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Special Section: Estimands, Design and Analysis of Clinical Trials with Time-to-Event Outcomes

Robust Design and Analysis of Clinical Trials With Nonproportional Hazards: A Straw Man Guidance From a Cross-Pharma Working Group

ORCID Icon, , &
Pages 280-294 | Received 03 Mar 2020, Accepted 06 Jan 2021, Published online: 04 Mar 2021

References

  • Anderson, K. M. (2020), “simtrial: Clinical Trial Simulation for Time-to-Event Endpoints,” available at https://github.com/keaven/simtrial.
  • Bartlett, J. W., Morris, T. P., Stensrud, M. J., Daniel, R. M., Vansteelandt, S. K., and Burman, C.-F. (2020), “The Hazards of Period Specific and Weighted Hazard Ratios,” Statistics in Biopharmaceutical Research, 12, 518–519. DOI: 10.1080/19466315.2020.1755722.
  • Borghaei, H., Paz-Ares, L., Horn, L., Spigel, D. R., Steins, M., Ready, N. E., Chow, L. Q., Vokes, E. E., Felip, E., Holgado, E., and Barlesi, F. (2015), “Nivolumab Versus Docetaxel in Advanced Nonsquamous Non-Small-Cell Lung Cancer,” New England Journal of Medicine, 373, 1627–1639. DOI: 10.1056/NEJMoa1507643.
  • Breslow, N. E., Edler, L., and Berger, J. (1984), “A Two-Sample Censored-Data Rank Test for Acceleration,” Biometrics, 40, 1049–1062. DOI: 10.2307/2531155.
  • Buckley, J., and James, I. (1979), “Linear Regression With Censored Data,” Biometrika, 66, 429–436. DOI: 10.1093/biomet/66.3.429.
  • Buyse, M. (2010), “Generalized Pairwise Comparisons of Prioritized Outcomes in the Two-Sample Problem,” Statistics in Medicine, 29, 3245–3257. DOI: 10.1002/sim.3923.
  • Callegaro, A., and Spiessens, B. (2017), “Testing Treatment Effect in Randomized Clinical Trials With Possible Nonproportional Hazards,” Statistics in Biopharmaceutical Research, 9, 204–211. DOI: 10.1080/19466315.2016.1257436.
  • Campbell, H., and Dean, C. (2014), “The Consequences of Proportional Hazards Based Model Selection,” Statistics in Medicine, 33, 1042–1056. DOI: 10.1002/sim.6021.
  • Chapman, J. W., O’Callaghan, C. J., Hu, N., Ding, K., Yothers, G. A., Catalano, P. J., Shi, Q., Gray, R. G., O’Connell, M. J., and Sargent, D. J. (2013), “Innovative Estimation of Survival Using Log-Normal Survival Modelling on ACCENT Database,” British Journal of Cancer, 108, 784–790. DOI: 10.1038/bjc.2013.34.
  • Chen, T.-T. (2013), “Statistical Issues and Challenges in Immuno-Oncology,” Journal for ImmunoTherapy of Cancer, 1, 1–9. DOI: 10.1186/2051-1426-1-18.
  • Chi, Y., and Tsai, M.-H. (2001), “Some Versatile Tests Based on the Simultaneous Use of Weighted Logrank and Weighted Kaplan-Meier Statistics,” Communications in Statistics—Simulation and Computation, 30, 743–759. DOI: 10.1081/SAC-100107779.
  • Cohen, E. E. W., Souliéres, D., Le Tourneau, C., Dinis, J., Licitra, L., Ahn, M. J., Soria, A., Machiels, J. P., Mach, N., Mehra, R., and Burtness, B. (2019), “Pembrolizumab Versus Methotrexate, Docetaxel, or Cetuximab for Recurrent or Metastatic Head-and-Neck Squamous Cell Carcinoma (KEYNOTE-040): A Randomised, Open-Label, Phase 3 Study,” The Lancet, 393, 156–167. DOI: 10.1016/S0140-6736(18)31999-8.
  • Cox, D. (1972), “Regression Models and Life-Tables,” Journal of the Royal Statistics Society, Series B, 34, 187–220. DOI: 10.1111/j.2517-6161.1972.tb00899.x.
  • Demets, D. L., and Lan, K. K. G. (1994), “Interim Analysis: The Alpha Spending Function Approach,” Statistics in Medicine, 13, 1341–1352. DOI: 10.1002/sim.4780131308.
  • Freidlin, B., and Korn, E. L. (2009), “Monitoring for Lack of Benefit: A Critical Component of a Randomized Clinical Trial,” Journal of Clinical Oncology, 27, 629–633. DOI: 10.1200/JCO.2008.17.8905.
  • Freidlin, B., and Korn, E. L. (2019), “Methods for Accommodating Nonproportional Hazards in Clinical Trials: Ready for the Primary Analysis?,” Journal of Clinical Oncology, 37, 3455–3459.
  • Genz, A. (1992), “Numerical Computation of Multivariate Normal Probabilities,” Journal of Computational and Graphical Statistics, 1, 141–149.
  • Grambsch, P., and Theneau, T. (1994), “Proportional Hazards Tests and Diagnostics Based on Weighted Residuals,” Biometrika, 81, 515–526. DOI: 10.1093/biomet/81.3.515.
  • Guyot, P., Ades, A. E., Ouwens, M. J., and Welton, N. J. (2012), “Enhanced Secondary Analysis of Survival Data: Reconstructing the Data From Published Kaplan-Meier Survival Curves,” BMC Medical Research Methodology, 12, 9. DOI: 10.1186/1471-2288-12-9.
  • Harrington, D., and Fleming, T. (1982), “A Class of Rank Test Procedures for Censored Survival Data,” Biometrika, 69, 553–566. DOI: 10.1093/biomet/69.3.553.
  • Hasegawa, T. (2014), “Sample Size Determination for the Weighted Log-Rank Test With the Fleming–Harrington Class of Weights in Cancer Vaccine Studies,” Pharmaceutical Statistics, 13, 128–135. DOI: 10.1002/pst.1609.
  • Hasegawa, T. (2016), “Group Sequential Monitoring Based on the Weighted Log-Rank Test Statistic With the Fleming–Harrington Class of Weights in Cancer Vaccine Studies,” Pharmaceutical Statistics, 15, 412–419.
  • Herbst, R. S., Baas, P., Kim, D.-W., Felip, E., Pérez-Gracia, J. L., Han, J. Y., Molina, J., Kim, J. H., Arvis, C. D., Ahn, M. J., and Majem, M. (2016), “Pembrolizumab Versus Docetaxel for Previously Treated, PD-L1-Positive, Advanced Non-Small-Cell Lung Cancer (KEYNOTE-010): A Randomised Controlled Trial,” The Lancet, 387, 1540–1550. DOI: 10.1016/S0140-6736(15)01281-7.
  • ICH (1998), “International Conference on Harmonization (ICH E9): Statistical Principles for Clinical Trials,” available at https://www.ich.org/fileadmin/Public/_Web_Site/ICH/_Products/Guidelines/Efficacy/E9/Step4/E9/_Guideline.pdf.
  • Kaplan, E., and Meier, P. (1958), “Nonparametric Estimation From Incomplete Observations,” Journal of the American Statistical Association, 53, 457–481. DOI: 10.1080/01621459.1958.10501452.
  • Karrison, T. (2016), “Versatile Tests for Comparing Survival Curves Based on Weighted Log-Rank Statistics,” Stata Journal, 16, 678–690. DOI: 10.1177/1536867X1601600308.
  • Kaufman, P. A., Awada, A., Twelves, C., Yelle, L., Perez, E. A., Velikova, G., Olivo, M. S., He, Y., Dutcus, C. E., and Cortes, J. (2015), “Phase III Open-Label Randomized Study of Eribulin Mesylate Versus Capecitabine in Patients With Locally Advanced or Metastatic Breast Cancer Previously Treated With an Anthracycline and a Taxane,” Journal of Clinical Oncology, 33, 594–601. DOI: 10.1200/JCO.2013.52.4892.
  • Klein, J. P., Logan, B., Harhoff, M., and Andersen, P. K. (2007), “Analyzing Survival Curves at a Fixed Point in Time,” Statistics in Medicine, 26, 4505–4519. DOI: 10.1002/sim.2864.
  • Koehler, E., Brown, E., and Haneuse, S. J.-P. A. (2009), “On the Assessment of Monte Carlo Error in Simulation-Based Statistical Analyses,” The American Statistician, 63, 155–162. DOI: 10.1198/tast.2009.0030.
  • Lee, J. W. (1996), “Some Versatile Tests Based on the Simultaneous Use of Weighted Log-Rank Statistics,” Biometrics, 52, 721–725. DOI: 10.2307/2532911.
  • Lee, S.-H. (2007), “On the Versatility of the Combination of the Weighted Log-Rank Statistics,” Computational Statistics and Data Analysis, 51, 6557–6564. DOI: 10.1016/j.csda.2007.03.006.
  • Lin, R. S., Lin, J., Roychoudhury, S., Anderson, K. M., Hu, T., Huang, B., Leon, L. F., Liao, J. J., Liu, R., Luo, X., and Mukhopadhyay, P. (2020a), “Rejoinder to Letter to the Editor ‘The Hazards of Period Specific and Weighted Hazard Ratios’,” Statistics in Biopharmaceutical Research, 12, 520–521. DOI: 10.1080/19466315.2020.1825522.
  • Lin, R. S., Lin, J., Roychoudhury, S., Anderson, K. M., Hu, T., Huang, B., Leon, L. F., Liao, J. J., Liu, R., Luo, X., and Mukhopadhyay, P. (2020b), “Alternative Analysis Methods for Time to Event Endpoints Under Nonproportional Hazards: A Comparative Analysis,” Statistics in Biopharmaceutical Research, 12, 187–198.
  • Logan, B. R., Klein, J. P., and Zhang, M.-J. (2008), “Comparing Treatments in the Presence of Crossing Survival Curves: An Application to Bone Marrow Transplantation,” Biometrics, 64, 733–740. DOI: 10.1111/j.1541-0420.2007.00975.x.
  • Logan, B. R., and Mo, S. (2015), “Group Sequential Tests for Long-Term Survival Comparisons,” Lifetime Data Analysis, 21, 218–240. DOI: 10.1007/s10985-014-9298-4.
  • Magirr, D., and Burman, C.-F. (2019), “Modestly Weighted Logrank Tests,” Statistics in Medicine, 38, 3782–3790. DOI: 10.1002/sim.8186.
  • Moore, M. J., Goldstein, D., Hamm, J., Figer, A., Hecht, J. R., Gallinger, S., Au, H. J., Murawa, P., Walde, D., Wolff, R. A., and Campos, D. (2007), “Erlotinib Plus Gemcitabine Compared With Gemcitabine Alone in Patients With Advanced Pancreatic Cancer: A Phase III Trial of the National Cancer Institute of Canada Clinical Trials Group,” Journal of Clinical Oncology, 25, 1960–1966. DOI: 10.1200/JCO.2006.07.9525.
  • Morris, T. P., White, I. R., and Crowther, M. J. (2019), “Using Simulation Studies to Evaluate Statistical Methods,” Statistics in Medicine, 38, 2074–2102. DOI: 10.1002/sim.8086.
  • Pepe, M. S., and Fleming, T. R. (1989), “Weighted Kaplan-Meier Statistics: A Class of Distance Tests for Censored Survival Data,” Biometrics, 45, 497–507. DOI: 10.2307/2531492.
  • Perón, J., Roy, P., Ozenne, B., Roche, L., and Buyse, M. (2016), “The Net Chance of a Longer Survival as a Patient-Oriented Measure of Treatment Benefit in Randomized Clinical Trials,” JAMA Oncology, 2, 901–905. DOI: 10.1001/jamaoncol.2015.6359.
  • Peto, R., and Peto, J. (1972), “Asymptotically Efficient Rank Invariant Test Procedures,” Journal of the Royal Statistical Society, Series A, 135, 185–198. DOI: 10.2307/2344317.
  • Powles, T., Durán, I., van der Heijden, M. S., Loriot, Y., Vogelzang, N. J., De Giorgi, U., Oudard, S., Retz, M. M., Castellano, D., Bamias, A., and Fléchon, A. (2018), “Atezolizumab Versus Chemotherapy in Patients With Platinum-Treated Locally Advanced or Metastatic Urothelial Carcinoma (IMvigor211): A Multicentre, Open-Label, Phase 3 Randomised Controlled Trial,” The Lancet, 391, 748–757. DOI: 10.1016/S0140-6736(17)33297-X.
  • Powles, T., van der Heijden, M. S., Castellano, D., Galsky, M. D., Loriot, Y., Petrylak, D. P., Ogawa, O., Park, S. H., Lee, J. L., De Giorgi, U., and Bögemann, M. (2020), “Durvalumab Alone and Durvalumab Plus Tremelimumab Versus Chemotherapy in Previously Untreated Patients With Unresectable, Locally Advanced or Metastatic Urothelial Carcinoma (DANUBE): A Randomised, Open-Label, Multicentre, Phase 3 Trial,” The Lancet Oncology, 21, 1574–1588. DOI: 10.1016/S1470-2045(20)30541-6.
  • Prentice, R. L. (1978), “Linear Rank Tests With Right Censored Data,” Biometrika, 65, 167–179. DOI: 10.1093/biomet/65.1.167.
  • Putter, H., Sasako, M., Hartgrink, H. H., Van de Velde, C. J. H., and Van Houwelingen, J. C. (2005), “Long-Term Survival With Non-Proportional Hazards: Results From the Dutch Gastric Cancer Trial,” Statistics in Medicine, 24, 2807–2821. DOI: 10.1002/sim.2143.
  • Royston, P., and Parmar, M. K. (2011), “The Use of Restricted Mean Survival Time to Estimate the Treatment Effect in Randomized Clinical Trials When the Proportional Hazards Assumption Is in Doubt,” Statistics in Medicine, 30, 2409–2421. DOI: 10.1002/sim.4274.
  • Schemper, M. (1992), “Cox Analysis of Survival Data With Non-Proportional Hazard Functions,” Journal of the Royal Statistical Society, Series D, 41, 455–465. DOI: 10.2307/2349009.
  • Schemper, M., Wakounig, S., and Heinze, G. (2009), “The Estimation of Average Hazard Ratios by Weighted Cox Regression,” Statistics in Medicine, 28, 2473–2489. DOI: 10.1002/sim.3623.
  • Therneau, T. M., and Grambsch, P. M. (2000), Modeling Survival Data: Extending the Cox Model, New York: Springer.
  • Tian, L., Zhao, L., and Wei, L. J. (2014), “Predicting the Restricted Mean Event Time With the Subject’s Baseline Covariates in Survival Analysis,” Biostatistics, 15, 222–233. DOI: 10.1093/biostatistics/kxt050.
  • Tsiatis, A. A. (1982), “Repeated Significance Testing for a General Class of Statistics Used in Censored Survival Analysis,” Journal of the American Statistical Association, 77, 855–861. DOI: 10.1080/01621459.1982.10477898.
  • Uno, H., Claggett, B., Tian, L., Inoue, E., Gallo, P., Miyata, T., Schrag, D., Takeuchi, M., Uyama, Y., Zhao, L., and Skali, H. (2014), “Moving Beyond the Hazard Ratio in Quantifying the Between-Group Difference in Survival Analysis,” Journal of Clinical Oncology, 32, 2380–2385. DOI: 10.1200/JCO.2014.55.2208.
  • Wang, Y., Wu, H., Anderson, K., Roychoudhury, S., Hu, T., and Liu, H. (2019), “R package: nphsim,” available at http://github.com/keaven/nphsim.
  • Xu, R., and O’Quigley, J. (2000), “Estimating Average Regression Effect Under Non-Proportional Hazards,” Biostatistics, 1, 423–439. DOI: 10.1093/biostatistics/1.4.423.
  • Xu, Z., Park, Y., Zhen, B., and Zhu, B. (2018), “Designing Cancer Immunotherapy Trials With Random Treatment Time-Lag Effect,” Statistics in Medicine, 37, 4589–4609. DOI: 10.1002/sim.7937.
  • Xu, Z., Zhen, B., Park, Y., and Zhu, B. (2017), “Designing Therapeutic Cancer Vaccine Trials With Delayed Treatment Effect,” Statistics in Medicine, 36, 592–605. DOI: 10.1002/sim.7157.
  • Yang, S., and Prentice, R. (2010), “Improved Logrank-Type Tests for Survival Data Using Adaptive Weights,” Biometrics, 66, 30–38. DOI: 10.1111/j.1541-0420.2009.01243.x.

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