Score Estimating Equations from Embedded Likelihood Functions Under Accelerated Failure Time Model

• Published in: Journal of the American Statistical Association Vol. 109; no. 508; pp. 1625 - 1635
• Main Authors: Ning, Jing, Qin, Jing, Shen, Yu
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 01.12.2014; Taylor & Francis Group, LLC; Taylor & Francis Ltd
• Subjects: Analytical estimating; Censored data; Cox model; Data sampling; Dementia; equations; Estimation methods; Estimators; Failure analysis; Length-biased data; Mathematical functions; Mathematical models; Parameter estimation; Preliminary estimates; probability; Proportional odds model; Random variables; Regression analysis; Sampling bias; Score equation; Statistical bias; Statistical estimation; Statistics; Theory and Methods; Length-biased data; Accelerated failure time model; Proportional odds model; Cox model; Score equation; Likelihood function
• ISSN: 1537-274X; 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2014.946034

The semiparametric accelerated failure time (AFT) model is one of the most popular models for analyzing time-to-event outcomes. One appealing feature of the AFT model is that the observed failure time data can be transformed to identically independent distributed random variables without covariate effects. We describe a class of estimating equations based on the score functions for the transformed data, which are derived from the full likelihood function under commonly used semiparametric models such as the proportional hazards or proportional odds model. The methods of estimating regression parameters under the AFT model can be applied to traditional right-censored survival data as well as more complex time-to-event data subject to length-biased sampling. We establish the asymptotic properties and evaluate the small sample performance of the proposed estimators. We illustrate the proposed methods through applications in two examples.