RE: Mixture model for Disease Progression
Dear Dr. Holford,
Thank-you for the insightful comments. Since the last posting I have made some
progress; the updated code can be found below. The biological validity of the
mixture populations bothered me as well. Fortunately, the team measured several
biomarkers indicative of disease at baseline. One of these biomarkers (BIOM in
the code) has a distinct bimodal distribution. I made the biomarker a DV as
well and added a flag column to the dataset (PDT) to tell NONMEM the PD type. I
still have a few questions for the code below and I am hoping that you will
kindly answer some questions:
a) Would you still suggest using the biomarker simply as a covariate rather
than the mixture model below? The reason I chose the approach below is because
when I plot the eta for the slope (MET2) vs. the biomarker I see no
co-relation. It appears that the biomarker acts like an on-off switch. Low
levels of the biomarker as associated with no progression while high levels are
associated with progression. It may just make sense to convert the biomarker to
a categorical covariate and get rid of the mixture?
b) NONMEM acts strangely for the BSV of the biomarker in the code below. I
have only one observation for the biomarker per individual (only baseline
measurements right now) so only 1 level of random effect can be implemented for
the biomarker. I tried to first code it as an ETA (NONMEM crashed and gave
infinite objective function error). If I code the random effect for the
biomarker as an EPS (as shown below) NONMEM is happy. Why does NONMEM care and
wants the random effect as an EPS and not an ETA?
c) A quick question regarding your tutorial on PAGE. The random effect on the
slope is modeled in your lecture notes as a proportional error model. Why is it
proportional, why can't it be additive? An additive error model would also
allow negative slopes. I have used additive error in my code since it allows a
mean slope of zero with BSV around zero for the non-progressers.
Please advise,
Mahesh
$PRED
CALLFL=1
EST=MIXEST
MQ1 = 0
MQ2 = 0
IF (MIXNUM.EQ.1) MQ1 = 1
IF (MIXNUM.EQ.2) MQ2 = 1
MET1=THETA(1)*ETA(1)
MET2=THETA(2)*ETA(2)
BIOM1=THETA(3) ; PATHOLOGIC BIOM
BIOM2=THETA(4)
TVBM = ((BIOM1*MQ1) + (BIOM2*MQ2))
BIOM = TVBM
BASE1=THETA(5) ; PATHOLOGIC BASELINE
BASE2=THETA(6)
TVBA = ((BASE1*MQ1) + (BASE2*MQ2))
BASE = TVBA*EXP(MET1)
SLOP1=THETA(7) ; PATHOLOGIC PROGRESSION PARAMETER
SLOP2=THETA(8)
TVSL = ((SLOP1*MQ1) + (SLOP2*MQ2))
SLOP = TVSL+MET2
W1=THETA(9)
W2=THETA(10)
IPRED=BASE + SLOP*TIME
Y1=IPRED + W1*EPS(1)
Y2=BIOM + W2*EPS(2)
Q1=0
IF(PDT.EQ.1) Q1=1 ; PDT IS 1 FOR DISEASE SCORES
Q2=0
IF(PDT.EQ.2) Q2=1 ; PDT IS 2 FOR BIOMARKER
Y=Q1*Y1+Q2*Y2
$MIX
NSPOP=2
P(1)=THETA(11) ;PATHOLOGIC
P(2)=1-THETA(11) ;NON-PATHOLOGIC
$THETA
...
(0,FIX) ;THETA(8) FIXED TO ZERO FOR NON PROGRESSERS
...
$OMEGA
1 FIX
1 FIX
$SIGMA
1 FIX
1 FIX
Quoted reply history
________________________________
From: [email protected] on behalf of Nick Holford
Sent: Sun 1/16/2011 1:49 AM
To: [email protected]
Subject: Re: [NMusers] Mixture model for Disease Progression
Mahesh,
Do you have a good biological reason to divide your population into different
subpopulations?
If not then a more flexible way to describe an association between baseline and
slope is estimate the covariance between the random effects. This does carry
with it the explicit assumption that the mixture model makes about the
existence of different sub-populations.
Nick
On 15/01/2011 11:12 a.m., Samtani, Mahesh [PRDUS] wrote:
Hello,
I am trying some simple linear disease progression analysis and the
data suggests that there are 2 populations in the dataset (Low Baseline, Low
Slope vs. High Baseline, High Slope). It appears that that population consists
of progressers and non-progressers (The Pharmacometrics textbook describes some
code with 3 populations i.e. positive slope, zero slope, and negative slope but
I want to keep my model simple).
This is the only piece of the code that seems to work for my dataset.
If I try to estimate THETA(3) in my code it causes the model to either becomes
unstable or I get a very small negative value for THETA(3) with very poor
precision. I would really appreciate feedback from NMusers on the
parameterization of the slope parameter in this model (thetas and etas for the
2 populations).
Many thanks in advance...MNS
$PK
CALLFL =1
EST=MIXEST
IF (MIXNUM.EQ.2) THEN
BASE=THETA(2)*EXP(ETA(2))
SLOP=THETA(4)+ETA(4)
ELSE
BASE=THETA(1)*EXP(ETA(1)) ; PATHOLOGIC BASELINE
SLOP=THETA(3)*(1+ETA(3)) ; PATHOLOGIC PROGRESSION PARAMETER; ETA
PARAMETERIZATION BASED ON TUTURIAL FROM PAGE
ENDIF
$THETA
(0,15 ) ; BASELINE PATHOLOGIC
(0,7) ; BASELINE NON-PATHOLOGIC
(0,0.1) ; SLOPE PATHOLOGIC
(0 FIX ) ; SLOPE NON-PATHOLOGIC
$OMEGA BLOCK(1) 0.15
$OMEGA BLOCK(1) SAME
$OMEGA BLOCK(1) 0.35
$OMEGA BLOCK(1) 0.03
--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
email: [email protected]
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford