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This JAMA Guide to Statistics and Methods discusses E-value analysis, an alternative approach to sensitivity analyses for unmeasured confounding in observational studies that specifies the degree of unmeasured confounding that would need to be operative to negate observed results in a study.

Randomized trials serve as the standard for comparative studies of treatment effects. In many settings, it may not be feasible or ethical to conduct a randomized study,1 and researchers may pursue observational studies to better understand clinical outcomes. A central limitation of observational studies is the potential for confounding bias that arises because treatment assignment is not random. Thus, the observed associations may be attributable to differences other than the treatment being investigated and causality cannot be assumed.

In the October 16, 2018, issue of JAMA, results from a large, multisite observational study of the association between bariatric surgery and long-term macrovascular disease outcomes among patients with severe obesity and type 2 diabetes were reported by Fisher et al.2 Using data from 5301 patients aged 19 to 79 years who underwent bariatric surgery at 1 of 4 integrated health systems in the United States between 2005 and 2011 and 14934 matched nonsurgical patients, they found that bariatric surgery was associated with a 40% lower incidence of macrovascular disease at 5 years (2.1% in the surgical group and 4.3% in the nonsurgical group; hazard ratio [HR], 0.60 [95% CI, 0.42-0.86]).

Two strategies were used to mitigate confounding bias. In the first, a matched cohort design was used where nonsurgical patients were matched to surgical patients on the basis of a priori–identified potential confounders (study site, age, sex, body mass index, hemoglobin A1c level, insulin use, observed diabetes duration, and prior health care use). In the second strategy used to adjust for confounding bias, the primary results were based on the fit of a multivariable Cox model that adjusted for all of the factors used in the matching as well as a broader range of potential confounders (Table 1 in the article2). Thus, any imbalances in the observed potential confounders that remained after the matching process were controlled for by the statistical analysis. Despite these efforts, however, given the observational design, the potential for unmeasured confounding remained.


While matching and regression-based analysis provide some control of confounding, it can only be with respect to factors that are measured. The potential for confounding from factors that were not measured in the study still exists. To assess how much of a problem unmeasured confounding factors may pose, researchers may conduct a sensitivity or bias analysis.3 Common to most of these sensitivity analysis methods is the use of a formula for which 2 inputs are required: (1) the strength and direction of the association between the unmeasured confounder and treatment choice and (2) the strength ...

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