Typical statistical analysis of epidemiologic data captures uncertainty due to random sampling variation, but ignores more systematic sources of variation such as selection bias, measurement error, and unobserved confounding. Such sources are often only mentioned via qualitative caveats, perhaps under the heading of ‘study limitations.’ Recently, however, there has been considerable interest and advancement in probabilistic methodologies for more integrated statistical analysis. Such techniques hold the promise of replacing a confidence interval reflecting only random sampling variation with an interval reflecting all, or at least more, sources of uncertainty. We survey and appraise the recent literature in this area, giving some prominence to the use of Bayesian statistical methodology.
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