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

["Irwin T.S. Wang" <irwintswang@gmail.com>]

Paul,

Thanks for your information as well. As you pointed out, fitting a
model after using -stsplit, at(failures)- on a large data set becomes
very slow. I will try your -stmp2 suggestion.
Thanks again for your help.

TS

On Tue, Nov 9, 2010 at 9:21 AM, Lambert, Paul C. (Dr.)
<pl4@leicester.ac.uk> wrote:
> *
> 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).
>
>
> clear
> 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)
>
>
> Paul
>
>
> 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: paul.lambert@le.ac.uk
> Homepage: http://www2.le.ac.uk/Members/pl4/
> ________________________________________
> From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] On Behalf Of Wei-Kang Shih [wkshih@gmail.com]
> Sent: Tuesday, November 09, 2010 1:46 PM
> To: statalist@hsphsun2.harvard.edu
> 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.
>
> TS
>
> On Tue, Nov 9, 2010 at 3:29 AM, Maarten buis <maartenbuis@yahoo.co.uk> 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:
>> http://www.maartenbuis.nl/example_faq )
>>
>> Hope this helps,
>> Maarten
>>
>> --------------------------
>> Maarten L. Buis
>> Institut fuer Soziologie
>> Universitaet Tuebingen
>> Wilhelmstrasse 36
>> 72074 Tuebingen
>> Germany
>>
>> http://www.maartenbuis.nl
>> --------------------------
>>
>>
>>
>>
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