In heart failure (HF) trials efficacy is usually assessed by a composite endpoint including cardiovascular death (CVD) and heart failure hospitalizations (HFHs), which has traditionally been evaluated with a time-to-first-event analysis based on a Cox model. As a considerable fraction of events is ignored that way, methods for recurrent events were suggested, among others the semiparametric proportional rates models by Lin, Wei, Yang, and Ying (LWYY model) and Mao and Lin (Mao-Lin model). In our work we apply least false parameter theory to explain the behavior of the composite treatment effect estimates resulting from the Cox model, the LWYY model, and the Mao-Lin model in clinically relevant scenarios parameterized through joint frailty models. These account for both different treatment effects on the two outcomes (CVD, HFHs) and the positive correlation between their risk rates. For the important setting of beneficial outcome-specific treatment effects we show that the correlation results in composite treatment effect estimates, which are decreasing with trial duration. The estimate from the Cox model is affected more by the attenuation than the estimates from the recurrent event models, which both demonstrate very similar behavior. Since the Mao-Lin model turns out to be less sensitive to harmful effects on mortality, we conclude that, among the three investigated approaches, the LWYY model is the most appropriate one for the composite endpoint in HF trials. Our investigations are motivated and compared with empirical results from the PARADIGM-HF trial (ClinicalTrials.gov identifier: NCT01035255), a large multicenter trial including 8399 chronic HF patients.

中文翻译：

---

评估心力衰竭试验中复合终点的半参数方法的比较

在心力衰竭 (HF) 试验中，疗效通常通过复合终点进行评估，包括心血管死亡 (CVD) 和心力衰竭住院 (HFH)，传统上通过基于 Cox 模型的首次事件时间分析来评估。由于以这种方式忽略了相当一部分事件，因此建议了复发事件的方法，其中包括 Lin、Wei、Yang 和 Ying（LWYY 模型）以及 Chao 和 Lin（Mao-Lin 模型）的半参数比例模型。在我们的工作中，我们应用最小错误参数理论来解释由 Cox 模型、LWYY 模型和 Mao-Lin 模型产生的复合治疗效果估计在通过关节衰弱模型参数化的临床相关场景中的行为。这些解释了对两种结果（CVD、HFHs) 及其风险率之间的正相关关系。对于有益结果特定治疗效果的重要设置，我们表明相关性导致复合治疗效果估计，其随着试验持续时间而下降。来自 Cox 模型的估计比来自重复事件模型的估计更受衰减的影响，两者都表现出非常相似的行为。由于结果证明茂林模型对死亡率的有害影响不太敏感，因此我们得出结论，在三种研究方法中，LWYY 模型最适合用于 HF 试验中的复合终点。我们的调查是有动机的，并与 PARADIGM-HF 试验（ClinicalTrials.gov 标识符：NCT01035255）的实证结果进行了比较，这是一项包括 8399 名慢性 HF 患者的大型多中心试验。