Statistical methods for assessing differential vaccine protection against human immunodeficiency virus types

The human immunodeficiency virus type 1 (HIV-1) is extremely diverse. In assessing the utility of an HIV-1 vaccine, an important issue is the possibility of differential protection. We discuss statistical methods of inferring how the vaccine efficacy may vary with viral type from data that would be collected from a randomized, double-blind, placebo-controlled preventive vaccine efficacy trial. Detailed characterization of virus isolated from individuals infected during the trial will be available. We focus on the highly simplified case in which the viral characteristics are summarized by a single feature, which may be nominal, or a scalar quantity that represents distance between the isolate and the prototype virus or viruses used in the vaccine preparation. We consider discrete categorical and continuous response models for this quantity and identify models whose parameters can be interpreted as log ratios of strain-specific relative risks of infection in a prospective model for HIV-1 exposure and transmission. Methods of inference are described for the multinomial logistic regression (MLR) model for discrete categorical response, and a new semiparametric model which can be viewed as a continuous analog of the MLR model is introduced. The methods are illustrated by application to HIV-1 and hepatitis B vaccine trial data.