Survival Analysis and Interpretation of Time-to-Event Data: The Tortoise and the Hare

Survival analysis, or more generally, time-to-event analysis, refers to a set of methods for analyzing the length of time until the occurrence of a well-defined end point of interest. A unique feature of survival data is that typically not all patients experience the event (eg, death) by the end of the observation period, so the actual survival times for some patients are unknown. This phenomenon, referred to as censoring, must be accounted for in the analysis to allow for valid inferences. Moreover, survival times are usually skewed, limiting the usefulness of analysis methods that assume a normal data distribution. As part of the ongoing series in Anesthesia & Analgesia, this tutorial reviews statistical methods for the appropriate analysis of time-to-event data, including nonparametric and semiparametric methods—specifically the Kaplan-Meier estimator, log-rank test, and Cox proportional hazards model. These methods are by far the most commonly used techniques for such data in medical literature. Illustrative examples from studies published in Anesthesia & Analgesia demonstrate how these techniques are used in practice. Full parametric models and models to deal with special circumstances, such as recurrent events models, competing risks models, and frailty models, are briefly discussed. This is an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License 4.0 (CCBY-NC-ND), where it is permissible to download and share the work provided it is properly cited. The work cannot be changed in any way or used commercially without permission from the journal. Accepted for publication June 8, 2018. Funding: None. The authors declare no conflicts of interest. Reprints will not be available from the authors. Address correspondence to Patrick Schober, MD, PhD, MMedStat, Department of Anesthesiology, VU University Medical Center, De Boelelaan 1117, 1081 HV, Amsterdam, the Netherlands. Address e-mail to p.schober@vumc.nl. © 2018 International Anesthesia Research Society

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