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To reduce the cost and improve the efficiency of cohort studies, case-cohort design is a widely used biased-sampling scheme for time-to-event data. In modeling process, we may encounter the situation that actual covariates are not directly observed, but are contaminated with a multiplicative factor which is determined by a smooth unknown function of an observed covariate. In this paper, we study the inference methods for case-cohort data under the additive hazards model with covariate adjustment. We propose to estimate the distorting function by nonparametric regressing the contaminated covariates on the distorting factor. The estimators for the parameters can then be obtained based on the estimated covariates. A series of simulation studies are conducted to assess the finite-sample performance of the proposed estimator. An application to a pulmonary exacerbation study demonstrates the practicability of the proposed methods.

Statistical inference for case-cohort design under the additive hazards model with covariate adjustment