Causal inference in paired two‐arm experimental studies under noncompliance with application to prognosis of myocardial infarction

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 noncompliance in both treatment and control arms. We base the method 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 noncompliance, the model assumes the existence of three subpopulations of subjects: compliers, never‐takers, and always‐takers. We estimate the model using a two‐step estimator: at the first step, we estimate the probability that a subject belongs to one of the three subpopulations on the basis of the available covariates; at the second step, we estimate the causal effects through a conditional logistic method, the implementation of which depends on the results from the first step. The estimator is approximately consistent and, under certain circumstances, exactly consistent. We provide evidence that the bias is negligible in relevant situations. We compute standard errors 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 2 years, with a log‐odds of about  − 2. Given that noncompliance is significant for patients being given the treatment because of high‐risk conditions, classical estimators fail to detect, or at least underestimate, this effect. Copyright © 2013 John Wiley & Sons, Ltd.