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

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 pj < p < pj+1, and pj, pj+1 well defined percentiles (i.e with S(Q(pj)) = pj),

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

• i will add latex formulation, i just need to understand how to include it and i have an urging task to do besides, during this time i've set this question back to the original shape so that it's a bit readible Commented Feb 10, 2021 at 17:33