Difference between typical values and geometric mean of posthoc values

From: "Eleveld, DJ" d.j.eleveld@anest.umcg.nl Subject: [NMusers] Difference between typical values and geometric mean of posthoc values Date: Wed, March 30, 2005 5:54 am Hello everyone, Many thanks for all those who reacted to my question about the difference between the typical (theta) values and the geometric mean of the posthoc values. The comments seemed to have three main points: 1) The underlying data might not really be log-normal distributed 2) The sample being fitted will have sampling-error (I think thats what its called) 3) The thetas are the 'most-probable values', not the geometric mean The data I have been fitting comes from monte-carlo simulation so the parameters are really log-normally distributed. So 1) does not apply in this case. I see the point that this would definetly be applicable when fitting 'real' measured data (i.e. not simulated data). I think sampling error has been handeled as well as i can. The monte-carlo simulations are fittings of 10 simulated data sets from a 3 compartment PK model. The fitting are repeated 100 times, each time with different underlying PK parameters. If the difference between the typical values and the geometric mean of the posthoc values is a result of sampling-error then one would expect an 'on average' difference between these values to be zero. For one of the model parameters (CL) there is a 10% difference. This seems to me to be unusually large to be just 'random'. I'm not sure what exactly the difference is between the 'most-probable' values and the geometric mean. I thought that 'most-probable' value would be the maximum-likelihood value and that the maximum likelihood value and the geometric mean are the same for a log-normal distribution, although I dont have a definition handy. I'll try to find out this for sure. I remember reading that nonmem uses a linearization technique for estimation. Could this result in the bias i am seeing? Might LAPLACIAN make a difference here? Thank you very much for your replies, Doug Eleveld Just to check that I havent made any obvious errors the control stream is: $PROB Test fitting $DATA mcra.dat IGNORE=C $INPUT ID TIME WGT AMT RATE DV $SUBROUTINES ADVAN11 TRANS4 $PK V1=THETA(1)*EXP(ETA(1)) V2=THETA(2)*EXP(ETA(2)) V3=THETA(3)*EXP(ETA(3)) CL=THETA(4)*EXP(ETA(4)) Q3=THETA(6)*EXP(ETA(6)) Q2=(THETA(2)*(THETA(6)/THETA(3) + THETA(5)))*EXP(ETA(5)) S1=V1 $ERROR Y=F*EXP(ERR(1)) ; Starting at the exact values $THETA (0, 3.64)(0, 3.01)(0, 6.44)(0, 0.51)(0, 0.048)(0, 0.051) $OMEGA 0.0533 0.1217 0.1063 0.1245 0.2215 0.0650 $SIGMA 0.01 ;SIGMA 0.04 Some (12, 37, 44, 49, 54, 71, 84, 92) used this to get convergence $ESTIMATION MAX=9999 SIG=6 METHOD=COND NOABORT POSTHOC $TABLE TIME V1 V2 V3 CL Q2 Q3 DV $SCATTER PRED VS DV UNIT