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

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

I said it is a goof idea to use -punaf- after -cloglog-, but probably 
not a good idea to use -punafcc- after -cloglog-. This is because, in a 
cohort or cross-sectional study, or even in a discrete-time survival 
analysis, we want to estimate a PUF (ie a between-scenario ratio between 
means, which includes proportions), and subtract it and its confidence 
limits from 1 to get a CI for a PAF. The Greenland-Drescher PUF in a 
case-control study, or my definition of a PUF for continuous-time 
survival data modelled using Cox regression, is a mean ratio (eg a mean 
odds ratio for cases or a mean hazard ratio for deaths), which is not 
the same thing as a ratio between means. So, if you wanted a ratio 
between means, then you should use -punaf- (which estimates ratios 
between means), and not -punafcc- (which estimates mean ratios).

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/popgenetics/reph/

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

On 22/07/2013 10:43, S.Jenkins@lse.ac.uk wrote:
> As part of his reply to Angelo Belardi <angelo.belardi@unibas.ch>,
> Roger Newson <r.newson@imperial.ac.uk> wrote:
>
> > A. You can indeed use -punaf- after -cloglog-. (Or you should be able to
> > do so - let me know if you have any problems.) However, the
> > interpretation of the attributable and unattributable fractions will
> > then be similar to the interpretation of these parameters when you use
> > - -punaf- after -logit- or -logistic-. It is probably not a good idea to
> > use -punafcc- after -cloglog-. And -punafcc- should probably not be used
> > after -logit- or -logistic-, except if your data are from a case-control
> > study (for which -punafcc- was written). After a Cox regression, you may
> > use either -punaf- or -punafcc-, depending on what kind of population
> > unattributable and attributable fractions you wanted to estimate (ie my
> > kind or Samuelson and Eider's kind).
>
> My understanding is that Angelo is using -cloglog- to fit the discrete-time  proportional hazard model, i.e. the analogue of the Cox model - which is for continuous survival times -- for interval -censored survival time data. The estimated coefficients on the predictors from the -cloglog- model are exactly the coefficients from the underlying continuous time model, and exp(coeff) is the corresponding hazard ratio.
> Given this context, why is it not a good idea to use -punaf- after -cloglog-? Could you please clarify?
>
> Stephen
> ------------------
> Stephen P. Jenkins <s.jenkins@lse.ac.uk>
>
> Please access the attached hyperlink for an important electronic communications disclaimer: http://lse.ac.uk/emailDisclaimer
>
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