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. 2011 Mar 15;173(6):695-702.
doi: 10.1093/aje/kwq387. Epub 2011 Feb 8.

Hierarchical latency models for dose-time-response associations

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Hierarchical latency models for dose-time-response associations

David B Richardson et al. Am J Epidemiol. .

Abstract

Exposure lagging and exposure-time window analysis are 2 widely used approaches to allow for induction and latency periods in analyses of exposure-disease associations. Exposure lagging implies a strong parametric assumption about the temporal evolution of the exposure-disease association. An exposure-time window analysis allows for a more flexible description of temporal variation in exposure effects but may result in unstable risk estimates that are sensitive to how windows are defined. The authors describe a hierarchical regression approach that combines time window analysis with a parametric latency model. They illustrate this approach using data from 2 occupational cohort studies: studies of lung cancer mortality among 1) asbestos textile workers and 2) uranium miners. For each cohort, an exposure-time window analysis was compared with a hierarchical regression analysis with shrinkage toward a simpler, second-stage parametric latency model. In each cohort analysis, there is substantial stability gained in time window-specific estimates of association by using a hierarchical regression approach. The proposed hierarchical regression model couples a time window analysis with a parametric latency model; this approach provides a way to stabilize risk estimates derived from a time window analysis and a way to reduce bias arising from misspecification of a parametric latency model.

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Figures

Figure 1.
Figure 1.
Analysis of the association between lung cancer mortality and asbestos exposure among the cohort of asbestos textile workers employed at a Charleston, South Carolina, plant between 1940 and 1965. A, single-stage analysis with 8 exposure-time windows (light dotted lines) and a 10-year lag analysis (dark dashed line); gray bars indicate 95% credible intervals. B, a 2-stage model where the fitted first-stage model includes 8 exposure-time windows (light dotted lines), and the second-stage model is a 10-year lag model (dark dashed line); gray bars indicate 95% credible intervals. ERR, excess relative risk.
Figure 2.
Figure 2.
Analysis of the association between lung cancer mortality and radon exposure among the cohort of underground uranium miners in the Colorado Plateau first employed between 1950 and 1960. A, single-stage analysis with 6 exposure-time windows (light dotted lines) and a 10-year lag analysis (dark dashed line); gray bars indicate 95% credible intervals. B, a 2-stage model where the fitted first-stage model includes 6 exposure-time windows (light dotted lines), and the second-stage model is a 10-year lag model (dark dashed line); gray bars indicate 95% credible intervals. C, a 2-stage model where the fitted first-stage model includes 6 exposure-time windows (light dotted lines), and the second-stage model is a bilinear model (dark dashed line); gray bars indicate 95% credible intervals. D, a 2-stage model where the fitted first-stage model includes 20 exposure-time windows (light dotted lines), and the second-stage model is a bilinear model (dark dashed line); gray bars indicate 95% credible intervals. ERR, excess relative risk; WLM, working-level months.

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