Dropout in highly unbalanced longitudinal data (WGEE)

Question

I have found a lot of software and examples that uses Weighted Generalized Estimating Equations to deal with missing data in a balanced data set (equal time points). However, I have a very high unbalanced data set (patients just come and go whenever they like). How can I use WGEE to handle dropout in this case? Is there software available (R/SAS)?

Answer 1

The R package wgeesel implements weighted GEE approach for longitudinal data with dropout or monotone missingness under missing-at-random assumption. For weighted GEE, however, you need to specify a model for the missingness, which in some cases is not straightforward. Another way to deal with missing data would be multiple imputation. With clustered data, a multilevel multiple imputation approach would be appropriate. The R package jomo is a useful tool for this (see also an introduction to jomo by the maintainer here). Below is an example using the dataset cereb from package BCgee:

library(missForest)
library(magrittr)
library(dplyr)
library(jomo)
library(mitml)
library(BCgee)
library(gee)
data(cereb)

Introduce 10% missingness to variables Drug and y:

cereb.na <- cbind(cereb[1:2],prodNA(cereb[3:4],0.1))

Prepare data; make sure binomial variables are factor, then perform imputations.

cereb.na$Drug <- as.factor(cereb.na$Drug)
cereb.na$y <- as.factor(cereb.na$y)
cereb.na$Period <- as.factor(cereb.na$Period)
Y <- cereb.na %>% select(Drug,y)
clus <- cereb.na %>% select(id)
X<-Z<-cereb.na %>% select(Period)
X$const <- 1
Z$const <- 1
jomo.cereb <- jomo(Y,X=X,Z=Z,clus=clus,nimp=5,output=F)

Transform the imputations to a list:

listjomo.cereb <- jomo2mitml.list(jomo.cereb)

Apply GEE. Note that subject identification was id in the original dataset, but in the imputed dataset its name is clus.

imp.gee <- lapply(listjomo.cereb, function(x) {
    gee(as.numeric(y) - 1 ~ Period + Drug, id = as.factor(clus), data=x, family=binomial)
})

Create a function to extract covariance matrices from the GEE results. Then obtain pooled estimates using Rubin's rules:

vcov.gee <- function(x) {
    return(x$robust.variance)
}
testEstimates(imp.gee)