Constrained Estimation In Cox Model Under Failure-Time Outcome-Dependent Sampling Design

The failure-time outcome-dependent sampling (ODS) design is a cost-effective sampling scheme, which can improve the efficiency of the studies by selectively including certain failures to enrich the observed sample. In modeling process, taking some prior constraints on parameters into account may lead to more powerful and efficient inferences. In this paper, we study how to fit the proportional hazards model with parameter constraints to data from a failure-time ODS design. We propose constrained weighted estimation by conducting an optimization problem on a working likelihood function. The asymptotic properties of the proposed estimator are established. We develop a restricted minorization-maximization (MM) algorithm for the numerical calculation of the proposed estimator. Simulation studies are conducted to evaluate the finite-sample performance of the proposed estimator. An application to a data set from a Wilms tumor study is illustrated for the utility of the proposed method.