Efficiency of Naive Estimators for Accelerated Failure Time Models under Length-Biased Sampling

Area of Science:

• Biostatistics
• Epidemiology
• Survival Analysis

Background:

• Prevalent cohort studies often face length-biased sampling, where observed event times (forward recurrence, backward recurrence, or their sum) are influenced by study recruitment.
• Standard methods for accelerated failure time (AFT) models assume unbiased data, but their efficiency under length-biased sampling is uncertain.

Purpose of the Study:

• To investigate the efficiency of regression parameter estimators in semiparametric AFT models under length-biased sampling.
• To determine if the observed covariate distribution, itself subject to length-bias, provides additional information for parameter estimation.

Main Methods:

• The study considers a semiparametric AFT model where the intercept is absorbed into a nuisance parameter.
• It analyzes the invariance of the model under different observed data setups (forward, backward, or sum of recurrence times).
• Focuses on a naive estimator derived from the conditional likelihood given covariates.

Main Results:

• The semiparametric AFT model remains invariant under length-biased sampling, allowing standard fitting methods.
• The efficiency of naive estimators was previously unclear due to length-biased covariate distributions.
• Demonstrates that the naive estimator is fully efficient for the slope parameter when the true covariate distribution is unspecified.

Conclusions:

• Standard AFT model fitting methods can be applied despite length-biased sampling.
• The naive estimator, utilizing the conditional likelihood, achieves full efficiency for regression slopes in the presence of unknown covariate distributions under length-bias.