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

• Published in: Statistics in medicine Vol. 32; no. 25; pp. 4348 - 4366
• Main Authors: Bartolucci, Francesco, Farcomeni, Alessio
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 10.11.2013; Wiley Subscription Services, Inc
• Subjects: Aged; Bayes Theorem; Bias; Causality; conditional logistic regression; Control Groups; Coronary Angiography; counterfactuals; Electrocardiography; Estimating techniques; Female; finite mixture models; Glycemic Index; Heart attacks; Humans; Hydroxymethylglutaryl-CoA Reductase Inhibitors - therapeutic use; latent variables; Likelihood Functions; Logistic Models; Male; Mathematical models; Medical imaging; Multicenter Studies as Topic - methods; Multicenter Studies as Topic - statistics & numerical data; Myocardial Infarction - diagnostic imaging; Myocardial Infarction - prevention & control; Myocardial Infarction - therapy; Noncompliance; Patient Compliance - statistics & numerical data; potential outcomes; Probability; Prognosis; Randomized Controlled Trials as Topic - methods; Randomized Controlled Trials as Topic - statistics & numerical data; Recurrence; Research Design; Secondary Prevention; Treatment Outcome; potential outcomes; latent variables; finite mixture models; counterfactuals; conditional logistic regression
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.5856

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.