# Box-Cox tranformation

From: Leonid Gibiansky <lgibiansky>
Date: Fri, 6 Nov 2015 11:21:58 -0500

Dear All,
Could statisticians out there help me to understand the use of the
Box-Cox transformation? I found the old discussion here:

http://www.cognigencorp.com/nonmem/current/2010-June/1721.html

Specifically:

Box-Cox transformation
TVCL=THETA(1)
BXPAR=THETA(2)
PHI = EXP(ETA(1))
ETATR = (PHI**BXPAR-1)/BXPAR
CL=TVCL*EXP(ETATR)

I think the idea is to use transformation in cases when true CL is not
log-normal. However, here is what we do here
1: use normally distributed ETAs to create log-normal PHI
2: use Box-Cox to create ETATR (and the idea of Box-Cox is to make
normal out of something that is not normal)
3: Use ETATR (that is normal? at least that is what Box-Cox is supposed
to do) to create CL.

If it is working (and I suppose it is working as otherwise it would not
be used), it is working because exp() + Box-Cox create something
not-normal out of normal ETA(1). But this is not an intended use of this
transformation.

Would it be better to use the following:

1: Use normally-distributed
logCLbc=THETA(1)+ETA(1)

2: Use inverse Box-Cox to get something not normal:

logCL=(1+lambda*logCLbc)**(1/lambda)

(we need to make sure that logCLbc is positive, so we may shift it as
needed)

3: return back to CL scale
CL=EXP(logCL)

This version also has an advantage of being easily MU-referenced (that
is required for the application of the IMP/SAEM/etc. estimation methods)

Have anybody tried this second version and compared it with the first one?

Thanks!
Leonid

--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566

Received on Fri Nov 06 2015 - 11:21:58 EST

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