Characterizing quantile-varying covariate effects under the accelerated failure time model

TL;DR

This paper introduces a flexible framework for modeling covariate effects that vary across quantiles in the AFT survival analysis model, allowing for more nuanced understanding of covariate impacts on survival times.

Contribution

It develops a novel quantile-varying AFT model with a Bayesian estimation approach, enabling detailed analysis of covariate effects across the entire survival distribution.

Findings

The proposed model captures effects that differ across quantiles.

Simulation studies demonstrate accurate estimation of quantile-varying effects.

Application to Alzheimer's data reveals nuanced covariate impacts.

Abstract

An important task in survival analysis is choosing a structure for the relationship between covariates of interest and the time-to-event outcome. For example, the accelerated failure time (AFT) model structures each covariate effect as a constant multiplicative shift in the outcome distribution across all survival quantiles. Though parsimonious, this structure cannot detect or capture effects that differ across quantiles of the distribution, a limitation that is analogous to only permitting proportional hazards in the Cox model. To address this, we propose a general framework for quantile-varying multiplicative effects under the AFT model. Specifically, we embed flexible regression structures within the AFT model, and derive a novel formula for interpretable effects on the quantile scale. A regression standardization scheme based on the g-formula is proposed to enable estimation of both covariate-conditional and marginal effects for an exposure of interest. We implement a user-friendly Bayesian approach for estimation and quantification of uncertainty, while accounting for left truncation and complex censoring. We emphasize the intuitive interpretation of this model through numerical and graphical tools, and illustrate its performance through simulation and application to a study of Alzheimer's disease and dementia.