Notice: On April 23, 2014, Statalist moved from an email list to a forum, based at statalist.org.
| From | Angelo Belardi <angelo.belardi@unibas.ch> |
| To | "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |
| Subject | R: st: Population attributable fractions (PAFs) in discrete-time survival analysis. -punaf- |
| Date | Mon, 5 Aug 2013 10:33:47 +0100 |
Thanks again for your precise answers. I have now tried to run -punaf- after my -cloglog- analyses. However, -punaf- encountered a problem. The error message that comes up is: "expression (log(_b[_cons])) evaluates to missing". I assume that this might be connected to my use of the -noconstant- option in the -cloglog- commands. For analyses where the calculations are possible to run without the -nocons- option, -punaf- also gives me reasonable results and no error message. However, from what I know I have to use this option because of my fully non-parametric baseline hazard function. Is it possible that -punaf- has a problem with that or might the error be due to something else? How could I solve this issue? Best regards, Angelo 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 2013/7/21 Roger B. Newson <r.newson@imperial.ac.uk> > In reply to Angelo's queries: > > 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). > > B. If you are working with a dataset with 1 observation per person per period, and the outcome variable is binary, then you should use an estimation command that allows for the clustering of person-periods by persons. For instance, you might use -xtgee-, or you might use -logit-, -logistic-, or -cloglog- with an option like -vce(cluster person)-. The interpretation of the population unattributable and attributable fractions will then be the same as when -punaf- is used after binary data. That is to say, the PAF (or PUF) will be the fraction of the binary outcomes equal to 1 that is attributable (or unattributable) to living in Scenario 0 instead of Scenario 1. > > C. The WHO definition of a PAF is an extremely simple special case of the -punaf- definition of a PAF, for the special case of a binary outcome variable, a discrete-valued exposure variable with n levels, and no concomitant (or confounder) variables. And the WHO also assumes that "Scenario 0" is the real world that we live in, and that "Scenario 1" is a user-specified ideal scenario (eg a dream scenario where the whole world stopped smoking, or a dream scenario where the current smokers become ex-smokers, or a more realistic dream scenario where only a proportion of the current smokers quit smoking). The P_i specified by the WHO are the proportions of the population at the i'th exposure level in the real world (Scenario 0). And the P'_i are the proportions of the population that would have the i'th exposure level in the dream scenario (Scenario 1). And the RR_i are the relative risks (ie rate ratios) associated with the comparing the ith exposure level to the lowest exposu! re level. So, the -punaf- definition is a generalization of the WHO definition. There seems to be some controversy about how best to generalize the concept of a PAF (or a PUF) to the case of a Cox regression. (At least, I had a different idea from Samuelson and Eide.) > > > 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 16/07/2013 23:20, Angelo Belardi wrote: >> >> 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/ >> > * > * 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/ * * 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/