   0.010698    4.785 1.73e-06 ***
## countryportugal     0.008848   0.008868    0.998   0.3184    
## countryswitzerland  0.164635   0.010387   15.851  < 2e-16 ***
## countryuk          -0.036300   0.004795   -7.570 3.94e-14 ***
## countryusa         -0.032016   0.004978   -6.432 1.30e-10 ***
## bmi_z              -0.002867   0.001574   -1.822   0.0685 .  
## parenteducation    -0.015503   0.003760   -4.123 3.77e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -1.589966   0.008883 -178.99   <2e-16 ***
## icad_sexmale  0.020321   0.012783    1.59    0.112    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1.39636    0.04244  32.902   <2e-16 ***
## icad_sexmale -0.02359    0.05678  -0.415    0.678    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  15461 
## Degrees of Freedom for the fit:  16
##       Residual Deg. of Freedom:  15445 
##                       at cycle:  8 
##  
## Global Deviance:     177921.1 
##             AIC:     177953.1 
##             SBC:     178075.4 
## ******************************************************************

3.4.5 Summarizing Moderate

3.4.5.1 Plot

3.4.5.2 Table

Light as defined by Evenson Cut-offs, Summarised by Country

Gender	Count	Mean	Std Dev	Median	Skew
female	7998	31.19	15.73	29.83	0.71
male	7463	43.07	20.35	41.80	0.55

3.4.5.3 Unadjusted

3.4.5.3.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  
## gamlss(formula = moderate_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = gamlss_comp_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.440222   0.005637  610.31   <2e-16 ***
## icad_sexmale 0.322690   0.007853   41.09   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.755265   0.007907  348.47   <2e-16 ***
## icad_sexmale 0.257663   0.011380   22.64   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  15461 
## Degrees of Freedom for the fit:  4
##       Residual Deg. of Freedom:  15457 
##                       at cycle:  2 
##  
## Global Deviance:     132920.6 
##             AIC:     132928.6 
##             SBC:     132959.2 
## ******************************************************************

3.4.5.3.2 GAMLSS - Median + SE + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  
## gamlss(formula = moderate_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = gamlss_comp_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.386285   0.006352  533.08   <2e-16 ***
## icad_sexmale 0.335909   0.008812   38.12   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.622962   0.009325 -66.803  < 2e-16 ***
## icad_sexmale -0.069383   0.013503  -5.138  2.8e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.63555    0.01687  37.670   <2e-16 ***
## icad_sexmale  0.06274    0.02476   2.534   0.0113 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  15461 
## Degrees of Freedom for the fit:  6
##       Residual Deg. of Freedom:  15455 
##                       at cycle:  6 
##  
## Global Deviance:     131680.7 
##             AIC:     131692.7 
##             SBC:     131738.6 
## ******************************************************************

3.4.5.4 Adjusted

3.4.5.4.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = moderate_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = gamlss_comp_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         3.630140   0.010478 346.441  < 2e-16 ***
## icad_sexmale        0.323779   0.007256  44.623  < 2e-16 ***
## countrybrazil      -0.378481   0.027363 -13.832  < 2e-16 ***
## countrydenmark     -0.265633   0.015632 -16.993  < 2e-16 ***
## countryestonia      0.007721   0.017846   0.433 0.665272    
## countrynorway       0.068751   0.020453   3.361 0.000777 ***
## countryportugal    -0.118672   0.019346  -6.134 8.77e-10 ***
## countryswitzerland  0.192935   0.018455  10.454  < 2e-16 ***
## countryuk          -0.088250   0.010319  -8.552  < 2e-16 ***
## countryusa         -0.386845   0.011914 -32.469  < 2e-16 ***
## bmi_z              -0.037951   0.004046  -9.381  < 2e-16 ***
## parenteducation    -0.049061   0.008878  -5.526 3.33e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.686218   0.007915  339.38   <2e-16 ***
## icad_sexmale 0.265410   0.011405   23.27   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  15461 
## Degrees of Freedom for the fit:  14
##       Residual Deg. of Freedom:  15447 
##                       at cycle:  3 
##  
## Global Deviance:     130901.2 
##             AIC:     130929.2 
##             SBC:     131036.2 
## ******************************************************************

3.4.5.4.2 GAMLSS - Median + SE + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = moderate_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = gamlss_comp_adjusted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         3.530689   0.011809 298.972  < 2e-16 ***
## icad_sexmale        0.343220   0.008371  41.000  < 2e-16 ***
## countrybrazil      -0.279036   0.023968 -11.642  < 2e-16 ***
## countrydenmark     -0.168872   0.015298 -11.039  < 2e-16 ***
## countryestonia      0.092759   0.021073   4.402 1.08e-05 ***
## countrynorway       0.140057   0.025444   5.504 3.76e-08 ***
## countryportugal    -0.048776   0.020979  -2.325   0.0201 *  
## countryswitzerland  0.187525   0.024325   7.709 1.34e-14 ***
## countryuk          -0.069905   0.011261  -6.208 5.51e-10 ***
## countryusa         -0.308011   0.011680 -26.370  < 2e-16 ***
## bmi_z              -0.040617   0.003659 -11.101  < 2e-16 ***
## parenteducation    -0.051710   0.008865  -5.833 5.56e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.670646   0.009079 -73.868  < 2e-16 ***
## icad_sexmale -0.067479   0.013188  -5.117 3.15e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.61606    0.01535  40.122  < 2e-16 ***
## icad_sexmale  0.07302    0.02259   3.232  0.00123 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  15461 
## Degrees of Freedom for the fit:  16
##       Residual Deg. of Freedom:  15445 
##                       at cycle:  7 
##  
## Global Deviance:     130099.9 
##             AIC:     130131.9 
##             SBC:     130254.2 
## ******************************************************************

3.4.6 Summarizing Vigorous

3.4.6.1 Plot

3.4.6.2 Unadjusted

3.4.6.2.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  
## gamlss(formula = vigorous_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = gamlss_vig_adjusted,      trace = FALSE) 
## 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.460752   0.009826  250.44   <2e-16 ***
## icad_sexmale 0.499302   0.013100   38.12   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   2.33102    0.00791  294.69   <2e-16 ***
## icad_sexmale  0.33757    0.01139   29.63   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  15429 
## Degrees of Freedom for the fit:  4
##       Residual Deg. of Freedom:  15425 
##                       at cycle:  2 
##  
## Global Deviance:     120738 
##             AIC:     120746 
##             SBC:     120776.6 
## ******************************************************************

3.4.6.2.2 GAMLSS - Median + SE + Skew

3.4.6.3 Adjusted

3.4.6.3.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = vigorous_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = gamlss_vig_adjusted,      trace = FALSE) 
## 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         2.722086   0.017243 157.871  < 2e-16 ***
## icad_sexmale        0.498145   0.012233  40.721  < 2e-16 ***
## countrybrazil      -1.042826   0.078648 -13.259  < 2e-16 ***
## countrydenmark     -0.323085   0.025261 -12.790  < 2e-16 ***
## countryestonia     -0.126540   0.030598  -4.136 3.56e-05 ***
## countrynorway       0.085983   0.030985   2.775  0.00553 ** 
## countryportugal    -0.381271   0.037299 -10.222  < 2e-16 ***
## countryswitzerland  0.077505   0.031188   2.485  0.01296 *  
## countryuk          -0.177192   0.016680 -10.623  < 2e-16 ***
## countryusa         -0.437227   0.019355 -22.590  < 2e-16 ***
## bmi_z              -0.116344   0.007362 -15.803  < 2e-16 ***
## parenteducation    -0.045486   0.014754  -3.083  0.00205 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.288776   0.007931  288.57   <2e-16 ***
## icad_sexmale 0.336602   0.011456   29.38   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  15429 
## Degrees of Freedom for the fit:  14
##       Residual Deg. of Freedom:  15415 
##                       at cycle:  3 
##  
## Global Deviance:     119420 
##             AIC:     119448 
##             SBC:     119555 
## ******************************************************************

4 Sensitivity Analyses

Models are repeated using 1) an unrestricted dataset on the unadjusted model. 2) On the adjusted and restricted model, with the additional inclusions and restriction based on season being present, and finally 3) the process for season repeated for ethnicity.

4.0.1 Unrestricted Unadjusted

4.0.1.1 CPM

4.0.1.1.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = cpm_wear ~ icad_sex, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_unrestricted_cpm,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.273633   0.003910    1604   <2e-16 ***
## icad_sexmale 0.190021   0.005589      34   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  5.288482   0.007406  714.12   <2e-16 ***
## icad_sexmale 0.169317   0.010699   15.83   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  17504 
## Degrees of Freedom for the fit:  4
##       Residual Deg. of Freedom:  17500 
##                       at cycle:  2 
##  
## Global Deviance:     237653.5 
##             AIC:     237661.5 
##             SBC:     237692.6 
## ******************************************************************

4.0.1.1.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = cpm_wear ~ icad_sex, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_unrestricted_cpm,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.237125   0.004229  1475.0   <2e-16 ***
## icad_sexmale 0.201095   0.006058    33.2   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  -0.965166   0.007783 -124.004   <2e-16 ***
## icad_sexmale -0.015227   0.011428   -1.332    0.183    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.48724    0.01894  25.724  < 2e-16 ***
## icad_sexmale  0.15043    0.02735   5.501 3.83e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  17504 
## Degrees of Freedom for the fit:  6
##       Residual Deg. of Freedom:  17498 
##                       at cycle:  6 
##  
## Global Deviance:     236685.8 
##             AIC:     236697.8 
##             SBC:     236744.4 
## ******************************************************************

4.0.1.2 MVPA

4.0.1.2.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = mvpa_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_unrestricted_mvpa,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.773192   0.005611  672.52   <2e-16 ***
## icad_sexmale 0.353293   0.007801   45.29   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.185351   0.007141  446.04   <2e-16 ***
## icad_sexmale 0.285736   0.010271   27.82   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  18980 
## Degrees of Freedom for the fit:  4
##       Residual Deg. of Freedom:  18976 
##                       at cycle:  2 
##  
## Global Deviance:     180022.7 
##             AIC:     180030.7 
##             SBC:     180062.1 
## ******************************************************************

4.0.1.2.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = mvpa_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_unrestricted_mvpa,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.695626   0.006382  579.11   <2e-16 ***
## icad_sexmale 0.370456   0.008847   41.88   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.519239   0.008327 -62.359  < 2e-16 ***
## icad_sexmale -0.069919   0.012051  -5.802 6.67e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.55526    0.01364  40.702   <2e-16 ***
## icad_sexmale  0.05955    0.02026   2.939   0.0033 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  18980 
## Degrees of Freedom for the fit:  6
##       Residual Deg. of Freedom:  18974 
##                       at cycle:  7 
##  
## Global Deviance:     177579.5 
##             AIC:     177591.5 
##             SBC:     177638.6 
## ******************************************************************

4.0.1.3 Sedentary

4.0.1.3.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  
## gamlss(formula = sedentary_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_unrestricted_cpm,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   5.910484   0.002802 2109.40   <2e-16 ***
## icad_sexmale -0.051109   0.004137  -12.35   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   4.592002   0.007406 620.074   <2e-16 ***
## icad_sexmale -0.010045   0.010699  -0.939    0.348    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  17504 
## Degrees of Freedom for the fit:  4
##       Residual Deg. of Freedom:  17500 
##                       at cycle:  2 
##  
## Global Deviance:     210262.5 
##             AIC:     210270.5 
##             SBC:     210301.6 
## ******************************************************************

4.0.1.3.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  
## gamlss(formula = sedentary_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_unrestricted_cpm,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   5.894741   0.003052 1931.26   <2e-16 ***
## icad_sexmale -0.052884   0.004510  -11.73   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  -1.304365   0.007689 -169.646  < 2e-16 ***
## icad_sexmale  0.042197   0.011118    3.795 0.000148 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.56967    0.02987  19.070   <2e-16 ***
## icad_sexmale -0.01025    0.04225  -0.243    0.808    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  17504 
## Degrees of Freedom for the fit:  6
##       Residual Deg. of Freedom:  17498 
##                       at cycle:  6 
##  
## Global Deviance:     209851.1 
##             AIC:     209863.1 
##             SBC:     209909.7 
## ******************************************************************

4.0.1.4 Light

4.0.1.4.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = light_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_unrestricted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  5.882154   0.002205 2667.962  < 2e-16 ***
## icad_sexmale 0.010648   0.003187    3.342 0.000835 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.360281   0.007141 610.564   <2e-16 ***
## icad_sexmale 0.020199   0.010271   1.967   0.0492 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  18980 
## Degrees of Freedom for the fit:  4
##       Residual Deg. of Freedom:  18976 
##                       at cycle:  2 
##  
## Global Deviance:     219749.9 
##             AIC:     219757.9 
##             SBC:     219789.3 
## ******************************************************************

4.0.1.4.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = light_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_unrestricted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  5.889209   0.002308 2551.799  < 2e-16 ***
## icad_sexmale 0.011168   0.003317    3.366 0.000763 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  -1.541969   0.007965 -193.588   <2e-16 ***
## icad_sexmale  0.006883   0.011462    0.601    0.548    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1.29391    0.03536  36.588   <2e-16 ***
## icad_sexmale  0.01555    0.04905   0.317    0.751    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  18980 
## Degrees of Freedom for the fit:  6
##       Residual Deg. of Freedom:  18974 
##                       at cycle:  7 
##  
## Global Deviance:     219575.9 
##             AIC:     219587.9 
##             SBC:     219635 
## ******************************************************************

4.0.1.5 Moderate

4.0.1.5.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  
## gamlss(formula = moderate_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_unrestricted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.453885   0.005132  672.99   <2e-16 ***
## icad_sexmale 0.299492   0.007155   41.86   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.776922   0.007141  388.85   <2e-16 ***
## icad_sexmale 0.237515   0.010271   23.12   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  18980 
## Degrees of Freedom for the fit:  4
##       Residual Deg. of Freedom:  18976 
##                       at cycle:  2 
##  
## Global Deviance:     163633.8 
##             AIC:     163641.8 
##             SBC:     163673.2 
## ******************************************************************

4.0.1.5.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  
## gamlss(formula = moderate_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_unrestricted,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.397386   0.005777  588.07   <2e-16 ***
## icad_sexmale 0.312358   0.008024   38.93   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.615813   0.008364  -73.63  < 2e-16 ***
## icad_sexmale -0.065996   0.012087   -5.46 4.82e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.61930    0.01474  42.003  < 2e-16 ***
## icad_sexmale  0.05723    0.02166   2.642  0.00825 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  18980 
## Degrees of Freedom for the fit:  6
##       Residual Deg. of Freedom:  18974 
##                       at cycle:  7 
##  
## Global Deviance:     161985.1 
##             AIC:     161997.1 
##             SBC:     162044.2 
## ******************************************************************

4.0.1.6 Vigorous

4.0.1.6.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  
## gamlss(formula = vigorous_evenson ~ icad_sex, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_unrestricted_vig,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.470928   0.008834  279.72   <2e-16 ***
## icad_sexmale 0.472493   0.011851   39.87   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.336651   0.007144  327.08   <2e-16 ***
## icad_sexmale 0.326124   0.010283   31.71   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  18936 
## Degrees of Freedom for the fit:  4
##       Residual Deg. of Freedom:  18932 
##                       at cycle:  2 
##  
## Global Deviance:     148192.6 
##             AIC:     148200.6 
##             SBC:     148232 
## ******************************************************************

4.0.2 Adjusted for Season

4.0.2.1 CPM

4.0.2.1.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = cpm_wear ~ icad_sex + country + bmi_z +  
##     parenteducation + season, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_season_cpm,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         6.489962   0.011386 569.975  < 2e-16 ***
## icad_sexmale        0.187012   0.006380  29.311  < 2e-16 ***
## countrydenmark     -0.263721   0.011647 -22.643  < 2e-16 ***
## countryestonia     -0.132477   0.014714  -9.003  < 2e-16 ***
## countrynorway      -0.029012   0.016158  -1.795   0.0726 .  
## countryportugal    -0.230397   0.015820 -14.564  < 2e-16 ***
## countryswitzerland -0.015128   0.026870  -0.563   0.5734    
## countryuk          -0.205224   0.008091 -25.365  < 2e-16 ***
## bmi_z              -0.028633   0.003736  -7.664 1.96e-14 ***
## parenteducation    -0.033664   0.008175  -4.118 3.85e-05 ***
## seasonspring        0.055515   0.009165   6.057 1.43e-09 ***
## seasonsummer        0.080648   0.010686   7.547 4.84e-14 ***
## seasonwinter       -0.062601   0.009968  -6.280 3.52e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   5.21222    0.00967  538.99   <2e-16 ***
## icad_sexmale  0.17104    0.01406   12.16   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  10191 
## Degrees of Freedom for the fit:  15
##       Residual Deg. of Freedom:  10176 
##                       at cycle:  3 
##  
## Global Deviance:     136809.3 
##             AIC:     136839.3 
##             SBC:     136947.7 
## ******************************************************************

4.0.2.1.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = cpm_wear ~ icad_sex + country + bmi_z +  
##     parenteducation + season, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_season_cpm,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         6.452963   0.011509 560.681  < 2e-16 ***
## icad_sexmale        0.196195   0.006866  28.573  < 2e-16 ***
## countrydenmark     -0.213402   0.011078 -19.264  < 2e-16 ***
## countryestonia     -0.111358   0.014792  -7.528 5.57e-14 ***
## countrynorway       0.004735   0.018174   0.261    0.794    
## countryportugal    -0.200813   0.015310 -13.117  < 2e-16 ***
## countryswitzerland -0.014958   0.030095  -0.497    0.619    
## countryuk          -0.211920   0.008377 -25.299  < 2e-16 ***
## bmi_z              -0.031635   0.003602  -8.783  < 2e-16 ***
## parenteducation    -0.035238   0.008421  -4.185 2.88e-05 ***
## seasonspring        0.069981   0.008751   7.997 1.41e-15 ***
## seasonsummer        0.098281   0.010372   9.476  < 2e-16 ***
## seasonwinter       -0.060633   0.009219  -6.577 5.03e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  -1.106345   0.010244 -108.001   <2e-16 ***
## icad_sexmale -0.008439   0.015152   -0.557    0.578    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.61869    0.02649  23.352  < 2e-16 ***
## icad_sexmale  0.16390    0.03760   4.359 1.32e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  10191 
## Degrees of Freedom for the fit:  17
##       Residual Deg. of Freedom:  10174 
##                       at cycle:  6 
##  
## Global Deviance:     136423.8 
##             AIC:     136457.8 
##             SBC:     136580.7 
## ******************************************************************

4.0.2.2 MVPA

4.0.2.2.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = mvpa_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + season, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_season_mvpa,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         3.964435   0.016015 247.541  < 2e-16 ***
## icad_sexmale        0.355839   0.008718  40.817  < 2e-16 ***
## countrybrazil      -0.569588   0.034188 -16.661  < 2e-16 ***
## countrydenmark     -0.260919   0.017128 -15.234  < 2e-16 ***
## countryestonia     -0.014630   0.019741  -0.741 0.458656    
## countrynorway       0.083411   0.021517   3.877 0.000107 ***
## countryportugal    -0.184991   0.022329  -8.285  < 2e-16 ***
## countryswitzerland  0.156976   0.021768   7.211 5.91e-13 ***
## countryuk          -0.112876   0.011612  -9.721  < 2e-16 ***
## bmi_z              -0.049083   0.005264  -9.324  < 2e-16 ***
## parenteducation    -0.043721   0.011243  -3.889 0.000101 ***
## seasonspring        0.072845   0.012549   5.805 6.62e-09 ***
## seasonsummer        0.036885   0.014295   2.580 0.009885 ** 
## seasonwinter       -0.074887   0.013876  -5.397 6.92e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.109140   0.009279  335.09   <2e-16 ***
## icad_sexmale 0.299779   0.013471   22.25   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11109 
## Degrees of Freedom for the fit:  16
##       Residual Deg. of Freedom:  11093 
##                       at cycle:  3 
##  
## Global Deviance:     103774.1 
##             AIC:     103806.1 
##             SBC:     103923.2 
## ******************************************************************

4.0.2.2.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = mvpa_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + season, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_season_mvpa,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         3.884304   0.016268 238.769  < 2e-16 ***
## icad_sexmale        0.365385   0.009843  37.122  < 2e-16 ***
## countrybrazil      -0.503856   0.024593 -20.488  < 2e-16 ***
## countrydenmark     -0.171735   0.015625 -10.991  < 2e-16 ***
## countryestonia      0.034540   0.021151   1.633    0.102    
## countrynorway       0.131917   0.025596   5.154 2.60e-07 ***
## countryportugal    -0.120305   0.021691  -5.546 2.98e-08 ***
## countryswitzerland  0.146820   0.025530   5.751 9.12e-09 ***
## countryuk          -0.107081   0.011797  -9.077  < 2e-16 ***
## bmi_z              -0.051387   0.005016 -10.244  < 2e-16 ***
## parenteducation    -0.053012   0.011578  -4.579 4.73e-06 ***
## seasonspring        0.093984   0.012301   7.641 2.34e-14 ***
## seasonsummer        0.060290   0.014020   4.300 1.72e-05 ***
## seasonwinter       -0.069169   0.013032  -5.308 1.13e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.68164    0.01054 -64.666  < 2e-16 ***
## icad_sexmale -0.04964    0.01559  -3.185  0.00145 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.59960    0.01719  34.885  < 2e-16 ***
## icad_sexmale  0.10065    0.02640   3.813 0.000138 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11109 
## Degrees of Freedom for the fit:  18
##       Residual Deg. of Freedom:  11091 
##                       at cycle:  6 
##  
## Global Deviance:     102893.8 
##             AIC:     102929.8 
##             SBC:     103061.5 
## ******************************************************************

4.0.2.3 Sedentary

4.0.2.3.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = sedentary_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + season, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_season_cpm,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         5.711091   0.009693 589.190  < 2e-16 ***
## icad_sexmale       -0.050285   0.004980 -10.098  < 2e-16 ***
## countrydenmark      0.243220   0.008647  28.128  < 2e-16 ***
## countryestonia      0.130687   0.012268  10.653  < 2e-16 ***
## countrynorway       0.098900   0.015354   6.441 1.24e-10 ***
## countryportugal     0.207806   0.012335  16.847  < 2e-16 ***
## countryswitzerland  0.104428   0.026225   3.982 6.88e-05 ***
## countryuk           0.183206   0.007300  25.096  < 2e-16 ***
## bmi_z               0.010464   0.002841   3.684 0.000231 ***
## parenteducation     0.039131   0.007062   5.541 3.09e-08 ***
## seasonspring       -0.033266   0.006915  -4.811 1.52e-06 ***
## seasonsummer       -0.095216   0.008535 -11.156  < 2e-16 ***
## seasonwinter        0.031516   0.007063   4.462 8.19e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   4.471290   0.009678  462.03   <2e-16 ***
## icad_sexmale -0.011407   0.014084   -0.81    0.418    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  10191 
## Degrees of Freedom for the fit:  15
##       Residual Deg. of Freedom:  10176 
##                       at cycle:  3 
##  
## Global Deviance:     119944.4 
##             AIC:     119974.4 
##             SBC:     120082.8 
## ******************************************************************

4.0.2.3.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = sedentary_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + season, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_season_cpm,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         5.701706   0.009368 608.648  < 2e-16 ***
## icad_sexmale       -0.050197   0.005407  -9.283  < 2e-16 ***
## countrydenmark      0.251683   0.008682  28.989  < 2e-16 ***
## countryestonia      0.140667   0.011827  11.894  < 2e-16 ***
## countrynorway       0.100206   0.014256   7.029 2.21e-12 ***
## countryportugal     0.210151   0.011978  17.545  < 2e-16 ***
## countryswitzerland  0.115376   0.024214   4.765 1.92e-06 ***
## countryuk           0.168753   0.006799  24.819  < 2e-16 ***
## bmi_z               0.011130   0.002832   3.931 8.52e-05 ***
## parenteducation     0.036646   0.006642   5.517 3.53e-08 ***
## seasonspring       -0.026212   0.006987  -3.752 0.000177 ***
## seasonsummer       -0.087730   0.008276 -10.601  < 2e-16 ***
## seasonwinter        0.032107   0.007291   4.404 1.08e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -1.39255    0.01003 -138.85  < 2e-16 ***
## icad_sexmale  0.04437    0.01464    3.03  0.00245 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.59086    0.04421  13.366   <2e-16 ***
## icad_sexmale  0.05474    0.05900   0.928    0.354    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  10191 
## Degrees of Freedom for the fit:  17
##       Residual Deg. of Freedom:  10174 
##                       at cycle:  6 
##  
## Global Deviance:     119640.7 
##             AIC:     119674.7 
##             SBC:     119797.6 
## ******************************************************************

4.0.2.4 Light

4.0.2.4.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = light_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + season, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_season,      trace = FALSE) 
## 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         5.925017   0.006753 877.374  < 2e-16 ***
## icad_sexmale        0.004549   0.003635   1.251  0.21090    
## countrybrazil      -0.076248   0.010336  -7.377 1.73e-13 ***
## countrydenmark     -0.054421   0.006620  -8.221 2.24e-16 ***
## countryestonia      0.064868   0.008372   7.748 1.02e-14 ***
## countrynorway       0.026710   0.010290   2.596  0.00945 ** 
## countryportugal    -0.028417   0.008989  -3.161  0.00158 ** 
## countryswitzerland  0.153812   0.009609  16.007  < 2e-16 ***
## countryuk          -0.047352   0.005024  -9.425  < 2e-16 ***
## bmi_z               0.000305   0.002102   0.145  0.88463    
## parenteducation    -0.014720   0.004816  -3.057  0.00224 ** 
## seasonspring        0.033421   0.005260   6.354 2.18e-10 ***
## seasonsummer        0.053632   0.005935   9.036  < 2e-16 ***
## seasonwinter       -0.015100   0.005641  -2.677  0.00744 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.244576   0.009287 457.020   <2e-16 ***
## icad_sexmale 0.028626   0.013498   2.121    0.034 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11109 
## Degrees of Freedom for the fit:  16
##       Residual Deg. of Freedom:  11093 
##                       at cycle:  3 
##  
## Global Deviance:     126134.6 
##             AIC:     126166.6 
##             SBC:     126283.7 
## ******************************************************************

4.0.2.4.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = light_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + season, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_season,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         5.9203488  0.0062808 942.618  < 2e-16 ***
## icad_sexmale        0.0045907  0.0037283   1.231 0.218239    
## countrybrazil      -0.0352517  0.0094266  -3.740 0.000185 ***
## countrydenmark      0.0093988  0.0060143   1.563 0.118141    
## countryestonia      0.0896530  0.0080469  11.141  < 2e-16 ***
## countrynorway       0.0515132  0.0097011   5.310 1.12e-07 ***
## countryportugal     0.0111232  0.0082448   1.349 0.177327    
## countryswitzerland  0.1538487  0.0098384  15.638  < 2e-16 ***
## countryuk          -0.0418662  0.0045166  -9.269  < 2e-16 ***
## bmi_z               0.0007776  0.0018912   0.411 0.680971    
## parenteducation    -0.0162561  0.0044284  -3.671 0.000243 ***
## seasonspring        0.0286138  0.0047492   6.025 1.74e-09 ***
## seasonsummer        0.0530258  0.0053981   9.823  < 2e-16 ***
## seasonwinter       -0.0135712  0.0049876  -2.721 0.006519 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -1.69747    0.01042 -162.98   <2e-16 ***
## icad_sexmale  0.02198    0.01505    1.46    0.144    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1.55740    0.05471  28.467   <2e-16 ***
## icad_sexmale -0.07769    0.07180  -1.082    0.279    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11109 
## Degrees of Freedom for the fit:  18
##       Residual Deg. of Freedom:  11091 
##                       at cycle:  8 
##  
## Global Deviance:     125921.1 
##             AIC:     125957.1 
##             SBC:     126088.8 
## ******************************************************************

4.0.2.5 Moderate

4.0.2.5.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = moderate_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + season, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_season,      trace = FALSE) 
## 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         3.612909   0.014807 244.006  < 2e-16 ***
## icad_sexmale        0.310392   0.007997  38.814  < 2e-16 ***
## countrybrazil      -0.405945   0.027673 -14.669  < 2e-16 ***
## countrydenmark     -0.248126   0.015913 -15.592  < 2e-16 ***
## countryestonia      0.016472   0.018142   0.908 0.363926    
## countrynorway       0.068202   0.020489   3.329 0.000875 ***
## countryportugal    -0.111227   0.019697  -5.647 1.67e-08 ***
## countryswitzerland  0.189989   0.019935   9.531  < 2e-16 ***
## countryuk          -0.088751   0.010763  -8.246  < 2e-16 ***
## bmi_z              -0.028484   0.004733  -6.018 1.82e-09 ***
## parenteducation    -0.044339   0.010337  -4.289 1.81e-05 ***
## seasonspring        0.077942   0.011605   6.716 1.96e-11 ***
## seasonsummer        0.046843   0.013107   3.574 0.000353 ***
## seasonwinter       -0.063423   0.012808  -4.952 7.46e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.689430   0.009278  289.88   <2e-16 ***
## icad_sexmale 0.266959   0.013468   19.82   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11109 
## Degrees of Freedom for the fit:  16
##       Residual Deg. of Freedom:  11093 
##                       at cycle:  3 
##  
## Global Deviance:     94102.02 
##             AIC:     94134.02 
##             SBC:     94251.07 
## ******************************************************************

4.0.2.5.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = moderate_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + season, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_season,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         3.544774   0.014709 241.001  < 2e-16 ***
## icad_sexmale        0.318623   0.008905  35.781  < 2e-16 ***
## countrybrazil      -0.308852   0.022464 -13.749  < 2e-16 ***
## countrydenmark     -0.147498   0.014125 -10.442  < 2e-16 ***
## countryestonia      0.100367   0.019331   5.192 2.12e-07 ***
## countrynorway       0.125903   0.023110   5.448 5.20e-08 ***
## countryportugal    -0.036505   0.019632  -1.859    0.063 .  
## countryswitzerland  0.177563   0.023006   7.718 1.28e-14 ***
## countryuk          -0.079012   0.010610  -7.447 1.03e-13 ***
## bmi_z              -0.027631   0.004511  -6.126 9.34e-10 ***
## parenteducation    -0.052211   0.010499  -4.973 6.69e-07 ***
## seasonspring        0.093457   0.011104   8.416  < 2e-16 ***
## seasonsummer        0.066601   0.012662   5.260 1.47e-07 ***
## seasonwinter       -0.062090   0.011739  -5.289 1.25e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.78248    0.01064 -73.541   <2e-16 ***
## icad_sexmale -0.04671    0.01568  -2.979   0.0029 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.68394    0.01945  35.164  < 2e-16 ***
## icad_sexmale  0.09238    0.02902   3.183  0.00146 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11109 
## Degrees of Freedom for the fit:  18
##       Residual Deg. of Freedom:  11091 
##                       at cycle:  6 
##  
## Global Deviance:     93609.55 
##             AIC:     93645.55 
##             SBC:     93777.23 
## ******************************************************************

4.0.2.6 Vigorous

4.0.2.6.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = vigorous_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + season, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_season_vig,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         2.750722   0.024286 113.266  < 2e-16 ***
## icad_sexmale        0.457057   0.013470  33.932  < 2e-16 ***
## countrybrazil      -1.065290   0.079193 -13.452  < 2e-16 ***
## countrydenmark     -0.308700   0.025829 -11.952  < 2e-16 ***
## countryestonia     -0.122986   0.031114  -3.953 7.77e-05 ***
## countrynorway       0.091753   0.030960   2.964  0.00305 ** 
## countryportugal    -0.367990   0.037910  -9.707  < 2e-16 ***
## countryswitzerland  0.070956   0.033684   2.107  0.03518 *  
## countryuk          -0.176268   0.017414 -10.122  < 2e-16 ***
## bmi_z              -0.100509   0.008471 -11.865  < 2e-16 ***
## parenteducation    -0.043637   0.017183  -2.539  0.01112 *  
## seasonspring        0.049991   0.019031   2.627  0.00863 ** 
## seasonsummer        0.008474   0.022028   0.385  0.70048    
## seasonwinter       -0.098574   0.021017  -4.690 2.76e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.302329   0.009283  248.01   <2e-16 ***
## icad_sexmale 0.321637   0.013488   23.85   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11085 
## Degrees of Freedom for the fit:  16
##       Residual Deg. of Freedom:  11069 
##                       at cycle:  3 
##  
## Global Deviance:     85888.62 
##             AIC:     85920.62 
##             SBC:     86037.63 
## ******************************************************************

4.0.3 Adjusted for Ethnicity

4.0.3.1 CPM

4.0.3.1.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = cpm_wear ~ icad_sex + country + bmi_z +  
##     parenteducation + ethnicity, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_ethnicity_cpm,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      6.322144   0.016385 385.855  < 2e-16 ***
## icad_sexmale     0.205845   0.006812  30.217  < 2e-16 ***
## countryestonia   0.040328   0.016968   2.377  0.01748 *  
## countrynorway    0.155414   0.018814   8.261  < 2e-16 ***
## countryportugal -0.046206   0.018953  -2.438  0.01479 *  
## countryuk       -0.013019   0.011512  -1.131  0.25812    
## countryusa      -0.156225   0.014525 -10.756  < 2e-16 ***
## bmi_z           -0.036870   0.003688  -9.997  < 2e-16 ***
## parenteducation -0.024650   0.008715  -2.828  0.00469 ** 
## ethnicitywhite  -0.018725   0.011679  -1.603  0.10888    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  5.215479   0.009342  558.27   <2e-16 ***
## icad_sexmale 0.202022   0.013516   14.95   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11050 
## Degrees of Freedom for the fit:  12
##       Residual Deg. of Freedom:  11038 
##                       at cycle:  3 
##  
## Global Deviance:     148762.1 
##             AIC:     148786.1 
##             SBC:     148873.8 
## ******************************************************************

4.0.3.1.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = cpm_wear ~ icad_sex + country + bmi_z +  
##     parenteducation + ethnicity, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_ethnicity_cpm,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      6.299346   0.016276 387.036  < 2e-16 ***
## icad_sexmale     0.216855   0.007337  29.555  < 2e-16 ***
## countryestonia   0.032656   0.018079   1.806 0.070901 .  
## countrynorway    0.164585   0.022114   7.443 1.06e-13 ***
## countryportugal -0.051448   0.019217  -2.677 0.007435 ** 
## countryuk       -0.041888   0.011962  -3.502 0.000464 ***
## countryusa      -0.157671   0.014218 -11.089  < 2e-16 ***
## bmi_z           -0.038865   0.003277 -11.859  < 2e-16 ***
## parenteducation -0.022913   0.008517  -2.690 0.007151 ** 
## ethnicitywhite  -0.017425   0.011073  -1.574 0.115590    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##                Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  -1.0035483  0.0097743 -102.672   <2e-16 ***
## icad_sexmale -0.0005017  0.0144041   -0.035    0.972    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.49823    0.02305  21.619  < 2e-16 ***
## icad_sexmale  0.16590    0.03270   5.073 3.97e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11050 
## Degrees of Freedom for the fit:  14
##       Residual Deg. of Freedom:  11036 
##                       at cycle:  6 
##  
## Global Deviance:     148118.8 
##             AIC:     148146.8 
##             SBC:     148249.2 
## ******************************************************************

4.0.3.2 MVPA

4.0.3.2.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = mvpa_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + ethnicity, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_ethnicity_mvpa,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      3.459927   0.035607  97.170  < 2e-16 ***
## icad_sexmale     0.393800   0.009637  40.862  < 2e-16 ***
## countrydenmark   0.377191   0.038091   9.902  < 2e-16 ***
## countryestonia   0.547874   0.039043  14.033  < 2e-16 ***
## countrynorway    0.646331   0.039848  16.220  < 2e-16 ***
## countryportugal  0.381999   0.039781   9.602  < 2e-16 ***
## countryuk        0.458029   0.035629  12.855  < 2e-16 ***
## countryusa       0.120104   0.035901   3.345 0.000824 ***
## bmi_z           -0.070887   0.005550 -12.773  < 2e-16 ***
## parenteducation -0.041424   0.012311  -3.365 0.000768 ***
## ethnicitywhite  -0.080001   0.016649  -4.805 1.57e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.121633   0.009023  345.98   <2e-16 ***
## icad_sexmale 0.313637   0.012975   24.17   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11989 
## Degrees of Freedom for the fit:  13
##       Residual Deg. of Freedom:  11976 
##                       at cycle:  3 
##  
## Global Deviance:     112525.8 
##             AIC:     112551.8 
##             SBC:     112647.9 
## ******************************************************************

4.0.3.2.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = mvpa_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + ethnicity, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_ethnicity_mvpa,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      3.402781   0.028090 121.136  < 2e-16 ***
## icad_sexmale     0.422472   0.011103  38.051  < 2e-16 ***
## countrydenmark   0.375782   0.030726  12.230  < 2e-16 ***
## countryestonia   0.530180   0.033956  15.614  < 2e-16 ***
## countrynorway    0.641209   0.038026  16.862  < 2e-16 ***
## countryportugal  0.373344   0.033064  11.291  < 2e-16 ***
## countryuk        0.400944   0.027563  14.547  < 2e-16 ***
## countryusa       0.107000   0.027655   3.869  0.00011 ***
## bmi_z           -0.073733   0.004715 -15.640  < 2e-16 ***
## parenteducation -0.039673   0.012104  -3.278  0.00105 ** 
## ethnicitywhite  -0.085532   0.015604  -5.481 4.31e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.50865    0.01033 -49.262  < 2e-16 ***
## icad_sexmale -0.08376    0.01502  -5.577  2.5e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.52116    0.01472   35.41  < 2e-16 ***
## icad_sexmale  0.08345    0.02237    3.73 0.000192 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11989 
## Degrees of Freedom for the fit:  15
##       Residual Deg. of Freedom:  11974 
##                       at cycle:  7 
##  
## Global Deviance:     110656.2 
##             AIC:     110686.2 
##             SBC:     110797.1 
## ******************************************************************

4.0.3.3 Sedentary

4.0.3.3.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = sedentary_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + ethnicity, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_ethnicity_cpm,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      5.875982   0.011720 501.342  < 2e-16 ***
## icad_sexmale    -0.048817   0.004880 -10.004  < 2e-16 ***
## countryestonia  -0.006945   0.013869  -0.501  0.61658    
## countrynorway   -0.051728   0.017425  -2.969  0.00300 ** 
## countryportugal  0.063420   0.014240   4.454 8.52e-06 ***
## countryuk        0.024880   0.008986   2.769  0.00563 ** 
## countryusa       0.090923   0.010387   8.754  < 2e-16 ***
## bmi_z            0.004522   0.002345   1.928  0.05385 .  
## parenteducation  0.033487   0.006163   5.434 5.63e-08 ***
## ethnicitywhite  -0.030690   0.007710  -3.981 6.92e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   4.536e+00  9.341e-03 485.596   <2e-16 ***
## icad_sexmale -5.323e-05  1.351e-02  -0.004    0.997    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11050 
## Degrees of Freedom for the fit:  12
##       Residual Deg. of Freedom:  11038 
##                       at cycle:  2 
##  
## Global Deviance:     131598.6 
##             AIC:     131622.6 
##             SBC:     131710.3 
## ******************************************************************

4.0.3.3.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = sedentary_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + ethnicity, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_ethnicity_cpm,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      5.8722768  0.0115819 507.021  < 2e-16 ***
## icad_sexmale    -0.0492981  0.0052534  -9.384  < 2e-16 ***
## countryestonia  -0.0009632  0.0128859  -0.075  0.94042    
## countrynorway   -0.0470853  0.0155789  -3.022  0.00251 ** 
## countryportugal  0.0589055  0.0135377   4.351 1.37e-05 ***
## countryuk        0.0015202  0.0085688   0.177  0.85919    
## countryusa       0.0920615  0.0101134   9.103  < 2e-16 ***
## bmi_z            0.0051007  0.0023696   2.153  0.03137 *  
## parenteducation  0.0304092  0.0060030   5.066 4.13e-07 ***
## ethnicitywhite  -0.0229452  0.0078633  -2.918  0.00353 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##               Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  -1.382268   0.009816 -140.822  < 2e-16 ***
## icad_sexmale  0.051049   0.014242    3.584 0.000339 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.70557    0.04012  17.588   <2e-16 ***
## icad_sexmale  0.02100    0.05489   0.383    0.702    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11050 
## Degrees of Freedom for the fit:  14
##       Residual Deg. of Freedom:  11036 
##                       at cycle:  6 
##  
## Global Deviance:     131335.7 
##             AIC:     131363.7 
##             SBC:     131466 
## ******************************************************************

4.0.3.4 Light

4.0.3.4.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = light_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + ethnicity, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_ethnicity,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      5.888659   0.011231 524.325  < 2e-16 ***
## icad_sexmale     0.013703   0.003945   3.473 0.000516 ***
## countrydenmark   0.079089   0.012386   6.385 1.77e-10 ***
## countryestonia   0.119524   0.013395   8.923  < 2e-16 ***
## countrynorway    0.084080   0.015021   5.598 2.22e-08 ***
## countryportugal  0.037270   0.013498   2.761 0.005769 ** 
## countryuk        0.020207   0.011291   1.790 0.073524 .  
## countryusa      -0.032327   0.011275  -2.867 0.004148 ** 
## bmi_z           -0.005790   0.002012  -2.878 0.004008 ** 
## parenteducation -0.009233   0.004958  -1.862 0.062571 .  
## ethnicitywhite  -0.020665   0.006376  -3.241 0.001195 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.338427   0.009019 481.043  < 2e-16 ***
## icad_sexmale 0.034737   0.012964   2.679  0.00738 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11989 
## Degrees of Freedom for the fit:  13
##       Residual Deg. of Freedom:  11976 
##                       at cycle:  3 
##  
## Global Deviance:     138454.6 
##             AIC:     138480.6 
##             SBC:     138576.7 
## ******************************************************************

4.0.3.4.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = light_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + ethnicity, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_ethnicity,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      5.904925   0.010283 574.251  < 2e-16 ***
## icad_sexmale     0.012645   0.004087   3.094  0.00198 ** 
## countrydenmark   0.070438   0.011435   6.160 7.52e-10 ***
## countryestonia   0.105758   0.012649   8.361  < 2e-16 ***
## countrynorway    0.071247   0.014088   5.057 4.32e-07 ***
## countryportugal  0.035009   0.012324   2.841  0.00451 ** 
## countryuk       -0.011593   0.010289  -1.127  0.25987    
## countryusa      -0.016850   0.010230  -1.647  0.09956 .  
## bmi_z           -0.005268   0.001790  -2.942  0.00327 ** 
## parenteducation -0.012916   0.004515  -2.860  0.00424 ** 
## ethnicitywhite  -0.015287   0.005746  -2.660  0.00782 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  -1.56872    0.01012 -154.999   <2e-16 ***
## icad_sexmale  0.02054    0.01453    1.414    0.157    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1.37404    0.04654  29.522   <2e-16 ***
## icad_sexmale -0.01925    0.06245  -0.308    0.758    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11989 
## Degrees of Freedom for the fit:  15
##       Residual Deg. of Freedom:  11974 
##                       at cycle:  8 
##  
## Global Deviance:     138323.5 
##             AIC:     138353.5 
##             SBC:     138464.3 
## ******************************************************************

4.0.3.5 Moderate

4.0.3.5.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = moderate_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + ethnicity, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_ethnicity,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      3.276964   0.028957 113.168  < 2e-16 ***
## icad_sexmale     0.336439   0.008834  38.086  < 2e-16 ***
## countrydenmark   0.223865   0.031500   7.107 1.25e-12 ***
## countryestonia   0.406607   0.032393  12.552  < 2e-16 ***
## countrynorway    0.462114   0.033767  13.685  < 2e-16 ***
## countryportugal  0.283675   0.032660   8.686  < 2e-16 ***
## countryuk        0.311167   0.028896  10.769  < 2e-16 ***
## countryusa      -0.024825   0.029256  -0.849    0.396    
## bmi_z           -0.046268   0.004942  -9.362  < 2e-16 ***
## parenteducation -0.045808   0.011292  -4.057 5.01e-05 ***
## ethnicitywhite  -0.059899   0.015370  -3.897 9.78e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.708164   0.009013  300.48   <2e-16 ***
## icad_sexmale 0.277371   0.012946   21.43   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11989 
## Degrees of Freedom for the fit:  13
##       Residual Deg. of Freedom:  11976 
##                       at cycle:  3 
##  
## Global Deviance:     102189.4 
##             AIC:     102215.4 
##             SBC:     102311.5 
## ******************************************************************

4.0.3.5.2 GAMLSS - Median + Skew

## ******************************************************************
## Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.") 
## 
## Call:  gamlss(formula = moderate_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + ethnicity, sigma.formula = ~icad_sex,  
##     nu.formula = ~icad_sex, family = BCCGo, data = sensitivity_ethnicity,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      3.254311   0.025546 127.391  < 2e-16 ***
## icad_sexmale     0.355492   0.010072  35.296  < 2e-16 ***
## countrydenmark   0.201778   0.027971   7.214 5.76e-13 ***
## countryestonia   0.387939   0.030953  12.533  < 2e-16 ***
## countrynorway    0.434359   0.034539  12.576  < 2e-16 ***
## countryportugal  0.254034   0.030029   8.460  < 2e-16 ***
## countryuk        0.228501   0.025173   9.077  < 2e-16 ***
## countryusa      -0.046620   0.025137  -1.855 0.063673 .  
## bmi_z           -0.047120   0.004276 -11.020  < 2e-16 ***
## parenteducation -0.044548   0.011004  -4.048 5.19e-05 ***
## ethnicitywhite  -0.053401   0.014043  -3.803 0.000144 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.61300    0.01043 -58.758  < 2e-16 ***
## icad_sexmale -0.06702    0.01511  -4.435 9.27e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Nu link function:  identity 
## Nu Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.59808    0.01667  35.877  < 2e-16 ***
## icad_sexmale  0.06950    0.02462   2.823  0.00476 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11989 
## Degrees of Freedom for the fit:  15
##       Residual Deg. of Freedom:  11974 
##                       at cycle:  7 
##  
## Global Deviance:     100973.2 
##             AIC:     101003.2 
##             SBC:     101114.1 
## ******************************************************************

4.0.3.6 Vigorous

4.0.3.6.1 GAMLSS - Mean + SD

## ******************************************************************
## Family:  c("NO", "Normal") 
## 
## Call:  gamlss(formula = vigorous_evenson ~ icad_sex + country +  
##     bmi_z + parenteducation + ethnicity, sigma.formula = ~icad_sex,  
##     family = NO(mu.link = log), data = sensitivity_ethnicity_vig,  
##     trace = FALSE) 
## 
## Fitting method: RS() 
## 
## ------------------------------------------------------------------
## Mu link function:  log
## Mu Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      1.724764   0.080492  21.428  < 2e-16 ***
## icad_sexmale     0.525559   0.014770  35.583  < 2e-16 ***
## countrydenmark   0.833019   0.083127  10.021  < 2e-16 ***
## countryestonia   0.961668   0.084517  11.378  < 2e-16 ***
## countrynorway    1.162603   0.084093  13.825  < 2e-16 ***
## countryportugal  0.720208   0.086372   8.338  < 2e-16 ***
## countryuk        0.911777   0.080645  11.306  < 2e-16 ***
## countryusa       0.571057   0.080739   7.073 1.60e-12 ***
## bmi_z           -0.132401   0.008978 -14.747  < 2e-16 ***
## parenteducation -0.029261   0.018661  -1.568    0.117    
## ethnicitywhite  -0.128659   0.024834  -5.181 2.24e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## Sigma link function:  log
## Sigma Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   2.28375    0.00904   252.6   <2e-16 ***
## icad_sexmale  0.34269    0.01303    26.3   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------------------------------
## No. of observations in the fit:  11960 
## Degrees of Freedom for the fit:  13
##       Residual Deg. of Freedom:  11947 
##                       at cycle:  4 
##  
## Global Deviance:     92542.77 
##             AIC:     92568.77 
##             SBC:     92664.83 
## ******************************************************************