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RE: st: Question about Baseline Hazard in Parametric Hazard Models

From   "Lambert, Paul C. (Dr.)" <[email protected]>
To   "[email protected]" <[email protected]>
Subject   RE: st: Question about Baseline Hazard in Parametric Hazard Models
Date   Tue, 9 Nov 2010 14:21:04 +0000

I think Maarten  needs to add an -stsplit- to his code before generating the polynomals, i.e.

sysuse cancer, clear
gen id = _n
stset studytime, failure(died) id(id)
stsplit, at(failures) 
orthpoly _t, gen(t*) degree(3)
streg t*, dist(exp)

However, I agree with both Maarten and Steve that polynomials are not a good way to model the hazard function. Restricted cubic splines are a useful alternative and you could calulate splines rather than polynomials in the above example. However, fitting a model after using -stsplit, at(failures)- on a large data set becomes paintfully slow. If you want to use splines and not have to use -stsplit- then you can use -stpm2- (available from SSC), which models on the log cumulative hazard scale. Below is an example of estimating a hazard function which has a turning point using a restriced cubic splines with 4 knots (3 df).

webuse brcancer
stset rectime, f(censrec=1) scale(365.25) exit(time 5*365.25) id(id)
stpm2, scale(hazard) df(3) 
predict h, hazard ci
twoway (rarea h_lci h_uci _t, sort pstyle(ci)) (line h  _t, sort)


Dr Paul C Lambert
Reader in Medical Statistics
Centre for Biostatistics & Genetic Epidemiology
Department of Health Sciences
University of Leicester
2nd Floor, Adrian Building
University Road
Leicester LE1 7RH
Tel: +44 (0)116 229 7265, Fax: +44 (0)116 229 7250
e-mail: [email protected]
From: [email protected] [[email protected]] On Behalf Of Wei-Kang Shih [[email protected]]
Sent: Tuesday, November 09, 2010 1:46 PM
To: [email protected]
Subject: Re: st: Question about Baseline Hazard in Parametric Hazard Models

Marrten and Steven,

Thank you both for your suggestions. And yes, the reason I want to
impose a third polynomial baseline hazard is to reproduce some work
done by others. I will try both your suggestion to see what I can get.

Thanks so much again.


On Tue, Nov 9, 2010 at 3:29 AM, Maarten buis <[email protected]> wrote:
> --- On Nov 8, 2010, at 5:33 PM, Irwin T.S. Wang wrote:
>> > I would like to specify/estimate a baseline hazard
>> > function, which is not among the distribution provided
>> > by Stata, e.g. exponential, Gompertz, in a Proportional
>> > Hazard (PH) models. For example, I want to restrict the
>> > shape of the the baseline hazard to a third degree
>> > polynomial in time
> --- On Tue, 9/11/10, Steven Samuels wrote:
>> Two suggestions:  1) -stpm2- from SSC, which uses
>> restricted cubic splines; and 2) -stcox-, followed by
>> -stcurve-, which will smooth the Cox baseline hazard. I
>> recommend against third degree polynomials, because they can
>> curve up or down at the ends unpredictably and implausibly.
> Another option you could investigate is a piecewise constant
> model, see -ssc d stpiece-.
> I agree with Steven that such a polynomial would often impose
> too much unrealistic structure on your baseline hazard. The
> only reason I can imagine why you would want use the cubic
> polynomial baseline hazard would be when you want to reproduce
> an analysis made by someone else who used that baseline hazard
> (typically to follow that with a "better" analysis to show
> that they were wrong...). If that is what you want to do, then
> below is an example of how to do that (I used -orthpoly- to
> avoid problems with colinearity):
> *-------- begin example ---------
> sysuse cancer, clear
> stset studytime, failure(died)
> orthpoly _t, gen(t*) degree(3)
> streg t*, dist(exp)
> *--------- end example ----------
> (For more on examples I sent to the Statalist see:
> )
> Hope this helps,
> Maarten
> --------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
> --------------------------
> *
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