In evaluating the benefit of a treatment on survival, it is often of interest to compare post-treatment survival with the survival function that would have been observed in the absence of treatment. In many practical settings, treatment is time-dependent in the sense that subjects typically begin follow-up untreated, with some going on to receive treatment at some later time point. In observational studies, treatment is not assigned at random and, therefore, may depend on various patient characteristics. We have developed semi-parametric matching methods to estimate the average treatment effect on the treated (ATT) with respect to survival probability and restricted mean survival time. Matching is based on a prognostic score which reflects each patient’s death hazard in the absence of treatment. Specifically, each treated patient is matched with multiple as-yet-untreated patients with similar prognostic scores. The matched sets do not need to be of equal size, since each matched control is weighted in order to preserve risk score balancing across treated and untreated groups. After matching, we estimate the ATT non-parametrically by contrasting pre- and post-treatment weighted Nelson–Aalen survival curves. A closed-form variance is proposed and shown to work well in simulation studies. The proposed methods are applied to national organ transplant registry data.

中文翻译：

---

用于估计不可逆二进制时间依赖性治疗对生存函数的平均影响的预后评分匹配方法。

在评估治疗对生存的益处时，将治疗后的生存与在没有治疗的情况下观察到的生存函数进行比较通常是有意义的。在许多实际环境中，治疗是时间依赖性的，因为受试者通常在开始随访时未经治疗，有些会在稍后的某个时间点接受治疗。在观察性研究中，治疗不是随机分配的，因此可能取决于患者的各种特征。我们已经开发了半参数匹配方法来估计对被治疗者 (ATT) 的平均治疗效果，即生存概率和受限平均生存时间。匹配基于反映每位患者在没有治疗的情况下的死亡风险的预后评分。具体来说，每个接受治疗的患者都与多个具有相似预后评分的尚未接受治疗的患者相匹配。匹配的集合不需要具有相同的大小，因为每个匹配的控件都被加权以保持治疗组和未治疗组之间的风险评分平衡。匹配后，我们通过对比治疗前和治疗后加权 Nelson-Aalen 生存曲线来非参数地估计 ATT。提出了一种封闭形式的方差，并证明其在模拟研究中工作良好。所提出的方法应用于国家器官移植登记数据。我们通过对比治疗前和治疗后加权 Nelson-Aalen 生存曲线来非参数地估计 ATT。提出了一种封闭形式的方差，并证明其在模拟研究中工作良好。所提出的方法应用于国家器官移植登记数据。我们通过对比治疗前和治疗后加权 Nelson-Aalen 生存曲线来非参数地估计 ATT。提出了一种封闭形式的方差，并证明其在模拟研究中工作良好。所提出的方法应用于国家器官移植登记数据。