Event History- HW 3

#read in data from DHS in Uganda 2011 and 2016 and combine into one data-set
library(haven)
library(knitr)
library(tidyverse)

── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
✔ ggplot2 3.3.6      ✔ purrr   0.3.4 
✔ tibble  3.1.8      ✔ dplyr   1.0.10
✔ tidyr   1.2.0      ✔ stringr 1.4.1 
✔ readr   2.1.2      ✔ forcats 0.5.2 
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()

library(car)

Loading required package: carData

Attaching package: 'car'

The following object is masked from 'package:dplyr':

    recode

The following object is masked from 'package:purrr':

    some

ugtotal <- read_dta("C:/Users/rlutt/Downloads/UGIR7BFL.DTA")

ugtotal<-zap_labels(ugtotal)

-My outcome used in this analysis is the event of a second birth. For this part of the analysis, I considers the covariates of martial status, age, and use of contraception. The original grouping variable emotional partner violence is not included here, but it will be included later on in a larger variable that accounts for all intimate partner violence as the main predictor. This analysis focuses on covariates known to affect likelihood of a second birth.

#emotional ipv & births & covariates

library(dplyr)
library(tibble)

#check what is censored
table(is.na(ugtotal$bidx_01))


FALSE  TRUE 
13745  4761

#cutdown data-set to only use variables of interest
sub<-ugtotal%>%
    filter(bidx_01==1&b0_01==0)%>%
  transmute(int.cmc=v008,
            emoipv=d104,
              fbir.cmc=b3_01,
                 sbir.cmc=b3_02, 
            contraception=v313, 
            marital=v501, 
            age=v012,
                weight=v005/1000000,
                 psu=v021,
                 strata=v022)%>%
select(int.cmc, emoipv, fbir.cmc, sbir.cmc, contraception, marital, emoipv, age, weight, psu, strata)%>%
  filter(emoipv==1)%>%
  mutate(agefb = (age - (int.cmc - fbir.cmc)/12))

#calculate birth intervals 

sub2<-sub%>%
  mutate(secbi = ifelse(is.na(sbir.cmc)==T,
                   int.cmc - fbir.cmc, 
                   fbir.cmc - sbir.cmc),
         b2event = ifelse(is.na(sbir.cmc)==T,0,1))

#drop na
library(tidyr)
drop_na(sub2, secbi)

# A tibble: 2,986 × 13
   int.cmc emoipv fbir.cmc sbir.cmc contrace…¹ marital   age weight   psu strata
     <dbl>  <dbl>    <dbl>    <dbl>      <dbl>   <dbl> <dbl>  <dbl> <dbl>  <dbl>
 1    1400      1     1364     1316          0       2    26  1.10      1      1
 2    1400      1     1384       NA          0       2    38  1.10      1      1
 3    1400      1     1384     1342          3       1    24  1.10      1      1
 4    1400      1     1377     1310          0       2    33  1.10      1      1
 5    1400      1     1325     1199          0       5    43  1.10      1      1
 6    1400      1     1396     1345          3       1    23  0.996     2      1
 7    1400      1     1395     1324          3       1    34  0.996     2      1
 8    1400      1     1290     1248          0       5    40  0.996     2      1
 9    1400      1     1392     1378          0       1    31  0.996     2      1
10    1400      1     1398     1366          0       5    36  0.996     2      1
# … with 2,976 more rows, 3 more variables: agefb <dbl>, secbi <dbl>,
#   b2event <dbl>, and abbreviated variable name ¹contraception

 complete.cases(sub2)

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[2881]  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE
[2893]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE
[2905]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE FALSE  TRUE  TRUE
[2917]  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE
[2929]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE FALSE
[2941]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
[2953]  TRUE FALSE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE
[2965]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE
[2977]  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE FALSE FALSE

#check distributions of event 

smoothScatter(sub2$secbi)

#kernel-density method of hazard
library(muhaz)
fit.haz.sm<-muhaz(sub2$secbi, sub2$b2event)

Did you choose an AFT or PH model and why?

I chose parametric hazard function because framing the event of giving birth using the proportional hazard model because literature on birth spacing that uses event history analysis usually uses a hazard framework rather than a survival framework.

Fit the parametric model of your choosing to the data.

#build model

#design
library(survey)

Loading required package: grid

Loading required package: Matrix


Attaching package: 'Matrix'

The following objects are masked from 'package:tidyr':

    expand, pack, unpack

Loading required package: survival


Attaching package: 'survey'

The following object is masked from 'package:graphics':

    dotchart

options(survey.lonely.psu = "adjust")

des<-svydesign(ids=~psu, strata=~strata,
               data=sub2, weight=~weight)

#use eha package and survival packages
library(eha)
library(survival)



#use weibull first
day<-1/365

fit.1<-phreg(Surv(secbi+day, b2event)~marital+contraception+age,
             data=sub2,
             dist="weibull",
             shape = 1)

summary(fit.1)

Covariate             Mean       Coef     Rel.Risk   S.E.    LR p
marital               2.158    -0.052     0.950     0.014   0.0002 
contraception         1.032     0.040     1.040     0.014   0.0038 
age                  33.450    -0.008     0.992     0.002   0.0005 

Events                    2671 
Total time at risk        118376 
Max. log. likelihood      -12778 
LR test statistic         39.78 
Degrees of freedom        3 
Overall p-value           1.18664e-08

#plot
plot(fit.1)
lines(fit.haz.sm, col=2)

Justify what parametric distribution you choose

First I tried Weibull then I tried piecewise because it allows for me to set the parameters for the shape of the distribution. I compared the AICs at the end which showed that piecewise is the better fit.

Carry out model fit diagnostics for the model
Include all main effects in the model
Test for an interaction between at least two of the predictors

#interaction between marriage and contraception

fit.2<-phreg(Surv(secbi+day, b2event)~marital+marital*contraception+contraception+age,
             data=sub2,
             dist="weibull",
             shape = 1)
summary(fit.2)

Single term deletions

Model:
Surv(secbi + day, b2event) ~ marital + marital * contraception + 
    contraception + age
                      Df   AIC   LRT Pr(>Chi)    
<none>                   25566                   
age                    1 25576 12.08  0.00051 ***
marital:contraception  1 25564  0.02  0.87698    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Covariate             Mean       Coef     Rel.Risk   S.E.    Wald p
marital               2.158    -0.053     0.948     0.017   0.0021 
contraception         1.032     0.037     1.037     0.024   0.1315 
age                  33.450    -0.008     0.992     0.002   0.0005 
marital:contraception 
   :                          0.002     1.002     0.010    0.8769 

Events                    2671 
Total time at risk        118376 
Max. log. likelihood      -12778 
LR test statistic         39.80 
Degrees of freedom        4 
Overall p-value           4.75328e-08

plot(fit.2, fn="haz")
lines(fit.haz.sm, col=2)

Interpret your results and write them up
Provide tabular and graphical output to support your conclusions

#try piecewise model
fit.3<-pchreg(Surv(secbi, b2event)~marital+contraception+age,
             data=sub2,
             cuts=seq(1, 300, 12))
summary(fit.3)

Covariate             Mean       Coef     Rel.Risk   S.E.    LR p
marital               2.158    -0.067     0.935     0.014   0.0000 
contraception         1.032     0.036     1.037     0.014   0.0084 
age                  33.450    -0.016     0.984     0.003   0.0000 

Events                    2671 
Total time at risk        118368 
Max. log. likelihood      -11765 
LR test statistic         74.33 
Degrees of freedom        3 
Overall p-value           5.55112e-16

Restricted mean survival:  27.80497 in (1, 289]

plot(fit.3, fn="haz")
lines(fit.haz.sm, col=2)

fit.4<-pchreg(Surv(secbi, b2event)~marital*contraception+age+marital+contraception,
             data=sub2,
             cuts=seq(1, 300, 12))
summary(fit.4)

Single term deletions

Model:
Surv(secbi, b2event) ~ marital * contraception + age + marital + 
    contraception
                      Df   AIC  LRT Pr(>Chi)    
<none>                   23586                  
age                    1 23622 38.8  4.7e-10 ***
marital:contraception  1 23584  0.0      0.9    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Covariate             Mean       Coef     Rel.Risk   S.E.    Wald p
marital               2.158    -0.068     0.934     0.017   0.0001 
contraception         1.032     0.034     1.034     0.024   0.1645 
age                  33.450    -0.016     0.984     0.003   0.0000 
marital:contraception 
   :                          0.001     1.001     0.010    0.9006 

Events                    2671 
Total time at risk        118368 
Max. log. likelihood      -11765 
LR test statistic         74.34 
Degrees of freedom        4 
Overall p-value           2.77556e-15

Restricted mean survival:  27.77653 in (1, 289]

plot(fit.4, fn="haz")
lines(fit.haz.sm, col=2)

#compare AICs
AIC(fit.1)

[1] 25563.96

AIC(fit.2)

[1] 25565.93

-2*fit.3$loglik[2]+length(fit.3$coefficients)

[1] 23532.59

-2*fit.4$loglik[2]+length(fit.4$coefficients)

[1] 23533.58

The piecewise distribution without an interaction term seems to be the best fit given the lowest AIC score.

The results show that martial status has a negative effect on the hazard of giving birth as does age. I would not expect marital status to have this effect. Secondly, contraception has a small, but positive effect on the hazard of giving birth, which seems to be against what you would expect, however in the context of second births in sub-Saharan Africa it makes sense because of the prevalence of using short term contraception to space out births rather than to stop having children altogether.