title: Nonparametric estimation of the survival function for ordered multivariate failure time data: A comparative study.
abstract: In longitudinal studies of disease, patients may experience several events through a follow-up period. In these studies, the sequentially ordered events are often of interest and lead to problems that have received much attention recently. Issues of interest include the estimation of bivariate survival, marginal distributions, and the conditional distribution of gap times. In this work, we consider the estimation of the survival function conditional to a previous event. Different nonparametric approaches will be considered for estimating these quantities, all based on the Kaplan-Meier estimator of the survival function. We explore the finite sample behavior of the estimators through simulations. The different methods proposed in this article are applied to a dataset from a German Breast Cancer Study. The methods are used to obtain predictors for the conditional survival probabilities as well as to study the influence of recurrence in overall survival.
authors.affiliation: Centre of Mathematics and Department of Mathematics and Applications, University of Minho, Campus de Azurem, 4800-058 Guimarães, Portugal.
authors.forename: Luís
authors.initials: L
authors.lastname: Meira-Machado
authors.affiliation: Centre of Mathematics and Department of Mathematics and Applications, University of Minho, Campus de Azurem, 4800-058 Guimarães, Portugal.|SiDOR Research Group and CINBIO, University of Vigo, Spain.
authors.forename: Marta
authors.initials: M
authors.lastname: Sestelo
authors.affiliation: Centre of Mathematics and Department of Mathematics and Applications, University of Minho, Campus de Azurem, 4800-058 Guimarães, Portugal.
authors.forename: Andreia
authors.initials: A
authors.lastname: Gonçalves
mesh_terms: D001699:Biometry / Q000379:methods*; D001943:Breast Neoplasms / Q000175:diagnosis / Q000453:epidemiology; D005260:Female; D005858:Germany / Q000453:epidemiology; D006801:Humans; D015233:Models, Statistical; D015999:Multivariate Analysis; D011336:Probability; D012008:Recurrence; D018709:Statistics, Nonparametric; D016019:Survival Analysis; D013997:Time Factors
keywords: Conditional survival; Gap times; Kaplan-Meier; Nonparametric estimation; Recurrent events