A Heteroscedastic Accelerated Failure Time Model for Survival Analysis

TL;DR

This paper introduces a heteroscedastic accelerated failure time (HAFT) model for survival analysis that accounts for covariate-dependent variances, improving estimation in heavily censored data.

Contribution

It extends the AFT model to include heteroscedasticity and develops an efficient ECM algorithm for maximum likelihood estimation with censored data.

Findings

HAFT model reduces outliers compared to homoscedastic models

Method effectively handles heavily censored clinical trial data

Proposes new residuals for model diagnostics

Abstract

Nonparametric and semiparametric methods are commonly used in survival analysis to mitigate the bias due to model misspecification. However, such methods often cannot estimate upper-tail survival quantiles when a sizable proportion of the data are censored, in which case parametric likelihood-based estimators present a viable alternative. In this article, we extend a popular family of parametric survival models which make the Accelerated Failure Time (AFT) assumption to account for heteroscedasticity in the survival times. The conditional variances can depend on arbitrary covariates, thus adding considerable flexibility to the homoscedastic model. We present an Expectation-Conditional-Maximization (ECM) algorithm to efficiently compute the HAFT maximum likelihood estimator with right-censored data. The methodology is applied to the heavily censored data from a colon cancer clinical trial, for which a new type of highly stringent model residuals is proposed. Based on these, the HAFT model was found to eliminate most outliers from its homoscedastic counterpart.