Repeated Measures for HAPPI

#Loading the dataset that has been reset into a long version
data.test4 <- read.csv("/Volumes/TOSHIBA EXT/Dropbox/ADULT STUDY/adult_study011615.csv")
#Creating a new variable that is the mean of all HAPPI questions
data.test4$HAPPI <- apply(data.test4[, c ("HAPPI1" ,"HAPPI2", "HAPPI3")], 1, mean, na.rm = TRUE)
library(reshape2); library(car)

## Warning: package 'car' was built under R version 3.1.2

data <- data.test4[,c("ID", "GROUP", "wave", "HAPPI")]
data <- dcast(data, ID + GROUP ~ wave, mean, value.var = "HAPPI")
data[,3:5] <- apply(data[,3:5],2,function(x) recode(x, "NaN = NA") )

data2 <- as.data.frame(mapply(c,data[,1:4], data[,c(1:3,5)]))
data2$wave <- rep(1:2, each=89)
names(data2) <- c("ID", "GROUP", "BASELINE", "HAPPI", "WAVE")

Drop the cases where participants did not complete the intervention completely

#data2 <- data2[-c(which(data2$GROUP ==2)),]

Intention to treat model (ITT) where we keep the cases who dropped out and did not complete the study (http://en.wikipedia.org/wiki/Intention-to-treat_analysis).

data2[which(data2$GROUP ==2), "GROUP"] <- 1

For lme to work GROUP and ID need to be seen as factors

data2$GROUP <-as.factor(data2$GROUP)
data2$ID <-as.factor(data2$ID)

Load the psych package

library(psych)

## 
## Attaching package: 'psych'
## 
## The following object is masked from 'package:car':
## 
##     logit

Describe the HAPPI variable by the GROUP variable

describeBy(data2[,3:4], group = data2$GROUP)

## group: 0
##          vars  n mean   sd median trimmed  mad min max range  skew
## BASELINE    1 86 5.03 1.32   5.33    5.16 0.99   2   7     5 -0.92
## HAPPI       2 59 5.23 1.24   5.33    5.37 0.99   1   7     6 -1.31
##          kurtosis   se
## BASELINE    -0.11 0.14
## HAPPI        1.72 0.16
## -------------------------------------------------------- 
## group: 1
##          vars  n mean   sd median trimmed  mad  min max range skew
## BASELINE    1 88 4.83 1.32   4.67    4.85 1.48 1.67   7  5.33 -0.1
## HAPPI       2 54 5.72 0.81   5.67    5.73 0.99 4.00   7  3.00  0.0
##          kurtosis   se
## BASELINE    -0.68 0.14
## HAPPI       -0.88 0.11

Create a plot that visualizes HAPPI variable by the GROUP variable

library(ggplot2)

## 
## Attaching package: 'ggplot2'
## 
## The following object is masked from 'package:psych':
## 
##     %+%

Take a look at the residuals

residual <- lm(HAPPI ~ BASELINE, data=data2)$residual

Plot the residuals to see that they are random

plot(density(residual))# A density plot

qqnorm(residual) # A quantile normal plot to checking normality
qqline(residual)

Checking the different between intervention and control groups residuals. This allows us to control for individual unsystematic differences.

data2$residual <- NA
sel1 <- which(!is.na(data2$HAPPI)) 
sel2 <- which(!is.na(data2$BASELINE))
data2$residual[intersect(sel1,sel2)] <- residual
qplot(GROUP, HAPPI, data=data2, geom="boxplot")

## Warning: Removed 65 rows containing non-finite values (stat_boxplot).

Plot of the difference between intervention and control groups.

qplot(GROUP, residual, data=data2, geom="boxplot")

## Warning: Removed 69 rows containing non-finite values (stat_boxplot).

# Load the nlme package
library(nlme)

Two way repeated measures Graphing the Two-Way Interaction.

with(data2, boxplot(HAPPI ~ WAVE + GROUP))

with(data2, boxplot(residual ~ WAVE + GROUP))

Linear Mixed-Effects Model

Comparing Basline to Wave 2 and 3 by Group.

fullModel <- lme(HAPPI ~ GROUP * WAVE + BASELINE, random = ~1 | ID, data = data2, method = "ML", na.action = "na.omit")

Results

Explanation of significance:

We asses the significance of our models by comparing them from the baseline model using the anova() function.
(Intercept): Where everything is 0
GROUP1: Is there a difference between group. If it is significant than there is a difference and the treatment had an effect.
WAVE: Asseses whether the effects gets bigger beteen time 2 and 3 (does not have to be significant)
BASELINE: Should not be significant. If it is then it shows that there is a difference between groups before the treatment.
GROUP1:WAVE: If this is significant then it means that the effect was either fleeting or it happened after the treatment i.e. between time 2 and 3.

summary(fullModel)

## Linear mixed-effects model fit by maximum likelihood
##  Data: data2 
##     AIC   BIC logLik
##   242.5 261.4 -114.3
## 
## Random effects:
##  Formula: ~1 | ID
##         (Intercept) Residual
## StdDev:      0.6351   0.4394
## 
## Fixed effects: HAPPI ~ GROUP * WAVE + BASELINE 
##               Value Std.Error DF t-value p-value
## (Intercept)  2.4086    0.4120 66   5.847  0.0000
## GROUP1       0.2790    0.3210 66   0.869  0.3879
## WAVE        -0.1458    0.1319 38  -1.106  0.2759
## BASELINE     0.5707    0.0690 66   8.277  0.0000
## GROUP1:WAVE  0.2483    0.1923 38   1.291  0.2045
##  Correlation: 
##             (Intr) GROUP1 WAVE   BASELI
## GROUP1      -0.369                     
## WAVE        -0.414  0.562              
## BASELINE    -0.849  0.012 -0.029       
## GROUP1:WAVE  0.288 -0.825 -0.686  0.014
## 
## Standardized Within-Group Residuals:
##      Min       Q1      Med       Q3      Max 
## -2.31795 -0.35922  0.02431  0.41902  1.90238 
## 
## Number of Observations: 109
## Number of Groups: 69

Table with P-values

	Value	Std.Error	DF	t-value	p-value
(Intercept)	2.4086	0.4120	66.0000	5.8468	0.0000
GROUP1	0.2790	0.3210	66.0000	0.8692	0.3879
WAVE	-0.1458	0.1319	38.0000	-1.1055	0.2759
BASELINE	0.5707	0.0690	66.0000	8.2770	0.0000
GROUP1:WAVE	0.2483	0.1923	38.0000	1.2911	0.2045

``` Table with confidence intervals

	est.	lower	upper
(Intercept)	2.4086	1.6052	3.2120
GROUP1	0.2790	-0.3470	0.9051
WAVE	-0.1458	-0.4066	0.1150
BASELINE	0.5707	0.4363	0.7052
GROUP1:WAVE	0.2483	-0.1320	0.6286