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On comparing competing risks using the ratio of their cumulative incidence functions
Annals of the Institute of Statistical Mathematics ( IF 1 ) Pub Date : 2022-05-14 , DOI: 10.1007/s10463-022-00823-9
Hammou El Barmi

For \( 1\le i \le r\), let \(F_i\) be the cumulative incidence function (CIF) corresponding to the ith risk in an r-competing risks model. We assume a discrete or a grouped time framework and obtain the maximum likelihood estimators (m.l.e.) of these CIFs under the restriction that \(F_i(t)/F_{i+1}(t)\) is nondecreasing, \(1 \le i \le r-1.\) We also derive the likelihood ratio tests for testing for and against this restriction and obtain their asymptotic distributions. The theory developed here can also be used to investigate the association between a failure time and a discretized or ordinal mark variable that is observed only at the time of failure. To illustrate the applicability of our results, we give examples in the competing risks and the mark variable settings.



中文翻译:

关于使用累积发生率函数的比率比较竞争风险

对于\( 1\le i \le r\),令\(F_i\)是对应于r竞争风险模型中第 i 个风险的累积关联函数 (CIF)。我们假设一个离散或分组的时间框架,并在\(F_i(t)/F_{i+1}(t)\) 不减的限制下获得这些 CIF 的最大似然估计量 (mle) ,\(1\ le i \le r-1.\)我们还推导出似然比检验来检验和反对这种限制,并获得它们的渐近分布。这里开发的理论也可用于研究故障时间与仅在故障时观察到的离散或有序标记变量之间的关联。为了说明我们结果的适用性,我们给出了竞争风险和标记变量设置的例子。

更新日期:2022-05-17
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