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

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

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

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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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