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Biometrika 2006 93(4):747-762; doi:10.1093/biomet/93.4.747
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© 2006 Biometrika Trust

Censored linear regression for case-cohort studies

Bin Nan1, Menggang Yu2 and John D. Kalbfleisch3

1 Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A. bnan{at}umich.edu, 2 Division of Biostatistics, Indiana University, Indianapolis, Indiana 46202, U.S.A. meyu{at}iupui.edu, 3 Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A. jdkalbfl{at}umich.edu


  Abstract

Right-censored data from a classical case-cohort design and a stratified case-cohort design are considered. In the classical case-cohort design the subcohort is obtained as a simple random sample of the entire cohort, whereas in the stratified design this subcohort is elected by independent Bernoulli sampling with arbitrary selection probabilities. For each design and under a linear regression model, methods for estimating the regression parameters are proposed and analysed. These methods are derived by modifying the linear ranks tests and estimating equations that arise from full-cohort data using methods that are similar to the pseudolikelihood estimating equation that has been used in relative risk regression for these models. The estimators so obtained are shown to be consistent and asymptotically normal. Variance estimation and numerical illustrations are also provided.

Key Words: Case-cohort design; Censored linear regression; Counting process; Martingale; Rank statistic.

Received October 2004. Revised February 2006.


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