Sensitivity analysis for unmeasured confounding for a joint effect with an application to survey data

Abstract In observational studies, performing a sensitivity analysis for unmeasured confounding is recommended alongside estimating the causal effect of an exposure on an outcome. This study extended sensitivity analysis frameworks to evaluate the joint effects of two binary exposures, accounting for potential unmeasured confounders. We applied this approach to assess the joint impact of household wealth and maternal education on child nutritional status using data from the 2019 Bangladesh Multiple Indicator Cluster Survey (MICS). A log-binomial regression model was employed to estimate the causal effect in the relative risk scale after adjusting for observed confounders by inverse probability weighting (IPW). Sensitivity analysis explored the robustness of the estimated causal effect under different scenarios of unmeasured confounding. The findings indicate that higher levels of wealth and maternal education significantly reduce the risk of child malnutrition independently and jointly, and the joint effects are robust against unmeasured confounders. Such conclusions underscore the need to account for both exposures in causal inference and provide a framework to assess robustness when unmeasured confounders are a concern in public health studies.