Bonetti Marco, Gigliarano Chiara, Muliere Pietro
Department of Decision Sciences, Bocconi University, via Roentgen 1, 20136 Milan, Italy.
Lifetime Data Anal. 2009 Dec;15(4):493-518. doi: 10.1007/s10985-009-9125-5. Epub 2009 Sep 2.
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.
我们将著名的基尼指数应用于测量患者组内生存时间的集中度，并以此作为比较临床研究中不同患者组生存时间分布的一种方法。特别地，我们从右删失数据中提出了该指数受限版本的一个估计量。我们推导了所得基尼统计量的渐近分布，并构建了其渐近方差的一个估计量。我们利用这些结果提出了一种用于检验生存分布异质性差异的新方法，这可能表明某些患者组存在差异治疗效果。我们特别关注传统和广义治愈率模型，即治愈患者寿命分布在无穷远处退化或具有密度的混合模型。模拟研究结果表明，基尼指数在某些情况下是有用的，并且应该与现有检验（特别是对数秩检验、威尔科克森检验和格雷 - 齐亚蒂斯检验）一起考虑。通过东部肿瘤协作组黑色素瘤临床试验E1690产生的经典数据说明了该检验的应用。
