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Efficiency of naive estimators for accelerated failure time models under length‐biased sampling

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  • Pourab Roy
  • Jason P. Fine
  • Michael R. Kosorok

Abstract

In prevalent cohort studies where subjects are recruited at a cross‐section, the time to an event may be subject to length‐biased sampling, with the observed data being either the forward recurrence time, or the backward recurrence time, or their sum. In the regression setting, assuming a semiparametric accelerated failure time model for the underlying event time, where the intercept parameter is absorbed into the nuisance parameter, it has been shown that the model remains invariant under these observed data setups and can be fitted using standard methodology for accelerated failure time model estimation, ignoring the length bias. However, the efficiency of these estimators is unclear, owing to the fact that the observed covariate distribution, which is also length biased, may contain information about the regression parameter in the accelerated life model. We demonstrate that if the true covariate distribution is completely unspecified, then the naive estimator based on the conditional likelihood given the covariates is fully efficient for the slope.

Suggested Citation

  • Pourab Roy & Jason P. Fine & Michael R. Kosorok, 2022. "Efficiency of naive estimators for accelerated failure time models under length‐biased sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 525-541, June.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:2:p:525-541
    DOI: 10.1111/sjos.12526
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    References listed on IDEAS

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    4. Niels Keiding & Katrine Lykke Albertsen & Helene Charlotte Rytgaard & Anne Lyngholm Sørensen, 2019. "Prevalent cohort studies and unobserved heterogeneity," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(4), pages 712-738, October.
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