# Is the Kaplan-Meier estimator appropriate when I have observed only one event?

Let's say I have a database with 21 patients and one of these patients has died. In such a scenario, can we apply overall survival analysis using the Kaplan-Meier model or no? Meaning that does it have any statistical interest or it would be just a waste of time ? why / why not ?

Maybe "appropriate" but "not very useful."

The Kaplan-Meier estimator will show a single drop in the survival curve, at the time of the death event. It will only use information from the individuals at risk at that particular time. If $$Y$$ individuals are at risk at that time, the drop will be to a survival fraction of $$(Y-1)/Y$$, with a variance (by the Greenwood formula) of $$(Y-1)/Y^3$$. The Kaplan-Meier curve will be flat at that value thereafter.

That has the merit of displaying your data sample in a useful way, but it wouldn't provide much reason to trust your results beyond your particular data sample.

• thank you so much Feb 12 at 10:36

Just to give a very intuitive perspective: in survival analysis the main unit we care about is the "case", as in the subject who experienced the event in study. Contrarily, when we analyze a continuous outcome we care about all the subjects with a measure of the outcome.

To make a parallel between the two types of analyses, having only one case in survival it's like having only one observation in a continuous outcome setting. You cannot do much statistics on that..

• thank you so much Feb 12 at 10:36