How efficiently does a study design or method of analysis use the available sample size to distinguish causal effects and unmeasured confounding? The design sensitivity tells us about the limit as the sample size goes to infinity, but it does not address efficient use of a finite sample size. The answer is provided by the Bahadur efficiency of a sensitivity analysis. The efficiency declines to zero as the sensitivity parameter increase to the design sensitivity. Methods that are efficient under the assumption that there are not unmeasured confounders may be very inefficient when a sensitivity analysis allows for a degree of unmeasured confounding.
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Rosenbaum PR. Bahadur efficiency of observational block designs. Journal of the American Statistical Association. 2024 Jul 2;119(547):1871-81. https://doi.org/10.1080/01621459.2023.2221402