The Annals of Statistics

Methods for the Analysis of Sampled Cohort Data in the Cox Proportional Hazards Model

O. Borgan, L. Goldstein, and B. Langholz

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Methods are provided for regression parameter and cumulative baseline hazard estimation in the Cox proportional hazards model when the cohort is sampled according to a predictable sampling probability law. The key to the methodology is to define counting processes which count joint failure and sampled risk sets occurrences and to derive the appropriate intensities for these counting processes, leading to estimation methods parallel to those for full cohort data. These techniques are illustrated for a number of sampling designs, including three novel designs: counter-matching with additional randomly sampled controls; quota sampling of controls; and nested case-control sampling with number of controls dependent on the failure's exposure status. General asymptotic theory is developed for the maximum partial likelihood estimator and cumulative baseline hazard estimator and is used to derive the asymptotic distributions for estimators from a large class of designs.

Article information

Ann. Statist. Volume 23, Number 5 (1995), 1749-1778.

First available in Project Euclid: 11 April 2007

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Primary: 62D05: Sampling theory, sample surveys
Secondary: 62F12: Asymptotic properties of estimators 62G05: Estimation 62M99: None of the above, but in this section 62P10: Applications to biology and medical sciences

Case-control study cohort sampling counting process Cox's regression model epidemiology marked process martingale partial likelihood survival analysis


Borgan, O.; Goldstein, L.; Langholz, B. Methods for the Analysis of Sampled Cohort Data in the Cox Proportional Hazards Model. Ann. Statist. 23 (1995), no. 5, 1749--1778. doi:10.1214/aos/1176324322.

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