How large must an associational mean difference be to support a causal effect?

An observational study might support a causal claim if the association found cannot be explained by bias due to unconsidered confounders. This bias depends on how strongly the common predisposition, a summary of unconsidered confounders, is related to the factor and the outcome. For a positive effect to be supported, the product of these two relations must be smaller than the left boundary of the confidence interval for, e.g., a standardised mean difference (d). We suggest means to derive heuristics for how large this product must be to serve as a confirmatory threshold. We also provide non-technical, visual means to express researchers’ assumptions on the two relations to assess whether a finding on d is explainable by omitted confounders. The ViSe tool, available as an R package and Shiny application, allows users to choose between various effect sizes and apply it to their own data or published summary results.