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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 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
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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.]
Professor Stephen Duffull
Chair of Clinical Pharmacy
School of Pharmacy
University of Otago
PO Box 56 Dunedin
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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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