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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.

Keywords

Delayed effects group sequential designs immuno-oncology log-rank test modestly-weighted log-rank test time-to-event

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References

Harrington

Fleming

. A class of rank test procedures for censored survival data. Biometrika 1982; 69(3): 553–566.

Yang

Prentice

. Improved logrank-type tests for survival data using adaptive weights. Biometrics 2010; 66(1): 30–38.

Garès

Andrieu

Dupuy

, et al. A comparison of the constant piecewise weighted logrank and Fleming-Harrington tests. Electron J Stat 2014; 8(1): 841–860.

Karrison

. Versatile tests for comparing survival curves based on weighted log-rank statistics. Stat J 2016; 16(3): 678–690.

Roychoudhury

Anderson

, et al. Robust design and analysis of clinical trials with nonproportional hazards: A straw man guidance from a cross-pharma working group. In: Statistics in Biopharmaceutical Research. Taylor & Francis, 2021, pp. 1–15.

Freidlin

Korn

. Methods for accommodating nonproportional hazards in clinical trials: ready for the primary analysis? J Clin Oncol 2019; 37(35): 3455–3459.

Magirr

Burman

. Modestly weighted logrank tests. Stat Med 2019; 38(20): 3782–3790.

Magirr

. Non-proportional hazards in immuno-oncology: is an old perspective needed? Pharm Stat 2021; 20: 512–527.

Fleming

Harrington

. Counting processes and survival analysis, vol. 169. Hoboken, NJ: John Wiley & Sons, 2011.

10.

Tsiatis

. Repeated significance testing for a general class of statistics used in censored survival analysis. J Am Stat Assoc 1982; 77(380): 855–861.

11.

Jennison

Turnbull

. Group sequential methods with applications to clinical trials. Boca Raton, FL: CRC Press, 1999.

12.

Whitehead

. The design and analysis of sequential clinical trials. Hoboken, NJ: John Wiley & Sons, 1997.

13.

Gillen

Emerson

. Information growth in a family of weighted logrank statistics under repeated analyses. Sequent Anal 2005; 24(1): 1–22.

14.

Fehrenbacher

Spira

Ballinger

, et al. Atezolizumab versus docetaxel for patients with previously treated non-small-cell lung cancer (POPLAR): a multicentre, open-label, phase 2 randomised controlled trial. Lancet 2016; 387(10030): 1837–1846.

15.

Gandara

Paul

Kowanetz

, et al. Blood-based tumor mutational burden as a predictor of clinical beneﬁt in non-small-cell lung cancer patients treated with atezolizumab. Nat Med 2018; 24(9): 1441–1448.

16.

Rahman

Fell

Ventz

, et al. Deviation from the proportional hazards assumption in randomized phase 3 clinical trials in oncology: prevalence, associated factors, and implications. Clin Cancer Res 2019; 25(21): 6339–6345.

17.

Jiménez

Stalbovskaya

Jones

. Properties of the weighted log-rank test in the design of conﬁrmatory studies with delayed effects. Pharm Stat 2019; 18(3): 287–303.

18.

Hwang

Shih

De Cani

. Group sequential designs using a family of type I error probability spending functions. Stat Med 1990; 9(12): 1439–1445.

19.

Gray

Tsiatis

. A linear rank test for use when the main interest is in differences in cure rates. Biometrics 1989; 45: 899–904.

20.

Food and Drug Administration. Adaptive designs for clinical trials of drugs and biologics: guidance for industry, https://www.fda.gov/media/78495/download

21.

Gallo

Mao

Shih

. Alternative views on setting clinical trial futility criteria. J Biopharm Stat 2014; 24(5): 976–993.

22.

Pampallona

Tsiatis

Kim

. Interim monitoring of group sequential trials using spending functions for the type I and type II error probabilities. Drug Inform J 2001; 35(4): 1113–1121.

23.

Lachin

. A review of methods for futility stopping based on conditional power. Stat Med 2005; 24(18): 2747–2764.

24.

Spiegelhalter

Freedman

Blackburn

. Monitoring clinical trials: conditional or predictive power? Control Clin Trials 1986; 7(1): 8–17.

25.

DeMets

Lan

. Interim analysis: the alpha spending function approach. Stat Med 1994; 13(13–14): 1341–1352.

26.

Rufibach

. Treatment effect quantification for time-to-event endpoints–estimands, analysis strategies, and beyond. Pharm Stat 2019; 18(2): 145–165.

27.

Jiménez

. Quantifying treatment differences in conﬁrmatory trials under non-proportional hazards. J Appl Stat. Epub ahead of print 3 September 2020. DOI: 10.1080/02664763.2020.1815673.

28.

Lin

León

. Estimation of treatment effects in weighted log-rank tests. Contemp Clin Trials Commun 2017; 8: 147–155.

29.

Bartlett

Morris

Stensrud

, et al. The hazards of period speciﬁc and weighted hazard ratios. Stat Biopharm Res 2020; 12(4): 518–519.

30.

Lin

Roychoudhury

, et al. Rejoinder to letter to the editor ‘The hazards of period specific and weighted hazard ratios’. Stat Biopharm Res 2020; 12(4): 520–521.

31.

Pinheiro

DeMets

. Estimating and reducing bias in group sequential designs with Gaussian independent increment structure. Biometrika 1997; 84(4): 831–845.

32.

Fan

DeMets

Lan

KKG

. Conditional bias of point estimates following a group sequential test. J Biopharm Stat 2004; 14(2): 505–530.

33.

Walter

Guyatt

Bassler

, et al. Randomised trials with provision for early stopping for beneﬁt (or harm): the impact on the estimated treatment effect. Stat Med 2019; 38(14): 2524–2543.

34.

Freidlin

Korn

. Stopping clinical trials early for beneﬁt: impact on estimation. Clin Trials 2009; 6(2): 119–125.

35.

Robertson

Choodari-Oskooei

Dimairo

, et al. Point estimation for adaptive trial designs, https://orca.cardiff.ac.uk/141478/1/2105.08836.pdf

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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:

Methods:

Conclusion:

Keywords

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References

Supplementary Material