Sensitivity analyses to estimate the potential impact of unmeasured confounding in causal research

Background: The impact of unmeasured confounders on causal associations can be studied by means of sensitivity analyses. Although several sensitivity analyses are available, these are used infrequently. This article is intended as a tutorial on sensitivity analyses, in which we discuss three methods to conduct sensitivity analysis. Methods: Each method is based on assumed associations between confounder and exposure, confounder and outcome and the prevalence of the confounder in the population at large. In the first method an unmeasured confounder is simulated and subsequently adjusted. The other two methods are analytical methods, in which either the (adjusted) effect estimate is multiplied with a factor based on assumed confounder characteristics, or the (adjusted) risks for the outcome among exposed and unexposed subjects are adjusted by such a factor. These methods are illustrated with a clinical example on influenza vaccine effectiveness. Results: When applied to a dataset constructed to assess the effect of influenza vaccination on mortality, the three reviewed methods provided similar results. After adjustment for observed confounders, influenza vaccination reduced mortality by 42% [odds ratio (OR) 0.58, 95% confidence interval (CI) 0.46-0.73]. To arrive at a 95% CI including one requires a very common confounder (40% prevalence) with strong associations with both vaccination status and mortality, respectively OR ≥0.3 and OR ≥3.0 (OR 0.79, 95% CI 0.62-1.00). Conclusions: In every non-randomized study on causal associations the robustness of the results with respect to unmeasured confounding can, and should, be assessed using sensitivity analyses.