Comparing OFV from MCMC Bayesian models

Dear Baysian modellers We have generated a nine compartment model from extremely rich imaging data using MCMC Baysian analysis (and also SAEM during burn-in). For model evaluation we skip single or multiple compartments and compare the numerical outcomes such as the conditional weighted residuals, the Bayes trend or caterpillar plots and the objective function value (OFV). Let's now assume we want to compare model 1 ($PRIOR NWPRI NTHETA=14, NETA=14, NTHP=0, NETP=14) with model 2 ($PRIOR NWPRI NTHETA=18, NETA=18, NTHP=0, NETP=18) More details on the models can be found below (sorry for the many lines of text) For model 1, two peripheral compartments were omitted from model 2. Thus, model 1 has 8 model parameters less than model 2 (as can be seen from NTHETA and NETA). CONCERN and QUESTION: Giving the fact that we estimate the full covariance matrix, I am not quite certain if I am allowed to compare the OFV values from these two model using the F-Test. Could anyone give an advise or comment on this? Many thanks for your help Andreas ______________________________________________________ MODEL 1 $PK MU_1 = THETA(1) MU_2 = THETA(2) MU_3 = THETA(3) MU_4 = THETA(4) MU_5 = THETA(5) MU_6 = THETA(6) MU_7 = THETA(7) MU_8 = THETA(8) MU_9 = THETA(9) MU_10 = THETA(10) MU_11 = THETA(11) MU_12 = THETA(12) MU_13 = THETA(13) MU_14 = THETA(14) MU_15 = THETA(15) MU_16 = THETA(16) MU_17 = THETA(17) MU_18 = THETA(18) ; CENTRAL CL = 0.04 VC = EXP(MU_1+ETA(1)) S2 = VC S3 = VC S5 = VC ; C K10 = CL/VC ; M K19 = EXP(MU_2+ETA(2)) K91 = EXP(MU_3+ETA(3)) K92 = EXP(MU_4+ETA(4)) K29 = EXP(MU_5+ETA(5)) K24 = EXP(MU_6+ETA(6)) K42 = EXP(MU_7+ETA(7)) ; TL K16 = EXP(MU_8+ETA(8)) K61 = EXP(MU_9+ETA(9)) ; T K63 = EXP(MU_10+ETA(10)) K36 = EXP(MU_11+ETA(11)) K37 = EXP(MU_12+ETA(12)) K73 = EXP(MU_13+ETA(13)) ; L K65 = EXP(MU_14+ETA(14)) K56 = EXP(MU_15+ETA(15)) K58 = EXP(MU_16+ETA(16)) K85 = EXP(MU_17+ETA(17)) ALAG1 = EXP(MU_18+ETA(18)) $ERROR Y=F+F*ERR(2)+ERR(1) IPRED = F IRES = DV-IPRED ; INDIVIDUAL-SPECIFIC RESIDUAL IWRES = IRES ; INDIVIDUAL-SPECIFIC WEIGHTED RESIDUAL $THETA 1.3 ; VC -1.4 ; K19 -4.4 ; K91 0.8 ; K92 5.2 ; K29 -1.8 ; K24 -6.3 ; K42 1.0 ; K16 -0.5 ; K61 -3 ; K63 -1.25 ; K36 1.2 ; K37 -0.37 ; K73 -5.2; K65 -5.0 ; K56 -3.2 ; K58 -10. ; K85 2.35 ; ALAG1 $OMEGA BLOCK(17) 0.1 ; VC 0.01 0.1 ; K19 0.01 0.01 0.1 ; K91 0.01 0.01 0.01 0.1 ; K92 0.01 0.01 0.01 0.01 0.1 ; K29 0.01 0.01 0.01 0.01 0.01 0.1 ; K24 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K42 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K16 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K61 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K63 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K36 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K37 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K73 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K65 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K56 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K58 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K85 $OMEGA 0.04 ; ALAG1 $SIGMA 5.5E-05 0.0068 $OMEGA BLOCK(17) 0.1 FIX 0 0.1 0 0 0.1 0 0 0 0.1 0 0 0 0 0.1 0 0 0 0 0 0.1 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1 $OMEGA 0.1 FIX ; ALAG1 $THETA (17.0 FIXED) (1 FIXED) _______________________________________________ MODEL 2 $PK MU_1 = THETA(1) MU_2 = THETA(2) MU_3 = THETA(3) MU_4 = THETA(4) MU_5 = THETA(5) MU_6 = THETA(6) MU_7 = THETA(7) MU_8 = THETA(8) MU_9 = THETA(9) MU_10 = THETA(10) MU_11 = THETA(11) MU_12 = THETA(12) MU_13 = THETA(13) MU_14 = THETA(14) ; CENTRAL CL = 0.04 VC = EXP(MU_1+ETA(1)) S2 = VC S3 = VC S5 = VC ; C K10 = CL/VC ; M K17 = EXP(MU_2+ETA(2)) K71 = EXP(MU_3+ETA(3)) K72 = EXP(MU_4+ETA(4)) K27 = EXP(MU_5+ETA(5)) K24 = EXP(MU_6+ETA(6)) K42 = EXP(MU_7+ETA(7)) ; TL K16 = EXP(MU_8+ETA(8)) K61 = EXP(MU_9+ETA(9)) ; T K63 = EXP(MU_10+ETA(10)) K36 = EXP(MU_11+ETA(11)) ; L K65 = EXP(MU_12+ETA(12)) K56 = EXP(MU_13+ETA(13)) ALAG1 = EXP(MU_14+ETA(14)) $ERROR Y=F+F*ERR(2)+ERR(1) IPRED = F IRES = DV-IPRED ; INDIVIDUAL-SPECIFIC RESIDUAL IWRES = IRES ; INDIVIDUAL-SPECIFIC WEIGHTED RESIDUAL $THETA 1.3 ; VC -1.4 ; K17 -4.4 ; K71 0.8 ; K72 5.2 ; K27 -1.8 ; K24 -6.3 ; K42 1.0 ; K16 -0.5 ; K61 -3 ; K63 -1.25 ; K36 -5.2; K65 -5.0 ; K56 2.35 ; ALAG1 $OMEGA BLOCK(13) 0.1 ; VC 0.01 0.1 ; K17 0.01 0.01 0.1 ; K71 0.01 0.01 0.01 0.1 ; K72 0.01 0.01 0.01 0.01 0.1 ; K27 0.01 0.01 0.01 0.01 0.01 0.1 ; K24 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K42 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K16 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K61 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K63 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K36 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K65 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K56 $OMEGA 0.04 ; ALAG1 $SIGMA 5.5E-05 0.0068 $OMEGA BLOCK(13) 0.1 FIX 0 0.1 0 0 0.1 0 0 0 0.1 0 0 0 0 0.1 0 0 0 0 0 0.1 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0.1 $OMEGA 0.1 FIX ; ALAG1 $THETA (13.0 FIXED) (1 FIXED) $EST PRINT=1 METHOD=SAEM INTERACTION NBURN=100 NITER=20 FILE=SAEM.EXT NOPRIOR=1 $EST METHOD=BAYES FILE=BAYES.EXT NBURN = 4000 NSIG = 3 NITER= 3000 NOPRIOR=0 $COV MATRIX=R PRINT=E UNCONDITIONAL SIGL=12 ---------------------------------------------------------------------------------------------------------------------------------------- Andreas Steingötter, PhD Division for Gastroenterology and Hepatology Institut for Biomedical Engineering Department of Internal Medicine Divisions of Bioimaging and MRI Technology University Hospital Zurich University and ETH Zurich Rämistrasse 100 Gloriastrasse 35 CH - 8091 Zurich CH - 8092 Zurich Tel. +41 44 255 5684 Tel. +41 44 255 5684 Fax +41 44 255 4591 Fax +41 44 632 1193 Email [email protected] Email [email protected]