Weighted likelihood method for grouped survival data in case-cohort studies with application to HIV vaccine trials

Grouped failure time data arise often in HIV studies. In a recent preventive HIV vaccine efficacy trial, immune responses generated by the vaccine were measured from a case-cohort sample of vaccine recipients, who were subsequently evaluated for the study endpoint of HIV infection at prespecified follow-up visits. Gilbert et al. (2005, Journal of Infectious Diseases 191, 666-677) and Forthal et al. (2007, Journal of Immunology 178, 6596-6603) analyzed the association between the immune responses and HIV incidence with a Cox proportional hazards model, treating the HIV infection diagnosis time as a right-censored random variable. The data, however, are of the form of grouped failure time data with case-cohort covariate sampling, and we propose an inverse selection probability-weighted likelihood method for fitting the Cox model to these data. The method allows covariates to be time dependent, and uses multiple imputation to accommodate covariate data that are missing at random. We establish asymptotic properties of the proposed estimators, and present simulation results showing their good finite sample performance. We apply the method to the HIV vaccine trial data, showing that higher antibody levels are associated with a lower hazard of HIV infection.