NONMEM Analysis for Future Bayesian Estimation

I'm trying to work through the cycle of analyzing clinical data (as for an aminoglycoside) using a one compartment model with elimination rate described by: kel = a * CR-CL + b and V with the intent of being able to use the results for Bayesian analysis of future data. My understanding is that I would like to calculate population mean and standard deviation values for 'a', 'b', and V. Thus I simulated 256 data sets (one dose and two data points per set) and analyzed the combined data using NONMEM. Model: One compartment model with a one hour infusion. 256 data set generated One time point between 1.25 and 2.5 and one time point between 6 and 12 hours. Model parameters used for the simulation CR-Cl = 65 +/- 20 (std.dev.) between 5 - 125 kel = a*CR-Cl + b a = 0.005 +/- 10 % (c.v.) between 0.0001 - 0.1 b = 0.01 +/- 20 % (c.v.) between 0.0001 - 1.0 V = 15 +/- 5 % (c.v) between 1 - 200 Data for first 5 subjects... 1 90 90 0.0 0.0 69.16 1 0.0 0.0 1.75 3.44664 69.16 1 0.0 0.0 9.00 0.27351 69.16 2 60 60 0.0 0.0 67.25 2 0.0 0.0 2.00 2.64588 67.25 2 0.0 0.0 8.00 0.35496 67.25 3 60 60 0.0 0.0 113.72 3 0.0 0.0 2.50 1.34226 113.72 3 0.0 0.0 8.00 0.06132 113.72 4 50 50 0.0 0.0 74.7 4 0.0 0.0 1.75 1.78155 74.7 4 0.0 0.0 9.00 0.05505 74.7 5 60 60 0.0 0.0 22.85 5 0.0 0.0 2.00 3.2508 22.85 5 0.0 0.0 6.00 2.38014 22.85 ...... My first attempt was to include ETA's for both the 'a' and 'b' values. Thus after analysis I could include these in the Bayesian analysis. The control file and the (some) output are below: NONMEM control file > nmtran > nonmem $PROBLEM Aminoglycoside example $INPUT ID AMT RATE TIME DV CRCL $DATA TEST $SUBROUTINES ADVAN1 $PK TA = THETA(1)*(1.+ETA(1)) TB = THETA(2)*(1.+ETA(2)) K = TA*CRCL + TB V = THETA(3)*(1.+ETA(3)) S1 = V $ERROR Y = F*(1. + ERR(1)) $THETA (0.,.005,0.1) (0.,.01,1.0) (1,15,100) $OMEGA .2 .2 .2 $SIGMA .2 $ESTIMATION PRINT=5 MAXEVALS=900 $COVARIANCE $TABLE ID TIME AMT DV $SCAT PRED VS DV UNIT $SCAT WRES VS DV TIME CRCL Partial output from NONMEM *** MINIMUM VALUE OF OBJECTIVE FUNCTION *** -1266.431 *** FINAL PARAMETER ESTIMATE THETA - VECTOR OF FIXED EFFECTS ********************* TH 1 TH 2 TH 3 4.93E-03 8.75E-03 1.50E+01 OMEGA - COV MATRIX FOR RANDOM EFFECTS - ETAS ******** ETA1 ETA2 ETA3 ETA1 9.29E-03 ETA2 0.00E+00 1.54E-08 ETA3 0.00E+00 0.00E+00 3.02E-03 SIGMA - COV MATRIX FOR RANDOM EFFECTS - EPSILONS **** EPS1 EPS1 5.06E-03 This gives: Theta(1) = a = 4.93E-03 +/- 9.64 % sqrt(9.29E-03) * 100 Theta(2) = b = 8.75E-03 +/- 0.0124 % sqrt(1.54E-08) * 100 Theta(3) = V = 15.0 +/- 5.50 % sqrt(3.02E-03) * 100 Data = +/- 7.11 % sqrt(5.06E-03) * 100 These are all similar to the input parameters (except the c.v. for 'b'). Modeling these data as apparently suggested in the manual etc., I used the control file below: $PROBLEM Aminoglycoside example $INPUT ID AMT RATE TIME DV CRCL $DATA TEST $SUBROUTINES ADVAN1 $PK TA = THETA(1) TB = THETA(2) TK = TA*CRCL + TB K = TK*(1.+ETA(1)) V = THETA(3)*(1.+ETA(2)) S1 = V $ERROR Y = F*(1. + ERR(1)) $THETA (0.,.005,0.1) (0.,.01,1.0) (1,15,100) $OMEGA .2 .2 $SIGMA .2 $ESTIMATION PRINT=5 MAXEVALS=900 $COVARIANCE $TABLE ID TIME AMT DV $SCAT PRED VS DV UNIT $SCAT WRES VS DV TIME CRCL This produced the results: *** MINIMUM VALUE OF OBJECTIVE FUNCTION *** -1265.415 *** FINAL PARAMETER ESTIMATE THETA - VECTOR OF FIXED EFFECTS ********************* TH 1 TH 2 TH 3 4.94E-03 8.04E-03 1.50E+01 OMEGA - COV MATRIX FOR RANDOM EFFECTS - ETAS ******** ETA1 ETA2 ETA1 8.82E-03 ETA2 0.00E+00 3.02E-03 SIGMA - COV MATRIX FOR RANDOM EFFECTS - EPSILONS **** EPS1 EPS1 5.05E-03 This gives: Theta(1) = a = 4.94E-03 Theta(2) = b = 8.04E-03 kel = a * CR-CL + b +/- 9.39 % sqrt(8.82E-03) * 100 Theta(3) = V = 1.50E+01 +/- 5.50 % sqrt(3.02E-03) * 100 Data = +/- 7.11 % sqrt(5.06E-03) * 100 These are all similar to the input parameters (except for the meaning of the kel c.v.). This seemed to be a satisfactory approach except for the input into the subsequent Bayesian analysis. Any comments or suggestions. Thanks.

Note that even when CRCL is 5 (your lowest value) the renal comntribution to k is twice that of the "intercept": the contribution to total variability in k from 20% variability in intercept is, even for this most extreme case, (.2)(.01)/.025 = 8%. The contribution (of 1 SD of intercept) when CRCL = 100 is (.2)(.01)/.51 = .4%. It seems to me no wonder at all that you are unable to detect such a trivial component of variance. When NONMEM can't estimate a component of variance it drives it towards zero which is what happened to you. The proof is that the obj function is only trivially altered when this component is deleted. Bayesan adjustment with your smaller model should work just fine.