  The Health and Retirement Study is a longitudinal study of US adults enrolled
at age 50 and older. We were interested in investigating the effect of a sudden
large decline in wealth on the cognitive score of subjects. Our analysis was
complicated by the lack of randomization, confounding by indication, and a
substantial fraction of the sample and population will die during follow-up
leading to some of our outcomes being censored. Common methods to handle these
problems for example marginal structural models, may not be appropriate because
it upweights subjects who are more likely to die to obtain a population that
over time resembles that would have been obtained in the absence of death. We
propose a refined approach by comparing the treatment effect among subjects who
would survive under both sets of treatment regimes being considered. We do so
by viewing this as a large missing data problem and impute the survival status
and outcomes of the counterfactual. To improve the robustness of our
imputation, we used a modified version of the penalized spline of propensity
methods in treatment comparisons approach. We found that our proposed method
worked well in various simulation scenarios and our data analysis.
