#### Abstract

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 on the HIV sequences that infect vaccine efficacy trial participants to 1) test for vaccine efficacy more powerfully than procedures that ignore the sequence data; and 2) evaluate the dependence of vaccine efficacy on the divergence of infecting HIV strains 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. Problems 1) and 2) can then be approached by testing whether the ratio of the mark-specific hazard functions for the vaccine and placebo groups is unity or independent of the mark, respectively. We develop nonparametric and semiparametric tests for these null hypotheses, based on contrasts of Nelson–Aalen-type estimates of cumulative mark-specific hazard functions for the two groups. Techniques for nonparametric estimation of mark-specific vaccine efficacy based on the cumulative mark-specific incidence functions are also developed. Numerical studies show satisfactory performance of the procedures. The methods are illustrated with application to HIV genetic sequence data collected in the first HIV vaccine efficacy trial. The methodology applies generally to the study of relative risks of failure wherein a continuous mark variable accompanies each failure event.

#### Disciplines

Statistical Methodology | Statistical Theory | Survival Analysis

#### Suggested Citation

Gilbert, Peter B.; McKeague, Ian W.; and Sun, Yanqing, "The Two-sample Problem for Failure Rates Depending on a Continuous Mark: An Application to Vaccine Efficacy" (March 2006). *UW Biostatistics Working Paper Series.* Working Paper 280.

http://biostats.bepress.com/uwbiostat/paper280