Journal Article

Bias due to Aggregation of Individual Covariates in the Cox Regression Model

Michal Abrahamowicz, Roxane du Berger, Daniel Krewski, Richard Burnett, Gillian Bartlett, Robyn M. Tamblyn and Karen Leffondré

in American Journal of Epidemiology

Published on behalf of Johns Hopkins Bloomberg School of Public Health

Volume 160, issue 7, pages 696-706
Published in print October 2004 | ISSN: 0002-9262
Published online October 2004 | e-ISSN: 1476-6256 | DOI:
Bias due to Aggregation of Individual Covariates in the Cox Regression Model

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The impact of covariate aggregation, well studied in relation to linear regression, is less clear in the Cox model. In this paper, the authors use real-life epidemiologic data to illustrate how aggregating individual covariate values may lead to important underestimation of the exposure effect. The issue is then systematically assessed through simulations, with six alternative covariate representations. It is shown that aggregation of important predictors results in a systematic bias toward the null in the Cox model estimate of the exposure effect, even if exposure and predictors are not correlated. The underestimation bias increases with increasing strength of the covariate effect and decreasing censoring and, for a strong predictor and moderate censoring, may exceed 20%, with less than 80% coverage of the 95% confidence interval. However, covariate aggregation always induces smaller bias than covariate omission does, even if the two phenomena are shown to be related. The impact of covariate aggregation, but not omission, is independent of the covariate-exposure correlation. Simulations involving time-dependent aggregates demonstrate that bias results from failure of the baseline covariate mean to account for nonrandom changes over time in the risk sets and suggest a simple approach that may reduce the bias if individual data are available but have to be aggregated.

Keywords: aggregation bias; confidentiality; Cox model; ecological bias; epidemiologic methods; simulation

Journal Article.  6255 words.  Illustrated.

Subjects: Public Health and Epidemiology

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