Between Subject Random Effect Transformations with NONMEM VI

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Between Subject Random Effect Transformations
with NONMEMVI

• Bill Frame
• 09/11/2009

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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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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?
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• 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. Fishers Z transformation for the Pearson
product moment correlation coefficient (?).
Z ½loge((1?)/(1-?)) 2.
The response (YDV) Change Y to ZY1/2 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)SHOETHETA(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(y3)/mean(y2)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(y4)/mean(y2)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 KATHETA(1)EXP(ETA(1))
ET2(EXP(ETA(2)THETA(4))-1)/THETA(4) THETA(4)
LAMBDA KTHETA(2)EXP(ET2)
S2THETA(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 YF(1EPS(1)) SIGMA .013
PROPORTIONAL ERROR ESTIMATION MAXEVALS9000
PRINT1 METHOD1 INTERACTION
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Results with nmv or nm6?
C6.TXT Drop in MOF of 16 points. ? Estimate
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