$PROBLEM MULTISTATE TB DISEASE MODEL WITH CLINICAL DATA ; Author: Robin Svensson 2015-10 UPPSALA UNIVERSITY ;; 1. Based on: 179 ;; 2. Description: ;; SLOPE MODELS ON INCREASED DEATH OF S AND N. ON/OFF EFFECT ON GROWTH OF F. INCLUDED SMYTHE RIF PK MODEL. IMPLEMENTATION OF SPUTUM SAMPLE COMPARTMENT. ;; 3. Label: ;; DRUG DATA WITH MULTISTATE TB DISEASE MODEL AND RIF PK, SLOPE MODELS ON S AND N. ON/OFF EFFECT ON FG. IMPLEMENTATION OF SPUTUM SAMPLE COMPARTMENT. ;; 4. Structural model: ;; 4 BACTERIAL COMPARTMENTS 1-COMP ENZYME TURNOVER PK MODEL FOR RIF AND SPUTUM SAMPLE COMPARTMENT. ;; 5. Covariate model: ;; FFM AND WT ON CL AND V2 IN RIF PK MODEL. ;; 6. Inter-individual variability: ;; LOG-NORMAL OMEGA ON BMAX ;; 7. Inter-occasion variability: ;; 8. Residual variability: ;; ADDITIVE (PROPORTIONAL ON NORMAL SCALE) AND ADDITIVE (PROPORTIONAL ON NORMAL SCALE) REPLICATE ERROR BOTH AS EPS ;; 9. Estimation: ;; FIRST ORDER CONDITIONAL ESTIMATION (FOCE) METHOD ; BASED ON (run413) MULTISTATE TB DISEASE MODEL WITH RIF BY CLEWE. ALSO INCLUDING SMYTHE RIF PK MODEL (run106) ; Fixed parameters: KG, KFN, KSN, KSF, KNF, KNS, KD, SLOPE, AF, AS, CL, V2, MTT, NN, EC50, EMAX, KENZ, BIO and FGOO $DATA Simulated_clinical_rif_pkpd.csv IGNORE=@ ; TIME=hours after infection, NDV=CFU, DV=natural log of CFU, AMT=mg, ; LOQ (0= observation is not LOQ, 1=observation is LOQ, 2=dummy time point), ; REGI = abbreviated regimen (R5 = rifampicin 5 mg/kg, R10 = rifampicin 10 mg/kg, R20 = rifampicin 20 mg/kg, Nil = negative control group) ; TAD = time after first dose, in days, DOSE=mg/kg (only when first dose have been given), DGRP = dose in mg/kg displayed for all records ; L2 = L2 data item, shared by replicates from each unique time point (and ID), REP = replicate at each time point (1 or 2) ; CMT = needed to turn on and off the sputum sample compartment, SDUR = duration of sputum sampling in hours, SVOL = volume of sputum sample in mL $INPUT ID TIME NDV DV EVID AMT DRUG FLAG LOQ REGI=DROP TAD DOSE DGRP L2 REP CMT SDUR SVOL $SUBROUTINE ADVAN13 TOL=9 $MODEL NCOMP=7 COMP=(F) COMP=(S) COMP=(N) COMP = (DEPOT,DEFDOSE) COMP = (CPK) COMP = (ENZ) COMP =(SPU) $PK ;----BACTERIAL SYSTEM PARAMETERS---- TVKG = THETA(1) ; GROWTH RATE OF F TVKFSLIN = THETA(2)/100 ; RATE PARAMETER, KFS, TIME DEPENDENT TVKFN = THETA(3)/1000000 ; F -> N TVKSF = THETA(4)/10 ; S -> F TVKSN = THETA(5) ; S -> N TVKNS = THETA(6)/100 ; N -> S TVBMAX = THETA(7)*10000000 ; SYSTEM CARRYING CAPACITY (ML-1) System carrying capacity (cfu/ml) TVF0 = THETA(8) ; INITIAL F BACTERIAL NUMBER (ML-1) Initial TVS0 = THETA(9) ; INITIAL S BACTERIAL NUMBER (ML-1) Initial ;----DRUG PK PARAMETERS------------- IF(NEWIND.NE.2)PD = 0 IF(AMT.GT.0)PD = AMT ; PD = (PER)ORAL DOSE, FOR TRANSIT ABSORPTION MODEL IF(NEWIND.NE.2)TDOS = 0 IF(AMT.GT.0)TDOS = TIME ; TDOS = time of DOSE, FOR TRANSIT ABSORPTION MODEL TSLD = TIME - TDOS ; TSLD = time since last DOSE, FOR TABLE OUTPUT CLFFAT = THETA(18) ; CONTRIBUTION OF FAT-FREE MASS AND BODY WEIGHT TO CL/F NFMCL = 45 + CLFFAT*(56-45) ; FFM and WT changed to median originating from: FFM + CLFFAT*(WT - FFM) ALLMCL = (NFMCL/70)**0.75 ; ALLOMETRIC SCALING OF CL/F VFFAT = THETA(19) ; CONTRIBUTION OF FAT-FREE MASS AND BODY WEIGHT TO V/F NFMV = 45 + VFFAT*(56-45) ; FFM and WT changed to median originating from: FFM + VFFAT*(WT-FFM) ALLMV = (NFMV/70) ; ALLOMETRIC SCALING OF V/F TVCL = THETA(10)*ALLMCL ; ORAL CLEARANCE AT THE PREINDUCED STATE (L*H-1) TVV2 = THETA(11)*ALLMV ; APPARENT VOLUME OF DISTRIBUTION (L) TVMTT = THETA(12) ; MEAN TRANSIT TIME (H) TVNN = THETA(13) ; NUMBER OF TRANSIT COMPARTMENTS TVEMAX = THETA(14) ; MAXIMAL INCREASE IN ENZYME PRODUCTION RATE TVEC50 = THETA(15) ; RIFAMPICIN CONCENTRATION AT WHICH HALF THE EMAX (FOR THE PRODUCTION RATE) IS REACHED (MG/L) TVKENZ = THETA(16) ; RATE CONSTANT FOR FIRST-ORDER DEGRADATION OF THE ENZYME POOL (H-1) TVBIO = THETA(17) ; BIOAVAILABILITY ;----DRUG EFFECT PARAMETERS---- TVSDK = THETA(20) ; SLOPE, INCREASED DEATH RATE, S (L*MG-1*DAY-1) TVNDK = THETA(21) ; SLOPE, INCREASED DEATH RATE, N (L*MG-1*DAY-1) TVFGOO = THETA(22) ; ON/OFF, INHIBITION OF KG, F (DAY-1) KG = TVKG KFN = TVKFN KSN = TVKSN BMAX = TVBMAX*EXP(ETA(1)) KSF = TVKSF KNS = TVKNS KFSLIN = TVKFSLIN F0 = TVF0 S0 = TVS0 CL = TVCL V2 = TVV2 MTT = TVMTT NN = TVNN EC50 = TVEC50 EMAX = TVEMAX KENZ = TVKENZ BIO = TVBIO K = CL/V2 S2 = V2 SDK = TVSDK NDK = TVNDK FGOO = TVFGOO S7 = SVOL IF(SDUR.EQ.0) THEN KPROD = 0 ELSE KPROD = SVOL/SDUR ; SPUTUM PRODUCTION RATE (ML*H-1) ENDIF KTR = (NN + 1) / MTT ; SPEED UP CALCULATIONS L = 0.9189385 + (NN + 0.5)*LOG(NN) - NN + LOG(1 + 1/(12*NN)) ; LOGARITHM OF THE APPROXIMATION TO THE GAMMA FUNCTION LBPD = LOG(BIO*PD) LKTR = LOG(KTR) CUMUL = LBPD + LKTR - L KA = KTR ;----INITIALIZATION OF COMPARTMENTS---- A_0(1) = F0 ; INITIAL NUMBER, F A_0(2) = S0 ; INITIAL NUMBER, S A_0(3) = 0.00001 ; INITIAL NUMBER, N F4 = 0 ; INITIAL AMOUNT TRANSIT DOSE COMPARTMENT A(4) A_0(5) = 0.0001 ; INITIAL AMOUNT CENTRAL COMPARTMENT A_0(6) = 1 ; INITIAL AMOUNT INDUCTION COMPARTMENT A_0(7) = 0.00001 ; INITIAL AMPUNT SPUTUM SAMPLE COMPARTMENT $DES ;----GOMPERTZ GROWTH FUNCTION, FAST MULTIPLYING BACTERIA---- GROWTH = KG*LOG(BMAX/(A(1)+A(2)+A(3))) ; GOMPERTZ GROWTH FUNCTION IF(GROWTH.LT.0) GROWTH=0 ; KEEP GROWTH FROM TURNING NEGATIVE ;----TIME DEPENDENT KFS---- KFS = KFSLIN*T/24 ; TIME DEPENDENT LINEAR (SLOPE) TRANSFER, TIME IS SCALED TO DAYS ;----DRUG EFFECTS---------- IF(DOSE.GT.0) THEN RIFCP = A(5) / V2 ; RIF PLASMA CONCENTRATION (MG/L) ELSE RIFCP=0 ENDIF IF(RIFCP.GT.0) THEN EFG = 1-FGOO ; INHIBITION OF KG, F, ON/OFF ESD = SDK*RIFCP ; INCREASED DEATH RATE, S, SLOPE END = NDK*RIFCP ; INCREASED DEATH RATE, N, SLOPE ELSE EFG=1 ESD=0 END=0 ENDIF DADT(1)=( A(1)*GROWTH*EFG+KSF*A(2)-KFS*A(1)-KFN*A(1) )/24 ; F DADT(2)=( KFS*A(1)+KNS*A(3)-KSN*A(2)-KSF*A(2)-ESD*A(2) )/24 ; S DADT(3)=( KSN*A(2)+KFN*A(1)-KNS*A(3)-END*A(3) )/24 ; N ;----DRUG CONCENTRATION---- TEMPO = T - TDOS IF(TEMPO.GT.0)THEN KTT = KTR*TEMPO DADT(4) = EXP(CUMUL + NN*LOG(KTT) - KTT) - KA*A(4) ; TRANSIT ABSORPTION COMPARTMENT ELSE DADT(4) = 0 ENDIF DADT(5) = KA*A(4) - K*A(5)*A(6) ; CENTRAL COMPARTMENT EFF = (EMAX*(RIFCP)) / (EC50 + RIFCP) ; EFFECT, INCREASED ENZYME PRODUCTION RATE, EMAX DADT(6) = KENZ*(1 + EFF) - KENZ*A(6) ; ENZYME POOL, INDUCTION COMPARTMENT DADT(7) = KPROD*(A(1)+A(2)) ; SPUTUM SAMPLE COMPARTMENT $ERROR ;----OUTPUT--------------- FBAC = A(1) ; NUMBER OF F (ML-1) SBAC = A(2) ; NUMBER OF S (ML-1) NBAC = A(3) ; NUMBER OF N (ML-1) AA4 = A(4) ; ABSORPTION COMPARTMENT AA5 = A(5) ; CENTRAL RIFAMPICIN COMPARTMENT (MG/L) AA6 = A(6) ; AUTO-INDUCTION COMPARTMENT SPUT = A(7) ; SPUTUM COMPARTMENT IF(EVID.EQ.0) THEN IPRED = LOG(A(7)/S7+0.00001) ; LOG OF AMOUNT IN SPUTUM SAMPLE COMPARTMENT PER ML SPUTUM ELSE IPRED = 0.00001 ENDIF IRES = DV-IPRED ADD1 = SQRT(SIGMA(1,1)) ; ADD ERROR WITH LOG DV, I.E. PROP ERROR ADD2 = SQRT(SIGMA(2,2)) SD = SQRT(ADD1*ADD1+ADD2*ADD2) IWRES = IRES/SD IF(REP==1) Y = IPRED+EPS(1)+EPS(2) ; ADD REPLICATE ERROR WITH LOG DV, I.E. PROP ERROR IF(REP==2) Y = IPRED+EPS(1)+EPS(3) ; ADD REPLICATE ERROR WITH LOG DV, I.E. PROP ERROR IF(AMT.GT.0) THEN TDOS = TIME PD = AMT ENDIF $THETA 2.06E-01 FIX ; 1 kG $THETA 1.66E-01 FIX ; 2 kFSLIN (/100) $THETA 8.97E-01 FIX ; 3 kFN (/1000000) $THETA 1.45E-01 FIX ; 4 kSF (/10) $THETA 1.86E-01 FIX ; 5 kSN $THETA 1.23E-01 FIX ; 6 kNS (/100) $THETA (0, 2.61E+02) ; 7 Bmax (*10000000) $THETA 4.10E+00 FIX ; 8 F0 $THETA 9.77E+03 FIX ; 9 S0 $THETA 1.00E+01 FIX ; 10 CL/F $THETA 8.67E+01 FIX ; 11 V2/F $THETA 7.13E-01 FIX ; 12 MTT $THETA 1.00E+00 FIX ; 13 NN $THETA 1.04E+00 FIX ; 14 EMAX $THETA 7.05E-02 FIX ; 15 EC50 $THETA 3.69E-03 FIX ; 16 KENZ $THETA 1.00E+00 FIX ; 17 BIO $THETA 3.11E-01 FIX ; 18 CLFFAT $THETA 1.88E-01 FIX ; 19 VFFAT $THETA (0,2.00E-01) ; 20 SDSL $THETA (0,1.06E-01) ; 21 NDSL $THETA 1.00E+00 FIX ; 22 FGOO $OMEGA 2.30E+00 ; IIV in BMAX $SIGMA 1.20E+00 ; ADD COMMON ERROR $SIGMA BLOCK(1) 5.35E-02 ; ADD REPLICATE CORRECTION ERROR $SIGMA BLOCK(1) SAME $ESTIMATION METHOD=1 MAXEVAL=9999 NSIG=3 SIGL=9 NOABORT PRINT=3 $COVARIANCE PRINT=E $TABLE ID TIME TAD DRUG PRED IPRED IRES IWRES CWRES NDV FBAC SBAC NBAC DOSE DGRP EVID AA4 AA5 AA6 RIFCP PD TDOS ESD EFG END SPUT ONEHEADER NOPRINT FILE=sdtab $TABLE ID TIME TAD GROWTH KG KFN KFS KSF KSN KNS BMAX DOSE DRUG BIO CL V2 KA K EMAX EC50 KENZ MTT KTR SDK NDK FGOO ETA1 ONEHEADER NOPRINT FILE=patab $TABLE ID TIME ONEHEADER NOPRINT FILE=cotab $TABLE ID TIME ONEHEADER NOPRINT FILE=catab