Planning and Analyzing Adaptive Clinical Trials with Multiple Correlated Survival Endpoints

经典的事件时间自适应设计是为只有一个主要终点的研究情况而开发的。在这些经典方法中，样本量适应的数据依赖性受到很强的限制。从本质上讲，只有关于所选的主要时间到事件端点的临时信息可以用于设计修改，而不能使用来自其他时间到事件端点的附加信息，因为否则通常不能保证对第一类错误概率的控制。在2010年代，开发了自适应程序（基于患者分离原则），甚至可以基于多个相关的事件时间端点进行广泛的设计修改。然而，通过构造，这些过程要么不能在最终测试决策中充分利用可用的时间到事件数据，要么导致保守的测试过程。在之前的项目（No. 413730122）中，我们开发了多变量自适应检验，用于检验k≥2个（相关）时间到事件端点联合分布的假设，允许基于所有k个时间到事件端点的数据相关设计修改，在最终的测试决策中充分利用可用的时间到事件数据，并完全控制和耗尽显著性水平。与此不同的是，Bauer和Posch在2004年已经要求对一个选定的时间到事件端点的边际分布进行单变量自适应假设检验，其中允许基于多个事件时间端点的数据相关设计修改。基于上述项目的结果，出现了明确和一般地解决鲍尔-波施问题的可能性。这是这里申请的延续项目的中心目标（目标1）。其次，在前一个项目中开发的多变量自适应生存测试被设计为非参数测试。在这里申请的延续项目的背景下，这些多变量适应生存检验的参数对应物也将在不同程度的参数分布假设下提供和研究。虽然由于分布假设的自由，非参数检验具有特殊的鲁棒性，但如果所做的分布假设是适当的，参数检验承诺比非参数检验具有更高的功率。这对于招聘潜力低的学习情况特别重要（目标2）。为了使临床试验具有普遍适用性，将要开发的方法将在免费软件（R包）中发布和实施。这代表了当前软件的扩展，用于规划和实施自适应设计。

Classical adaptive designs for event times were developed for study situations with only one primary endpoint. In these classical methods, the data dependence of sample size adaptations is subject to strong restrictions. Essentially, only interim information regarding the selected primary time-to-event endpoint may be used for design modifications, but no additional information from further time-to-event endpoints, because otherwise the control of the type one error probability is generally not guaranteed. In the 2010s, adaptive procedures were developed (based on the principle of patientwise separation) that allow extensive design modifications even based on multiple correlated event-time endpoints. However, by construction, these procedures either cannot fully utilize the available time-to-event data in the final test decision or result in conservative testing procedures. In the preceding project (No. 413730122), multivariate adaptive tests were developed for testing hypotheses about the joint distribution of k≥2 (correlated) time-to-event endpoints, allowing data-dependent design modifications based on all k time-to-event endpoints, making full use of the available time-to-event data in the final test decision and with full control and exhaustion of the significance level. Deviating from this, Bauer and Posch already in 2004 asked for univariate adaptive hypothesis tests about the marginal distribution of one selected time-to-event endpoint, where data-dependent design modifications based on multiple event-time endpoints are allowed. Based on the results of the preceding project, the possibility arises to solve the Bauer-Posch problem explicitly and in general. This is a central goal of the continuation project applied for here (objective 1). Second, the multivariate adaptive survival tests developed in the preceding project were designed as non-parametric tests. In the context of the continuation project applied for here, parametric counterparts of these multivariate adaptive survival tests will also be provided and investigated with different degrees of parametric distribution assumptions. While non-parametric tests are characterized by particular robustness due to the freedom of distributional assumptions, parametric tests promise higher power compared to their non-parametric counterparts if the distributional assumptions made are appropriate. This is of particular importance for study situations with low recruitment potential (objective 2). To enable general applicability in clinical trials, the methodology to be developed will be published and implemented in freely available software (R packages). This represents an extension of current software for the planning and implementation of adaptive designs.