Semiparametric Analysis of Nested Case-Control Design

Studying rare diseases often deals with small percentage of cases requiring a large amount of subjects in the medical study. The common analysis by the Cox proportional hazards model may be very time-consuming and financially inefficient. Nested case- control design presents a sampling method offering fewer data needed for the analysis while keeping the estimator of the Cox model consistent and asymptotic normal. In this thesis, we introduce nested case-control design, we describe in detail the method for sampling controls for cases, we present the partial likelihood and the maximum partial likelihood estimator of the regression parameter and we prove the consistency and the asymptotic normality of the estimator. Then, we introduce the counter-matching design as an extension of the nested case-control design and the pseudolikelihood approach under nested case-control design. In the last chapter, we perform a simulation study comparing the four designs. The contribution of this thesis is the detailed introduction to nested case- control design and its alternatives, more detailed proofs of the asymptotic properties of the maximum partial likelihood of the regression parameter of nested case-control design and the comparison of the four approaches through the simulation study.