The nested case-control (NCC) design is a cost-effective sampling method to study the relationship between a disease and its risk factors in epidemiologic studies. NCC data are commonly analyzed using Thomas' partial likelihood approach under Cox's s proportional hazards model with constant covariate effects. In this talk, I will present an extension, the Cox regression with time-varying coefficients, in NCC studies and discuss why the implementation of this model in NCC studies needs different handling from cohort studies. Both simulation studies and an application to the NCC study of breast cancer in the New York University Women's Health Study are used to illustrate the usefulness of the proposed methods. Furthermore, I will discuss another extension, the Cox regression with nonlinear covariate effects, and issues regarding different techniques to handle these two different models in NCC studies.
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