Regression analysis for the proportional hazards model with parameter constraints under case-cohort design

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, case-cohort studies can benefit further from taking parameters' prior information, such as the histological type and disease stage of the cancer in medical, the liquidity and market demand of the enterprise in finance. Regression analysis of the proportional hazards model with parameter constraints under case-cohort design is studied. Asymptotic properties are derived by applying the Lagrangian method based on Karush-Kuhn-Tucker conditions. The consistency and asymptotic normality of the constrained estimator are established. A modified minorization-maximization algorithm is developed for the calculation of the constrained estimator. Simulation studies are conducted to assess the finite-sample performance of the proposed method. An application to a Wilms tumor study demonstrates the utility of the proposed method in practice.