Threshold-based subgroup testing in logistic regression models in two-phase sampling designs.

The effect of treatment on binary disease outcome can differ across subgroups characterized by other covariates. Testing for the existence of subgroups that are associated with heterogeneous treatment effects can provide valuable insight regarding the optimal treatment recommendation in practice. Our research in this paper is motivated by the question of whether host genetics could modify a vaccine's effect on HIV acquisition risk. To answer this question, we used data from an HIV vaccine trial with a two-phase sampling design and developed a general threshold-based model framework to test for the existence of subgroups associated with the heterogeneity in disease risks, allowing for subgroups based on multivariate covariates. We developed a testing procedure based on maximum of likelihood-ratio statistics over change planes and demonstrated its advantage over alternative methods. We further developed the testing procedure to account for bias sampling of expensive (i.e. resource-intensive to measure) covariates through the incorporation of inverse probability weighting techniques. We used the proposed method to analyze the motivating HIV vaccine trial data. Our proposed testing procedure also has broad applications in epidemiological studies for assessing heterogeneity in disease risk with respect to univariate or multivariate predictors.