Causal inference in paired two-arm experimental studies under non-compliance with application to prognosis of myocardial infarction

TL;DR

This paper introduces a new causal inference method for two-arm studies with non-compliance, applying it to assess the impact of prompt coronary angiography on myocardial infarction prognosis, revealing significant treatment effects overlooked by traditional methods.

Contribution

The paper develops a novel two-step estimator for causal effects in non-compliance settings, incorporating latent heterogeneity and subpopulation classification, with application to medical treatment evaluation.

Findings

Prompt coronary angiography reduces risk of subsequent events.

Classical estimators underestimate effects due to non-compliance.

Method effectively accounts for unobserved heterogeneity and compliance types.

Abstract

Motivated by a study about prompt coronary angiography in myocardial infarction, we propose a method to estimate the causal effect of a treatment in two-arm experimental studies with possible non-compliance in both treatment and control arms. The method is based on a causal model for repeated binary outcomes (before and after the treatment), which includes individual covariates and latent variables for the unobserved heterogeneity between subjects. Moreover, given the type of non-compliance, the model assumes the existence of three subpopulations of subjects: compliers, never-takers, and always-takers. The model is estimated by a two-step estimator: at the first step the probability that a subject belongs to one of the three subpopulations is estimated on the basis of the available covariates; at the second step the causal effects are estimated through a conditional logistic method, the implementation of which depends on the results from the first step. Standard errors for this estimator are computed on the basis of a sandwich formula. The application shows that prompt coronary angiography in patients with myocardial infarction may significantly decrease the risk of other events within the next two years, with a log-odds of about -2. Given that non-compliance is significant for patients being given the treatment because of high risk conditions, classical estimators fail to detect, or at least underestimate, this effect.