# Bayesian inference on average treatment effects in the PreventS trial data in the presence of unmeasured confounding

## TL;DR

This paper develops a Bayesian causal inference framework to estimate the effects of health interventions in complex trial data with unmeasured confounding, demonstrating its application to the PreventS trial.

## Contribution

It introduces a novel Bayesian approach for causal effect estimation in the presence of multiple exposures and unmeasured confounding, addressing model non-identifiability issues.

## Key findings

- HWC intervention improves cardiovascular health scores.
- HWC reduces systolic blood pressure.
- No clear effect on mental health.

## Abstract

Using the PreventS trial data, our objective is to estimate average effects of a Health Wellness Coaching (HWC) intervention on improvement of cardiovascular health at 9 months post randomization and in three consecutive 3-month periods over 9 months post randomization. Conventional approaches, including instrumental variable models, are not applicable in the presence of multiple correlated multivalued exposures and unmeasured confounding. We propose a causal framework and its Bayesian modelling procedures to identify and estimate average effects of one or multiple multivalued exposures on one outcome in the presence of unmeasured confounding, noncompliance and missing data, in a two-arm randomized trial. We also propose estimation methods of unmeasured confounders, where the exposure and outcome distributions are conditional on unmeasured confounders and then unmeasured confounders are imputed as completely missing variables. Several types of model non-identifiability and possible solutions are described. There is a risk that estimation methods of unmeasured confounders can fail when multiple contradictory posterior solutions are produced. The random intercept outcome models that only adjust for unmeasured confounding in the outcome distribution are proposed as a good surrogate causal model in this case, and they need further development. There is evidence that the HWC intervention is beneficial to cardiovascular health at 9 months post randomization. On average, completing one HWC session improves the Life's Simple Seven total score by 0.16 (0.09, 0.22) and reduces systolic blood pressure by 0.54 (0.19, 0.90) mm Hg. There is also evidence that the HWC intervention has a larger beneficial effect on cardiovascular health during 3 months post randomization. There is no clear evidence that the HWC intervention benefits or harms mental health. The complete abstract is in the article.