Statistical analysis of length-biased and right-censored data

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Biased sampling arises when the observations are not randomly selected from the target population. When the sampling probability is proportional to the underlying outcome of interest, this is known as length-biased sampling. Length-biased sampling has been well recognized in economics, industrial reliability, etiology applications, epidemiological studies and cancer screening trials. Right-censored time-to-event data are often observed from a cohort of prevalent cases that are subject to length-biased sampling, which are termed as length-biased and right-censored data. It has a unique data structure different from traditional survival data and thus requires different inference methods for both nonparametric and semiparametric estimations. In this thesis, we will exploit these unique aspects and discuss the statistical analysis of length-biased and right-censored data. The first part of this dissertation discusses a goodness-of-fit test for checking the parametric model with length-biased and right-censored data. The second part of this dissertation considers the regression analysis of length-biased and right-censored data in the context of the novel two sample short-term and long-term hazard ratios model. The third part of this dissertation proposes an inverse probability weighted (IPW) method and a reweighted method for estimating the regression parameters in the Cox model with missing covariates under length-biased sampling. The performance of the proposed approaches are demonstrated through simulation studies and we apply the approaches to the survival data from the Canadian Study of Health and Aging(CSHA).