A cause-specific cumulative incidence function (CIF) is the probability of failure from a specific cause as a function of time. In randomized trials, a difference of cause-specific CIFs (treatment minus control) represents a treatment effect. Cause-specific CIF in each intervention arm can be estimated based on the usual non-parametric Aalen-Johansen estimator which generalizes the Kaplan-Meier estimator of CIF in the presence of competing risks. Under random censoring, asymptotically valid Wald-type confidence intervals (CIs) for a difference of cause-specific CIFs at a specific time point can be constructed using one of the published variance estimators. Unfortunately, these intervals can suffer from substantial under-coverage when the outcome of interest is a rare event, as may be the case for example in the analysis of uncommon adverse events. We propose two new approximate interval estimators for a difference of cause-specific CIFs estimated in the presence of competing risks and random censoring. Theoretical analysis and simulations indicate that the new interval estimators are superior to the Wald CIs in the sense of avoiding substantial under-coverage with rare events, while being equivalent to the Wald CIs asymptotically. In the absence of censoring, one of the two proposed interval estimators reduces to the well-known Agresti-Caffo CI for a difference of two binomial parameters. The new methods can be easily implemented with any software package producing point and variance estimates for the Aalen-Johansen estimator, as illustrated in a real data example.

中文翻译：

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在存在竞争风险和随机审查的情况下估计的两个特定原因累积发生率函数的差异的置信区间得到改善

特定原因累积发生率函数 (CIF) 是作为时间函数的特定原因导致的故障概率。在随机试验中，原因特异性 CIF（治疗减去对照）的差异代表治疗效果。可以基于通常的非参数 Aalen-Johansen 估计量来估计每个干预组中特定原因的 CIF，该估计量在存在竞争风险的情况下概括了 CIF 的 Kaplan-Meier 估计量。在随机审查下，可以使用已发布的方差估计量之一构建特定时间点特定原因 CIF 差异的渐近有效 Wald 型置信区间 (CI)。不幸的是，当感兴趣的结果是罕见事件时，这些间隔可能会受到严重覆盖不足的影响，例如在分析罕见的不良事件时可能就是这种情况。我们提出了两个新的近似区间估计量，用于在存在竞争风险和随机审查的情况下估计的特定原因 CIF 的差异。理论分析和模拟表明，新的区间估计量在避免罕见事件的严重覆盖不足的意义上优于 Wald CI，同时渐近地等效于 Wald CI。在没有审查的情况下，对于两个二项式参数的差异，两个提议的区间估计量之一简化为众所周知的 Agresti-Caffo CI。新方法可以使用任何软件包轻松实现，为 Aalen-Johansen 估计器生成点和方差估计，如真实数据示例所示。