# Posterior Predictive Treatment Assignment Methods for Causal Inference in the Context of Time-Varying Treatments

## TL;DR

This paper introduces a Bayesian approach using posterior predictive treatment assignment methods to improve causal inference in time-varying treatment settings, especially when covariate overlap is limited.

## Contribution

It extends the ATO estimand and develops a stochastic pruning method based on PPTA for better causal effect estimation in longitudinal studies.

## Key findings

- Simulations show improved bias and coverage over traditional IPW methods.
- The method effectively handles low overlap scenarios in time-varying treatments.
- Application to Medicare data reveals insights into pollution's impact on heart disease.

## Abstract

Marginal structural models (MSM) with inverse probability weighting (IPW) are used to estimate causal effects of time-varying treatments, but can result in erratic finite-sample performance when there is low overlap in covariate distributions across different treatment patterns. Modifications to IPW which target the average treatment effect (ATE) estimand either introduce bias or rely on unverifiable parametric assumptions and extrapolation. This paper extends an alternate estimand, the average treatment effect on the overlap population (ATO) which is estimated on a sub-population with a reasonable probability of receiving alternate treatment patterns in time-varying treatment settings. To estimate the ATO within a MSM framework, this paper extends a stochastic pruning method based on the posterior predictive treatment assignment (PPTA) as well as a weighting analogue to the time-varying treatment setting. Simulations demonstrate the performance of these extensions compared against IPW and stabilized weighting with regard to bias, efficiency and coverage. Finally, an analysis using these methods is performed on Medicare beneficiaries residing across 18,480 zip codes in the U.S. to evaluate the effect of coal-fired power plant emissions exposure on ischemic heart disease hospitalization, accounting for seasonal patterns that lead to change in treatment over time.