Composite estimator of mean residual lifetime with length-biased and right-censored data

Abstract

Length-biased data are very common in prevalent cases by cross-sectional sampling when studying time-to-event data, the distribution of length bias data changes from the population distribution and the censoring is informative censoring. But it is difficult to estimate lifetime exactly from such biased observational data with censoring. Bias and the informative censoring in the length-biased data make many classical statistical methods invalid. In this paper, we study a mean residual lifetime model when sample is subject to length-biased and rightcensored data. Nonparametric estimation methods are proposed based on estimating equations. To improve the efficiency of the estimator, we take account into the informative censoring and auxiliary information of length-bias data. Although the maximum likelihood estimation is efficient, its computation has so many iterations. Thus we propose a simple way to add the auxiliary information, where the new estimator needs less calculation times. At the same time, asymptotic properties of nonparametric estimators for the mean residual lifetime are established. In simulation studies, it can be seen that our estimator is more effective and simpler.