Analysis of censored discrete longitudinal data: estimation of mean response

The study of longitudinal data is usually concerned with one or several response variables measured, possibly along with some covariates, at different points in time. In real-life situations this is often complicated by missing observations due to what we usually refer to as 'censoring'. In this paper we consider missingness of a monotone kind; subjects that dropout, i.e. are censored, fail to participate in the study at any of the subsequent observation times. Our scientific objective is to make inference about the mean response in a hypothetical population without any dropouts. There are several methods and approaches that address this problem, and we will present two existing methods (the linear-increments method and the inverse-probability-weighting method), as well as propose a new method, based on a discrete Markov process. We examine the performance of the corresponding estimators and compare these with respect to bias and variability. To demonstrate the effectiveness of the approaches in estimating the mean of a response variable, we analyse simulated data of different multistate models with a Markovian structure. Analyses of substantive data from (1) a study of symptoms experienced after a traumatic brain injury, and (2) a study of cognitive function among the elderly, are used as illustrations of the methods presented.