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Regression Models for the Effects of Exposure Rate and Cumulative Exposure

Richardson, David B.a; Cole, Stephen R.a; Langholz, Bryanb

doi: 10.1097/EDE.0b013e31826c3149

Epidemiologic studies that collect detailed exposure histories often incorporate this information into a regression model through a time-dependent cumulative exposure metric. This summary metric obscures variations in exposure rates among people and within persons over time. To disentangle the effects of cumulative exposure and exposure rate, one standard approach is to simultaneously model both cumulative exposure and average exposure rate. We propose an alternative regression model that uses a person’s detailed exposure history information to describe the effect of the history of exposure increments on the relative hazard function. We illustrate this approach using data from a cohort study of radon exposure and lung cancer mortality among uranium miners. Compared with a standard cumulative exposure-average exposure rate model, our proposed approach yielded somewhat stronger evidence that the radon-lung cancer mortality association is modified by exposure rate. At low exposure rates, the estimated excess relative hazard per 100 working-level months was 0.63 (95% confidence interval = 0.32–1.37) under the standard approach, whereas under the proposed approach it was 1.23 (0.53–3.76). The proposed approach may provide better understanding of relationships between a protracted exposure and disease and is readily implemented using existing statistical software.

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From the aDepartment of Epidemiology, School of Public Health, University of North Carolina at Chapel Hill, Chapel Hill, NC; and bDepartment of Preventive Medicine, Division of Biostatistics, Keck School of Medicine, University of Southern California, CA.

Submitted 13 January 2012; accepted 22 May 2012; posted 21 September 2012.

Supported by grant R01-CA117841 from the National Cancer Institute, National Institutes of Health.

Editors’ note: A commentary on this article appears on page 900.

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Correspondence: David B. Richardson, Department of Epidemiology, School of Public Health, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599. E-mail:

© 2012 Lippincott Williams & Wilkins, Inc.