Analyzing longitudinal data in the presence of informative drop-out: The jmre1 command

Many studies in various research areas have designs that involve repeated measurements over time of a continuous variable across a group of subjects. A frequent and serious problem in such studies is the occurrence of missing data. In many cases, missing data are caused by an event that leads to a premature termination of the series of repeated measurements on some subjects. When the probability of the occurrence of this event is related to the subject-specific underlying trend of the variable of interest, this missingness process is called informative censoring or informative drop-out. Standard likelihood-based methods (for example, linear mixed models) fail to give consistent estimates. In such cases, one needs to apply methods that simultaneously model the observed data and the missingness process. In this article, we review a method proposed by Touloumi et al. (1999, Statistics in Medicine 18: 1215-1233) to adjust for informative drop-out in longitudinal data analysis. We also present the jmre1 command, which can be used to fit the proposed model. The estimation method combines the restricted iterative generalized least-squares method with a nested expectation-maximization algorithm. The method is implemented mainly using Stata's matrix programming language, Mata. Our example is derived from the epidemiology of the HIV infection.