The causal interpretation of acceleration factors

TL;DR

This paper formalizes the causal interpretation of acceleration factors in AFT models, demonstrating their validity as causal effect measures and comparing them to hazard ratios through simulations.

Contribution

It provides a formal causal framework for acceleration factors in AFT models, extending their interpretation to time-dependent effects and highlighting their advantages over hazard ratios.

Findings

Acceleration factors are valid causal effect measures even with heterogeneity.

AFT models better capture causal effects than hazard ratios under certain conditions.

Time-dependent acceleration factors cannot distinguish between effect heterogeneity and homogeneous effects.

Abstract

In studies of time-to-event outcomes with unmeasured heterogeneity, the hazard ratio for treatment is known to have a complex causal interpretation. Accelerated failure time (AFT) models, which assess the effect on the survival time ratio scale, are often suggested as a better alternative because they model a parameter with direct causal interpretation while allowing straightforward adjustment for measured confounders. In this work, we formalize the causal interpretation of the acceleration factor in AFT models using structural causal models and data under independent censoring. We prove that the acceleration factor is a valid causal effect measure, even in the presence of frailty and treatment effect heterogeneity. Through simulations, we show that the acceleration factor better captures the causal effect than the hazard ratio when both AFT and conditional proportional hazards models apply. Additionally, we extend the interpretation to systems with time-dependent acceleration factors, illustrating the impossibility of distinguishing between a time-varying homogeneous effect and unmeasured effect heterogeneity. While the causal interpretation of acceleration factors is promising, we caution practitioners about potential challenges for the interpretation in the presence of effect heterogeneity.