Nonparametric estimation for length-biased and right-censored data

摘要

This paper considers survival data arising from length-biased sampling, where the survivalntimes are left truncated by uniformly distributed random truncation times. We propose annonparametric estimator that incorporates the information about the length-biased samplingnscheme. The new estimator retains the simplicity of the truncation product-limit estimator withna closed-form expression, and has a small efficiency loss compared with the nonparametricnmaximum likelihood estimator, which requires an iterative algorithm. Moreover, the asymptoticnvariance of the proposed estimator has a closed form, and a variance estimator is easilynobtained by plug-in methods. Numerical simulation studies with practical sample sizes arenconducted to compare the performance of the proposed method with its competitors. A datananalysis of the Canadian Study of Health and Aging is conducted to illustrate the methodsnand theory.