Planning and Analyzing Adaptive Clinical Trials with Multiple Correlated Survival Endpoints

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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.