Statistical analysis for the survival data with non-proportional hazard in oncology clinical trials_Chinese Journal of Evidence-Based Medicine

Authors：

 HUANG Lihong ^1,2 , YAN Fangrong ^2,3 , MAI Yabing ^2,4 , LIU Meiruo ^2,4 , HU Hanzhao ^2,4 , CHEN Feng ^2,5

1. Zhongshan Hospital Fudan University, Shanghai 200032, P. R. China;
2. CSCO Biostatistics Expert Committee KEYNOTE Working Group, Shanghai 200032, P. R. China;
3. Collage of Science of China Medical University, Nanjing 211198, P. R. China;
4. Boehringer Ingelheim (China) Investment Co., Ltd., Shanghai 200040, P. R. China;
5. School of Public Health of Nanjing Medical University, Nanjing 211166, P. R. China;

Corresponding author：

HUANG Lihong, Email: huang.lihong@zs-hospital.sh.cn

Keywords：

Non-proportional hazard; Clinical trial; Non-proportional hazard survival analysis method; Sensitivity analysis

DOI：

10.7507/1672-2531.202209119

Video：

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Abstract Full text Figures/Tables Video References Cited by

Survival data were widely used in oncology clinical trials. The methods used, such as the log-rank test and Cox regression model, should meet the assumption of proportional hazards. However, the survival data with non-proportional hazard (NPH) are also quite usual, which will decrease the power of these methods and conceal the true treatment effect. Therefore, during the trial design, we need to test the proportional hazard assumption and plan different analysis methods for different testing results. This paper introduces some methods that are widely used for proportional hazard testing, and summarizes the application condition, advantages and disadvantages of analysis methods for non-proportional hazard survival data. When the non-proportional hazard occurs, we need to choose the suitable method case by case and to be cautious in the interpretation of the results.

Citation： HUANG Lihong, YAN Fangrong, MAI Yabing, LIU Meiruo, HU Hanzhao, CHEN Feng. Statistical analysis for the survival data with non-proportional hazard in oncology clinical trials. Chinese Journal of Evidence-Based Medicine, 2023, 23(7): 826-833. doi: 10.7507/1672-2531.202209119 Copy

1.	Goel MK, Khanna P, Kishore J. Understanding survival analysis: Kaplan-Meier estimate. Int J Ayurveda Res, 2010, 1(4): 274-278.
2.	Xue X, Xie X, Gunter M, et al. Testing the proportional hazards assumption in case-cohort analysis. BMC Med Res Methodol, 2013, 13: 88.
3.	Therneau TM, Grambsch PM, Fleming TR. Martingale-based residuals for survival models. Biometrika, 1990, 77(1): 147-160.
4.	Tarone RE. On the distribution of the maximum of the logrank statistic and the modified Wilcoxon statistic. Biometrics, 1981, 37(1): 79-85.
5.	Lee JW. Some versatile tests based on simultaneous use of weighted log-rank statistics. Biometrics, 1996, 52(2): 721-725.
6.	Karrison TG. Versatile tests for comparing survival curves based on weighted log-rank statistics. Stata J, 2016, 16(3): 678-690.
7.	Xu Z, Zhen B, Park Y, et al. Designing therapeutic cancer vaccine trials with delayed treatment effect. Stat Med, 2017, 36(4): 592-605.
8.	Xu Z, Park Y, Zhen B, et al. Designing cancer immunotherapy trials with random treatment time-lag effect. Stat Med, 2018, 37(30): 4589-4609.
9.	Ding X, Wu J. Designing cancer immunotherapy trials with delayed treatment effect using maximin efficiency robust statistics. Pharm Stat, 2020, 19(4): 424-435.
10.	Duke University, US Food and Drug Administration. Public workshop: oncology clinical trials in the presence of non-proportional hazards.
11.	Miyahara S, Wahed AS. Weighted Kaplan-Meier estimators for two-stage treatment regimes. Stat Med, 2010, 29(25): 2581-2591.
12.	Karrison TG. Restricted mean life with adjustment for covariates. J Am Stat Assoc, 1987, 82: 1169-1176.
13.	Pepe MS, Fleming TR. Weighted Kaplan-Meier statistics: a class of distance tests for censored survival data. Biometrics, 1989, 45: 497-507.
14.	Royston P, Parmar MK. The use of restricted mean survival time to estimate the treatment effect in randomized clinical trials when the proportional hazards assumption is in doubt. Stat Med, 2011, 30(19): 2409-2421.
15.	Seruga B, Pond GR, Hertz PC, et al. Comparison of absolute benefits of anticancer therapies determined by snapshot and area methods. Ann Oncol, 2012, 23(11): 2977-2982.
16.	Horiguchi M, Cronin AM, Takeuchi M, et al. A flexible and coherent test/estimation procedure based on restricted mean survival times for censored time-to-event data in randomized clinical trials. Stat Med, 2018, 37(15): 2307-2320.
17.	Royston P, Parmar MK. 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: 16.
18.	Yang S, Prentice R. Semiparametric analysis of short-term and long-term hazard ratios with two-sample survival data. Biometrika, 2005, 92(1): 1-17.
19.	Yang S, Zhao Y. Checking the short-term and long-term hazard ratio model for survival data. Scand J Sta, 2012, 39(3): 554-567.
20.	Lin RS, León LF. Estimation of treatment effects in weighted log-rank tests. Contemp Clin Trials Commun, 2017, 8: 147-155.
21.	Lin RS, Lin J, Roychoudhury S, et al. Alternative analysis methods for time to event endpoints under nonproportional hazards: a comparative analysis. Stat Biopharm Res, 2020, 12(2): 187-198.
22.	Li W, Chen SY, Rong A. Estimation of delay time in survival data with delayed treatment effect. J Biopharm Stat, 2019, 29(2): 229-243.
23.	Mok TSK, Wu YL, Kudaba I, et al. Pembrolizumab versus chemotherapy for previously untreated, PD-L1-expressing, locally advanced or metastatic non-small-cell lung cancer (KEYNOTE-042): a randomised, open-label, controlled, phase 3 trial. Lancet, 2019, 393(10183): 1819-1830.
24.	Guyot P, Ades AE, Ouwens MJ, et al. Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves. BMC Med Res Methodol, 2012, 12: 9.
25.	Freidlin B, Korn EL. Methods for accommodating nonproportional hazards in clinical trials: ready for the primary analysis. J Clin Oncol, 2019, 37(35): 3455-3459.
26.	Ananthakrishnan R, Green S, Previtali A, et al. Critical review of oncology clinical trial design under non-proportional hazards. Crit Rev Oncol Hematol, 2021, 162: 103350.

1. Goel MK, Khanna P, Kishore J. Understanding survival analysis: Kaplan-Meier estimate. Int J Ayurveda Res, 2010, 1(4): 274-278.
2. Xue X, Xie X, Gunter M, et al. Testing the proportional hazards assumption in case-cohort analysis. BMC Med Res Methodol, 2013, 13: 88.
3. Therneau TM, Grambsch PM, Fleming TR. Martingale-based residuals for survival models. Biometrika, 1990, 77(1): 147-160.
4. Tarone RE. On the distribution of the maximum of the logrank statistic and the modified Wilcoxon statistic. Biometrics, 1981, 37(1): 79-85.
5. Lee JW. Some versatile tests based on simultaneous use of weighted log-rank statistics. Biometrics, 1996, 52(2): 721-725.
6. Karrison TG. Versatile tests for comparing survival curves based on weighted log-rank statistics. Stata J, 2016, 16(3): 678-690.
7. Xu Z, Zhen B, Park Y, et al. Designing therapeutic cancer vaccine trials with delayed treatment effect. Stat Med, 2017, 36(4): 592-605.
8. Xu Z, Park Y, Zhen B, et al. Designing cancer immunotherapy trials with random treatment time-lag effect. Stat Med, 2018, 37(30): 4589-4609.
9. Ding X, Wu J. Designing cancer immunotherapy trials with delayed treatment effect using maximin efficiency robust statistics. Pharm Stat, 2020, 19(4): 424-435.
10. Duke University, US Food and Drug Administration. Public workshop: oncology clinical trials in the presence of non-proportional hazards.
11. Miyahara S, Wahed AS. Weighted Kaplan-Meier estimators for two-stage treatment regimes. Stat Med, 2010, 29(25): 2581-2591.
12. Karrison TG. Restricted mean life with adjustment for covariates. J Am Stat Assoc, 1987, 82: 1169-1176.
13. Pepe MS, Fleming TR. Weighted Kaplan-Meier statistics: a class of distance tests for censored survival data. Biometrics, 1989, 45: 497-507.
14. Royston P, Parmar MK. The use of restricted mean survival time to estimate the treatment effect in randomized clinical trials when the proportional hazards assumption is in doubt. Stat Med, 2011, 30(19): 2409-2421.
15. Seruga B, Pond GR, Hertz PC, et al. Comparison of absolute benefits of anticancer therapies determined by snapshot and area methods. Ann Oncol, 2012, 23(11): 2977-2982.
16. Horiguchi M, Cronin AM, Takeuchi M, et al. A flexible and coherent test/estimation procedure based on restricted mean survival times for censored time-to-event data in randomized clinical trials. Stat Med, 2018, 37(15): 2307-2320.
17. Royston P, Parmar MK. 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: 16.
18. Yang S, Prentice R. Semiparametric analysis of short-term and long-term hazard ratios with two-sample survival data. Biometrika, 2005, 92(1): 1-17.
19. Yang S, Zhao Y. Checking the short-term and long-term hazard ratio model for survival data. Scand J Sta, 2012, 39(3): 554-567.
20. Lin RS, León LF. Estimation of treatment effects in weighted log-rank tests. Contemp Clin Trials Commun, 2017, 8: 147-155.
21. Lin RS, Lin J, Roychoudhury S, et al. Alternative analysis methods for time to event endpoints under nonproportional hazards: a comparative analysis. Stat Biopharm Res, 2020, 12(2): 187-198.
22. Li W, Chen SY, Rong A. Estimation of delay time in survival data with delayed treatment effect. J Biopharm Stat, 2019, 29(2): 229-243.
23. Mok TSK, Wu YL, Kudaba I, et al. Pembrolizumab versus chemotherapy for previously untreated, PD-L1-expressing, locally advanced or metastatic non-small-cell lung cancer (KEYNOTE-042): a randomised, open-label, controlled, phase 3 trial. Lancet, 2019, 393(10183): 1819-1830.
24. Guyot P, Ades AE, Ouwens MJ, et al. Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves. BMC Med Res Methodol, 2012, 12: 9.
25. Freidlin B, Korn EL. Methods for accommodating nonproportional hazards in clinical trials: ready for the primary analysis. J Clin Oncol, 2019, 37(35): 3455-3459.
26. Ananthakrishnan R, Green S, Previtali A, et al. Critical review of oncology clinical trial design under non-proportional hazards. Crit Rev Oncol Hematol, 2021, 162: 103350.

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