PharmPK Discussion - a priori and a posteriori

• On 29 Jul 2013 at 20:32:01, Roger W. Jelliffe sent the message
  

  
  Dear Steve:
  
  In your communication to Xinting on July 24, You said that a priori covariate models were developed
  from data usually by others, for example, allometric scaling, and Cockcroft-Gault for CCr, etc. OK.
  But then you said “A posteriori covariate models are derived based on your data only to provide the
  best fit for your current data set”.
  Did you mean this literally? I don’t think so, as anything a posteriori would presumably have a
  Bayesian prior beforehand. It sounds more like least-squares regression to me, and I know you too
  well to think you really meant that.  Yes – your individual data set, after a Bayesian prior
  covariate model, would result in an aposteriori covariate model, I think.
  All the best,
  Roger
  
  Roger W. Jelliffe, M.D., F.C.P., F.A.A.C.P.
  Professor of Medicine Emeritus,
  Founder and Director Emeritus
  Laboratory of Applied Pharmacokinetics
  USC School of Medicine
  Consultant in Infectious Diseases,
  Children’s Hospital of Los Angeles
  4650 Sunset Blvd, MS 51
  Los Angeles CA 90027
  Jelliffe.at.usc.edu
  www.lapk.org
  
  

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• On 29 Jul 2013 at 23:20:11, Stephen Duffull sent the message
  

  
  Hi Roger
  
  Thank you for keeping me honest...
  
  You said: "OK. But then you said “A posteriori covariate models are derived based on your data only
  to provide the best fit for your current data set”.
                Did you mean this literally? I don’t think so, as anything a posteriori would
  presumably have a Bayesian prior beforehand."
  
  If your Bayesian prior was uninformative, for instance, and hence no particular covariate
  representation carried any more weight than any other (for instance wearing glasses was considered
  to be equally important a covariate as CLCr) then the data would dominate the prior and the Bayesian
  approach would be equivalent to a likelihood based approach, then I think this would be reasonable
  to call this an a posteriori covariate model approach.
  
  Admittedly when I wrote the email I was intending this as a conceptual framework rather than a
  formal one - but it still works for me.  Obviously if you have a strong prior on a particular model
  but still update the parameters then this is subjective Bayesian and doesn't fit into my framework
  above which I think is your point.
  
  So to recast my framework we could suggest:
  A priori covariate models (where current data will not change your opinion)
  Subjective a posteriori covariate models (where current data may update your opinion)
  Objective a posteriori covariate models (where only current data is used to form your opinion)
  
  [If we use a Maximum A Posteriori (MAP) then objective a posteriori covariate models are equivalent
  to maximum likelihood based models.]
  
  Regards
  
  Steve
  --
  Professor Stephen Duffull
  Chair of Clinical Pharmacy
  School of Pharmacy
  University of Otago
  PO Box 56 Dunedin
  New Zealand
  E: stephen.duffull.-a-.otago.ac.nz
  
  

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• On 31 Jul 2013 at 09:33:56, A.J. Rossini sent the message
  

  
  Actually, I would have taken a general view of this subject from how you describe it, Roger.
  Ignore the Bayesian/non-bayesian use of prior probabilities and posterior probabilities, and think
  about a-priori models where the form is precisely prespecified and , and a-posteriori models as
  those where there is a bit of data-driven model fitting.   ie, the decision on the appropriate model
  comes after (a-posteriori) rather than before (a-priori).
  
  Even for frequentist approaches, this holds.
  
  

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