M&M: A maximum duration design with the Maxcombo test for a group sequential trial of an immunotherapy with a random delayed treatment effect

Abstract

A random delayed treatment effect is expected in a confirmatory clinical trial for an immunotherapy due to the individual heterogeneity of physiological conditions. For this reason, the delay time will be assumed to follow a continuous distribution that is difficult to estimate accurately based on the early-phase data, which hinders the specification of the most powerful weighted log-rank test. Therefore, we propose a simulation-based maximum duration design with a robustly powerful Maxcombo test for a group sequential trial for the immunotherapy with the random delayed treatment effect. The design obtains the group sequential boundaries by a simulation procedure and determines the required maximum sample size using a one-dimensional search in which another simulation procedure is used to calculate empirical power. The simulation researches proved the accuracy of the group sequential boundaries and their robustness against the misspecified maximum sample sizes for large samples and revealed their moderate sensitivity against the misspecified survival distributions under the null hypothesis of no difference. The studies investigated whether the type I error rate would inflate under the "inferior" null hypothesis and evaluated the robustness against different distributions of the delay time in terms of the empirical power among the Maxcombo tests and component weighted log-rank tests.

Group sequential design with maximin efficiency robust test for immunotherapy with generalized delayed treatment effect

“…This subsection provides a summary of the additional simulation studies. First, we evaluated performance of two alternative approaches for determining the group sequential boundaries: integration-based 18 and simulation-based 34 approaches in Web Appendix A. We determined the group sequential boundaries using both approaches and calculated the empirical type 1 error rates using a Monte-Carlo simulation procedure under the same scenarios as those specified in the subsection 4.1.…”

“…35,36 However, the strong null hypothesis is of clinical interest in some cases, especially when the crossing hazard pattern may occur. 34 In such cases, the modestly weighted log-rank test may be used as an alternative to MERT. 35 Third, we evaluated the validity of the group sequential boundaries against misspecifications of the survival function of the control group, S 0 t ð Þ, when using the calendar-driven and event-driven approaches, respectively, in Web Appendix C. The calendar-driven approach was employed in our research, while the event-driven approach, utilized by Wang el al., 37 was independent from the determination of group sequential boundaries.…”

“…ð Þ, as described by Li et al 34 and Xu et al 38 The maximum sample size estimation and the corresponding empirical power are presented in Table S2. It is evident that the empirical power values closely align with the corresponding values in Table 2, indicating the compatibility of the proposed generalized delayed treatment effect mechanism with the aforementioned random delay mechanism.…”

New late‐emphasis and combination tests based on infimum and supremum logrank statistics with application in oncology trials

“…More recently, the MaxCombo test based on the combination of the F‐H test statistics, $$$ {\mathrm{FH}}^{0,0},{\mathrm{FH}}^{1,0},{\mathrm{FH}}^{0,1}\kern.5em \mathrm{and}\kern.5em {\mathrm{FH}}^{1,1} $$$, have been recommended in oncology trials to provide robust performance under more general alternatives 8,10 10 . It has also been shown that the combination of $$$ {\mathrm{FH}}^{0,0} $$$ with a sequence of piecewise weighted logrank test statistics created after successively deleting events during an initial period provide robust performance under PH and general delayed treatment alternatives 13‐15 . Since all these combination tests follow an asymptotic multivariate normal approximation with independent increments covariance structure, the P ‐values can be obtained using algorithms originally designed for group sequential testing.…”

“…10 It has also been shown that the combination of FH 0,0 with a sequence of piecewise weighted logrank test statistics created after successively deleting events during an initial period provide robust performance under PH and general delayed treatment alternatives. [13][14][15] Since all these combination tests follow an asymptotic multivariate normal approximation with independent increments covariance structure, the P-values can be obtained using algorithms originally designed for group sequential testing.…”