Sample size and power for the weighted log‐rank test and Kaplan‐Meier based tests with allowance for nonproportional hazards

Yung, Godwin; Liu, Yi

doi:10.1111/biom.13196

Cited by 19 publications

(27 citation statements)

References 21 publications

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“…Many sample size procedures have been developed for the log-rank test in superiority 1–3,6–17,19 and NI trials. 4,5 These methods will be compared on the basis of the way of approximating the mean and variance of the log-rank statistic, and extended to the NI, equivalence and maximum combination tests whenever appropriate in sections 3.1, 3.2 and 3.3.…”

Section: Power and Sample Size Formulae For The Log-rank Testmentioning

confidence: 99%

“…The analytic expressions for μ and σ02 are well known 1,5,10,14–16 …”

Section: Power and Sample Size Formulae For The Log-rank Testmentioning

confidence: 99%

“…18 The computation of (μ,σ02) will be discussed in Section 3.4. Yung and Liu 16 recently derived σ12 for superiority trials based on the work of Luo et al. 15 Appendix A.2 gives the analytic expression σ12 for NI trials.…”

Section: Power and Sample Size Formulae For The Log-rank Testmentioning

confidence: 99%

“…For oncology trials, it involves determining an appropriate combination of the sample size, patient accrual rate, and trial duration to ensure a sufficient power for detecting a clinically important effect. Since the seminal work of Schoenfeld, 1 many sample size methods have been developed under proportional hazards (PH 1–5 ) and non-proportional hazards (NPH 3,6–19 ). Most works focus on a somewhat different scenario (i.e.…”

Section: Introductionmentioning

confidence: 99%

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A unified approach to power and sample size determination for log-rank tests under proportional and nonproportional hazards

Tang

2021

Stat Methods Med Res

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Log-rank tests have been widely used to compare two survival curves in biomedical research. We describe a unified approach to power and sample size calculation for the unweighted and weighted log-rank tests in superiority, noninferiority and equivalence trials. It is suitable for both time-driven and event-driven trials. A numerical algorithm is suggested. It allows flexible specification of the patient accrual distribution, baseline hazards, and proportional or nonproportional hazards patterns, and enables efficient sample size calculation when there are a range of choices for the patient accrual pattern and trial duration. A confidence interval method is proposed for the trial duration of an event-driven trial. We point out potential issues with several popular sample size formulae. Under proportional hazards, the power of a survival trial is commonly believed to be determined by the number of observed events. The belief is roughly valid for noninferiority and equivalence trials with similar survival and censoring distributions between two groups, and for superiority trials with balanced group sizes. In unbalanced superiority trials, the power depends also on other factors such as data maturity. Surprisingly, the log-rank test usually yields slightly higher power than the Wald test from the Cox model under proportional hazards in simulations. We consider various nonproportional hazards patterns induced by delayed effects, cure fractions, and/or treatment switching. Explicit power formulae are derived for the combination test that takes the maximum of two or more weighted log-rank tests to handle uncertain nonproportional hazards patterns. Numerical examples are presented for illustration.

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Section: Power and Sample Size Formulae For The Log-rank Testmentioning

confidence: 99%

“…The analytic expressions for μ and σ02 are well known 1,5,10,14–16 …”

Section: Power and Sample Size Formulae For The Log-rank Testmentioning

confidence: 99%

Section: Power and Sample Size Formulae For The Log-rank Testmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A unified approach to power and sample size determination for log-rank tests under proportional and nonproportional hazards

Tang

2021

Stat Methods Med Res

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“…However, it is recognized that these alternative measures of efficacy pose their own challenges (Freidlin and Korn 2019 ). A comparison to the HR in superiority trials with a time-to-event endpoint is provided in Huang and Kuan ( 2018 ) and Yung and Liu ( 2019 ).…”

Section: Analysis Considerationsmentioning

confidence: 99%

Assessing the Impact of COVID-19 on the Clinical Trial Objective and Analysis of Oncology Clinical Trials—Application of the Estimand Framework

Degtyarev

Rufibach

Shentu

et al. 2020

Statistics in Biopharmaceutical Research

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– Coronavirus disease 2019 (COVID-19) outbreak has rapidly evolved into a global pandemic. The impact of COVID-19 on patient journeys in oncology represents a new risk to interpretation of trial results and its broad applicability for future clinical practice. We identify key intercurrent events (ICEs) that may occur due to COVID-19 in oncology clinical trials with a focus on time-to-event endpoints and discuss considerations pertaining to the other estimand attributes introduced in the ICH E9 addendum. We propose strategies to handle COVID-19 related ICEs, depending on their relationship with malignancy and treatment and the interpretability of data after them. We argue that the clinical trial objective from a world without COVID-19 pandemic remains valid. The estimand framework provides a common language to discuss the impact of COVID-19 in a structured and transparent manner. This demonstrates that the applicability of the framework may even go beyond what it was initially intended for.

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Sample Size Calculation Under Nonproportional Hazards Using Average Hazard Ratios

Dormuth,

Pauly,

Rauch

et al. 2024

Biometrical J

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Many clinical trials assess time‐to‐event endpoints. To describe the difference between groups in terms of time to event, we often employ hazard ratios. However, the hazard ratio is only informative in the case of proportional hazards (PHs) over time. There exist many other effect measures that do not require PHs. One of them is the average hazard ratio (AHR). Its core idea is to utilize a time‐dependent weighting function that accounts for time variation. Though propagated in methodological research papers, the AHR is rarely used in practice. To facilitate its application, we unfold approaches for sample size calculation of an AHR test. We assess the reliability of the sample size calculation by extensive simulation studies covering various survival and censoring distributions with proportional as well as nonproportional hazards (N‐PHs). The findings suggest that a simulation‐based sample size calculation approach can be useful for designing clinical trials with N‐PHs. Using the AHR can result in increased statistical power to detect differences between groups with more efficient sample sizes.

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Sample size and power for the weighted log‐rank test and Kaplan‐Meier based tests with allowance for nonproportional hazards

Cited by 19 publications

References 21 publications

A unified approach to power and sample size determination for log-rank tests under proportional and nonproportional hazards

A unified approach to power and sample size determination for log-rank tests under proportional and nonproportional hazards

Assessing the Impact of COVID-19 on the Clinical Trial Objective and Analysis of Oncology Clinical Trials—Application of the Estimand Framework

Sample Size Calculation Under Nonproportional Hazards Using Average Hazard Ratios

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