title: 'Smooth' inference for survival functions with arbitrarily censored data.
abstract: We propose a procedure for estimating the survival function of a time-to-event random variable under arbitrary patterns of censoring. The method is predicated on the mild assumption that the distribution of the random variable, and hence the survival function, has a density that lies in a class of 'smooth' densities whose elements can be represented by an infinite Hermite series. Truncation of the series yields a 'parametric' expression that can well approximate any plausible survival density, and hence survival function, provided the degree of truncation is suitably chosen. The representation admits a convenient expression for the likelihood for the 'parameters' in the approximation under arbitrary censoring/truncation that is straightforward to compute and maximize. A test statistic for comparing two survival functions, which is based on an integrated weighted difference of estimates of each under this representation, is proposed. Via simulation studies and application to a number of data sets, we demonstrate that the approach yields reliable inferences and can result in gains in efficiency over traditional nonparametric methods.
authors.affiliation: Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27402-6170, USA.
authors.forename: Kirsten
authors.initials: K
authors.lastname: Doehler
authors.forename: Marie
authors.initials: M
authors.lastname: Davidian
mesh_terms: D002986:Clinical Trials as Topic / Q000379:methods; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D018450:Disease Progression; D023381:Endpoint Determination; D006801:Humans; D016013:Likelihood Functions; D018709:Statistics, Nonparametric; D016019:Survival Analysis