Re: inclusion of covariates with $PRIOR
Dear Anna,
The times I have used SCM in combination with a frequentist prior, it has been
only to test if a new population is different (i.e. the data used to generate
the prior were all of a different population, e.g. healthy volunteers and other
indications than the currently-investigated population.
Or something similar where the covariate value is a nominal level which was not
present in the data used to generate the prior).
To use SCM in combination with NWPRI in that situation is straightforward.
With regards to your first question. If you use a prior only to support the
estimation of this specific covariate coefficient (no prior on other
parameters), then you do not need to center around the same covariate value.
The point estimate for the covariate coefficient will be the same, regardless
of how you center these covariate models (but standard errors, correlation
between estimates and the covariance matrix as a whole will be different
depending on how you center).
However, with prior across all model parameters, it would be important to
center across the same covariate value, since the population typical value is
with regards to this (e.g. the population typical clearance for a subject with
70 kg body weight).
Maybe this is what Gisleskog et al. were referring to?
With regards to model selection with a prior on all available parameters this
is not as straightforward.
If your prior is a full model (including all covariates that you want to test
in SCM), then in principle using prior on all fixed effects would be possible.
But due to correlation between the estimates in your prior you could end up
leaving a covariate out of the model, in a way that would not have happened in
a combined analysis.
An alternative may be to have separate priors for each model you test, but I do
not think there is any automated software to support that procedure.
If you have access to the data used to generate the prior, it may be easier to
combine all data, rather than using a frequentist prior.
I suspect this is not possible in your case, since you ask these questions?
Best regards
Jakob
Jakob Ribbing, Ph.D.
Senior Consultant, Pharmetheus AB
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