Monte Carlo Sensitivity Analysis and Bayesian Analysis of Smoking as an Unmeasured Confounder in a Study of Silica and Lung Cancer

Abstract

Conventional confidence intervals reflect uncertainty due to random error but omit uncertainty due to biases, such as confounding, selection bias, and measurement error. Such uncertainty can be quantified, especially if the investigator has some idea of the amount of such bias. A traditional sensitivity analysis produces one or more point estimates for the exposure effect hypothetically adjusted for bias, but it does not provide a range of effect measures given the likely range of bias. Here the authors used Monte Carlo sensitivity analysis and Bayesian bias analysis to provide such a range, using data from a US silica-lung cancer study in which results were potentially confounded by smoking. After positing a distribution for the smoking habits of workers and referents, a distribution of rate ratios for the effect of smoking on lung cancer, and a model for the bias parameter, the authors derived a distribution for the silica-lung cancer rate ratios hypothetically adjusted for smoking. The original standardized mortality ratio for the silica-lung cancer relation was 1.60 (95% confidence interval: 1.31, 1.93). Monte Carlo sensitivity analysis, adjusting for possible confounding by smoking, led to an adjusted standardized mortality ratio of 1.43 (95% Monte Carlo limits: 1.15, 1.78). Bayesian results were similar (95% posterior limits: 1.13, 1.84). The authors believe that these types of analyses, which make explicit and quantify sources of uncertainty, should be more widely adopted by epidemiologists.