Binary response models with M-phase case-control data

In this study, a more general single-index regression model was presented to characterize the relationship between a dichotomous response and covariates of interest. With M-phase (M≥2) case-control data supplemented by information on a response and certain covariates, we propose a pseudo maximum likelihood estimation for the index coefficients. In the receiver operating characteristic curve analysis, an estimation for the accuracy measure is further provided and is borrowed to seek an optimal linear predictor. As for the hypothesis of model correctness, a pseudo least squares approach is employed as an aid to devising suitable testing procedures. Moreover, the general theoretical frameworks of these estimators are well developed. Finally, extensive simulations and two empirical applications are used to illustrate the applicability of our methodology.