[R] Survival Rate Estimates

[David Winsemius]

On May 12, 2011, at 12:40 PM, Brian McLoone wrote:

> Dear List,
>
> Is there an automated way to use the survival package to generate  
> survival
> rate estimates and their standard errors?  To be clear, *not *the
> survivorship estimates (which are cumulative), but the survival  
> *rate *
> estimates...

Not entirely clear, but from context I suspect you mean instantaneous  
hazard?

(Survival is not a rate but rather a proportion. Mortality can be a  
rate. The instantaneous hazard is the decrement in survival per unit  
time divided by the survival to that time.)

So at each death the non-parametric estimate would divide current  
deaths (often 1 but ties are possible) by time since last death and  
then divide by proportion surviving.

Or if you have a semi-parametric estimated function for survival (such  
as might be output from `basehaz` which calls `survfit`) take:

  -delta_survival/delta_time/survival

tdata <- data.frame(time =c(1,1,1,2,2,2,3,3,3,4,4,4),  
status=rep(c(1,0,2),4), n =c(12,3,2,6,2,4,2,0,2,3,3,5))
fit <- survfit(Surv(time, time, status, type='interval') ~1,  
data=tdata, weight=n)
 > T <- c(0, fit$time)
 > S <- c(1, fit$surv)
 > (-diff(S)/diff(T) )/fit$surv
[1] 0.8602308 0.8247746 0.4044324 1.2115931

I don't know if Therneau's opinion about estimating smoothed hazards  
has changed:
http://finzi.psych.upenn.edu/Rhelp10/2009-March/193104.html
There is also a muhaz package which may generate standard errors for  
its estimates but I have read elsewhere that is does not do Cox models.
http://finzi.psych.upenn.edu/R/library/muhaz/html/00Index.html
--

David Winsemius, MD
West Hartford, CT