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252 Statistical Methods for Estimating Cumulative CTL Probabilities
M. Hudgens*
Fred Hutchinson Cancer Res. Ctr., Seattle, WA, USA
Background: In addition to safety, vaccine-induced CD8+ cytotoxic T-lymphocyte (CTL) responses to HIV-1 proteins are an outcome of interest in Phase I and II HIV vaccine trials. To this end, volunteers enrolled in such trials are often tested for CTL responses at periodic time points after enrollment. In summarizing these data, 3 quantities are typically of interest: the marginal probability of a positive response at a particular time point, the cumulative probability of at least 1 positive CTL response by some time point, and the cumulative repeat probability (i.e., the probability of at least 2 positive CTL responses by some time point). In previous HIV vaccine trials these quantities have been estimated using observed proportions. For example, the cumulative probability of a positive response in the vaccine arm at a particular time point is traditionally estimated by the proportion of vaccinees who had at least 1 positive CTL test among those that had at least 1 conclusive CTL test by that time point. We propose an alternative method of estimation.
Methods: Nonparametric maximum likelihood estimates (NPMLEs) of the marginal, cumulative, and cumulative repeat probabilities are developed. Comparisons of the NPMLEs and traditional estimates are investigated using data from simulations and AVEG vCP205 trials.
Results: In the presence of missing data, the traditional estimator is shown to yield biased estimates of the cumulative and cumulative repeat success probabilities that tend to underestimate the vaccine's ability to induce CTL responses. Conversely, the NPMLEs are shown to have little bias, even in the presence of a substantial amount of missing data.
Conclusions: Traditional estimators of cumulative and cumulative repeat CTL probabilities based on observed proportions should not be employed further as they can misleadingly underestimate a vaccine's ability to induce a CTL response. Maximum likelihood estimation offers an alternative method that yields more accurate estimates, which is especially important if cumulative CTL responses are used as a criterion for efficacy trial qualification.
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