Comparing Treatments in the Presence of Crossing Survival Curves: An Application to Bone Marrow Transplantation
Abstract
Summary In some clinical studies comparing treatments in terms of their survival curves, researchers may anticipate that the survival curves will cross at some point, leading to interest in a long‐term survival comparison. However, simple comparison of the survival curves at a fixed point may be inefficient, and use of a weighted log‐rank test may be overly sensitive to early differences in survival. We formulate the problem as one of testing for differences in survival curves after a prespecified time point, and propose a variety of techniques for testing this hypothesis. We study these methods using simulation and illustrate them on a study comparing survival for autologous and allogeneic bone marrow transplants.
Citing Literature
Number of times cited according to CrossRef: 34
- Elsa Hansen, Andrew F. Read, Cancer therapy: Attempt cure or manage drug resistance?, Evolutionary Applications, 10.1111/eva.12994, 13, 7, (1660-1672), (2020).
- Xinghui Huang, Jingjing Lyu, Yawen Hou, Zheng Chen, A nonparametric statistical method for two crossing survival curves, Communications in Statistics - Simulation and Computation, 10.1080/03610918.2020.1753075, (1-10), (2020).
- Ray S. Lin, Ji Lin, Satrajit Roychoudhury, Keaven M. Anderson, Tianle Hu, Bo Huang, Larry F Leon, Jason J.Z. Liao, Rong Liu, Xiaodong Luo, Pralay Mukhopadhyay, Rui Qin, Kay Tatsuoka, Xuejing Wang, Yang Wang, Jian Zhu, Tai-Tsang Chen, Renee Iacona, Alternative Analysis Methods for Time to Event Endpoints Under Nonproportional Hazards: A Comparative Analysis, Statistics in Biopharmaceutical Research, 10.1080/19466315.2019.1697738, (1-12), (2020).
- Philippe Flandre, John O’Quigley, Comparing Kaplan–Meier curves with delayed treatment effects: applications in immunotherapy trials, Journal of the Royal Statistical Society: Series C (Applied Statistics), 10.1111/rssc.12345, 68, 4, (915-939), (2019).
- Ulrike Pötschger, Harald Heinzl, Maria Grazia Valsecchi, Martina Mittlböck, Assessing the effect of a partly unobserved, exogenous, binary time-dependent covariate on survival probabilities using generalised pseudo-values, BMC Medical Research Methodology, 10.1186/s12874-017-0430-5, 18, 1, (2018).
- Frank Peinemann, Alexander Michael Labeit, Issues possibly associated with misinterpreting survival data: A method study, Journal of Evidence-Based Medicine, 10.1111/jebm.12301, 11, 3, (208-215), (2018).
- Philippe R. Bauer, Ognjen Gajic, Rahul Nanchal, Rahul Kashyap, Ignacio Martin-Loeches, Yasser Sakr, Stephan M. Jakob, Bruno François, Xavier Wittebole, Richard G. Wunderink, Jean-Louis Vincent, Association between timing of intubation and outcome in critically ill patients: A secondary analysis of the ICON audit, Journal of Critical Care, 10.1016/j.jcrc.2017.06.010, 42, (1-5), (2017).
- Haiming Zhou, Timothy Hanson, Jiajia Zhang, Generalized accelerated failure time spatial frailty model for arbitrarily censored data, Lifetime Data Analysis, 10.1007/s10985-016-9361-4, 23, 3, (495-515), (2016).
- Chatree Chai-Adisaksopha, Alfonso Iorio, Christopher Hillis, Wendy Lim, Mark Crowther, A systematic review of using and reporting survival analyses in acute lymphoblastic leukemia literature, BMC Hematology, 10.1186/s12878-016-0055-7, 16, 1, (2016).
- Florica Gadalean, Daniel Lighezan, Dana Stoian, Oana Schiller, Romulus Timar, Bogdan Timar, Flaviu Bob, Mihaela Dora Donciu, Mircea Munteanu, Adelina Mihaescu, Adrian Covic, Adalbert Schiller, The Survival of Roma Minority Patients on Chronic Hemodialysis Therapy - A Romanian Multicenter Survey, PLOS ONE, 10.1371/journal.pone.0155271, 11, 5, (e0155271), (2016).
- Curly Morris, Simona Iacobelli, Gösta Gahrton, Anja van Biezen, Mary Drake, Laurent Garderet, Michael Potter, Anton V. Schattenberg, Jan J. Cornelissen, Rose-Marie Hamladji, Massimo Martelli, Eefke Petersen, Montserrat Rovira, Giuseppe Bandini, Nicolaus Kroger, Theo de Witte, Efficacy and Outcome of Allogeneic Transplantation in IgD and Nonsecretory Myeloma. A Report on Behalf of the Myeloma Subcommittee of the Chronic Malignancies Working Party of the European Group for Blood and Marrow Transplantation, Biology of Blood and Marrow Transplantation, 10.1016/j.bbmt.2015.02.012, 21, 6, (1054-1058), (2015).
- Youn Ju Lee, Jae Won Lee, A comparison of the statistical methods for testing the equality of crossing survival functions, Journal of the Korean Data and Information Science Society, 10.7465/jkdi.2015.26.3.569, 26, 3, (569-580), (2015).
- Huimin Li, Dong Han, Yawen Hou, Huilin Chen, Zheng Chen, Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods, PLOS ONE, 10.1371/journal.pone.0116774, 10, 1, (e0116774), (2015).
- Brent R. Logan, Shuyuan Mo, Group sequential tests for long-term survival comparisons, Lifetime Data Analysis, 10.1007/s10985-014-9298-4, 21, 2, (218-240), (2014).
- Takahiro Hasegawa, Sample size determination for the weighted log‐rank test with the Fleming–Harrington class of weights in cancer vaccine studies, Pharmaceutical Statistics, 10.1002/pst.1609, 13, 2, (128-135), (2014).
- Liang Li, A Class of Permutation Tests for the Equality of Two Marginal Survival Functions Using Paired Censored Data, Communications in Statistics - Simulation and Computation, 10.1080/03610918.2012.755196, 43, 10, (2498-2507), (2014).
- Michael Coory, Karen E. Lamb, Michael Sorich, Risk-difference curves can be used to communicate time-dependent effects of adjuvant therapies for early stage cancer, Journal of Clinical Epidemiology, 10.1016/j.jclinepi.2014.03.006, 67, 9, (966-972), (2014).
- Seungbong Han, Adin-Cristian Andrei, Kam-Wah Tsui, A flexible semiparametric modeling approach for doubly censored data with an application to prostate cancer, Statistical Methods in Medical Research, 10.1177/0962280213498325, 25, 4, (1718-1735), (2013).
- H. Campbell, C.B. Dean, The consequences of proportional hazards based model selection, Statistics in Medicine, 10.1002/sim.6021, 33, 6, (1042-1056), (2013).
- Simona Iacobelli, Suggestions on the use of statistical methodologies in studies of the European Group for Blood and Marrow Transplantation, Bone Marrow Transplantation, 10.1038/bmt.2012.282, 48, S1, (S1-S37), (2013).
- Stefania Galimberti, Maria Grazia Valsecchi, Multivariate permutation test to compare survival curves for matched data, BMC Medical Research Methodology, 10.1186/1471-2288-13-16, 13, 1, (2013).
- G. Gahrton, S. Iacobelli, B. Bjorkstrand, U. Hegenbart, A. Gruber, H. Greinix, L. Volin, F. Narni, A. M. Carella, M. Beksac, A. Bosi, G. Milone, P. Corradini, S. Schonland, K. Friberg, A. van Biezen, H. Goldschmidt, T. de Witte, C. Morris, D. Niederwieser, L. Garderet, N. Kroger, Autologous/reduced-intensity allogeneic stem cell transplantation vs autologous transplantation in multiple myeloma: long-term results of the EBMT-NMAM2000 study, Blood, 10.1182/blood-2012-11-469452, 121, 25, (5055-5063), (2013).
- Fredrik B. Thorén, Harald Anderson, Örjan Strannegård, Late divergence of survival curves in cancer immunotherapy trials: interpretation and implications, Cancer Immunology, Immunotherapy, 10.1007/s00262-013-1458-y, 62, 10, (1547-1551), (2013).
- Ameina Tressler, Alan Chow, Multiple pairwise comparison procedures based on the Lin and Wang test for right censored survival data, Statistica Neerlandica, 10.1111/j.1467-9574.2012.00535.x, 67, 1, (112-120), (2012).
- I. Borges, J.-L. Hemptinne, A. O. Soares, Contrasting population growth parameters of the aphidophagous Scymnus nubilus and the coccidophagous Nephus reunioni, BioControl, 10.1007/s10526-012-9490-y, 58, 3, (351-357), (2012).
- José Jayme Galvão Lima, Luís Henrique Wolff Gowdak, Flávio Jota Paula, Luiz Antonio Machado César, José Antonio Franchini Ramires, Luiz A. Bortolotto, Which patients are more likely to benefit from renal transplantation?, Clinical Transplantation, 10.1111/j.1399-0012.2012.01631.x, 26, 6, (820-825), (2012).
- Seungbong Han, Adin-Cristian Andrei, Kam-Wah Tsui, A Flexible Modeling Approach for Current Status Survival Data via Pseudo-Observations, Korean Journal of Applied Statistics, 10.5351/KJAS.2012.25.6.947, 25, 6, (947-958), (2012).
- Tahani Coolen-Maturi, Pauline Coolen-Schrijner, Frank P. A. Coolen, Nonparametric Predictive Multiple Comparisons of Lifetime Data, Communications in Statistics - Theory and Methods, 10.1080/03610926.2011.569863, 41, 22, (4164-4181), (2012).
- Gisela Tunes-da-Silva, John P. Klein, Cutpoint selection for discretizing a continuous covariate for generalized estimating equations, Computational Statistics & Data Analysis, 10.1016/j.csda.2010.02.016, 55, 1, (226-235), (2011).
- Bo Björkstrand, Simona Iacobelli, Ute Hegenbart, Astrid Gruber, Hildegard Greinix, Liisa Volin, Franco Narni, Pellegrino Musto, Meral Beksac, Alberto Bosi, Giuseppe Milone, Paolo Corradini, Hartmut Goldschmidt, Theo de Witte, Curly Morris, Dietger Niederwieser, Gösta Gahrton, Tandem Autologous/Reduced-Intensity Conditioning Allogeneic Stem-Cell Transplantation Versus Autologous Transplantation in Myeloma: Long-Term Follow-Up, Journal of Clinical Oncology, 10.1200/JCO.2010.32.7312, 29, 22, (3016-3022), (2011).
- Pei-Fang Su, Yunchan Chi, Chung-I Li, Yu Shyr, Yi-De Liao, Analyzing survival curves at a fixed point in time for paired and clustered right-censored data, Computational Statistics & Data Analysis, 10.1016/j.csda.2010.10.001, 55, 4, (1617-1628), (2011).
- Jenny Zilberberg, Thea M. Friedman, Glenn Dranoff, Robert Korngold, Treatment with GM-CSF Secreting Myeloid Leukemia Cell Vaccine Prior to Autologous-BMT Improves the Survival of Leukemia-Challenged Mice, Biology of Blood and Marrow Transplantation, 10.1016/j.bbmt.2010.09.020, 17, 3, (330-340), (2011).
- T. Ian Barron, Kathleen Bennett, John Feely, A Competing Risks Prescription Refill Model of Compliance and Persistence, Value in Health, 10.1111/j.1524-4733.2010.00741.x, 13, 6, (796-804), (2010).
- Vito M. R. Muggeo, Miriam Tagliavia, A flexible approach to the crossing hazards problem, Statistics in Medicine, 10.1002/sim.3959, 29, 18, (1947-1957), (2010).




