Comparison of Mark-specific Relative Risks with Application to Viral Divergence in Vaccine Efficacy Trials

The efficacy of an HIV vaccine to prevent infection is likely to depend on the genetic variation of the exposing virus. This paper addresses the problem of using data from an HIV vaccine efficacy trial to detect such dependence in terms of the divergence of infecting HIV viruses in trial participants from the HIV strain that is contained in the vaccine. Because hundreds of amino acid sites in each HIV genome are sequenced, it is natural to treat the divergence (defined in terms of Hamming distance say) as a continuous mark variable that accompanies each failure (infection) time. The problem can then be approached by testing whether the ratio of the mark-specific hazard functions for the vaccine and placebo groups is independent of the mark. We develop nonparametric tests for this null hypothesis, using test statistics sensitive to ordered and two-sided alternatives. The test statistics are functionals of a bivariate test process that contrasts Nelson–Aalen-type estimates of cumulative mark-specific hazard functions for the two groups. Asymptotically correct critical values are obtained through a Gaussian multipliers simulation technique. Techniques for estimating mark-specific vaccine efficacy based on the cumulative mark-specific incidence functions are also developed. Numerical studies show good performance of the procedures. The methods are illustrated with application to HIV genetic sequence data collected in the first HIV vaccine efficacy trial. Some key words: Competing risks; genetic data; nonparametric statistics; survival analysis. Peter B. Gilbert is Research Associate Professor, Department of Biostatistics, University of Washington and Associate Member, Fred Hutchinson Cancer Research Center, Seattle, WA 98109 (E-mail: [email protected]); Ian W. McKeague is Professor of Biostatistics, Columbia University Mailman School of Public Health, 722 West 168th Street, 6th Floor, New York, NY 10032 (E-mail: [email protected]); and Yanqing Sun is Professor of Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223 (E-mail: [email protected]).