Copyright © 2004 by the Johns Hopkins Bloomberg School of Public Health
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Bias due to Aggregation of Individual Covariates in the Cox Regression Model
1 Department of Epidemiology and Biostatistics, McGill University, Montreal, Quebec, Canada.
2 Division of Clinical Epidemiology, The Montreal General Hospital, Montreal, Quebec, Canada.
3 McLaughlin Centre for Population Health Risk Assessment, University of Ottawa, Ottawa, Ontario, Canada.
4 Biostatistics and Epidemiology Division, Safe Environments Directorate, Healthy Environments and Consumer Safety Branch, Health Canada, Ottawa, Ontario, Canada.
5 Department of Medicine, McGill University, Montreal, Quebec, Canada.
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.
aggregation bias; confidentiality; Cox model; ecological bias; epidemiologic methods; simulation
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