HAZARD RATES AND RESTRICTED MEAN SURVIVAL TIME
DOI:
https://doi.org/10.29244/ijsa.v3i3.520Keywords:
effect size, research design, exponential distributionAbstract
Restricted Mean Survival Time (RMST) is well-established, but underutilized measure that can be interpreted as the average event-free survival time up to a pre-specified time point. In the last decade RMST received substantial attention and was advocated as an alternative for the Hazard Rate when the proportionality assumption is not met. Currently studies with time-to-evet outcomes routinely report survival curves and hazard rates. Research planning assumes extraction of comparative effect measures and variances that facilitates sample size calculations. Here we assessed the possibility of extracting clinically meaningful effect size estimates for RMST based research plans from studies that report survival curves and hazard rates. This assessment was based on simulations using Exponential and Weibull distributions. The simulations suggest that under certain conditions meaningful RMST effect size estimates can be extrapolated form published hazard rates. However, in cases when the proportionality assumption is in doubt (i.e. when RMST have most utility) extraction of meaningful estimates is not feasible.
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Allegra, C. J., Yothers, G., O'Connell, M. J., Sharif, S., Petrelli, N. J., Lopa, S. H., & Wolmark, N. (2012). Bevacizumab in Stage II-III Colon Cancer: 5-Year Update of the National Surgical Adjuvant Breast and Bowel Project C-08 Trial. Journal of Clinical Oncology, 31(3): 359-364. doi:10.1200/JCO.2012.44.4711
Andersen, P. K., Hansen, M. G., & Klein, J. P. (2004). Regression Analysis of Restricted Mean Survival Time Based on Pseudo-Observations. Lifetime Data Analysis, 10(4): 335-350. doi:10.1007/s10985-004-4771-0
Conner, S. C., Sullivan, L. M., Benjamin, E. J., LaValley, M. P., Galea, S., & Trinquart, L. (2019). Adjusted restricted mean survival times in observational studies. Statistics in Medicine, 38(20): 3832-3860. doi:10.1002/sim.8206
Couchoud, C., Dantony, E., Elsensohn, M.-H., Rabilloud, M., Ecochard, R., Villar, E., . . . Moranne, O. (2017). Restricted mean survival time over 15 years for patients starting renal replacement therapy. Nephrology Dialysis Transplantation, 32(suppl_2): ii60-ii67. doi:10.1093/ndt/gfw386
Guyot, P., Ades, A. E., Ouwens, M. J. N. M., & Welton, N. J. (2012). Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves. BMC Medical Research Methodology, 12(1): 9. doi:10.1186/1471-2288-12-9
Huang, B., & Kuan, P.-F. (2018). Comparison of the restricted mean survival time with the hazard ratio in superiority trials with a time-to-event end point. Pharmaceutical Statistics, 17(3): 202-213. doi:10.1002/pst.1846
Kim, D. H., Uno, H., & Wei, L. J. (2017). Restricted Mean Survival Time as a Measure to Interpret Clinical Trial Results. JAMA Cardiol, 2(11): 1179-1180. doi:10.1001/jamacardio.2017.2922
Lawrence, J., Qiu, J., Bai, S., & Hung, H. M. J. (2019). Difference in Restricted Mean Survival Time: Small Sample Distribution and Asymptotic Relative Efficiency. Statistics in Biopharmaceutical Research, 11(1): 61-66. doi:10.1080/19466315.2018.1527249
Lehmann, E. L. (1953). The Power of Rank Tests. Ann. Math. Statist., 24(1): 23-43. doi:10.1214/aoms/1177729080
Rajkumar, S. V., Jacobus, S., Callander, N. S., Fonseca, R., Vesole, D. H., Williams, M. E., . . . Greipp, P. R. (2010). Lenalidomide plus high-dose dexamethasone versus lenalidomide plus low-dose dexamethasone as initial therapy for newly diagnosed multiple myeloma: an open-label randomised controlled trial. The Lancet Oncology, 11(1): 29-37. doi:https://doi.org/10.1016/S1470-2045(09)70284-0
Royston, P., & Parmar, M. K. (2013). Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome. BMC Medical Research Methodology, 13(1): 152. doi:10.1186/1471-2288-13-152
Royston, P., & Parmar, M. K. B. (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(19): 2409-2421. doi:10.1002/sim.4274
Rulli, E., Ghilotti, F., Biagioli, E., Porcu, L., Marabese, M., D’Incalci, M., . . . Torri, V. (2018). Assessment of proportional hazard assumption in aggregate data: a systematic review on statistical methodology in clinical trials using time-to-event endpoint. British Journal of Cancer, 119(12): 1456-1463. doi:10.1038/s41416-018-0302-8
Stensrud, M. J., Aalen, J. M., Aalen, O. O., & Valberg, M. (2018). Limitations of hazard ratios in clinical trials. European Heart Journal, 40(17): 1378-1383. doi:10.1093/eurheartj/ehy770
Trinquart, L., Jacot, J., Conner, S. C., & Porcher, R. (2016). Comparison of Treatment Effects Measured by the Hazard Ratio and by the Ratio of Restricted Mean Survival Times in Oncology Randomized Controlled Trials. Journal of Clinical Oncology, 34(15): 1813-1819. doi:10.1200/jco.2015.64.2488
Uno, H., Claggett, B., Tian, L., Inoue, E., Gallo, P., Miyata, T., . . . Wei, L. J. (2014). Moving beyond the hazard ratio in quantifying the between-group difference in survival analysis. Journal of Clinical Oncology, 32(22): 2380-2385. doi:10.1200/jco.2014.55.2208
Uno, H., Wittes, J., Fu, H., Solomon, S. D., Claggett, B., Tian, L., . . . Wei, L.-J. (2015). Alternatives to Hazard Ratios for Comparing the Efficacy or Safety of Therapies in Noninferiority StudiesAlternatives to Hazard Ratios. Annals of Internal Medicine, 163(2), 127-134. doi:10.7326/M14-1741 %J Annals of Internal Medicine
Weir, I. R., & Trinquart, L. (2018). Design of non-inferiority randomized trials using the difference in restricted mean survival times. 15(5): 499-508. doi:10.1177/1740774518792259
Zukin, M., Barrios, C. H., Rodrigues Pereira, J., De Albuquerque Ribeiro, R., de Mendonça Beato, C. A., do Nascimento, Y. N., . . . Lilenbaum, R. C. (2013). Randomized Phase III Trial of Single-Agent Pemetrexed Versus Carboplatin and Pemetrexed in Patients With Advanced Non–Small-Cell Lung Cancer and Eastern Cooperative Oncology Group Performance Status of 2. Journal of Clinical Oncology, 31(23): 2849-2853. doi:10.1200/JCO.2012.48.1911
