$PROBLEM PKPD FPG-FI ;;1. Based on run276.mod ;;2. Data ;; FPG and FI: ;; GALANT6 with EBE-CL and V from Phase-II model ;; re-estimated on GALAN6 ;;3. Structural Model ;; BIG-Model ;;4. Covariate Model ;; PRET on SI and baseline-SI ;;5. Interindividual Variability ;; IIV on all BIG parameters and on Res-FPG ;;6. Residual Variability ;; Additive (after Log-transformation of both sides) ;; IIV on EPS for FPG ;;7. Fixed Parameters ;; variance parameters and some BIG parameters ;;8. Purpose of Run ;; As run276, but allowing glucose toxicity ;; Estimate structural and IIV params simultaneously. ;;9. Results and Conclusion ;; Terminates with 2.7 sigdigs, which is considered successful. ;; THIS IS THE FINAL MODEL! ;; 1. UPDATE IE:s ;; 2. CLEAN MODEL: for publication ;; 3. QUESTION FINAL MODEL: Check that sigmoidicity in Emax is still needed ;; 4. Re-estimate with sigdigs=4 ;; $INPUT ID TRMT=DROP DOSE AMT RATE TIME CMT ORIG EVID LIDV=DROP CLI VI DV STUD OID=DROP VIST TAD=DROP AGE SEX WGT=DROP HT=DROP RACE=DROP ETHN=DROP PRET MDRD=DROP CRCL=DROP HISD DAYS=DROP STRA ATAD $ABBREVIATED DERIV2=NO $DATA NM7DecTimeCatTad_simulated.csv IGNORE=@ IGNORE(ID.EQ.270, ID.EQ.252) $SUBROUTINE ADVAN8 TOL=6 $MODEL COMP=(BETA) ;Concentration instead of AMT COMP=(SensRat);Insulin sensitivity COMP=(PK) $PK (CALLFL=-1) ;Called for each new record CL = CLI V = VI K = CL/V ;DS1 = 0 ;None-diabetics in SIR-study ;IF (STUD.NE.1) DS1=1 ;DS2=0 ;Naive diabetics in GLAD and GALLANT ;IF (PRET.NE.1) DS2=1 ;Pre-treated diabetics DST = 5 IF(PRET.GT.1.AND.STUD.EQ.2) DST = 4 IF (PRET.EQ.1) THEN DST = STUD ; SIR GLAD GALLANT IF (STUD.EQ.6) DST=3 ;NAIVE 1 2 3 ENDIF ;PRET 4 5 ;--------ASSUMING IMMEDIATE SS IN PK--------------- CSS = 0 IF(AMT.GT.0) CSS = RATE/CLI ;----BIG PARAMETERS-------------------------------- TVSI = THETA(1)/24 ;1. Insulin sensitivity for SIR TVEG = THETA(2)/24 ;2. Glucose effectiveness (NID) TVRO = THETA(3)/24 ;3. Glucose production (at G0) TVSG = THETA(4)/24 ;4. Sigma, Max insulin secretion (per mg) TVAL = THETA(5)**2 ;5. Alpha, EC50**2 for insulin secretion TVKI = THETA(6)/24 ;6. Insulin-elimination-rate constant TVDE = THETA(7)/24 ;7. Death rate (at G0) TVRA = THETA(8)/24 ;8. Glucose dependent "replication" TVRB = THETA(9)/24 ;9. Glucose dependent "death" TVKO = THETA(12)/24 ;12. Rate constant for FPG turnover TVPS = THETA(13) ;13. Change in SI due to pre-treatment TVMS = THETA(15) ;15. Emax Insulin sensitivity for Galida TV5S = THETA(16) ;16. EC50 Insulin sensitivity for Galida TVPO = THETA(18) ;18. Reduced offset due to PRE TVMO = THETA(19) ;19. Emax On offset for Galida TV5O = THETA(20) ;20. EC50 On offset for Galida TVRL = THETA(34) ;34. Eponential relation KI~SI/TVSI TVAD = THETA(14) ;14. Change in betacell-adaptation rate TVSL = THETA(35) ;35. Slope ;---------Covariate Model-------- SICOV = (1+THETA(21)) IF(DST.EQ.2) SICOV = (1+THETA(21))*(1+THETA(22)) IF(DST.EQ.3) SICOV = (1+THETA(21))*(1+THETA(22))*(1+THETA(23)) IF(DST.EQ.4) SICOV = (1+THETA(21))*(1+THETA(22))* (1+THETA(24)) IF(DST.EQ.5) SICOV = (1+THETA(21))*(1+THETA(22))*(1+THETA(23))*(1+THETA(25)) IF(STUD.EQ.6) THEN TVPS = TVPS*(1+THETA(31)) TVPO = TVPO*(1+THETA(33)) ENDIF ;-------------------------------- SLOP=TVSL ADAP= (1+TVAD) KOUT= TVKO PRES= TVPS PREI= 0;TVPI PHI = LOG(TVPO/(1-TVPO)) DENOM = 1 + EXP(PHI + ETA(1)) PREO = EXP(PHI + ETA(1)) / DENOM KIN = KOUT SI = TVSI*EXP(ETA(4))*SICOV EGO = TVEG RO = TVRO SG = TVSG AL = TVAL KI = TVKI DE = TVDE RA = TVRA RB = TVRB RLKI= TVRL CORR=THETA(32) ;---DRUG-EFFECT MODEL----------------------- EMAS=TVMS EC5S=TV5S*EXP(ETA(2)*THETA(36)) EMAO=TVMO EC5O=TV5O*EXP(ETA(2)*THETA(37)) ;----Covariate Model, Part 2------------------------------ IF(PRET.EQ.1) THEN ;Drug naive PRES = 0 PREI = 0 PREO = 0 ENDIF A_0(2) = 1+PRES TVOF = THETA(26) IF (DST.EQ.2) TVOF = THETA(26)+THETA(27) IF (DST.EQ.3) TVOF = THETA(26)+THETA(27)+THETA(28) IF (DST.EQ.4) TVOF = THETA(26)+THETA(27)+ THETA(29) IF (DST.EQ.5) TVOF = THETA(26)+THETA(27)+THETA(28)+THETA(30) MAGN = 1 IF (PRET.GT.1) MAGN = 1+THETA(17) OFFG = CORR+(TVOF-CORR)*EXP(MAGN*ETA(3));Baseline offset DOFF = TVOF*EXP(MAGN*ETA(3)) ;Drug-effects can only reduce this portion ;-------------------------------------------------------- ;---INITIAL SS SOLUTION FOR FPG, FI AND BETA-CELLS------- ROOT = (RA/(2*RB))**2-DE/RB IF (ROOT.LT.0) ROOT=0;Saddle and fixed point collapsed BASG = RA/(2*RB) - SQRT(ROOT) + OFFG - PREO*DOFF;SS is offset by OFFG IF (BASG.LE.0) EXIT 1 3 BASI = (RO-EGO*BASG)/(SI*(1+PRES)*BASG) IF (BASI.LE.0) EXIT 1 4 BASB = BASI*KI*((SI*(1+PRES)/TVSI)**RLKI)*(AL+BASG**2)/(SG*(1+PREI)*BASG**2) IF (BASB.LE.0) EXIT 1 5 A_0(1) = BASB ;--------------------------------------------- ;DEFINITIONS USED IN $DES FOR PSEUDO-SS (FPG AND FI) AS=RO**2 DAYS = TIME/24 ; TIME as days $DES ;---SS SOLUTION FOR FPG AND FI--- S = SI*A(2) KID = KI*(S/TVSI)**RLKI;Dynamic KI for insulin elimination BS = KID**2 AX = S*SG*A(1) XX = KID*EGO+AX XY = AS*KID-3*EGO*XX*AL XO = (18*BS*EGO**2+45*KID*EGO*AX+27*AX**2)*AL XZ = SQRT(BS*(4*KID*(-XY)**3+AS*(2*(RO*KID)**2+XO)**2)) ZW = 2*RO**3*KID**3+18*RO*KID**3*EGO**2*AL+45*RO*BS*EGO*AX*AL+27*RO*KID*AX**2*AL FPG = (2*RO*KID+(2*2**(1/3)*KID*XY)/(ZW+XZ)**(1/3)+2**(2/3)*(ZW+XZ)**(1/3))/(6*XX) IF(FPG.LE.0) EXIT 1 6 FI = (RO-EGO*FPG)/(S*FPG) IF(FI.LE.0) FI=0.001 ;-------------------------------- DADT(3) = -K*A(3);Drug amount CP = A(3)/V IF(CP.LT.0) CP=0;Rounding error in $DES EFFS= EMAS*CP/(CP+EC5S) ;--------INSULIN-SENSITIVITY RATIO--------------- DADT(2) = KIN*(1+EFFS)-KOUT*A(2) ;--------BETA-CELL CONCENTRATION--------------- EFFB = EMAO*CP**SLOP/(CP**SLOP+EC5O**SLOP) GLUC = FPG - OFFG+EFFB*DOFF;Betacells adapting to this DADT(1) = A(1)*(-DE+RA*GLUC-RB*GLUC**2)*ADAP $ERROR ;---SS SOLUTION AGAIN------------ SIN = SI*A(2) DD = SIN*SG*A(1) KIDY= KI*(SIN/TVSI)**RLKI BS2 = KIDY**2 DX = KIDY*EGO+DD DY = AS*KIDY-3*EGO*DX*AL X0 = (18*BS2*EGO**2+45*KIDY*EGO*DD+27*DD**2)*AL DZ = SQRT(BS2*(4*KIDY*(-DY)**3+AS*(2*(RO*KIDY)**2+X0)**2)) DW = 2*RO**3*KIDY**3+18*RO*KIDY**3*EGO**2*AL+45*RO*BS2*EGO*DD*AL+27*RO*KIDY*DD**2*AL FPG2= (2*RO*KIDY+(2*2**(1/3)*KIDY*DY)/(DW+DZ)**(1/3)+2**(2/3)*(DW+DZ)**(1/3))/(6*DX) IF(FPG2.LE.0) FPG2=0.000001 FI2 = (RO-EGO*FPG2)/(SIN*FPG2) IF(FI2.LE.0) FI2 =0.000001 ;-----FOR OUTPUT-------- C = A(3)/V EFFS2 = EMAS*C/(C+EC5S) EFFB2 = EMAO*C/(C+EC5O) BETA = A(1) SENSR = A(2) ;--FPG PREDICTION (ORIG 2)------------ IPRED = LOG(FPG2) W = THETA(10)*EXP(ETA(5)) ;FPG Res ;--FI PREDICTION (ORIG 4)------------ IF (ORIG.EQ.4) THEN IPRED = LOG(FI2) W = THETA(11)*EXP(ETA(6));FI Res ENDIF IRES = DV - IPRED IWRES=IRES/W Y=IPRED+EPS(1)*W $THETA (0, 0.103672) FIX ;1. Insulin sensitivity $THETA (0, 1.44) FIX ;2. Glucose effectiveness (NID) $THETA (0, 47.95737) FIX ;3. Glucose production (at G0) $THETA (0, 300.024) FIX ;4. Sigma, Max insulin secretion (per mg) $THETA (0, 7.84976) FIX ;5. Alpha, EC50 for insulin secretion $THETA (0, 432) FIX ;6. Insulin-elimination-rate constant $THETA (0, 0.06) FIX ;7. Death rate (at G0) $THETA (0, 0.015133) FIX ;8. Glucose dependent "replication" $THETA (0, 0.000779) FIX ;9. Glucose dependent "death" $THETA (0, 0.0800) ;10. Res_FPG $THETA (0, 0.309) ;11. Res FI $THETA (0, 0.0599) ;12. Rate constant for Insulin Sensitivity (/day) $THETA (-1,0.196) ;13. Change in SI due to pre-treatment $THETA (-0.91, 0) FIX ;14. Change in betacell-adaptation rate $THETA (0, 9.48) ;15. Emax, Insulin sensitivity for Galida $THETA (0, 7.43) ;16. EC50, Insulin sensitivity for Galida $THETA (-1,0.489) ;17. Change in OFFG-IIV magnitude for pretreated $THETA (0, 0.270, 2) ;18. Reduced offset due to PRE $THETA (0, 1) FIX ;19. Emax, change in offset for Galida $THETA (0, 0.463) ;20. EC50 On offset for Galida $THETA (-1, -0.190, 0) ;21. Change in SI for DST=1 $THETA (-1, -0.217, 0) ;22. Change in SI for DST=2 $THETA (-1, -0.206, 0) ;23. Change in SI for DST=3 $THETA (-1, -0.00919,1) ;24. Change in SI for DST=4 $THETA (-1, 0.195, 1) ;25. Change in SI for DST=5 $THETA (0, 0.199) ;26. Increased Offset FPG-adaptation for DST=1 $THETA (0, 2.92) ;27. Increased Offset FPG-adaptation for DST=2 $THETA (0, 0.388) ;28. Increased Offset FPG-adaptation for DST=3 $THETA (-3,0.800) ;29. Increased Offset FPG-adaptation for DST=4 $THETA (-3,-0.431) ;30. Increased Offset FPG-adaptation for DST=5 $THETA (-1, 0) FIX ;31. Change in PRES GLAD->GALLANT $THETA (-3, -1.64) ;32. Correction of the offset distribution $THETA (-1, 0.948) ;33. Change in PREO GLAD->GALLANT $THETA (0, 0.653) ;34. Eponential relation KI~SI/TVSI $THETA (0, 1.12) ;35. SLOP $THETA (0, 0.484) ;36. IIV-EFFECT-SI $THETA (0, 1.04) ;37. IIV-EFFECT-OFFSET $OMEGA 1.25 ;1. PREO $OMEGA 1 FIX ;2. EFFECTS $OMEGA BLOCK(2) 0.0674 ;3. OFFG -0.0547 0.32 ;4. Insulin sensitivity $OMEGA BLOCK(2) 0.223 ;5. RES FPG 0.0789 0.0577 ;6. RES FI $SIGMA 1 FIX $ESTIMATION MAXEVAL=0 PRINT=1 NOABORT MSFO=msfo286 METHOD=1 INTER ;$COVARIANCE UNCOND $TABLE ID ATAD TIME IPRED IWRES ONEHEADER NOPRINT FILE=sdtab286 $TABLE ID ETA1 ETA2 ETA3 ETA4 ETA5 ETA6 CSS ONEHEADER NOPRINT FILE=patab286 $TABLE ID SEX DOSE PRET VIST STUD ONEHEADER NOPRINT FILE=catab286 ;$TABLE ID AGE HISD ONEHEADER NOPRINT FILE=cotab286 ;$TABLE ID DV STUD DAYS ORIG IPRED FPG2 FI2 DST SIN BETA SENSR KIDY PRET PREO PRES PREI SICOV ; EFFS2 EFFB2 CMT AMT RATE C NOAPPEND ONEHEADER NOPRINT FILE=mytab286 $TABLE ID ETA1 ETA2 ETA3 ETA4 ETA5 ETA6 NOPRINT ONEHEADER NOAPPEND FIRSTRECONLY FILE=ebtab286