Design and analysis of group-sequential clinical trials based on a modestly weighted log-rank test in anticipation of a delayed separation of survival curves: A practical guidance

Abstract

Background: A common feature of many recent trials evaluating the effects of immunotherapy on survival is that non-proportional hazards can be anticipated at the design stage. This raises the possibility to use a statistical method tailored towards testing the purported long-term benefit, rather than applying the more standard log-rank test and/or Cox model. Many such proposals have been made in recent years, but there remains a lack of practical guidance on implementation, particularly in the context of group-sequential designs. In this article, we aim to fill this gap. Methods: We illustrate how the POPLAR trial, which compared immunotherapy versus chemotherapy in non-small-cell lung cancer, might have been re-designed to be more robust to the presence of a delayed effect using the modestly-weighted log-rank test in a group-sequential setting. Conclusion: We provide step-by-step instructions on how to analyse a hypothetical realization of the trial, based on this new design. Basic theory on weighted log-rank tests and group-sequential methods is covered, and an accompanying R package (including vignette) is provided.

Simultaneous inference procedures for the comparison of multiple characteristics of two survival functions

“…Also, weighted logrank statistics may be included in the inference framework as a further extension. One could also consider performing interim analyses to allow for early stopping 14 , 50 and adaptations such as sample size reassessment 51 and modification of the set of parameters, for example, adding milestone analyses at later time points. Depending on which type of data is considered for the adaptations, 51 , 52 appropriate adaptive tests have to be implemented.…”

Stratified modestly weighted log‐rank tests in settings with an anticipated delayed separation of survival curves

“…Some comments on the choice of $$t^*$$ or $$s^*$$ are warranted. A modestly weighted test in a single stratum i can be thought of as similar to an average milestone analysis from time $$t^*$$ (or $$\hat{S}_{i,P}^{-1}(s^*)$$) to the end of follow‐up (Magirr, 2021; Magirr & Jiménez, 2022), where a milestone analysis is a contrast of the survival probability at a specific follow‐up time on the two treatment arms. An important point is that if we anticipate a delay of, for example, 6 months, this does not necessarily mean that we should choose $$t^*=6$$.…”

“…It is important to mention that $$t^*=0$$ (or $$s^*=1$$) is the same as the standard log‐rank test and that, for values of $$t^*$$ close to 0 (or $$s^*$$ close to 1), there will be little difference between these two tests. For further discussion of the choice of $$t^*$$ and the choice of weights more generally, we refer the reader to the papers from Magirr and Burman (2019) and Magirr & Jiménez (2022).…”

“…In the top row, the within-strata weights are based on modestly weighted log-rank test with 𝑡 * = 12; in the bottom row, they are based on the modestly weighted test with 𝑠 * = 0.5. Jiménez, 2022), where a milestone analysis is a contrast of the survival probability at a specific follow-up time on the two treatment arms. An important point is that if we anticipate a delay of, for example, 6 months, this does not necessarily mean that we should choose 𝑡 * = 6.…”

The Inverse Log-Rank Test: A Versatile Procedure for Late Separating Survival Curves

“…However, under moderate to heavy censoring and noting the potentially high correlation among weighted LRTs, the family of combination procedures (including the Max-combo test) may not be more versatile than individual component LRT tests [8]. The extension to a group sequential analysis allows the Max-Combo procedure to accommodate multiple time point decisions, with the test statistic assuming a joint normal distribution under the null hypothesis (per the application of Slutsky's theorem) [41][42][43][44].…”