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| From | Angelo Belardi <angelo.belardi@unibas.ch> |
| To | "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |
| Subject | Re: R: st: Population attributable fractions (PAFs) in discrete-time survival analysis. -punaf- |
| Date | Wed, 17 Jul 2013 00:20:05 +0200 |
Roger, thanks a lot for the detailed answers and all the effort. After a discussion with my colleagues, I have a few follow-up questions on the subject: A: In your last reply you spoke about Cox regression. Would these statements also apply to hazard models with a non-parametric baseline hazard function (using -cloglog-)? B: We work with person-period formatted datasets we got from reorganising our initial data. Does that have an influence on the results we get out of -punaf- or can the results be interpreted similarly? C: How would the resulting AHFs have to be interpreted? Are they time-independent as suggested by Samuelsen and Eide (2008) in their Equation 4? And could these be interpreted in line with the WHO definition of PAFs, as a "proportional reduction in the hazard ratio"? Best regards and thanks already for any further help Angelo References: - Sven Ove Samuelsen and Geir Egil Eide. 2008. Attributable fractions with survival data. Statistics in Medicine 2008; 27:1447–1467. http://onlinelibrary.wiley.com/doi/10.1002/sim.3022/abstract - WHO definition of population attributable fraction, http://www.who.int/healthinfo/global_burden_disease/metrics_paf/en/index.html Angelo Belardi Ambizione research group (SNSF) Department of Clinical Psychology and Psychiatry University of Basel Missionsstrasse 60/62 CH-4055 Basel, Switzerland Email: angelo.belardi@unibas.ch 2013/7/1 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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/