Survival Analysis and the Kaplan-Meier Curve

Clinical trials describe how an outcome is affected by an exposure. But sometimes whether an event happens matters less than when it happens. That is what survival analysis is all about.

Most clinical studies are designed to reach their endpoint quickly enough that all observations can be made with minimal dropout and a fairly constant effect over time. In some cases, though, the final proportion of events in two treatment groups is identical, or the outcome cannot be observed in the short term.

Imagine one group has all its events shortly after randomization, while the other has no events until just before the end of follow-up. The two treatments clearly have different clinical effects, even though the proportions at the end are the same. Analysing the time until an event occurs captures this difference.

What is survival analysis?

Survival analysis is a collection of statistical procedures for data analysis where the outcome variable of interest is the time until an event occurs: the time between entering a study and a subsequent event.

The method originated in medical research to evaluate the impact of medicines or procedures on time until death. But “survival” does not only mean survival from death. It can also be the time “survived” from complete remission to relapse or progression.

Survival analysis can be explored through several techniques:

• Survivor and hazard functions
• Cox proportional hazards regression
• Parametric survival models
• Survival trees and survival random forests
• Life tables
• The Kaplan-Meier curve

Why survival data are tricky: censoring

These analyses are often complicated for two main reasons. First, survival times are unlikely to be normally distributed. Second, the total survival time for some subjects cannot be determined accurately. This can happen for negative reasons, such as dropout, loss to follow-up or lost data. It can also happen for positive ones, such as the study ending before the subject experiences the event.

The Kaplan-Meier curve

The Kaplan-Meier curve is a visual representation of the survival function. It shows the probability of remaining event-free over time, and is widely used in oncology trials. It relies on three assumptions:

1. Censored patients have the same chance of survival as those still being followed.
2. Subjects recruited early and late in the study have comparable survival probabilities.
3. The event happens at the specified time. This can be a problem when an event is only detected at a scheduled examination, since all we know is that it happened between two visits. More frequent follow-up gives more accurate estimates.

How to read the curve

Each horizontal step along the X-axis (time) shows the survival duration for that interval. The interval ends when an event occurs, and the vertical drop on the Y-axis shows the change in the survival rate.

Visual gaps alone do not prove a difference. Statistical significance should be confirmed with appropriate tests, such as the log-rank test, the hazard ratio and its 95% confidence interval. For a practical primer on these measures, read Basic Statistics Every MSL Should Master.