Sensitivity Analysis for Effects of Multiple Exposures in the Presence of Unmeasured Confounding

Epidemiological research aims to investigate how multiple exposures affect health outcomes of interest, but observational studies often suffer from biases caused by unmeasured confounders. In this study, we develop a novel sensitivity model to investigate the effect of correlated multiple exposures on the continuous health outcomes of interest. The proposed sensitivity analysis is model-agnostic and can be applied to any machine learning algorithm. The interval of single- or joint-exposure effects is efficiently obtained by solving a linear programming problem with a quadratic constraint. Some strategies for reducing the input burden in the sensitivity analysis are discussed. We demonstrate the usefulness of sensitivity analysis via numerical studies and real data application.