From: "Joern Loetsch"
Subject: [NMusers] covariate significance
Date: Thu, 18 Apr 2002 20:44:25 +0200
Dear NONMEM users,
say there is a covariate "COV" that can take the values of 0, 1 or 2 (nothing else).
There is a parameter X to which the covariate is connected by
either
(choice 1)
IF (COV.EQ.0) THEN
X=THETA(1)
ELSE
X=THETA(1)*THETA(2)
ENDIF
or
(choice 2)
IF (COV.EQ.0) THEN
X=THETA(1)
ELSE
X=THETA(1)*THETA(2)*COV
ENDIF
Would one go with the second choice when the fit is simply better or only when the objective function
decreases significantly as compared to choice 1. I'm not in clear because it looks to me as if both
choices had the same number of parameters.
Thanks in advance
Jorn
______________________________________________________
Jorn Lotsch, MD
pharmazentrum frankfurt, Dept. of Clinical Pharmacology
Johann Wolfgang Goethe-University Hospital
Theodor-Stern-Kai 7
D-60590 Frankfurt am Main
GERMANY
Tel.:+49-69-6301-4589
Fax.:+49-69-6301-7636
http://www.klinik.uni-frankfurt.de/zpharm/klin/
covariate significance
From: LSheiner
Subject: Re: [NMusers] covariate significance
Date: Thu, 18 Apr 2002 13:57:15 -0700
Looks like a peculiar model to me.
If COV is continuous (e.;g., dose) then the two models to compare
would be something like
FULL: X = THETA(1) + THETA(2)*COV
REDUCED: X = THETA(1)
If COV is categorical (e.g., "small" medium" "large"), then the models
to compare would be something like
Q1=0
Q2=0
IF(COV.EQ.1) Q1 = 1
IF(COV.EQ.2) Q2 = 1
FULL: X = THETA(1) + THETA(2)*Q1 + THETA(3)*Q2
REDUCED: X = THETA(1)
LBS.
--
_/ _/ _/_/ _/_/_/ _/_/_/ Professor Lewis B Sheiner, MD
_/ _/ _/ _/_ _/_/ mail: Box 0626, UCSF, SF, CA,94143
_/ _/ _/ _/ _/ courier: Rm C255, UCSF, SF, CA,94122
_/_/ _/_/ _/_/_/ _/ 415-476-1965 (v), 415-476-2796 (fax)
From: Nick Holford
Subject: Re: [NMusers] covariate significance
Date: Fri, 19 Apr 2002 09:09:44 +1200
Jorn,
My decision would be guided more by the biological/mechanistic plausibility of
considering the covariate as a dichotomous variable (choice 1) or a continuous scale
variable (choice 2). I would certainly want to try a model with an extra parameter to
test for each of the 3 values of X having its own independent effect on THETA(1) if the
biology was compatible.
Biology is about studying the signal. Statistics is about studying the noise. I find
signal based decisions more satisfying than those based on reducing the noise.
Nick
Nick Holford, Divn Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm
From: "Olofsen, E. (Anes)"
Subject: RE: [NMusers] covariate significance
Date: Thu, 18 Apr 2002 23:42:06 +0200
Dear Joern,
How about choice 3?
IF (COV.EQ.0) THEN
X=THETA(1)
ELSE IF (COV.EQ.1) THEN
X=THETA(1)*THETA(2)
ELSE
X=THETA(1)*THETA(3)
ENDIF
Best regards,
Erik Olofsen
From: "R. E. Port"
Subject: Re: [NMusers] covariate significance
Date: Fri, 19 Apr 2002 09:30:24 +0200 (CEST)
Dear Jrn:
It seems to me that your original question was about how to choose
between two models which differ in structure but not in the number
of parameters (Lewis, Nick, and E. Olofsen suggest more flexible
alternatives with an additional parameter). In the case of two models
with the same number of parameters there is no statistical criterion
for comparison - as far as I know. Thus, you should not only use
biological knowledge in making your choice but you have to.
With best regards, Ruedi
-------------------------------------------------------------------------------
Dr. R.E. Port, German Cancer Research Center, D-0200
P.O. Box 10 19 49, D-69009 Heidelberg, Germany
phone: +49-6221 42-3381
fax: -3382
e-mail: r.port@dkfz.de
From: "Piotrovskij, Vladimir [PRDBE]"
Subject: RE: [NMusers] covariate significance
Date: Sun, 21 Apr 2002 10:55:16 +0200
Jorn,
Your COV may represent levels of a categorical covariate (factor). E.g. COV is race and
0, 1 and 2 code the three basic races. In that case your choice 1 is the only one (if you
have sufficient evidences to assume that COV=1 and COV=2 produce equal effect of X).
Alternatively, COV may be a quantitative variable, and 0, 1 and 2 are values (e.g., doses),
not levels. Then, only choice 2 is applicable. You could write your expression, which is in
fact a linear model, as
follows:
X = THETA(1)*(1+THETA(2)*COV)
thereby avoiding the IF ... ELSE loop. The parameters are better tractable: THETA(1) is an
intercept and THETA(2) is a slope expressed in terms of the fractional change.
In any case you cannot select one of the two implementations based on goodness-of-fit
or other statistical criteria.
Best regards,
Vladimir