The additive hazard estimator is consistent for continuous-time marginal structural models

TL;DR

This paper demonstrates the consistency of additive hazard estimators in continuous-time marginal structural models, even when weights are estimated, and introduces transformation methods for hazard estimates to improve interpretability.

Contribution

It provides a sufficient condition for consistency of continuous-time MSMs with estimated weights and introduces a transformation strategy for hazard estimates using R packages.

Findings

Additive hazard models can reliably estimate weights in continuous-time MSMs.

Estimated weights outperform IPTW in continuous treatment processes.

Transformation of hazard estimates enhances interpretability in survival analysis.

Abstract

Marginal structural models (MSMs) allow for causal analysis of longitudinal data. The MSMs were originally developed as discrete time models. Recently, continuous-time MSMs were presented as a conceptually appealing alternative for survival analysis. In applied analyses, it is often assumed that the theoretical treatment weights are known, but these weights are usually unknown and must be estimated from the data. Here we provide a sufficient condition for a class of continuous-time MSMs to be consistent even when the weights are estimated, and we show how additive hazard models can be used to estimate such weights. Our results suggest that the continuous-time weights perform better than IPTW when the underlying treatment process is continuous. Furthermore, we may wish to transform effect estimates of hazards to other scales that are easier to interpret causally. We show that a general transformation strategy can be used on weighted cumulative hazard estimates to obtain a range of other parameters in survival analysis, and demonstrate how this strategy can be applied on data using our R packages ahw and transform.hazards.