author:
- |
    Yaoyuan V. Tan[^1]\
    Department of Biostatistics and Epidemiology, Rutgers University\
    and\
    Carol A.C. Flannagan\
     Transportation Research Institute, University of Michigan\
    Lindsay R. Pool\
    Department of Preventive Medicine, Northwestern University\
    and\
    Michael R. Elliott\
    Department of Biostatistics, University of Michigan
bibliography:
- 'references.bib'
title: Accounting for selection bias due to death in estimating the effect of wealth shock on cognition for the Health and Retirement Study
---

[**Keywords:**]{} Bayesian additive regression trees; Causal inference; Confounding by indication; Longitudinal Study; Missing data; Penalized spline of propensity methods in treatment comparisons.

Introduction
============

Late middle age adults commonly experience chronic health conditions like high blood pressure or diabetes as well as declining cognitive abilities. Factors known to be associated with accelerated decrease in cognitive abilities include smoking, high alcohol consumption, physical inactivity, high dietary intake of sodium and saturated fats, low dietary intake of fruits and vegetables [@lee_back; @stuck]; hypertension, elevated serum cholesterol, diabetes, obesity, cerebrovascular and cardiovascular disease [@plassman]; depression, lower socioeconomic status, and exposure to acute stressful life events and chronic perceived stress [@krieger]. In particular, the acute stress of a sudden decrease in wealth – “a negative wealth shock” – may have a negative impact on the 