Nelson-Aalen estimate of hazard

[Navid Asgari]

Hi,

I am struggling with understanding what Stata reports as Nelson-Aalen hazard estimate. This is supposed to be cumulative hazard function. Many papers/manuals that discuss "sts" command also suggest that what is calculated after "sts" is H(t) (i.e., integrated h(t)). However, the documentation of Stata on "sts" is not very clear in this regards.

An example of what Stata does can be seen using the following code:

.use http://www.stata-press.com/data/cggm3/hip2, clear
.sts generate Survival=s
.sts generate Hazard=h

The documentation says the following

h produces the estimated hazard component deltaH_j = H(t_j) - H(t_(j-1)), where t_j is the current failure time and t_(j-1) is the previous one. This is mainly a utility function used to calculate the estimated cumulative hazard H(t_j), yet you can estimate the hazard via a kernel smooth of the deltaH_j; see [ST] sts graph. It is recorded at all the points at which a failure occurs and is computed as d_j/n_j, where d_j is the number of failures occurring at time t_j and n_j is the number at risk at t_j before the occurrence of the failures.

Why is h? Is it value of cumulative function. Is it H(t)-H(t-1)? If so, assuming that delta t in my dataset is 1, does h correspond to hazard rate (i.e., derivative of H(t))?

The same manual introduces s as:

s produces the Kaplan-Meier product-limit estimate of the survivor function or, if adjustfor() is specified, the baseline survivor function from a Cox regression model on the adjustfor() variables.

How about S? Why s is not defined in the same way as h?

Thanks,
Navid