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Analysis of survival outcomes in haematopoietic cell transplant studies: Pitfalls and solutions

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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.

Abstract

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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Fig. 1: Kaplan-Meier curves for overall survival.
Fig. 2: Correct and incorrect Kaplan-Meier curves.
Fig. 3: Cumulative incidence curves for relapse (a) and non-relapse mortality (b) for experimental and standard treatment.
Fig. 4: Survival curves for two treatments with a Hazard Ratio of 1.55.
Fig. 5: Analyses for the impact of relapse on death.

Data availability

The data file used in this article can be obtained from the corresponding author on reasonable request.

Change history

  • 28 July 2022

    Abstract and Series Editor Introduction were not tagged correctly and were thus presented as one part.

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Acknowledgements

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 [42].

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LdW and HP designed the study, wrote the manuscript, and analyzed the data. JS critically reviewed the manuscript. All authors read and approved the final manuscript.

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Correspondence to Liesbeth C. de Wreede.

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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 (2022). https://doi.org/10.1038/s41409-022-01740-4

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