Nelson-Aalen estimator and interval censoring/tied events I just noticed that the Nelson-Aalen estimate of the cumulative hazard changes depends on the existence of tied events. As a toy example, consider a study with 3 patients. The patients die on day 1, 5, and 14 of the study. If we check the patients status daily, the Nelson-Aalen estimate for the cumulative hazard at the end of the study is $\frac{1}{3} + \frac{1}{2} + 1 = \frac{11}{6}$. If we check weekly (on day 7 and 14), the final estimate is $\frac{2}{3} + 1=\frac{10}{6}$. So the final estimate of the cumulative hazard differs, and I don't see why this is reasonable.
 A: The mean of 1.9, 2.9, and 3 is 2.6, but if I round them up to integers, then the mean is 2.667. Are you surprised by this? Looking less frequently is like rounding, so it changes the answer.
Handling of ties in survival analysis is always a problematic issue, and there are several possible approaches. The Nelson-Aalen estimator corresponds to the "Breslow" method of handling ties. The "Efron" method would give the answer you feel is more natural.
library(survival)
y1 <- c(1,5,14)  # look daily
y2 <- c(7,7,14)  # look weekly
cens <- c(1,1,1) # event indicator
#
# "correct" estimate of cumulative hazard
basehaz(coxph(Surv(y1, cens) ~ 1))  
     hazard time
1 0.3333333    1
2 0.8333333    5
3 1.8333333   14
#
# gives Nelson-Aalen estimator
basehaz(coxph(Surv(y2, cens) ~ 1, method="breslow"))  
     hazard time
1 0.6666667    7
2 1.6666667   14
#
# your preferred option
basehaz(coxph(Surv(y2, cens) ~ 1, method="efron"))  
     hazard time
1 0.8333333    7
2 1.8333333   14

In the big picture, if the method for handling ties makes a big difference for the results of the analyses, then it is probably not very robust.
