The Gini concentration test for survival data

• Published in: Lifetime data analysis Vol. 15; no. 4; pp. 493 - 518
• Main Authors: Bonetti, Marco, Gigliarano, Chiara, Muliere, Pietro
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.12.2009; Springer Nature B.V
• Subjects: Clinical trials; Clinical Trials as Topic - statistics & numerical data; Economics; Expected values; Finance; Health Sciences; Insurance; Management; Mathematics and Statistics; Medical treatment; Medicine; Melanoma; Models, Statistical; Oncology; Operations Research/Decision Theory; Power; Quality Control; Random variables; Reliability; Safety and Risk; Simulation; Statistics; Statistics for Business; Statistics for Life Sciences; Studies; Survival Analysis; Tests; Cure rate model; Gini index; Linear rank test; Right censored survival data; Melanoma
• ISSN: 1380-7870; 1572-9249
• DOI: 10.1007/s10985-009-9125-5

We apply the well known Gini index to the measurement of concentration in survival times within groups of patients, and as a way to compare the distribution of survival times across groups of patients in clinical studies. In particular, we propose an estimator of a restricted version of the index from right censored data. We derive the asymptotic distribution of the resulting Gini statistic, and construct an estimator for its asymptotic variance. We use these results to propose a novel test for differences in the heterogeneity of survival distributions, which may suggest the presence of a differential treatment effect for some groups of patients. We focus in particular on traditional and generalized cure rate models, i.e., mixture models with a distribution of the lifetimes of the cured patients that is either degenerate at infinity or has a density. Results from a simulation study suggest that the Gini index is useful in some situations, and that it should be considered together with existing tests (in particular, the Log-rank, Wilcoxon, and Gray–Tsiatis tests). Use of the test is illustrated on the classic data arising from the Eastern Cooperative Oncology Group melanoma clinical trial E1690.