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

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