Rejoinder to Letter to the Editor “The Hazards of Period Specific and Weighted Hazard Ratios”

Lin, Ray; Lin, Ji; Roychoudhury, Satrajit; Anderson, Keaven M.; Hu, Tianle; Huang, Bo; Leon, Larry; Liao, Jason J. Z.; Liu, Rong; Luo, Xiaodong; Mukhopadhyay, Pralay; Qin, Rui; Tatsuoka, Kay; Wang, Xuejing; Wang, Yang; Zhu, Jian; Chen, Tai-Tsang; Iacona, Renee

doi:10.1080/19466315.2020.1825522

Cited by 10 publications

(5 citation statements)

References 7 publications

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“…[8][9][10] The period-specific HR has been suggested as a way to describe the changing treatment effect over time but this approach has been criticized for its lack of interpretability. 11,12 It is now widely recognized that meaningful conclusions require more than just statistical significance testing based on p-values alone. 13,5 Alternative approaches that emphasize more on the interpretability and clinical relevance of treatment-effect measures have been proposed, including the integrated log-rank test (iLR) and the combined max (LR, iLR) test, which can detect the departure of the PH assumption over time and provide more powerful tests under various treatment effects.…”

Section: Introductionmentioning

confidence: 99%

“…The MaxCombo test, which is a combination of different WLR tests with a range of weight functions that maximize the Z‐statistic, yields a test procedure that tends to be more powerful than the standard weighted LR tests in the presence of NPH 8–10 . The period‐specific HR has been suggested as a way to describe the changing treatment effect over time but this approach has been criticized for its lack of interpretability 11,12 …”

Section: Introductionmentioning

confidence: 99%

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Two‐sample inference procedures under nonproportional hazards

Tai

Wang

Wells

2023

Pharmaceutical Statistics

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We introduce a new two‐sample inference procedure to assess the relative performance of two groups over time. Our model‐free method does not assume proportional hazards, making it suitable for scenarios where nonproportional hazards may exist. Our procedure includes a diagnostic tau plot to identify changes in hazard timing and a formal inference procedure. The tau‐based measures we develop are clinically meaningful and provide interpretable estimands to summarize the treatment effect over time. Our proposed statistic is a U‐statistic and exhibits a martingale structure, allowing us to construct confidence intervals and perform hypothesis testing. Our approach is robust with respect to the censoring distribution. We also demonstrate how our method can be applied for sensitivity analysis in scenarios with missing tail information due to insufficient follow‐up. Without censoring, Kendall's tau estimator we propose reduces to the Wilcoxon‐Mann–Whitney statistic. We evaluate our method using simulations to compare its performance with the restricted mean survival time and log‐rank statistics. We also apply our approach to data from several published oncology clinical trials where nonproportional hazards may exist.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two‐sample inference procedures under nonproportional hazards

Tai

Wang

Wells

2023

Pharmaceutical Statistics

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“…Weighted hazard ratios have also been proposed in this context, 28 although their interpretability has been debated. 29,30…”

Section: Methodsmentioning

confidence: 99%

“…Weighted hazard ratios have also been proposed in this context, 28 although their interpretability has been debated. 29,30 For all summary measures, a group sequential design introduces some bias, owing to the possibility to stop early on a random high. Various methods have been proposed that attempt to account for this bias.…”

Section: Methodsmentioning

confidence: 99%

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

Magirr

Jiménez

2022

Clinical Trials

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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.

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“…As commented in Lin et al, 6,22 it is better to describe the functional form of the hazard ratio over time if NPHs are suspected. The proposed estimation method provides a versatile tool to capture different shapes of hazard ratios.…”

Section: Example 2: Analysis Of a Mock Trial Datamentioning

confidence: 99%

A MCP‐Mod approach to designing and analyzing survival trials with potential non‐proportional hazards

Luo

Sun

2022

Pharmaceutical Statistics

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Non‐proportional hazards have been observed in many studies especially in immuno‐oncology clinical trials. Traditional analysis using the combined approach with log‐rank test as the significance test and Cox model for treatment effect estimation becomes questionable as this approach relies heavily on the proportional hazards assumption. Inspired by the MCP‐Mod (multiple comparisons and modeling approach) that has been widely used in dose‐finding studies, we propose a similar approach to handle non‐proportional hazards. Using this approach, efficacy signal is first established by a max‐combo test, after which hazard ratios across time will be estimated using a logically nested splines model. Simulations studies and real‐data examples are used to illustrate the use of this approach.

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Rejoinder to Letter to the Editor “The Hazards of Period Specific and Weighted Hazard Ratios”

Cited by 10 publications

References 7 publications

Two‐sample inference procedures under nonproportional hazards

Two‐sample inference procedures under nonproportional hazards

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

A MCP‐Mod approach to designing and analyzing survival trials with potential non‐proportional hazards

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