Coherent modeling of longitudinal causal effects on binary outcomes

TL;DR

This paper introduces a new reparametrization for multiplicative structural nested mean models (SNMMs) that enables coherent modeling of longitudinal causal effects with binary outcomes, overcoming previous variation dependence issues.

Contribution

The authors develop a variation independent parametrization for binary multiplicative SNMMs, facilitating better estimation and interpretation of heterogeneous treatment effects in longitudinal biomedical studies.

Findings

Reparametrization solves variation dependence in binary SNMMs.

Additive SNMMs with binary outcomes cannot be parametrized independently.

New framework enables doubly robust estimation of causal effects.

Abstract

Analyses of biomedical studies often necessitate modeling longitudinal causal effects. The current focus on personalized medicine and effect heterogeneity makes this task even more challenging. Towards this end, structural nested mean models (SNMMs) are fundamental tools for studying heterogeneous treatment effects in longitudinal studies. However, when outcomes are binary, current methods for estimating multiplicative and additive SNMM parameters suffer from variation dependence between the causal parameters and the non-causal nuisance parameters. This leads to a series of difficulties in interpretation, estimation and computation. These difficulties have hindered the uptake of SNMMs in biomedical practice, where binary outcomes are very common. We solve the variation dependence problem for the binary multiplicative SNMM via a reparametrization of the non-causal nuisance parameters. Our novel nuisance parameters are variation independent of the causal parameters, and hence allow for coherent modeling of heterogeneous effects from longitudinal studies with binary outcomes. Our parametrization also provides a key building block for flexible doubly robust estimation of the causal parameters. Along the way, we prove that an additive SNMM with binary outcomes does not admit a variation independent parametrization, thereby justifying the restriction to multiplicative SNMMs.