Macquarie University
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Nonparametric inference in the presence of biased sampling

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posted on 2022-03-28, 01:19 authored by Ali Shariati
Life expectancy is a key concept in survival analysis. When communicating with non-statisticians, average remaining lifespan is a more meaningful and comprehensible measure than the survival probability or the hazard rate. Therefore our research is centered on the mean residual lifetime function. Survival data collected in a cohort of prevalent cases may be used to draw statistical inference. Since non-random sampling of subjects is involved, the data collected in this sampling scheme are biased. The most common case of this bias, occurring when the so-called stationarity assumption is satisfied, is called length-bias. While prospective prevalent cohort studies are commonly conducted to evaluate the progression of some disease overtime, observations of many other sampling schemes have been reported to be length-biased. It is often necessary to take into account loss to follow-up of subjects, that is, the presence of censored data. In this thesis, we study the problem of statistical inference (i.e. confidence interval) for length-biased data via the empirical likelihood method. The results are extended to construct a confidence interval for length-biased random censored data. The performance of these methods are illustrated through a simulation study and a data set obtained from a study of shrubs.


Table of Contents

1. Preliminaries and background -- 2. Confidence interval for the MRL function based on length-biased data -- 3. Confidence interval based on length-biased and right-censored data -- 4.Discussion and future directions -- 5. Appendix I -- 6. Appendix II -- References.


Empirical thesis. Bibliography: pages 77-81

Awarding Institution

Macquarie University

Degree Type

Thesis MRes


MRes, Macquarie University, Faculty of Science and Engineering, Department of Mathematics and Statistics

Department, Centre or School

Department of Mathematics and Statistics

Year of Award


Principal Supervisor

Hassan Doosti

Additional Supervisor 1

Justin Wishart


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