By providing a probabilistic model for nested case-control sampling in epidemiologic cohort studies, consistency and asymptotic normality of the maximum partial likelihood estimator of regression parameters in a Cox proportional hazards model can be derived using process and martingale theory as in Andersen and Gill. A general expression for the asymptotic variance is given and used to calculate asymptotic relative efficiencies relative to the full cohort variance in some important special cases.
"Asymptotic Theory for Nested Case-Control Sampling in the Cox Regression Model." Ann. Statist. 20 (4) 1903 - 1928, December, 1992. https://doi.org/10.1214/aos/1176348895