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

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.