Rejoinder to Comments on “Non-Proportional Hazards – An Evaluation of the MaxCombo Test in Cancer Clinical Trials”

This rejoinder continues a discussion initiated by the Oncology Center of Excellence’s call (2016–2017) for statistical approaches to address the problem of assessing treatment effects in the presence of non-proportional hazards (NPH) (Duke-Margolis Workshop 2018; Lin et al. 2020a, Lin et al. 2020b; Roychoudhury et al. 2021). The publication of the method was met with much discussion, several commentary articles (Freidlin and Korn 2019; Bartlett et al. 2020; Lin et al. 2020a; Magirr and Burman 2021; Roychoudhury et al. 2021) and a rejoinder by the MaxCombo test coauthors (Lin et al. 2020b). After consideration of the proposed method and review of its accompanying responses and rejoinder, we expressed our views on the MaxCombo tests and provided general thoughts on design issues when NPH is expected in our article (Shen et al. 2021). In response to the publication of our article, the Cross-PhRMA working group (Lin et al. 2023) and Posch, Ristl, and König (2022) published additional commentary providing further clarification and views. We appreciate the great interest in NPH issues in the regulatory statistical community and would like to take this opportunity to provide additional clarifications and comments. Although the primary objective of our 2021 article was to focus on the MaxCombo test, as noted by Lin et al. (2023), a number of the issues are more general and are equally applicable when using many other methods and testing statistics, for example, the difficulty in interpretation or failure to incorporate underlying reasons of NPH. In fact, recognizing the shortcomings of the more commonly used tests such as log-rank test, etc., FDA initiated the dialogue and invited PhRMA to come together to develop methodology to address this issue. The MaxCombo test is presented as representing a flexible testing procedure impervious to a variety of shapes of curves under NPH. Cross-PhRMA working group suggested a 3-step method for evaluation of treatment effect when NPH is expected (Lin et al. 2020a, Lin et al. 2020b, Roychoudhury et al. 2021). Lin et al. (2023) clarified that in this scenario, a successful treatment effect would not be claimed based solely on results from the MaxCombo test, as the Cross-PhRMA working group recommends such decisions be based on the totality of data