Interpretation and assumptions of Kaplan-Meier survival rates

Question

A study followed 1000 patients for a 5-year period, but some patients may have been lost to follow-up or relocated during the study. The study's results indicate that:

• Kaplan-Meier survival rate at 1 year: 0.80
• Kaplan-Meier survival rate at 2 year: 0.60
• Kaplan-Meier survival rate at 5 year: 0.50

Questions:

1. Is it valid to interpret that there were 200 deaths out of 1000 participants at 1 year, 400 deaths at 2 years, and 500 deaths at 5 years?

2. Does that interpretation assume that no patients were censored?

3. What is the best approach to estimate the number of deaths out of 1000 participants - at 1,2 and 5 years? Can you provide your thoughts, pointing a few good references?

Answer 1

Survival analysis tries to represent the distribution of survival times among members of a population. If you took 1000 randomly sampled members of a population of patients and followed each of them from the time of study entry until the event of interest, then in your scenario (with death as the event) your interpretation in Question 1 would be obviously correct.

In practice, many individuals in the sample aren't followed all the way until the event occurs. Right censoring (having a lower limit to the time to the event) is common. The advantage of survival models is that they can estimate the survival curve over time for the population of patients even when some survival-time values are censored.

In terms of Questions 1 and 2 when there are censored survival times, the Kaplan-Meier method provides an estimate of what you would have found without censoring. You didn't record that many deaths in your data, but those are estimates of how many actually occurred out of the 1000 patients.

For Question 3, this article might be helpful in terms of how Kaplan-Meier curves are estimated. The main R survival vignette contains concise summaries of other extensions of survival analysis. As of today, this Cross Validated website has nearly 3000 pages on survival analysis. This page, for example, shows how survival analysis takes censored event times into account.