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.

中文翻译：

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长度偏差采样下加速故障时间模型的朴素估计器的效率

在以横截面招募受试者的流行队列研究中，事件发生的时间可能会受到长度偏差抽样的影响，观察到的数据要么是前向复发时间，要么是后向复发时间，或者是它们的总和。在回归设置中，假设基础事件时间的半参数加速故障时间模型，其中截距参数被吸收到滋扰参数中，已经表明该模型在这些观察到的数据设置下保持不变，并且可以使用标准方法进行拟合用于加速故障时间模型估计，忽略长度偏差。然而，这些估计量的效率尚不清楚，因为观察到的协变量分布也是长度偏差的，可能包含有关加速寿命模型中回归参数的信息。我们证明，如果真正的协变量分布是完全未指定的，那么基于给定协变量的条件似然的朴素估计对于斜率是完全有效的。