Influence of human immunodeficiency virus infection on neurological impairment: an analysis of longitudinal binary data with informative drop‐out

A study to investigate the human immunodeficiency virus (HIV) status on the course of neurological impairment, conducted by the HIV Center at Columbia University, followed a cohort of HIV positive and negative gay men for 5 years and assessed the presence or absence of neurological impairment every 6 months. Almost half of the subjects dropped out before the end of the study for reasons that might have been related to the missing neurological data. We propose likelihood‐based methods for analysing such binary longitudinal data under informative and non‐informative drop‐out. A transition model is assumed for the binary response, and several models for the drop‐out processes are considered which are functions of the response variable (neurological impairment). The likelihood ratio test is used to compare models with informative and non‐informative drop‐out mechanisms. Using simulations, we investigate the percentage bias and mean‐squared error (MSE) of the parameter estimates in the transition model under various assumptions for the drop‐out. We find evidence for informative drop‐out in the study, and we illustrate that the bias and MSE for the parameters of the transition model are not directly related to the observed drop‐out or missing data rates. The effect of HIV status on the neurological impairment is found to be statistically significant under each of the models considered for the drop‐out, although the regression coefficient may be biased in certain cases. The presence and relative magnitude of the bias depend on factors such as the probability of drop‐out conditional on the presence of neurological impairment and the prevalence of neurological impairment in the population under study.