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The case-cohort design is used in large cohort study to improve the efficiency and reduce the cost. In modeling process, we meet the situation that some covariates in a regression model are distorted by an unknown function of an observable confounding variable in a multiplicative form. In this paper, we consider fitting covariate-adjusted proportional hazards model for case-cohort studies. We propose to estimate the distorted function by non parametrically regressing the observed covariates on the distorted confounder, and then an estimator for the regression parameter is obtained by using the estimated covariates. Under some mild assumptions, we establish the asymptotic properties of the proposed estimator. The results from both artificial and real data demonstrate good performance and practicality of the proposed method.

Case-cohort and inference for the proportional hazards model with covariate adjustment