title: A robust semi-parametric warping estimator of the survivor function with an application to two-group comparisons.
abstract: In this note, we develop a new and novel semi-parametric estimator of the survival curve that is comparable to the product-limit estimator under very relaxed assumptions. The estimator is based on a beta parametrization that warps the empirical distribution of the observed censored and uncensored data. The parameters are obtained using a pseudo-maximum likelihood approach adjusting the survival curve accounting for the censored observations. In the univariate setting, the new estimator tends to better extend the range of the survival estimation given a high degree of censoring. However, the key feature of this paper is that we develop a new two-group semi-parametric exact permutation test for comparing survival curves that is generally superior to the classic log-rank and Wilcoxon tests and provides the best global power across a variety of alternatives. The new test is readily extended to the k group setting.
authors.affiliation: Department of Biostatistics, University at Buffalo, USA.
authors.forename: Alan D
authors.initials: AD
authors.lastname: Hutson
mesh_terms: D056808:Biostatistics; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D009010:Monte Carlo Method; D016019:Survival Analysis
keywords: Product-limit estimator; Wilcoxon-rank sum test; censored data; log-rank test