Causal inference under over-simplified longitudinal causal models

TL;DR

This paper investigates how simplified causal models in epidemiology, which ignore longitudinal data, can lead to biased estimates and emphasizes the importance of repeated measurements for accurate causal inference.

Contribution

It derives conditions under which simplified causal estimates relate to true effects and highlights the limitations and potential biases of over-simplified models.

Findings

Simplified models often do not reflect true longitudinal effects.

Bias can be substantial when using over-simplified models.

Repeated measurements are crucial for accurate causal inference.

Abstract

Many causal models of interest in epidemiology involve longitudinal exposures, confounders and mediators. However, repeated measurements are not always available or used in practice, leading analysts to overlook the time-varying nature of exposures and work under over-simplified causal models. Our objective is to assess whether - and how - causal effects identified under such misspecified causal models relates to true causal effects of interest. We derive sufficient conditions ensuring that the quantities estimated in practice under over-simplified causal models can be expressed as weighted averages of longitudinal causal effects of interest. Unsurprisingly, these sufficient conditions are very restrictive, and our results state that the quantities estimated in practice should be interpreted with caution in general, as they usually do not relate to any longitudinal causal effect of interest. Our simulations further illustrate that the bias between the quantities estimated in practice and the weighted averages of longitudinal causal effects of interest can be substantial. Overall, our results confirm the need for repeated measurements to conduct proper analyses and/or the development of sensitivity analyses when they are not available.