Sensitivity Analysis for Effects of Multiple Exposures in the Presence of Unmeasured Confounding: Non-Gaussian and Time-to-Event Outcomes

In epidemiological studies, evaluating the health impacts stemming from multiple exposures is one of the important goals. To analyze the effects of multiple exposures on discrete or time-to-event health outcomes, researchers often employ generalized linear models, Cox proportional hazards models, and machine learning methods. However, observational studies are prone to unmeasured confounding factors, which can introduce the potential for substantial bias in the multiple exposure effects. To address this issue, we propose a novel outcome model-based sensitivity analysis method for non-Gaussian and time-to-event outcomes with multiple exposures. All the proposed sensitivity analysis problems are formulated as linear programming problems with quadratic and linear constraints, which can be solved efficiently. Analytic solutions are provided for some optimization problems, and a numerical study is performed to examine how the proposed sensitivity analysis behaves in finite samples. We illustrate the proposed method using two real data examples.