| The human immunodeficiency virus type 1 (HIV-1) exhibits broad genotypic and phenotypic diversity. Thus in assessing the utility of a candidate HIV-1 vaccine, an important issue is the possibility of virus type-specific protection. Statistical methods of inferring how vaccine efficacy may vary with viral type from data that would be collected from a randomized, double blinded, placebo-controlled preventive vaccine efficacy trial are developed. Detailed characterization of virus isolated from individuals infected during the trial will be available. Treatment focuses on the highly simplified case in which the viral characteristics are summarized by a one-dimensional nominal categorization or a single scalar quantity that represents distance between the isolate and the prototype virus or viruses used in the vaccine preparation. Discrete categorical and continuous response models for this quantity are considered, and models whose parameters can be interpreted as log ratios of strain-specific relative per-contact transmission rates in a prospective model for HIV-1 exposure and transmission are identified. Methods of inference are described for the multinomial logistic regression (MLR) model (Anderson, J. A., 1972, Biometrika 59, 19-35; Cox, D. R., 1970, The Analysis of Binary Data) for discrete categorical response, and for a new semiparametric model, the continuous logistic regression (CLR) model, for continuous response. These models can be used either to infer if and how vaccine efficacy depends on a viral feature chosen a priori, or as exploratory tools for identifying features which are potential viral correlates of protection. Extensions of these models are considered, including incorporation of multidimensional viral features and endpoints other than prevention of infection.;The CLR model belongs to the class of semiparametric selection bias models, which have wide application. New statistical methodology is developed for this class of models. Nonparametric estimation in selection bias models has been successfully treated by the method of maximum likelihood (e.g. Vardi, 1985 and Gill, Vardi, and Wellner, 1988), and the methodology described here can be viewed as a semiparametric extension of the earlier work. Through semiparametric efficiency theory utilizing tools in functional analysis and empirical process theory, the semiparametric maximum likelihood estimator (MLE) is proved to be asymptotically optimal. Furthermore, through a simulation study in the CLR model, HIV vaccine trial setting, the MLE is shown to behave well in finite samples. Maximum likelihood estimation in semiparametric selection bias models is comparable to maximum likelihood estimation in Cox's (1972) semiparametric proportional hazards model. |
