Parametric vs Semi-parametric survival in prediction models

[Pedro Emmanuel Alvarenga Americano do Brasil]

Statistical masters,

 

Im looking for a reading, as breif as possible, about how to decide wether using paramentric or semi-parametric survival models when the objective is to develop a prediction model. 

 

I did read Steynberg's book it seems the parametric models are always prefereble... but if this is true, why cox is more popular?

Also, he makes a little comparison concerning only the models that assumes praportionality and additivity. But it is not clear to me in what situations parametric models can not be used or cox are prefereble.

 

I did look for an answer in two books around here but they were not clear enough! So far I guess assuming time distribution is such a guess that non parametric is 'safer' ... or fitting several parametric and semi-paramentric models to check which one fits better is so time consuming that using a "more general recipe" will work fine more often!  

 

Kind regards and happy hollidays,
--
Abraço forte e que a força esteja com você,

Dr. Pedro Emmanuel A. A. do Brasil
Instituto de Pesquisa Clínica Evandro Chagas
Fundação Oswaldo Cruz
Rio de Janeiro - Brasil

[Martin Holt]

Dear Dr. Pedro Emmanuel Alvarenga Americano do Brasil,

 

Maybe the following might help:

 

http://www.mail-archive.com/nmu...@globomaxnm.com/msg00398.html

 

It is a mailing list discussing the choice between parametric and semi-parametric approaches.

 

HTH,

 

Martin Holt

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[Steve Simon, P.Mean Consulting]

Pedro Emmanuel Alvarenga Americano do Brasil wrote:

> Im looking for a reading, as breif as possible, about how to decide
> wether using paramentric or semi-parametric survival models when the
> objective is to develop a prediction model.
>
> I did read Steynberg's book it seems the parametric models are always
> prefereble... but if this is true, why cox is more popular?
> Also, he makes a little comparison concerning only the models that
> assumes praportionality and additivity. But it is not clear to me in
> what situations parametric models can not be used or cox are prefereble.
>
> I did look for an answer in two books around here but they were not
> clear enough! So far I guess assuming time distribution is such a guess
> that non parametric is 'safer' ... or fitting several parametric and
> semi-paramentric models to check which one fits better is so time
> consuming that using a "more general recipe" will work fine more often!

This is a very difficult question to answer. There are others on this
list who can offer a more authoritative response, but let me share what
little I know.

It's not quite what you want, but there is a review article in JASA:

The Price of Kaplan-Meier. Meier P, Karrison T, Chappell R, Xie H.
Journal of the American Statistical Association 2004: 99(467); 890-896.

This article refers to another article by Rupert Miller published in
1983 with the provocative title "What Price Kaplan-Meier?".

Kaplan-Meier and Cox regression are not the same, but both do not rely
on parametric assumptions and thus pay a "price" relative to a correctly
specified parametric model.

Cox regression is popular because it is (a) easy and (b) (as you noted)
safe. By "safe" I mean "more likely to satisfy the underlying
assumptions than a parametric model". It's harder to make an
unsupportable assumption with Cox regression.

A parametric model allows you to incorporate Bayesian priors. I don't
think you can fit a Bayesian form of Cox regression, but I could be
wrong. Parametric models offer various goodness of fit measures that can
avoid some of the problems with unsupportable assumptions.

Frank Harrell gave a nice web seminar a few months ago about this issue,
but I missed it so can't share his perspective on the issue. The handout
from the webinar is at

http://www.biopharmnet.com/doc/2009_04_03_webinar.pdf

Since there is no strong consensus in the research community, you can
use either approach and get published. I also suspect that the
differences between the parametric and non-parametric models are small
in a practical sense, but can't offer any data to support this hunch. In
general, though, I think the research community focuses too much
attention on data analysis issues and not enough on data collection
issues. After all, if you collect the wrong data, it doesn't matter how
fancy your analysis is.

I hope this helps.
--
Steve Simon, Standard Disclaimer
"The first three steps in a descriptive
data analysis, with examples in PASW/SPSS"
Thursday, January 21, 2010, 11am-noon, CST.
Details at www.pmean.com/webinars

[Frank Harrell]

Steve,

A Bayesian Cox model is possible using a Poisson trick detailed in the
BUGS Example Guides.

Kaplan-Meier or Cox survival estimates are just as efficient as
parametric ones if you have to try more than 2 parametric models to
get an adequate fit. This is because of model uncertainty. Apparent
variances of parametric estimates will be smaller but actual variances
are not, unless you pre-specify the model and you're correct.

Frank

On Dec 23, 11:22 am, "Steve Simon, P.Mean Consulting" <n...@pmean.com>
wrote:

[BXC (Bendix Carstensen)]

The Poisson trick is the piecewise constant hazards assumption, that not only allows a Bayesian set up, but also allows multiple time-scales (such as: Mortality depends on current age and disease duration...). Moreover, it lets you estimate hazards as simple parametric functions directly, using only standard software. Taken ad absurdum (the pieces of constant hazard getting smaller and smaller) the Poisson trick gets you to the Cox-model, see: Carstensen, B: Demography and epidemiology: Practical use of the Lexis diagram in the computer age or: Who needs the Cox-model anyway? http://biostat.ku.dk/reports/2006/rr-06-2.pdf/

Bendix Carstensen

> -----Original Message-----
> From: meds...@googlegroups.com
> [mailto:meds...@googlegroups.com] On Behalf Of Frank Harrell
> Sent: 23. december 2009 22:02
> To: MedStats
> Subject: Re: {MEDSTATS} Parametric vs Semi-parametric
> survival in prediction models
>