  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. By using the information gathered
in the first phase, the second-phase subsample can be selected to enhance the
efficiency of 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. In this study, we propose an extension of the two-phase designs that
employs an optimal sampling scheme for estimating predictor effects with pseudo
conditional likelihood estimators in case-control studies. This approach is
applicable to both local and non-local effects. We demonstrate the
effectiveness of the proposed sampling scheme through simulation studies and
analysis of data from 170 patients hospitalized for treatment of COVID-19. The
results show a significant improvement in the estimation of the parameter of
interest.
