Is it safe to say that Variance for Nelson Aalen estimate is always > than variance for Kaplan Meier? I am drawing from the solution to question 8.14 and 8.16. Thanks!
Var (KM) and Var (NA) are calculated for KM estimator i.e. F(t) and NA integrated hazard respectively. As the sd's (derived from variances) are used to compute the confidence intervals of the survival function, Var (KM) can be straightaway used i.e. CI = S(t) +/- 1.96 x sd(KM estimator) but Var (NA) has to be adjusted: first, calculate the CI of the integrated hazard i.e. integrated hazard +/- 1.96 x sd of NA integrated hazard and then the CI i.e. exp {- lower bound of CI of integrated hazard, - higher bound of CI of integrated hazard}. I believe the variances of KM and NA are not comparable as they are applied to different means.
