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

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