Between Subject Random Effect Transformations with NONMEM VI

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# Between Subject Random Effect Transformations with NONMEM VI - PowerPoint PPT Presentation

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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### Between Subject Random Effect Transformations with NONMEMVI

Bill Frame

09/11/2009

Wolverine Pharmacometrics Corporation

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

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

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.

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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.

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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.

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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

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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.

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Transformations for Skewness Removal

Power Family:

Box - Cox (1964)

Manly (1976)

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Kurtosis Removal

John - Draper (1980):

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An Example, Finally!

Back to our second example: PopPK!

C1.TXT DATA1.TXT

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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

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Results with nmv or nm6

C6.TXT

Drop in MOF of ~ 16 points.

 Estimate = 0.9

Wolverine Pharmacometrics Corporation