Comparison of Methods for Sensitivity Analysis of Heterogeneous Treatment Effects in Observational Studies and...

In Alzheimer's disease (AD) research, many observational studies have shown that the effect of sleeping quality, a modifiable risk factor, on cognitive decline is heterogeneous, where some adults experience faster rates of cognitive decline compared to others. However, these effects are likely confounded by unmeasured confounders, and the sensitivity of these effects to unmeasured confounders may be heterogeneous, where one subgroup's treatment effect is more sensitive than that of another subgroup. Unfortunately, compared to the overall treatment effect, there are limited investigations about the sensitivity of heterogeneous treatment effects to unmeasured confounding. The paper presents and compares methods for sensitivity analysis of heterogeneous effects in observational studies based on Rosenbaum's model for sensitivity analysis. We show that, unlike the sensitivity analysis of the overall treatment effect, the sensitivity of heterogeneous treatment effects depends on the variation in the effect sizes across subgroups and the correction for multiple testing. The data analysis further supports our findings where the overall effect of sleep disturbances on cognitive decline is significant ( $p$ -value = $5.55\times 10^{-5}$ ). Also, the effect is more severe among males ( $p$ -value = $2.00\times 10^{-4}$ ) and insensitive to a moderate degree of unmeasured confounding. Finally, we offer an easy-to-use R software to carry out the sensitivity analyses for heterogeneous treatment effects.