Accounting for selection bias due to death in estimating the effect of wealth shock on cognition for the Health and Retirement Study

The Health and Retirement Study (HRS) is a longitudinal study of U.S. adults enrolled at age 50 and older. We were interested in investigating the effect of a sudden large decline in wealth on the cognitive ability of subjects measured using a dataset provided composite score. However, our analysis was complicated by the lack of randomization, time-dependent confounding, and a substantial fraction of the sample and population will die during follow-up leading to some of our outcomes being censored. The common method to handle this type of problem is marginal structural models (MSM). Although MSM produces valid estimates, this may not be the most appropriate method to reflect a useful real-world situation because MSM upweights subjects who are more likely to die to obtain a hypothetical population that over time, resembles that would have been obtained in the absence of death. A more refined and practical framework, principal stratification (PS), would be to restrict analysis to the strata of the population that would survive regardless of negative wealth shock experience. In this work, we propose a new algorithm for the estimation of the treatment effect under PS by imputing the counterfactual survival status and outcomes. Simulation studies suggest that our algorithm works well in various scenarios. We found no evidence that a negative wealth shock experience would affect the cognitive score of HRS subjects.