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Re: st: RE: Survival analysis - individual survival functions

From (Roberto G. Gutierrez, StataCorp)
Subject   Re: st: RE: Survival analysis - individual survival functions
Date   Thu, 16 Dec 2010 15:45:40 -0600

Paul Seed <> asks:

> Following a parametric survival regression, I can use -predict- with the
> -surv- option to get the survival function; but I only do not seem to have
> any choice over when it is calculated for.

> The help file promises me values for S(t|t_0), and I would like to set both
> t and t_0 myself.  But they seem to be set automatically, at the time of
> entry and exit of the subject.

> Is there a simple way of doing this?  If not, is there any chance of it
> being included in a future version of Stata?

Paul has received some good advice on alternatives to doing this directly, 
but doing it directly is possible by manipulating the variables that -predict-
uses to calculate S(t|t_0).  Of course, when you do this you have to be
careful to put everything back in place when you are done.

To illustrate, we fit a Weibull model on the cancer data that ships with
Stata, and we use one covariate, -age-

    . sysuse cancer, clear
    . streg age, dist(weibull)

The time variables that -predict- uses to predict the survival function are
stored in variables _t and _t0, as established by -stset-.  We proceed by
making back up versions of these variables.  We'll also back up -age- since we
want to set this at a fixed value for the predictions, too.

    . gen age_old = age
    . gen t_old = _t
    . gen t0_old = _t0

Once backed up, we are free to manipulate these.  We begin by resetting _t to
an evenly-spaced grid from 0 to 20

    . drop _t
    . range _t 0 20

Then we replace _t0 to be zero everywhere (it probably already is as this is a
simple dataset, but we do it anyway), and we set -age- to be 75 so that the 
corresponding survival prediction is for someone aged 75

    . replace _t0 = 0
    . replace age = 75

We can now predict S(t|_t0) for -age == 75- and at the time values as manually

    . predict s, surv
    . list _t0 _t s

Of course, remember to put everything back in place

    . replace age = age_old
    . replace _t = t_old
    . replace _t0 = t0_old

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