title: A practical divergence measure for survival distributions that can be estimated from Kaplan-Meier curves.
abstract: This paper introduces a new simple divergence measure between two survival distributions. For two groups of patients, the divergence measure between their associated survival distributions is based on the integral of the absolute difference in probabilities that a patient from one group dies at time t and a patient from the other group survives beyond time t and vice versa. In the case of non-crossing hazard functions, the divergence measure is closely linked to the Harrell concordance index, C, the Mann-Whitney test statistic and the area under a receiver operating characteristic curve. The measure can be used in a dynamic way where the divergence between two survival distributions from time zero up to time t is calculated enabling real-time monitoring of treatment differences. The divergence can be found for theoretical survival distributions or can be estimated non-parametrically from survival data using Kaplan-Meier estimates of the survivor functions. The estimator of the divergence is shown to be generally unbiased and approximately normally distributed. For the case of proportional hazards, the constituent parts of the divergence measure can be used to assess the proportional hazards assumption. The use of the divergence measure is illustrated on the survival of pancreatic cancer patients. Copyright © 2016 John Wiley & Sons, Ltd.
authors: Cancer Research UK Liverpool Cancer Trials Unit, University of Liverpool, Liverpool, U.K.
authors: Trevor F
authors: TF
authors: Cox
authors: Department of Biostatistics, University of Liverpool, Liverpool, U.K.|Department of Eye and Vision Science, University of Liverpool, U.K.
authors: Gabriela
authors: G
authors: Czanner
mesh_terms: D056808:Biostatistics; D006801:Humans; D053208:Kaplan-Meier Estimate; D015233:Models, Statistical; D010190:Pancreatic Neoplasms / Q000401:mortality / Q000628:therapy; D016016:Proportional Hazards Models; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data; D018709:Statistics, Nonparametric; D013810:Therapeutic Equivalency
keywords: Kaplan-Meier curves; Kullback-Leibler divergence; crossing hazard functions; divergence measures; multidimensional scaling