Bayesian linear mixed model repeated measurements PROC MCMC

[Clg]

Dear all,

I would like to create a Bayesian linear mixed model for repeated measurements (visits) with a random intercept for subjects.

I have 2 treatments (Placebo and Active). 

I have also interaction between treatment and visits and I would like to add a prior distribution for the placebo effect.

I am using the proc mcmc but I am not sure how to add the prior distribution for the placebo effect. 

I should create one indicator variable for treatment (1=active, 0=placebo) but for which beta I should specify the prior distribution?  Y=B0 + B1*treatment+ B2*Visit + B3*Visit*treatment

Is it for B0 only in this case?

or should I create 2 indicator variables: placebo (1, otherwise 0) and active (1, otherwise 0) and then add the prior distribution for the beta related to placebo indicator variable and for the beta related to the placebo indicator*visit variable?

Thank you in advance,

Best regards,

Clemence

[SAS_Rob]

Unless I am misunderstanding something, it would not be possible to have the placebo effect be defined by a single parameter, regardless of how you parameterize the model, because you are including it in the interaction.

It may also be easier to fit this model in Proc BGLIMM than Proc MCMC as well.  There is an example similar to what you are doing in the BGLIMM documentation.

SAS Help Center: Normal Regression with Repeated Measurements

[Clg]

Thank you for your reply. The example in a first step but I would like in additon specify a prior distribution for the placebo group (only). And we do not have this in the example of the SAS documentation attached with proc bglimm. 

Best regards

[SAS_Rob]

A point of clarification might help.  Typically, we refer to prior distributions of parameters and not of effects.  When an effect can be measured by a single parameter (like in a main effects only model) then these terms could be used somewhat interchangeably.  When you have an interaction, there is not a single parameter that captures the effect and so you cannot use the terms in that manner.  

More to the point, the model you are fitting assumes that there is not a single treatment effect, but instead the effect depends upon the visit number.  Thus there is not a single effect.