Robust Bayesian causal estimation for causal inference in medical diagnosis

TL;DR

This paper introduces a robust Bayesian group LASSO approach for variable selection in high-dimensional causal inference, emphasizing cautious selection and expert elicitation to improve stability and accuracy.

Contribution

It proposes a Bayesian group LASSO framework with prior sensitivity analysis for variable selection, incorporating abstention and expert input for better causal effect estimation.

Findings

The method improves stability in causal effect estimates with limited data.

Expert elicited variable selection enhances robustness against overfitting.

Comparative studies validate the approach on synthetic and real datasets.

Abstract

Causal effect estimation is a critical task in statistical learning that aims to find the causal effect on subjects by identifying causal links between a number of predictor (or, explanatory) variables and the outcome of a treatment. In a regressional framework, we assign a treatment and outcome model to estimate the average causal effect. Additionally, for high dimensional regression problems, variable selection methods are also used to find a subset of predictor variables that maximises the predictive performance of the underlying model for better estimation of the causal effect. In this paper, we propose a different approach. We focus on the variable selection aspects of high dimensional causal estimation problem. We suggest a cautious Bayesian group LASSO (least absolute shrinkage and selection operator) framework for variable selection using prior sensitivity analysis. We argue that in some cases, abstaining from selecting (or, rejecting) a predictor is beneficial and we should gather more information to obtain a more decisive result. We also show that for problems with very limited information, expert elicited variable selection can give us a more stable causal effect estimation as it avoids overfitting. Lastly, we carry a comparative study with synthetic dataset and show the applicability of our method in real-life situations.