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

Our plain-English summary of On the proportional hazards model for occupational and environmental case-control analyses, by H. Gauvin, A. Lacourt, K. Leffondré (BMC Medical Research Methodology, 2013).

The study

• Authors: H. Gauvin, A. Lacourt, K. Leffondré
• Journal: BMC Medical Research Methodology
• Published: 2013;13:18
• Cited by: 1 article, as counted by NIH iCite
• Read it: PubMed · Publisher · Free full text

Abstract

Background: Case-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.

Method: We 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.

Results: The 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.

Conclusion: The 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.

In plain English

This was a statistical methods paper, not a study designed to measure asbestos risk. The authors tested a weighted Cox model for case-control studies, with a new 'superpopulation' way of calculating confidence intervals. In simulations, this gave intervals much closer to the intended 95% coverage than the older robust method. With one control per case in simulated populations of 1000 subjects, the weighted Cox model was more efficient than standard logistic regression; this advantage did not persist with more controls. The authors then applied the methods to French data on 1041 male pleural mesothelioma cases and 1425 male controls, all ever exposed to asbestos at work. All exposure measures were significantly associated with pleural mesothelioma under all four methods. In the simplest model, the weighted Cox model's hazard ratio per 1.0 fiber/ml of exposure intensity was 1.75 (95% CI 1.65 to 1.85 with the new calculation, 1.66 to 1.84 with the older one). This was weaker than the logistic regression odds ratios of 2.55 and 2.33. The authors said these estimates were for methodological comparison only, not substantive epidemiological results.

We wrote this plain-English summary from the full article with the help of AI, and a second AI model checked each sentence against the article. It is not the authors' wording; the abstract and the article are their own account.

What the study did and found

• Design: Statistical methods study: computer simulations comparing analysis methods (weighted Cox model with two variance estimators, conditional and unconditional logistic regression), plus an application to existing population-based case-control data
• Who was studied: Simulations: 1000 simulated source populations of 1000 or 5000 individuals, each yielding about 100 cases with 1, 2 or 4 controls per case. Application: 1041 male cases of pleural mesothelioma and 1425 male controls, all ever exposed to asbestos at work, from a French population-based case-control study (cases from a 1987–1993 study and the French National Mesothelioma Surveillance Program 1998–2006)
• Exposure: Occupational asbestos exposure (fiber type not specified), estimated with a job-exposure matrix. It was expressed as intensity (mean index of exposure, fibers/ml), duration, age at first exposure and time since last exposure
• Main results:
  • In simulations, the superpopulation variance estimator (WC2) gave estimates closer to the true variance than the robust estimator (WC1), which systematically underestimated it
  • In simulated scenarios with one control per case and source populations of 1000, the weighted Cox model estimates were more efficient and more accurate than conditional and unconditional logistic regression
  • The advantage of the weighted Cox model did not persist when more than one control per case was selected
  • In the French data on ever-exposed males, all asbestos exposure variables were significantly associated with pleural mesothelioma under all four analysis methods
  • The estimated effect of exposure intensity was weaker with the weighted Cox model than with logistic regression, and the 95% CIs did not overlap. In Model 1, per 1.0 fiber/ml, the hazard ratio was 1.75, with a 95% CI of 1.65 to 1.85 for WC2 (superpopulation variance) and 1.66 to 1.84 for WC1 (robust variance). The odds ratios were 2.55 (2.29 to 2.83) for conditional and 2.33 (2.14 to 2.54) for unconditional logistic regression
  • In the mesothelioma data, the 95% CIs from the two variance estimators were almost identical. The authors attributed this to the rarity of the disease
• The authors' conclusion: The authors concluded that the weighted Cox model with the superpopulation variance estimator may offer an alternative method for case-control analyses with detailed exposure histories. They said this applies especially when many subjects have exposure intensity that changes over lifetime and only one control is available per case
• Limitations the authors state:
  • The mesothelioma estimates were meant only for comparing methods, not as substantive epidemiological results
  • Effects were assumed to be linear, although the authors' earlier results suggested they were not
  • The weights used general French male population probabilities, but the analysed men were all ever exposed and have much higher probability of pleural mesothelioma
  • Because of how controls were selected, hazard ratios from the weighted Cox model and odds ratios from logistic regression may not measure the same quantity
  • Frequency matching on birth year was handled as a covariate rather than in the weights. The authors suggest this needs further study

Topics

The National Library of Medicine indexes this study under subjects our site covers: Mesothelioma.

Medical terms in this study, explained in our Lexicon: confidence interval, Exposure History, Occupational Exposure, Mesothelioma.

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