Nonparametric inference in the presence of biased sampling

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.