244 SURVIVAL ANALYSIS Young et al. • SURVIVALANALYSIS SPECIAL CONTRIBUTIONS Statistical Methodology: IX. Survival Analysis KELLY D. YOUNG, MD, JAMES J. MENEGAZZI,PHD, ROGER J. LEWIS, MD, PHD Abstract. Survival analysis is a group of statistical methods used to analyze data representing the time to an event of interest, e.g., the duration of survival after an out-of-hospital cardiac arrest or the length of time a patient stays in the ED. Survival analysis properly accounts for patients who are lost to follow- up and for patients who have not yet experienced the event of interest at the end of the study’s observation period (censored data). This article acquaints the reader with the terminology, methodology, and limi- tations of survival analysis. Specific methods dis- cussed include life tables, the Kaplan-Meier product limit estimate, the log-rank test, and the multivariate Cox proportional hazards model. Key words: survival analysis; statistics; life tables; Kaplan-Meier product limit estimate; log-rank test; Cox proportional haz- ards model. ACADEMIC EMERGENCY MEDICINE 1999; 6:244 – 249 A GROUP of statistical analysis methods, termed ‘‘survival analysis,’’ is being used with increasing frequency in the medical litera- ture. To date, these methods have been used infre- quently in the emergency medicine (EM) litera- ture. The term survival analysis applies to techniques in which the data being analyzed rep- resent the time it takes for a certain event to occur, for example, the time it takes for a patient to ac- cess the emergency medical services (EMS) system after the onset of chest pain. The use of survival analysis, as opposed to the use of a different sta- tistical method, is most important when some sub- jects are lost to follow-up or when the period of observation is finite, such that not all patients ex- perience the event of interest during the study pe- riod. Clinical researchers usually associate sur- vival analysis with studies involving long-term patient survival, such as oncology studies compar- ing different cancer treatments. Because of the common misconception that survival analysis is From the Departments of Emergency Medicine (KDY, RJL) and Pediatrics (KDY), Harbor–UCLA Medical Center, UCLA School of Medicine, Torrance, CA; and the Center for Emer- gency Medicine of Western Pennsylvania (JJM), Department of Emergency Medicine and School of Medicine, University of Pittsburgh, Pittsburgh, PA. Series editor: Roger J. Lewis, MD, PhD, Department of Emer- gency Medicine, Harbor–UCLA Medical Center, Torrance, CA. Received August 22, 1995; revision received November 12, 1998; accepted November 12, 1998. Address correspondence and reprint requests to: Kelly D. Young, MD, Department of Emergency Medicine, Harbor– UCLA Medical Center, 1000 West Carson Street, Box 21, Torrance, CA 90509. Fax: 310-212-6101; e-mail: kyoung@ emedharbor.edu useful only in long-term longitudinal studies, EM researchers rarely consider using these tech- niques, despite the frequent measurement of time- to-event data in EM research. Survival analysis methods are useful, however, for analyzing any time-to-event data. The event of interest, traditionally death, can be replaced with any endpoint that occurs at a particular time, and can occur only once. Examples of such events in- clude death, first readmission to the ED, admission to a particular hospital unit, or administration of a key therapy (e.g., appropriate antibiotics for a patient with bacterial meningitis). In survival analysis, it is the duration of time until the end- point occurs that is the outcome of interest. Some specific examples of data amenable to survival analysis that might be of interest to emergency physicians include: the duration of survival after out-of-hospital cardiac arrest, the length of time spent in triage, the length of time until transport to a tertiary care facility, and the time to receipt of thrombolytic therapy for patients with acute myocardial infarction. The purpose of this article is to provide the reader with the basic terminology and methods used in survival analysis. Specific methods to be discussed include life tables, the Kaplan-Meier product limit estimate, the log-rank test, and the multivariate Cox proportional haz- ards model. SAMPLE DATA Table 1 gives hypothetical sample data for survival from out-of-hospital cardiac arrest in two groups of