MU referencing

Hi all, When using MU referencing, how do I code the situation where the typical value appears to be the same between two groups, but one group is more variable - how do I give these two groups different ETAs but essentially the same THETA? Is this legit? tvParam=THETA(.) MU_1=tvParam MU_2=tvParam Param1=MU_1+ETA(1) Param2=MU_2+ETA(2) Param=Param1*G1+Param2*G2 Where G1 and G2 equal 0 or 1 based on which group the subject belongs. Thanks for the advice, Brendan

Hi Brendan, I think the version that you presented does not follow the rules. I would try this: MU_1=THETA(1) MU_2=0 Param1 = EXP(MU_1+ETA(1)) Param2 = EXP(MU_2+ETA(2)) Param = Param1*Param2**G2 where G2 = 0 (population 1) or 1 (population 2) This is another (equivalent) option: MU_1=THETA(1) Param1 = EXP(MU_1+ETA(1)) Param = Param1*EXP(ETA(2)*G2) I would also try correlated ETA(1) and ETA(2), and I wonder whether they will be estimated as collinear. Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566

Hi, Could we modify the inter-occasion variability example (example. # 7 in the intro7 guide with NM7.1 installation) to inter-group situation ? MU_1=THETA(1) TVPAR = EXP(MU_1+ETA(1)) ; fix ETA(1) to a small value ? GRP0 = EXP(ETA(2)) GRP1 = EXP(ETA(3)) IF (GRP.EQ.0) GRPETA = GRP0 IF (GRP.EQ.1) GRPETA = GRP1 Param = TVPAR*GRPETA Thanks Navin Goyal

There is another theoretical issue - constraining two parameters to have the same mean (tvParam) but different etas (ETA(1) and ETA(2)) violates the fundamental assumption of MCPEM-like method that the parameters are multivariate normal. The basic update formula for the fixed effects based on the means of the posteriors for the random effects is no longer valid. For example, in a standard formulation the mean of the posteriors over all subjects must be zero (this is the basic EM first order stationarity condition for the derivative of the log likelihood function ). But if you have two different means associated with the same eta, both means in general cannot both be simultaneously zero.. It is unclear if MCPEM will converge under these conditions, and even if it does, there is no guarantee that the point corresponds to maximum likelihood.