Generalized case-cohort and inference for Cox's model with parameter constraints

To reduce the cost and improve the efficiency of studies, the generalized case-cohort design, in which the risk-factors include the subcohort members sampled by simple random sample from the full cohort, augmented with another subset sampled from the failure of interest outside the subcohort, has been widely used in many prevention trials and epidemiological cohort studies. In modeling process, including prior information about the parameters into consideration can further improve the study efficiency. In this article, regression analysis of Cox's model with parameter constraints under the generalized case-cohort design is studied. A working likelihood function is constructed for the estimation of the model parameters. The asymptotic properties of the constrained estimation are derived by using the Karush-Kuhn-Tucker conditions. A constrained minorization-maximization algorithm is developed for the calculation of the constrained estimator. Simulation studies are conducted to evaluate the finite-sample performance of our proposed estimator. We demonstrate the practicability of the proposed approach with a data set from a Wilms tumor study.