Simple and fast overidentified rank estimation for right-censored length-biased data and backward recurrence time.

Length-biased survival data subject to right-censoring are often collected from a prevalent cohort. However, informative right censoring induced by the sampling design creates challenges in methodological development. While certain conditioning arguments could circumvent the problem of informative censoring, related rank estimation methods are typically inefficient because the marginal likelihood of the backward recurrence time is not ancillary. Under a semiparametric accelerated failure time model, an overidentified set of log-rank estimating equations is constructed based on the left-truncated right-censored data and backward recurrence time. Efficient combination of the estimating equations is simplified by exploiting an asymptotic independence property between two sets of estimating equations. A fast algorithm is studied for solving non-smooth, non-monotone estimating equations. Simulation studies confirm that the overidentified rank estimator can have a substantially improved estimation efficiency compared to just-identified rank estimators. The proposed method is applied to a dementia study for illustration.