## INTRODUCTION

This JAMA Guide to Statistics and Methods discusses the use of time-to-event analysis to evaluate the risk of an adverse outcome from a medical treatment.

Time-to-event analysis, also called survival analysis, was used in the study by Nissen et al1 to compare the risk of major adverse cardiovascular events (MACE) in a noninferiority trial of a combination of naltrexone and bupropion vs placebo for overweight or obese patients with cardiovascular risk factors. The authors used a type of time-to-event analysis called Cox proportional hazards modeling to compare the risk of MACE in the 2 groups, concluding that the use of naltrexone-bupropion increased the risk of MACE per unit time by no more than a factor of 2.

## USE OF THE METHOD

### Why Is Time-to-Event Analysis Used?

One way to evaluate how a medical treatment affects patients’ risk of an adverse outcome is to analyze the time intervals between the initiation of treatment and the occurrence of such events. That information can be used to calculate the hazard for each treatment group in a clinical trial. The hazard is the probability that the adverse event will occur in a defined time interval. For example, Nissen et al1 could measure the number of patients who experience MACE while taking naltrexone-bupropion during week 8 of the study and calculate the risk that an individual patient will experience MACE during week 8, assuming that the patient has not had MACE before week 8. This concept of a discrete hazard rate can be extended to a hazard function, which is generally a continuous curve that describes how the hazard changes over time. The hazard function shows the risk at each point in time and is expressed as a rate or number of events per unit of time.2

Calculating the hazard function using time-to-event observations is challenging because the event of interest is usually not observed in all patients. Thus, the time to the event occurrence for some patients is invisible—or censored—and there is no way to know if the event will occur in the near future, the distant future, or never. Censoring may occur because the patient is lost to follow-up or did not experience the event of interest before the end of the study period. In the study by Nissen et al,1 only 243 patients experienced MACE before the termination of the study, resulting in 8662 censored observations, meaning there were 8662 patients for whom it is not known when they experienced MACE, if ever. Common nonparametric statistical tests, such as the Wilcoxon rank sum test, could be used to compare the time intervals seen in the 2 groups if the analysis was limited to only the 243 patients who had observed events; however, when censored data are excluded from analysis, the information contained in the experience of the other 8662 patients is lost. While ...

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