Population Approach. Pharmacokinetics. Analysis Approaches. Describing The Signal and the Noise
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1 1 Population Approach Describing The Signal and the Noise 2 Pharmacometrics Science Pharmacology Models Pharmacokinetics Pharmacodynamics Experiment Dose Concentration Effect 3 Analysis Approaches ANOVA Doses Mean/Linear Models Limited covariates Univariate dose-effect REGRESSION Concs Biology is non-linear Multiple unrestricted covariates Multivariate dose-conc-effect
2 4 Two Approaches Individual Self contained Obsi >> Parms Structural Mdl Residual Error Mdl Population Shared Obsi >= Parms Structural Mdl Residual Error Mdl Covariate Model Parameter Variability Mdl 5 Population Methods Naive Pooled Data» Mean (biased) Standard Two Stage» Mean + SD (biased) Full Population» Mean + SD 6 Mixed Effect Model Fixed Effects (predictable variability)» Covariates and parameters» e.g. renal function and clearance Random Effects (unpredictable variability)» Parameter variability e.g. in clearance» Residual error e.g. measurement error MIXED EFFECT = FIXED EFFECT + RANDOM EFFECT
3 7 Parameter Variability N.Sambol CDDS/SUMC Structural Model E = E0 + EMAX * THEO / (C50 + THEO) E0, Emax, C50 9 Residual Error Model RUV=Residual Unidentified Variability Additive Y = E + RUV_SD Proportional Y = E + E * RUV_CV Mixed Y = E + E * RUV_CV + RUV_SD RUV_SD, RUV_CV
4 10 Continuous Covariate Model Theoretical FWT=(WT/70)**(3/4) Empirical FAGE= 1 + SLOPE*(AGE-60) 3/4 (theory), SLOPE 11 Categorical Covariate Model IF (SEX.EQ.1) THEN FSEX=1 ; male ELSE FSEX=FFEM ; female ENDIF Parameter: FFEM 12 Multiplicative Covariate Effects GRP_EMAX=FWT * FAGE * FSEX * POP_EMAX FIXED EFFECTS: FWT, FAGE, FSEX
5 13 Parameter Variability Model PPV=Population Parameter Variability Normal (additive) EMAX = GRP_EMAX + PPV_SD Proportional EMAX = GRP_EMAX + GRP_EMAX*PPV_CV Log Normal EMAX = GRP_EMAX *EXP(PPV_CV) exp(x) ~= 1+x (small x) PPV_SD, PPV_CV 14 Methods Parametric Methods» Icon NONMEM (NONlinear Mixed Effects Model)» R nlme, SAS NLMIXED, Pharsight Phoenix nlme Non-Parametric Methods» NPML, NPEG Expectation Maximization Methods» WinBUGS, MCPEM, S-Adapt, Lixsoft Monolix 15 Uses Covariate Influences» Population Screen PKPD» Dose/Conc Response» Disease progress Limited Sampling» Paediatrics» Toxicology
6 16 NONMEM C THE NONMEM SYSTEM MAY BE DISTRIBUTED ONLY BY THE NONMEM C PROJECT GROUP. CONTACT: PROF. STUART BEAL, CLINICS 255, C UNIV. OF CALIFORNIA, SAN FRANCISCO, CA C COPYRIGHT BY THE REGENTS OF THE UNIVERSITY OF CALIFORNIA C 1979, 1984, 1985, 1989, 1992, 1998 ALL RIGHTS RESERVED C C DO NOT MODIFY CODE C WITHOUT FIRST CONSULTING WITH THE NONMEM PROJECT GROUP C PROGRAM NONMEM 17 $PROB THEOPHYLLINE PHARMACODYNAMICS STANDARD CONTROL STREAM $DATA theopd.dat IGNORE # $INPUT ID TIME THEO AGE WT SEX RACE DIAG DV $ESTIM METHOD=COND INTER $COV $THETA (0,150.,) ; POP_E0 (0,200.,) ; POP_EMAX (.001,10,) ; POP_C50 $OMEGA 0.5 ; PPV_E0 0.5 ; PPV_EMAX 0.5 ; PPV_C50 NONMEM $SIGMA 100 ; RUV_SD $PRED E0=THETA(1)*EXP(ETA(1)) EMAX=THETA(2)*EXP(ETA(2)) EC50=THETA(3)*EXP(ETA(3)) Y = E0 + EMAX*THEO/(C50 + THEO) + EPS(1) $TABLE ID TIME THEO AGE WT SEX RACE DIAG E0 EMAX EC50 Y NOPRINT ONEHEADER FILE=theopd.fit 18 NONMEM THETA: POP_E0 POP_EMAX POP_C50 ETA: PPV_E0 PPV_EMAX PPV_C50 ERR: RUV_SD theopd.lst eval=270 sig=+3.3 sub=153 obs=574 CCIL=NNNN NV1.1 THETA = ETASD = ERRSD = THETA:se% = OMEGA:se% = SIGMA:se% = 10.6 MINIMIZATION SUCCESSFUL user 0:1.76 real 0:1.76 tcl 0:1.31
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