Causal Inference for Continuous Multiple Time Point Interventions

TL;DR

This paper introduces a method for causal inference with continuous, multi-time point interventions, addressing positivity violations by using projection functions to redefine estimands and improve dose-response estimation.

Contribution

It develops projection functions and $g$-computation estimators to handle positivity violations in continuous interventions, with practical diagnostics and application to HIV treatment data.

Findings

Proposed methods accurately estimate dose-response curves in areas with sufficient support.

Standard g-computation can be biased when positivity is violated, while the new approach recovers the true estimand.

Simulations demonstrate the effectiveness of the proposed estimators under various scenarios.

Abstract

There are limited options to estimate the treatment effects of variables which are continuous and measured at multiple time points, particularly if the true dose-response curve should be estimated as closely as possible. However, these situations may be of relevance: in pharmacology, one may be interested in how outcomes of people living with -- and treated for -- HIV, such as viral failure, would vary for time-varying interventions such as different drug concentration trajectories. A challenge for doing causal inference with continuous interventions is that the positivity assumption is typically violated. To address positivity violations, we develop projection functions, which reweigh and redefine the estimand of interest based on functions of the conditional support for the respective interventions. With these functions, we obtain the desired dose-response curve in areas of enough support, and otherwise a meaningful estimand that does not require the positivity assumption. We develop $g$-computation type plug-in estimators for this case. Those are contrasted with g-computation estimators which are applied to continuous interventions without specifically addressing positivity violations, which we propose to be presented with diagnostics. The ideas are illustrated with longitudinal data from HIV positive children treated with an efavirenz-based regimen as part of the CHAPAS-3 trial, which enrolled children $<13$ years in Zambia/Uganda. Simulations show in which situations a standard g-computation approach is appropriate, and in which it leads to bias and how the proposed weighted estimation approach then recovers the alternative estimand of interest.