RE: Missing mixed continuous and categorical data
From: "Mats Karlsson" mats.karlsson@farmbio.uu.se
Subject: RE: [NMusers] Missing mixed continuous and categorical data
Date: Wed, May 4, 2005 4:10 am
Hi,
We have recently used a mixture model approach for missing categorical
covariates (see code below). If you have category observations in some but
not all individuals, the parameter values for the different categories and
corresponding mixture components will be the same (i.e. A known EM and a
mixture model assigned EM will have the same typical CL value). The observed
(or known from literature) subpopulation frequencies can be used as fixed
parameters. Thus, no additional parameters need to be estimated. This
approach can be extended (I think but have not tried) to the situation where
both a continuous and categorical are missing. If they are not correlated
the extension is trivial. For the continuous covariate you can use the
"data" method (for a discussion on implementation of that method see J
Pharmacokinet Biopharm. 1998 Apr;26(2):207-46) and the categorical the
method illustrated in code below. If they are correlated (and either or both
can be missing), the situation is trickier. However, also that can be done:
let's assume that the covariates instead are SEX and WT and you want to
model CL with different WT relations for the two sexes:
TVCL=THETA(1)*WT
IF(SEX.EQ.1) TVCL=THETA(2)*WT
;Lets assume the following:
WT(males) = 75 (mean) , 10 (SD BSV) , 0 (SD measurement error)
WT(females) = 65 (mean) , 10 (SD BSV) , 0 (SD measurement error)
Males=50% of target population
Categories for missing data are NOMISS, SEXMISS, WTMISS and BOTHMISS.
Everyone has a "1" in one of these categories and "0" in the three other.
For the solution below it is assumed that there are no BOTHMISS
SEX=0/1 for males/females
Assume $SIGMA and $OMEGA fixed to 1
Then an extended model would be:
IF(NOMISS.EQ.1) THEN
TVCL=THETA(1)*WT
IF(SEX.EQ.1) TVCL=THETA(2)*WT
ENDIF
IF(WTMISS.EQ.1) THEN
MWT=75+ETA(1)*10
FWT=65+ETA(1)*10
TVCL=THETA(1)*MWT
IF(SEX.EQ.1) TVCL=THETA(2)*FWT
ENDIF
IF(SEXMISS.EQ.1) THEN
IF(MIXNUM.EQ.1) TVCL=THETA(1)*WT
IF(MIXNUM.EQ.2) TVCL=THETA(2)*WT
ENDIF
$MIX
NSPOP=2
P(1)=EXP(0.0111+(WT-70)*0.0922)/(1+EXP(0.0111+(WT-70)*0.0922))
P(2)=1-P(1)
ENDIF
;the equation of P(1) comes from a logistic regression based on the
;different WT distributions for males and females
;----
Here is the code for the different genotype (VHAB) influences on CL:
IF(VHAB.EQ.1.OR.VHAB.EQ.-99) CLVHAB = 0
IF(VHAB.EQ.2) CLVHAB=THETA(8)
IF(VHAB.EQ.3) CLVHAB=THETA(9)
IF(MIXNUM.EQ.2) THEN
IF(VHAB.EQ.-99) CLVHAB =THETA(8)
ENDIF
IF(MIXNUM.EQ.3) THEN
IF(VHAB.EQ.-99) CLVHAB =THETA(9)
ENDIF
CL=TVCL*(1+CLVHAB)*EXP(ETACL)
$MIX
NSPOP=3
P(1)=0.253
P(2)=0.552
P(3)=0.195
P(1-3) Are observed frequencies of wild type, heterozygous and homozygous
variants in the studied population.
;-------
Best regards,
Mats
--
Mats Karlsson, PhD
Professor of Pharmacometrics
Div. of Pharmacokinetics and Drug Therapy
Dept. of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
SE-751 24 Uppsala
Sweden
phone +46 18 471 4105
fax +46 18 471 4003
mats.karlsson@farmbio.uu.se
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