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Between Subject Random Effect Transformations with NONMEM VI

Between Subject Random Effect Transformations with NONMEM VI. Bill Frame 09/11/2009. Between Subject Random Effect ( ) Transformations. Why bother with transformations? What is a transformation? Examples and Brief History . Implementation and examples in NONMEM (V or VI).

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Between Subject Random Effect Transformations with NONMEM VI

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  1. Between Subject Random Effect Transformations with NONMEMVI Bill Frame 09/11/2009 Wolverine Pharmacometrics Corporation

  2. Between Subject Random Effect () Transformations. • Why bother with transformations? • What is a transformation? • Examples and Brief History. • Implementation and examples in NONMEM (V or VI) Wolverine Pharmacometrics Corporation

  3. Why Bother with Transformations? Variance stabilization (Workshop 7). NONMEM assumes that ~ N(0,) A better statistical fit to the data? Perhaps simulations can be improved upon, as opposed to a model with no eta transformation? Wolverine Pharmacometrics Corporation

  4. Q: What is an ETA transformation? • A: A one to one function that maps ETA to a new random effect ET, as a function of a fixed effect parameter (). • Q: What are desirable properties of such a transformation? • Invertible, this means one to one. • Domain = Real line, the same as ETA. • Differentiable with respect to argument and parameter, more of a theoretical issue than a practical one. • Null value for lambda is not on boundary of parameter space. Wolverine Pharmacometrics Corporation

  5. Examples and Brief History Transformations can be applied to: 1. Statistics i.e. Fisher’s Z transformation for the Pearson product moment correlation coefficient (). Z = ½*loge((1+)/(1-)) 2. The response (Y=DV): Change Y to Z=Y1/2 if E(Y)  Var(Y) and model Z, this is sometimes done for Poisson data. Wolverine Pharmacometrics Corporation

  6. Examples and Brief History 3. Predictors (i.e. SHOE): Consider the simple linear (in the random effects) mixed model with the usual assumptions: Y = THETA(1) + THETA(2)*SHOE**THETA(3) + ETA(1) + EPS(1) 4. Random effects (): The rest of workshop 6. Wolverine Pharmacometrics Corporation

  7. What is Skewness? A number? This is pulled from the S-Plus 6.1 help API. If y = x - mean(x), then the "moment" method computes the skewness value as mean(y^3)/mean(y^2)^1.5 Wolverine Pharmacometrics Corporation

  8. What is Kurtosis? A number? This is pulled from the S-Plus 6.1 help API. If y = x - mean(x), then the "moment" method computes the kurtosis value as mean(y^4)/mean(y^2)^2 - 3. Wolverine Pharmacometrics Corporation

  9. Transformations for Skewness Removal Power Family: Box - Cox (1964) Manly (1976) Wolverine Pharmacometrics Corporation

  10. Kurtosis Removal John - Draper (1980): Wolverine Pharmacometrics Corporation

  11. An Example, Finally! Back to our second example: PopPK! C1.TXT DATA1.TXT Wolverine Pharmacometrics Corporation

  12. Much Data/Subject + Conditional Estimation = $PK KA=THETA(1)*EXP(ETA(1)) ET2=(EXP(ETA(2)*THETA(4))-1)/THETA(4) ;THETA(4) = LAMBDA K=THETA(2)*EXP(ET2) S2=THETA(3)*WT $THETA (0,1) ;KA (0,.12) ;K (0,.4) ;VD (.5) ;LAMBDA TRANSFORM PARAMETER $OMEGA .25 ;INTER-SUBJECT VARIATION KA $OMEGA BLOCK(1) .05 ;INTER-SUBJECT VARIATION K $ERROR Y=F*(1+EPS(1)) $SIGMA .013 ;PROPORTIONAL ERROR $ESTIMATION MAXEVALS=9000 PRINT=1 METHOD=1 INTERACTION Wolverine Pharmacometrics Corporation

  13. Results with nmv or nm6 C6.TXT Drop in MOF of ~ 16 points.  Estimate = 0.9 Wolverine Pharmacometrics Corporation

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