Estimating cumulative probabilities from incomplete longitudinal binary responses with application to HIV vaccine trials

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Abstract
When describing longitudinal binary response data, it may be desirable to estimate the cumulative probability of at least one positive response by some time point. For example, in phase I and II human immunodeficiency virus (HIV) vaccine trials, investigators are often interested in the probability of at least one vaccine‐induced CD8+ cytotoxic T‐lymphocyte (CTL) response to HIV proteins at different times over the course of the trial. In this setting, traditional estimates of the cumulative probabilities have been based on observed proportions. We show that if the missing data mechanism is ignorable, the traditional estimator of the cumulative success probabilities is biased and tends to underestimate a candidate vaccine's ability to induce CTL responses. As an alternative, we propose applying standard optimization techniques to obtain maximum likelihood estimates of the response profiles and, in turn, the cumulative probabilities of interest. Comparisons of the empirical and maximum likelihood estimates are investigated using data from simulations and HIV vaccine trials. We conclude that maximum likelihood offers a more accurate method of estimation, which is especially important in the HIV vaccine setting as cumulative CTL responses will likely be used as a key criterion for large scale efficacy trial qualification. Copyright © 2003 John Wiley & Sons, Ltd.