Marginal structural models with monotonicity constraints: A case study in out‐of‐hospital cardiac arrest patients

Abstract

This paper deals with estimating the probability of a binary counterfactual outcome as a function of a continuous covariate under monotonicity constraints. We are motivated by the study of out‐of‐hospital cardiac arrest patients which aims to estimate the counterfactual 30‐day survival probability if either all patients had received, or if none of the patients had received bystander cardiopulmonary resuscitation (CPR), as a function of the ambulance response time. It is natural to assume that the counterfactual 30‐day survival probability cannot increase with increasing ambulance response time. We model the monotone relationship with a marginal structural model and B‐splines. We then derive an estimating equation for the parameters of interest which however further relies on an auxiliary regression model for the observed 30‐day survival probabilities. The predictions of the observed 30‐day survival probabilities are used as pseudo‐values for the unobserved counterfactual 30‐day survival status. The methods are illustrated and contrasted with an unconstrained modeling approach in large‐scale Danish registry data.