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Empirical likelihood-based confidence intervals for length-biased data


Correspondence to: Jing Ning, Department of Biostatistics, The University of Texas M. D. Anderson Cancer Center, Houston, TX 77030, U.S.A.



Logistic or other constraints often preclude the possibility of conducting incident cohort studies. A feasible alternative in such cases is to conduct a cross-sectional prevalent cohort study for which we recruit prevalent cases, that is, subjects who have already experienced the initiating event, say the onset of a disease. When the interest lies in estimating the lifespan between the initiating event and a terminating event, say death for instance, such subjects may be followed prospectively until the terminating event or loss to follow-up, whichever happens first. It is well known that prevalent cases have, on average, longer lifespans. As such, they do not constitute a representative random sample from the target population; they comprise a biased sample. If the initiating events are generated from a stationary Poisson process, the so-called stationarity assumption, this bias is called length bias. The current literature on length-biased sampling lacks a simple method for estimating the margin of errors of commonly used summary statistics. We fill this gap by using the empirical likelihood-based confidence intervals by adapting this method to right-censored length-biased survival data. Both large and small sample behaviors of these confidence intervals are studied. We illustrate our method by using a set of data on survival with dementia, collected as part of the Canadian Study of Health and Aging. Copyright © 2012 John Wiley & Sons, Ltd.