Sensitivity analysis for attributable fraction in the presence of unmeasured confounding

A main goal of epidemiology is to provide an impact of an exposure on health outcomes. The attributable fraction (AF) is a widely used measure for quantifying its contribution. Various methods have been developed to estimate AF, including standardization, inverse probability of treatment weighting, and doubly robust methods. However, the validity of these methods is established based on the conditional exchangeability assumption, which cannot be tested using only observed data. To assess how vulnerable the research findings are to departures from this assumption, researchers need to conduct a sensitivity analysis. In this study, we propose novel sensitivity analysis methods for AF. Sensitivity analysis problems are formulated as optimization problems, and analytic solutions for the problem are derived. We illustrate our proposed sensitivity analysis methods with a publicly available data set and examine how the AF of the mother's smoking status during pregnancy for low birth weight changes to the degree of unmeasured confounding.