Series Editor Introduction
The final article in our Statistics Series by de Wreede and colleagues deals with the important issue of survival analyses in general and in recipients of haematopoietic cell transplants specifically. At first glance analyzing survival should be simple. The endpoint is clear with rare exception, the subject is either alive or dead. Compare this to other less well defined transplant-related outcomes such as who has acute graft-versus-host disease (GvHD) and of what grade or what is the cause of interstitial pneumonia. There is also the complexity of composite endpoints when one analyzes outcomes such as event-free (EFS) or relapse-free survival (RFS). Here you’re either alive or dead. Period. Alas, as it turns out things are not so simple. As the authours point out: it takes time to observe time. It is almost never possible to wait long enough for everyone in a study to die. (Some people who are cured by a transplant will outlive their physician and statistician.) Other subjects may not be followed until the end of the study, lost to follow-up or withdraw consent to participate. Often these are non-random events, muddy the water and make what seems a simple analysis of survival not so. Fortunately, de Wreede and colleagues discuss the issues of informative and non-informative censoring and time-dependent co-variates. And there are other nasty complexities such non-proportional hazards of death say when initially there is a survival disadvantage to transplants from transplant-related mortality followed in 1–2 years by a survival benefit. They emphasize the danger of considering only Hazard Ratio in this setting. Lastly, the authours discuss how to compare interventions such as conventional therapy versus a haematopoietic cell transplant when the endpoint of interest is survival. We think this article will be of considerable interest to readers of BONE MARROW TRANSPLANTATION and suggest you study it carefully. Survival analyses, seemingly simple, are a potential minefield. You don’t want to step on one. This article and the entire Statistics Series are available online at https://www.nature.com/collections/ejhigdbeeh.
Robert Peter Gale MD, PhD & Mei-Jie Zhang PhD.
The most important outcome of many studies of haematopoietic cell transplants is survival. The statistical field that deals with such outcomes is survival analysis. Methods developed in this field are also applicable to other outcomes where the occurrence and timing are important. Analysis of such time-to-event outcomes has special challenges because it takes time to observe time. The most important condition for unbiased estimation of a survival curve—non-informative censoring—is discussed along with methods to account for competing risks, a situation where multiple, mutually-exclusive endpoints are of interest. Techniques to compare survival outcomes between groups are reviewed, including the instance where it is unknown at baseline to which group a subject will belong later during follow-up (time-dependent covariates).
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Iacobelli S, EBMT Statistical Committee. Suggestions on the use of statistical methodologies in studies of the European Group for Blood and Marrow Transplantation. Bone Marrow Transpl. 2013;48:S1–37. Suppl 1
Klein JP, Moeschberger ML. Techniques for censored and truncated data. New York: Springer-Verlag; 2003.
Clark TG, Bradburn MJ, Love SB, Altman DG. Survival analysis part I: basic concepts and first analyses. Br J Cancer. 2003;89:232–8.
Bradburn MJ, Clark TG, Love SB, Altman DG. Survival Analysis Part II: Multivariate data analysis—an introduction to concepts and methods. Br J Cancer. 2003;89:431–6.
Bradburn MJ, Clark TG, Love SB, Altman DG. Survival Analysis Part III: Multivariate data analysis—choosing a model and assessing its adequacy and fit. Br J Cancer. 2003;89:605–11.
Clark TG, Bradburn MJ, Love SB, Altman DG. Survival Analysis Part IV: Further concepts and methods in survival analysis. Br J Cancer. 2003;89:781–6.
Satagopan JM, Ben-Porat L, Berwick M, Robson M, Kutler D, Auerbach AD. A note on competing risks in survival data analysis. Br J Cancer. 2004;91:1229–35.
Gale RP, Zhang MJ. Statistical analyses of clinical trials in haematopoietic cell transplantation or why there is a strong correlation between people drowning after falling out of a fishing boat and marriage rate in Kentucky. Bone Marrow Transpl. 2020;55:1–3.
Zheng C, Dai R, Gale RP, Zhang MJ. Causal inference in randomized clinical trials. Bone Marrow Transpl. 2020;55:4–8.
Hu ZH, Peter Gale R, Zhang MJ. Direct adjusted survival and cumulative incidence curves for observational studies. Bone Marrow Transpl. 2020;55:538–43.
Gauthier J, Wu QV, Gooley TA. Cubic splines to model relationships between continuous variables and outcomes: a guide for clinicians. Bone Marrow Transpl. 2020;55:675–80.
Othus M, Gale RP, Hourigan CS, Walter RB. Statistics and measurable residual disease (MRD) testing: uses and abuses in hematopoietic cell transplantation. Bone Marrow Transpl. 2020;55:843–50.
Moodie EEM, Krakow EF. Precision medicine: Statistical methods for estimating adaptive treatment strategies. Bone Marrow Transpl. 2020;55:1890–6.
Hu ZH, Wang HL, Gale RP, Zhang MJA. SAS macro for estimating direct adjusted survival functions for time-to-event data with or without left truncation. Bone Marrow Transpl. 2022;57:6–10.
Therneau TM, Grambsch PM. Modeling survival data: extending the Cox Model. New York: Springer Science & Business Media; 2000. 372 p.
Gerds TA. prodlim: Product-Limit estimation for censored event history analysis. 2019. Available from: https://CRAN.R-project.org/package=prodlim
Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. J Am Stat Assoc. 1958;53:457–81.
Cox DR. Regression models and life-tables. J R Stat Soc Ser B Methodol. 1972;34:187–220.
Snowden JA, Saccardi R, Orchard K, Ljungman P, Duarte RF, Labopin M, et al. Benchmarking of survival outcomes following haematopoietic stem cell transplantation: A review of existing processes and the introduction of an international system from the European Society for Blood and Marrow Transplantation (EBMT) and the Joint Accreditation Committee of ISCT and EBMT (JACIE). Bone Marrow Transpl. 2020;55:681–94.
Putter H, Eikema DJ, de Wreede LC, McGrath E, Sánchez-Ortega I, Saccardi R, et al. Benchmarking survival outcomes: A funnel plot for survival data. Stat Methods Med Res. 2022 Mar;09622802221084130.
Schetelig J, de Wreede LC, van Gelder M, Koster L, Finke J, Niederwieser D, et al. Late treatment-related mortality versus competing causes of death after allogeneic transplantation for myelodysplastic syndromes and secondary acute myeloid leukemia. Leukemia 2019;33:686–95.
Kim HT, Armand P. Clinical endpoints in allogeneic hematopoietic stem cell transplantation studies: the cost of freedom. Biol Blood Marrow Transpl. 2013;19:860–6.
Putter H, Fiocco M, Geskus RB. Tutorial in biostatistics: competing risks and multi-state models. Stat Med. 2007;26:2389–430.
Andersen PK, Geskus RB, de Witte T, Putter H. Competing risks in epidemiology: possibilities and pitfalls. Int J Epidemiol. 2012;41:861–70.
Greinix HT, Eikema DJ, Koster L, Penack O, Yakoub-Agha I, Montoto S, et al. Improved outcome of patients with graft-versus-host disease after allogeneic hematopoietic cell transplantation for hematologic malignancies over time: an EBMT mega-file study. Haematologica 2022;107:1054–63.
Latta RB. A Monte Carlo study of some two-sample rank tests with censored data. J Am Stat Assoc. 1981;76:713–9.
Kellerer AM, Chmelevsky D. Small-sample properties of censored-data rank tests. Biometrics 1983;39:675–82.
Hothorn T, Hornik K, van de Wiel MA, Zeileis A. Implementing a class of permutation tests: The coin Package. J Stat Softw. 2008;28:1–23.
van Houwelingen H, Putter H. Dynamic prediction in clinical survival analysis. Boca Raton: CRC Press; 2012. 250 p.
Schemper M. Cox analysis of survival data with non-proportional hazard functions. J R Stat Soc Ser Stat 1992;41:455–65.
Felizzi F, Paracha N, Pöhlmann J, Ray J. Mixture cure models in oncology: a tutorial and practical guidance. PharmacoEconomics - Open. 2021;5:143–55.
Pohar Perme M, Pavlic K. Nonparametric relative survival analysis with the R Package relsurv. J Stat Softw. 2018;87:1–27.
Hsieh PY, Liu CJ, Teng CJ. Immortal time bias in retrospective analysis: comment on “Efficacy and safety of long-term treatment with lenalidomide and dexamethasone in patients with relapsed/refractory multiple myeloma.”. Blood Cancer J 2015;5:e283.
Anderson JR, Cain KC, Gelber RD. Analysis of survival by tumor response. J Clin Oncol. 1983;1:710–9.
Fisher LD, Lin DY. Time-dependent covariates in the Cox proportional-hazards regression model. Annu Rev Public Health. 1999;20:145–57.
Zhang Z, Reinikainen J, Adeleke KA, Pieterse ME, Groothuis-Oudshoorn CGM. Time-varying covariates and coefficients in Cox regression models. Ann Transl Med. 2018;6:121.
Dafni U. Landmark analysis at the 25-year landmark point. Circ Cardiovasc Qual Outcomes. 2011;4:363–71.
Morgan CJ. Landmark analysis: A primer. J Nucl Cardiol. 2019;26:391–3.
Brand R, Putter H, van Biezen A, Niederwieser D, Martino R, Mufti G, et al. Comparison of allogeneic stem cell transplantation and non-transplant approaches in elderly patients with advanced myelodysplastic syndrome: optimal statistical approaches and a critical appraisal of clinical results using non-randomized data. PLOS ONE. 2013;8:e74368.
Robin M, de Wreede LC, Padron E, Bakunina K, Fenaux P, Koster L, et al. Role of allogeneic transplantation in chronic myelomonocytic leukemia: an international collaborative analysis. Blood (accepted 2022). https://doi.org/10.1182/blood.2021015173.
Kragh Andersen P, Pohar Perme M, van Houwelingen HC, Cook RJ, Joly P, Martinussen T, et al. Analysis of time-to-event for observational studies: Guidance to the use of intensity models. Stat Med. 2021;40:185–211.
de Wreede LC, Putter H. Valkuilen en oplossingen bij de overlevingsduuranalyse in hematologische studies/Pitfalls and solutions in survival analysis for hematological studies. NTVH. 2017;14:118–24.
We thank Robert P. Gale (Imperial College, London, UK) and Mei-Jie Zhang (Medical College of Wisconsin, Milwaukee, WI, USA) for their invitation to contribute to their series of papers about statistical topics and we thank Dr Gale for his suggestions about content and wording that have improved the manuscript. We thank Michel van Gelder (MUMC, Maastricht, the Netherlands) and Katharina Schmidt-Brücken (Technical University Dresden, Germany) for their critical review of previous versions of this manuscript. This article is a reworked version of an article in Dutch .
The author declares no competing interests.
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de Wreede, L.C., Schetelig, J. & Putter, H. Analysis of survival outcomes in haematopoietic cell transplant studies: Pitfalls and solutions. Bone Marrow Transplant 57, 1428–1434 (2022). https://doi.org/10.1038/s41409-022-01740-4