Semiparametric methods for multiple exposure mismeasurement and a bivariate outcome in HIV vaccine trials

Exposure to infection information is important for estimating vaccine efficacy, but it is difficult to collect and prone to missingness and mismeasurement. We discuss study designs that collect detailed exposure information from only a small subset of participants while collecting crude exposure information from all participants and treat estimation of vaccine efficacy in the missing data/measurement error framework. We extend the discordant partner design for HIV vaccine trials of Golm, Halloran, and Longini (1998, Statistics in Medicine, 17, 2335-2352.) to the more complex augmented trial design of Longini, Datta, and Halloran (1996, Journal of Acquired Immune Deficiency Syndromes and Human Retrovirology 13, 440-447) and Datta, Halloran, and Longini (1998, Statistics in Medicine 17, 185-200). The model for this design includes three exposure covariates and both univariate and bivariate outcomes. We adapt recently developed semiparametric missing data methods of Reilly and Pepe (1995, Biometrika 82, 299 314), Carroll and Wand (1991, Journal of the Royal Statistical Society, Series B 53, 573-585), and Pepe and Fleming (1991, Journal of the American Statistical Association 86, 108-113) to the augmented vaccine trial design. We demonstrate with simulated HIV vaccine trial data the improvements in bias and efficiency when combining the different levels of exposure information to estimate vaccine efficacy for reducing both susceptibility and infectiousness. We show that the semiparametric methods estimate both efficacy parameters without bias when the good exposure information is either missing completely at random or missing at random. The pseudolikelihood method of Carroll and Wand (1991) and Pepe and Fleming (1991) was the more efficient of the two semiparametric methods.