Estimation of relative and absolute risk
from nested case-control studies


Örnulf Borgan
Institute of Mathematics, University of Oslo
P.O. Box 1053 Blindern, N-0316 Oslo 3, Norway

Abstract

Estimation in proportional hazards models, like Cox's regression model, is based on a partial likelihood which compares the covariate values of a failing individual to those of all individuals at risk at the time of the failure. In large epidemiological cohort studies of a rare disease, these methods require the collection of information on exposure variables and other covariates of interest for all individuals in the cohort even though only a small fraction of these actually get diseased. This may be very expensive, or even logistically impossible. Cohort sampling methods, in which each failing individual (case) is compared to a (small) sample of controls from those at risk at the case's failure time, may give a substantial reduction in the resources (time and money) that need to be allocated to a study.

In the talk I will describe a general framework for such cohort sampling methods [1], incorporating classical nested case-control sampling (with simple random sampling of the controls) [5], [6] and counter-matched sampling (with stratified random sampling of the controls) [3] as special cases. Further, I will review methods for estimation of the regression parameters [1],[5] and the integrated baseline hazard [1],[2] and indicate how one may estimate absolute risk, without and in the presence of competing risks, for given time-dependent covariate histories [4]. The methods will be illustrated by data on lung cancer deaths in a cohort of uranium miners from the Colorado Plateau.

References

[1] Borgan, {\O}., Goldstein L., and Langholz (1995). Methods for the analysis of sampled cohort data in the Cox proportional hazards model. Annals of Statistics 23, 1749--1778.

[2] Borgan, {\O}. and Langholz, B. (1993). Non-parametric estimation of relative mortality from nested case-control studies. Biometrics 49, 593-602.

[3] Langholz, B. and Borgan, {\O}. (1995). Counter-matching: A stratified nested case-control sampling method. Biometrika 82, 69-79.

[4] Langholz, B. and Borgan, {\O}. (1997). Estimation of absolute risk from nested case-control data. Biometrics 53, to appear June 1997.

[5] Oakes, D. (1981). Survival times: Aspects of partial likelihood (with discussion). International Statistical Review 49, 235--264.

[6] Thomas, D.C. (1977). Addendum to: Methods of cohort analysis: Appraisal by application to asbestos mining. {By F. D. K. Liddell, J. C. McDonald and D. C. Thomas}. Journal of the Royal Statistical Society A 140, 469--491.