A semiparametric pseudo-score method for analysis of two-phase studies with continuous phase-I covariates

Two-phase study designs can reduce cost and other practical burdens associated with large scale epidemiologic studies by limiting ascertainment of expensive covariates to a smaller but informative sub-sample (phase-II) of the main study (phase-I). During the analysis of such studies, however, subjects who are selected at phase-I but not at phase-II, remain informative as they may have partial covariate information. A variety of semi-parametric methods now exist for incorporating such data from phase-I subjects when the covariate information can be summarized into a finite number of strata. In this article, we consider extending the pseudo-score approach proposed by Chatterjee et al. (J Am Stat Assoc 98:158–168, 2003) using a kernel smoothing approach to incorporate information on continuous phase-I covariates. Practical issues and algorithms for implementing the methods using existing software are discussed. A sandwich-type variance estimator based on the influence function representation of the pseudo-score function is proposed. Finite sample performance of the methods are studies using simulated data. Advantage of the proposed smoothing approach over alternative methods that use discretized phase-I covariate information is illustrated using two-phase data simulated within the National Wilms Tumor Study (NWTS).