Abstract: Associations between an exposure and multiple competing events are typically described by cause-specific hazard ratios (csHR) or subdistribution hazard ratios (sHR). However, diagnostic tools to assess differences between them have not been described. Under the proportionality assumption for both, it can be shown mathematically that the sHR and csHR must be equal, so reporting different time-constant sHR and csHR implies non-proportionality for at least one. We propose a simple, intuitive approach using the ratio of sHR/csHR to nonparametrically compare these metrics. In general, for the non-null case, there must be at least one event type for which the sHR and csHR differ, and the proposed diagnostic will be useful to identify these cases. Furthermore, once standard methods are used to estimate the csHR, multiplying it with our nonparametric estimate for the sHR/csHR ratio will yield estimates of sHR which fulfill intrinsic linkages of the subhazards that separate analysis may violate. In addition, for non-null cases, at least one must be time dependent (i.e., non-proportional), and thus our tool serves as an indirect test of the proportionality assumption. We applied this proposed diagnostic tool to data from a cohort of children with congenital kidney disease to describe racial differences in the time to first dialysis or first transplant and extend methods to include adjustment for socioeconomic factors.

Keywords: survival analysis, nonparametric methods, competing risk analysis, cause-specific hazard ratios, sub-distribution hazard ratios, chronic kidney disease


中文翻译：

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竞争风险危险比之间的差异的非参数评估：在小儿慢性肾脏疾病进展中的种族差异中的应用。

摘要：暴露与多个竞争事件之间的关联通常由特定原因的危险比（csHR）或子分布危险比（sHR）描述。但是，尚未描述评估它们之间差异的诊断工具。在两者的比例假设下，可以从数学上证明sHR和csHR必须相等，因此报告不同的时间常数sHR和csHR意味着至少有一个不成比例。我们提出一种简单，直观的方法，使用sHR / csHR的比率对这些指标进行非参数比较。通常，对于非空病例，必须至少存在一种sHR和csHR不同的事件类型，建议的诊断方法将有助于识别这些病例。此外，一旦使用标准方法估算csHR，将其与我们的sHR / csHR比的非参数估计值相乘将得出sHR的估计值，这些估计值满足了单独分析可能违反的亚危害的内在联系。另外，对于非空的情况，至少一个必须与时间相关（即非比例），因此我们的工具可作为对比例假设的间接检验。我们将该拟议的诊断工具应用于一组先天性肾脏疾病患儿的数据，以描述初次透析或首次移植时的种族差异，并扩展方法以包括对社会经济因素的调整。因此我们的工具可以作为对比例假设的间接检验。我们将该拟议的诊断工具应用于一组先天性肾脏疾病患儿的数据，以描述初次透析或首次移植时的种族差异，并扩展方法以包括对社会经济因素的调整。因此我们的工具可以作为对比例假设的间接检验。我们将该拟议的诊断工具应用于一组先天性肾脏疾病患儿的数据，以描述初次透析或首次移植时的种族差异，并扩展方法以包括对社会经济因素的调整。

关键字：生存分析，非参数方法，竞争风险分析，特定原因的危险比，子分布危险比，慢性肾脏病