Optimal Designs of Two-Phase Case-Control Studies for General Predictor Effects

Under two-phase designs, the outcome and several covariates and confounders are measured in the first phase, and a new predictor of interest, which may be costly to collect, can be measured on a subsample in the second phase, without incurring the costs of recruiting subjects. Information in the first phase can be used to select the second-phase subsample with the goal of improving the efficiency in testing and estimating the effect of the new predictor on the outcome. Past studies have focused on optimal two-phase sampling schemes for statistical inference on local ($\beta = o(1)$) effects of the predictor of interest. Here we extend the two-phase designs with an optimal sampling scheme in case-control studies for estimation predictor effects with pseudo conditional likelihood estimators. The proposed approach is applicable to both local and non-local effects. We demonstrate that the proposed sampling scheme can lead to a substantive improvement in the estimation of the parameter of interest simulation studies and an analysis of data from 170 patients hospitalized for COVID-19.