A martingale approach to estimating confidence band with censored data

Lee Seung-Hwan () and Lee Eun-Joo ()
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Lee Seung-Hwan: Department of Mathematics, Illinois Wesleyan University, Bloomington, Illinois 61701, USA
Lee Eun-Joo: Department of Mathematics, Millikin University, Decatur, Illinois 62522, USA

Monte Carlo Methods and Applications, 2014, vol. 20, issue 4, 237-243

Abstract: This paper develops some non-parametric simultaneous confidence bands for survival function when data are randomly censored on the right. To construct the confidence bands, a computer-assisted method is utilized and this approach requires no distributional assumptions, so the confidence bands can be easily estimated. The procedures are based on the integrated martingale whose distribution is approximated by a Gaussian process. The supremum distribution of the Gaussian process generated by simulation techniques leads to the construction of the confidence bands. To improve the estimation procedures for the finite sample sizes, the log-minus-log transformation is employed. The proposed confidence bands are assessed using numerical simulations and applied to a real-world data set regarding leukemia.

Keywords: Censored data; Kaplan–Meier estimate; martingale; simultaneous confidence band; survival function (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1515/mcma-2014-0003

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