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October, 1995 Methods for the Analysis of Sampled Cohort Data in the Cox Proportional Hazards Model
O. Borgan, L. Goldstein, B. Langholz
Ann. Statist. 23(5): 1749-1778 (October, 1995). DOI: 10.1214/aos/1176324322


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.


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O. Borgan. L. Goldstein. B. Langholz. "Methods for the Analysis of Sampled Cohort Data in the Cox Proportional Hazards Model." Ann. Statist. 23 (5) 1749 - 1778, October, 1995.


Published: October, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0843.62094
MathSciNet: MR1370306
Digital Object Identifier: 10.1214/aos/1176324322

Primary: 62D05
Secondary: 62F12 , 62G05 , 62M99 , 62P10

Keywords: case-control study , cohort sampling , counting process , Cox's regression model , epidemiology , Marked process , martingale , partial likelihood , Survival analysis

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 5 • October, 1995
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