Group sequential methods based on supremum logrank statistics under proportional and nonproportional hazards

Abstract

Despite the widespread use of Cox regression for modeling treatment effects in clinical trials, in immunotherapy oncology trials and other settings therapeutic benefits are not immediately realized thereby violating the proportional hazards assumption. Weighted logrank tests and the so-called Maxcombo test involving the combination of multiple logrank test statistics have been advocated to increase power for detecting effects in these and other settings where hazards are nonproportional. We describe a testing framework based on supremum logrank statistics created by successively analyzing and excluding early events, or obtained using a moving time window. We then describe how such tests can be conducted in a group sequential trial with interim analyses conducted for potential early stopping of benefit. The crossing boundaries for the interim test statistics are determined using an easy-to-implement Monte Carlo algorithm. Numerical studies illustrate the good frequency properties of the proposed group sequential methods.

Keywords

Group sequential analysis supremum logrank statistics versatile tests nonproportional hazards oncology clinical trials

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References

Cox

. Regression models and life-tables (1994). J R Stat Soc Ser B 1972; 34: 187–122.

Kalbfleish

Prentice

. The statistical analysis of failure time data. Wiley Series in Probability and Statistics, Reading. Massachusetts: Wiley New York, 2002.

Castañon

Sanchez-Arraez

Alvarez-Manceñido

et al. Critical reappraisal of phase III trials with immune checkpoint inhibitors in non-proportional hazards settings. Eur J Cancer 2020; 136: 159–168.

Barnett

Taylor

Eliasziw

et al. Benefit of carotid endarterectomy in patients with symptomatic moderate or severe stenosis. New Eng J Med 1998; 339: 1415–1425.

Hortobagyi

Theriault

Lipton

et al. Long-term prevention of skeletal complications of metastatic breast cancer with pamidronate. Protocol 19 aredia breast cancer study group. J Clin Oncol 1998; 16: 20238–22044.

Stensrud

Hernán

. Why test for proportional hazards? J Am Med Assoc 2020; 323: 1401–1402.

Lin

Wei

. The robust inference for the Cox proportional hazards model. J Am Stat Assoc 1989; 84: 1074–1078.

Harrington

Fleming

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

Fine

. Consequences of delayed treatment effects on analysis of time-to-event endpoints. Drug Inf J 2007; 4: 535–539.

10.

Hasegawa

. Sample size determination for the weighted logrank test with the Fleming-Harrington class of weights in cancer vaccine studies. Pharm Stat 2014; 13: 128–135.

11.

Lin

Roychoudhury

et al. Alternative analysis methods for time to event endpoints under nonproportional hazards: a comparative analysis. Stat Biopharm Res 2020; 12: 187–198.

12.

Boher

Filleron

Bunouf

et al. New late-emphasis and combination tests based on infimum and supremum versions of logrank statistics with applications in oncology trials. Stat Med 2023; 42: 1981–1994.

13.

Prior

. Group sequential monitoring based on the maximum of weighted logrank statistics with the Fleming-Harrington class of weights in oncology clinical trials. Stat Methods Med Res 2020; 29: 3525–3532.

14.

Tsiatis

Rosmer

Tritchler

. Group sequential tests with censored survival data adjusting for covariates. Biometrika 1985; 72: 365–373.

15.

Fleming

Harrington

. Counting Processes and Survival Analysis. New York: John Wiley and Sons Inc., 1991.

16.

Freidlin

Korn

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

17.

Lee

. Some versatile tests based on the simultaneous use of weighted logrank statistics. Biometrics 1996; 29: 721–725.

18.

Fleming

Harrington

O’Sullivan

. Supremum versions of the logrank and generalized Wilcoxon statistics. J Am Stat Assoc 1987; 82: 312–332.

19.

Gilbert

. Flexible weighted logrank tests optimal for detecting early and/or late survival differences. Biometrics 2002; 58: 997–1004.

20.

Lee

. On the versatility of the combination of the weighted logrank statistics. Comput Stat Data Anal 2007; 51: 6557–6564.

21.

Logan

Klein

Zhang

. Comparing treatments in the presence of crossing survival curves: an application to bone marrow transplantation. Biometrics 2008; 64: 733–774.

22.

Royston

Parmar

MKB

. Augmenting the logrank test in the design of clinical trials in which non-proportional hazards of the treatment effect may be anticipated. BMC Med Res Methodol 2016; 16.

23.

Karrison

. Versatile tests for comparing survival curves based on weighted logrank statistics. Stata J 2016; 16: 678–669.

24.

Royston

Parmar

MKB

. A simulation study comparing the power of nine tests of the treatment effect in randomized controlled trials with a time-to-event outcome. Trials 2020; 21: 315.

25.

Kim KyungMann

Tsiatis

TAA

. Independent increments in group sequential tests: a review. SORT 2020; 2: 223–264.

26.

Ying

. Group sequential meethods for survival data using partial likelihood score processes with covariate adjustment. Stat Sin 1995; 5: 793–804.

27.

Park

Zhen

, et al. Designing cancer immunotherapy trials with random treatment time-lag effect. Stat Med 2018; 37: 4589–4609.

28.

Logan

Wang

Zhang

. Pairwise multiple adjustment in survival analysis. Statistics in Medecine 2005; 24: 2509–2523.

29.

Magirr

Burman

. Modestly weighted logrank tests. Stat Med 2019; 38: 3782–3379.

30.

Wang

Anderson

et al. nphsim: sample size and simulations for non-proportional hazards. Clinical trials, 2017. URL https://github.com/keaven/nphsim.git. Package nphsim version.1.1.90.

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