Nonparametric linear tests with multiple events

• Published in: Computational statistics & data analysis Vol. 53; no. 12; pp. 4279 - 4289
• Main Authors: Pinçon, Claire, Pons, Odile
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.2009; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Exact sciences and technology; General topics; Mathematics; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Parametric inference; Probability and statistics; Sciences and techniques of general use; Statistics; Rank statistic; Breast disease; Paired comparison; Statistical distribution; Vector distribution; Non parametric estimation; Multivariate analysis; Statistical simulation; Linear test; Parametric method; Hypothesis test; Statistical test; Covariance; Survival function; Marginal distribution; Distribution function; Logrank test; Approximation theory; Sample survey; Censored data; Discriminant analysis; Data analysis; Non parametric test; Martingale; Multiple test; Statistical estimation; Multiple comparison; Covariance matrix; Joint distribution; Survival; Statistical method; Statistical regression; Selection problem; Sampling theory; Statistical computation
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2009.05.022

A generalization of the nonparametric linear rank statistics is presented to handle the two-group comparison with multiple events. For a sample divided into two groups, in which each subject may experience at least two distinct failures, the logrank tests are extended to test the null hypothesis that the vector of the marginal survival distributions of the first group equals that of the second group. Two cases are distinguished depending on whether the null hypothesis does or does not imply the equality of the joint survival functions. In both cases, under the null hypothesis, the asymptotic joint distribution of the vector of the marginal statistics is shown to be Gaussian with covariance matrix consistently estimated using martingale properties. These theoretical results are illustrated by a simulation study and an application on the German Breast Cancer data. An extension to multiple hypotheses testing in multivariate proportional hazards models is also developed.