Re: R: st: Population attributable fractions (PAFs) in discrete-time survival analysis. -punaf-

["Roger B. Newson" <r.newson@imperial.ac.uk>]

PS I have had a look at the Sauelsen and Eide paper, and would like to 
make a minor correction. The AHF of Equation 4 looks like the PAF that 
you would get by using -punaf- after a Cox regression, and is equal (in 
their notation) to

AHF = 1 - E[exp(beta'Z*)]/E[exp(beta'Z)]

where Z is the covariate vector in the real-world scenario, and Z* is 
the covariate vector in the fantasy-intervention scenario. If you use 
-punafcc- after a Cox regression, then you should instead get

PAF = 1 - E[exp(beta'Z*)/exp(beta'Z)]

which is not exactly the same thing. However, whichever formula we use, 
we should probably use the option -vce(unconditional)- if we use it 
after a Cox regression, because the covariates at the time of each death 
are subject to sampling error.

Best wishes

Roger

Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

Opinions expressed are those of the author, not of the institution.

On 01/07/2013 13:09, Roger B. Newson wrote:
> Thanks to Carlo for this reference. Yes, the attributable hazard
> fraction (AHF) in Equation (4) of Samuelsen and Eide (2008) is the same
> as the population attributable fraction (PAF) produced by -punafcc-
> after using -stcox-. The confidence interval formulas are a little
> different. Samuelson and Eide use the percentile bootstrap, whereas the
> online help for -punafcc- recommends the user to use Shah variances by
> specifying the option -vce(unconditional)-. You could presumably write a
> program to use the percentile bootstrap with -punafcc-, though.
>
> Best wishes
>
> Roger
>
> References
>
> Sven Ove Samuelsen and Geir Egil Eide. 2008. Attributable fractions with
> survival data. Statistics in Medicine 2008; 27:1447–1467.
>
> Roger B Newson BSc MSc DPhil
> Lecturer in Medical Statistics
> Respiratory Epidemiology and Public Health Group
> National Heart and Lung Institute
> Imperial College London
> Royal Brompton Campus
> Room 33, Emmanuel Kaye Building
> 1B Manresa Road
> London SW3 6LR
> UNITED KINGDOM
> Tel: +44 (0)20 7352 8121 ext 3381
> Fax: +44 (0)20 7351 8322
> Email: r.newson@imperial.ac.uk
> Web page: http://www.imperial.ac.uk/nhli/r.newson/
> Departmental Web page:
> http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/
>
>
> Opinions expressed are those of the author, not of the institution.
>
> On 01/07/2013 12:21, Carlo Lazzaro wrote:
> > I suppose that Angelo refers to the following reference (access to the
> > full
> > text conditional on subscription to Stat Med):
> >
> > Samuelsen SO, Eide GE. Attributable fractions with survival data. Stat
> > Med.
> > 2008 Apr 30;27(9):1447-67.
> >
> > Kind regards,
> > Carlo
> > -----Messaggio originale-----
> > Da: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Roger B.
> > Newson
> > Inviato: lunedì 1 luglio 2013 12:57
> > A: statalist@hsphsun2.harvard.edu
> > Oggetto: Re: st: Population attributable fractions (PAFs) in
> > discrete-time
> > survival analysis. -punaf-
> >
> > Yes, you can use -punaf- after a generalized linear model (GLM) with a
> > complementary log-log link and a binomial error function. Or after any
> > other
> > GLM that gives positive-valued conditional expectations (which includes
> > proportions and also Gamma and inverse-Gaussian means).
> >
> > For proportional-hazard models (and also for case-control data), there
> > is a
> > package -punafcc-, which you can also download from SSC, and which
> > estimates
> > population attributable hazard factions (after proportional-hazard
> > regressions), or population attributable fractions (after logit
> > regressions
> > on case-control data).
> >
> > Angelo has not given the Samuelsen & Eide (2008) reference on PAHFs in
> > full.
> > However, I would guess that the PAHFs of that reference would be
> > either the
> > same as, or similar to, those produced by -punafcc-. I would very much
> > like
> > to know the full reference, so I can read it and find out more.
> >
> > I hope this helps.
> >
> > Best wishes
> >
> > Roger
> >
> > Roger B Newson BSc MSc DPhil
> > Lecturer in Medical Statistics
> > Respiratory Epidemiology and Public Health Group National Heart and Lung
> > Institute Imperial College London Royal Brompton Campus Room 33, Emmanuel
> > Kaye Building 1B Manresa Road London SW3 6LR UNITED KINGDOM
> > Tel: +44 (0)20 7352 8121 ext 3381
> > Fax: +44 (0)20 7351 8322
> > Email: r.newson@imperial.ac.uk
> > Web page: http://www.imperial.ac.uk/nhli/r.newson/
> > Departmental Web page:
> > http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgene
> >
> > tics/reph/
> >
> > Opinions expressed are those of the author, not of the institution.
> >
> > On 01/07/2013 00:13, Angelo Belardi wrote:
> > > Dear All,
> > >
> > > I am working on discrete-time proportional hazard models with a
> > > non-parametric baseline hazard function, using -cloglog- in
> > > person-period formatted datasets.
> > >
> > > I would like to additionally calculate population attributable
> > > fractions (PAFs) in these models.
> > > However, I have never worked with PAFs in survival analyses before and
> > > therefore don't know which functions to use and how to correctly
> > > interpret the results.
> > >
> > > Previously, I calculated PAFs in STATA with the -punaf- package from
> > > Roger Newson, e.g.
> > > for logistic regressions.
> > >
> > > Can I use -punaf- here as well, just after calculating the estimates
> > > over -cloglog-?
> > >
> > > Or is there another function/package for this situation?
> > >
> > > Or would it be better to calculate population attributable hazard
> > > fractions (PAHFs) as described in Samuelsen & Eide (2008)?
> > >
> > >
> > > Thanks for any help or advice on the subject.
> > >
> > > Regards,
> > > Angelo
> > >
> > >
> > > Ref:
> > > S. O. Samuelsen, G. E. Eide, Statist. Med. 27, 1447 (2008).
> > > http://onlinelibrary.wiley.com/doi/10.1002/sim.3022/abstract
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