On the proportional hazards model for occupational and environmental case-control analyses

Héloïse Gauvin,Aude Lacourt,Karen Leffondré

doi:10.1186/1471-2288-13-18

Abstract

BackgroundCase-control studies are generally designed to investigate the effect of exposures on the risk of a disease. Detailed information on past exposures is collected at the time of study. However, only the cumulated value of the exposure at the index date is usually used in logistic regression. A weighted Cox (WC) model has been proposed to estimate the effects of time-dependent exposures. The weights depend on the age conditional probabilities to develop the disease in the source population. While the WC model provided more accurate estimates of the effect of time-dependent covariates than standard logistic regression, the robust sandwich variance estimates were lower than the empirical variance, resulting in a low coverage probability of confidence intervals. The objectives of the present study were to investigate through simulations a new variance estimator and to compare the estimates from the WC model and standard logistic regression for estimating the effects of correlated temporal aspects of exposure with detailed information on exposure history.MethodWe proposed a new variance estimator using a superpopulation approach, and compared its accuracy to the robust sandwich variance estimator. The full exposure histories of source populations were generated and case-control studies were simulated within each source population. Different models with selected time-dependent aspects of exposure such as intensity, duration, and time since cessation were considered. The performances of the WC model using the two variance estimators were compared to standard logistic regression. The results of the different models were finally compared for estimating the effects of correlated aspects of occupational exposure to asbestos on the risk of mesothelioma, using population-based case-control data.ResultsThe superpopulation variance estimator provided better estimates than the robust sandwich variance estimator and the WC model provided accurate estimates of the effects of correlated aspects of temporal patterns of exposure.ConclusionThe WC model with the superpopulation variance estimator provides an alternative analytical approach for estimating the effects of time-varying exposures with detailed history exposure information in case-control studies, especially if many subjects have time-varying exposure intensity over lifetime, and if only one control is available for each case.

Highlights

Case-control studies are generally designed to investigate the effect of exposures on the risk of a disease
The weighted Cox (WC) model with the superpopulation variance estimator provides an alternative analytical approach for estimating the effects of time-varying exposures with detailed history exposure information in case-control studies, especially if many subjects have time-varying exposure intensity over lifetime, and if only one control is available for each case
The first objective of the present study is to investigate through extensive simulations the accuracy of the Lin variance estimator for estimating the effects of timevarying covariates in case-control data, using the weights proposed in the WC model [4]

Summary

Introduction

Case-control studies are generally designed to investigate the effect of exposures on the risk of a disease. While the WC model provided more accurate estimates of the effect of time-dependent covariates than standard logistic regression, the robust sandwich variance estimates were lower than the empirical variance, resulting in a low coverage probability of confidence intervals. Only the cumulated estimated dose of exposure at the index age (age at diagnosis for cases and at interview for controls) is usually used in standard logistic regression analyses Such approach does not use the (retrospective) dynamic information available on the exposure at different ages during lifetime. A time-dependent weighted Cox (WC) model has recently been proposed to incorporate this dynamic information on exposure, in order to more accurately estimate the effect of time-dependent exposures in population-based case-control studies [4]. The average robust sandwich variance estimates based on dfbetas residuals [5] were systematically lower than the empirical variance of the parameter estimates, which resulted in too narrow confidence intervals (CI) and low coverage probabilities [4]

Objectives

Methods

Results

Discussion

Conclusion