Can we take the kaplan-meier estimate to construct a piecewise linear estimate of survival?

Question

I intend to perform simulation based on a kaplan-meier estimation of survival on a dataset. I planned to use uniform simulation over [0,1] and the percentile function that i obtain from the kaplan-meier estimate.

Nevertheless, the fact that the kaplan-meier estimate S(t) is piecewise constant, and the use of the "classical" percentile function Q(p) = inf { t | S(t) ≤ 1-p } bring me to simulate only over a set of different time points. To add a more flexible approach, i would like to use weighted percentiles : with p_j < p < p_j+1, and p_j, p_j+1 well defined percentiles (i.e with S(Q(p_j)) = p_j),

Q*(p) = [(p-p_j)/(p_j+1-p_j)]*Q(p_j) + [(p_j+1-p)/(p_j+1-p_j)]*Q(p_j+1)

The fact is that it is equivalent to use a modification of the kaplan-meier estimate to construct our percentile function, where all the depression in the stairs representing this piecewise-constant estimator are linked by a straight line. So here is my question : does such an estimator exist in the litterature, and why don't we use it, as the hypothesis of constant survival seems in most practical case a bit far-fetched ?

thanks for reading

Answer 1

The Kaplan-Meier estimate makes jumps where there are observed event times.

Suppose there is an event on Day 150 and the next time of event is Day 200.
The K-M estimate of probability of surviving beyond Day 151 is the same as that of surviving beyond Day 199 because there is no data to tell me that they should be different. I did not observe anybody having an event in any of those days between 151 and 199. Maybe the truth is that no events can happen on those days for some scenarios.

If you really have a good feeling for what the curve should look like and there is not much data, then parametric survival analysis may work better in those scenarios. Another possible alternative is using piecewise constant hazard functions. Those will give you an estimated survival curve that is continuously decreasing.