On May 12, 2011, at 2:19 PM, David Winsemius wrote:


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)

I was doing something else in this session and realized that using 'T' was _not_ a good choice here.

> T == TRUE
[1] FALSE  TRUE FALSE FALSE FALSE

I (almost) always spell out TRUE but not everyone does. Better to use 'sT' or <almost anything else>. (But don't use: c, df, C, F, pi, rm, t, qt, pt, rt, dt,, df, rf, qf, ... )

> rm(T)
> T == TRUE
[1] TRUE

--
David.


> 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

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David Winsemius, MD
West Hartford, CT

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