From: "HUTMACHER, MATTHEW [Non-Pharmacia/1825]" <matthew.hutmacher@pharmacia.com>

Subject: Mixture model at the IOV level?

Date: Thu, 17 May 2001 10:53:51 -0500

 

Hello,

 

I was wondering if it is possible (or anyone had any experience) to fit a mixture model, where the different likelihoods originate at the IOV level and not the IIV level (between subject). In essence, I believe that different means (likelihoods) need to be fit within the individual at for different sampling periods in a random way.

 

Matt

 

*****

 

From: LSheiner <lewis@c255.ucsf.edu>

Subject: Re: Mixture model at the IOV level?

Date: Thu, 17 May 2001 12:02:04 -0700

 

We recently had to do this. There is at present almost no way to take advantage of NONMEMs mixture model option to accomplish this. The most general solution is to write your own PRED or $PRED and compute the mixture likelihood yourself. Unfortunately this means you give up the ability to use any ADVANs ... To see our recent example, look in

ftp://pkpd.icon.palo-alto.med.va.gov/nonmem.dir/COMPLIANCE2.dir/

 

If your mixture situation is very simple, you may be able to get away with the following, which does allow fukller use of NONMEMs capacities. For concreteness, I'll use the following example:

A patient is seen on (at most) two occasions, and a dose of drug is given on each and the Cp followed. The patient can be "sick or "not sick" on any occasion (these are the 2 mixture classes), and this might affect his clearance of the dose administered on the occasion.

 

In this simple case, one can define 4 mixture classes (NSPOIP=4) at the individual level:

 

Individual Occasion Occasion

Mixture class mixture class

------------- ---------- --------------

1 1 not-sick

2 1 sick

3 2 not-sick

4 2 sick

 

THEN

1. $PK might have code such as

IF (MIXNUM.EQ.1.OR MIXNUM.EQ.3) THEN

CL=THETA(1)*EXP(ETA(1))

ELSE

CL=THETA(2)*EXP(ETA(2))

ENDIF

 

2. $MIX might have code such as

$MIX

NSPOP=4

P(1)=THETA(5)

P(2)=1-THETA(5)

P(3)=THETA(5)

P(4)=1-THETA(5)

 

In the end, MIXEST will be 1,2,3,4 according as the fit finds the sick/'not-sick status on the 2 occasions.

 

Note that if you have m mixture classes and k occasions, this requires m**k separate individual-level micture clasaes, which quickly gets unweildy!

 

--

_/ _/ _/_/ _/_/_/ _/_/_/ Lewis B Sheiner, MD (lewis@c255.ucsf.edu)

_/ _/ _/ _/_ _/_/ Professor: Lab. Med., Bioph. Sci., Med.

_/ _/ _/ _/ _/ Box 0626, UCSF, SF, CA, 94143-0626

_/_/ _/_/ _/_/_/ _/ 415-476-1965 (v), 415-476-2796 (fax)

 

 

****

 

 

From: "Piotrovskij, Vladimir [JanBe]" <VPIOTROV@janbe.jnj.com>

Subject: RE: Mixture model at the IOV level?

Date: Fri, 18 May 2001 14:15:12 +0200

 

One more example.

 

If the drug is given orally it is not uncommon that ALAG can be seen in some patients and not seen in others. One way to model this is using the mixture, e.g.:

...

SUBP = MIXEST

SP1 = 0

SP2 = 0

IF (MIXNUM.EQ.1) SP1 = 1

IF (MIXNUM.EQ.2) SP2 = 1

ALAG1 = (SP1*THETA(1) + SP2*THETA(2))*EXP(ETA(1))

...

$MIX

NSPOP = 3

P(1) = THETA(3)

P(2) = 1-P(1)

 

$THETA 0 FIX (0 1)

 

Suppose now there are two occasions with the same drug. One can imagine a situation when in some patients ALAG is observable at one occasion and not observable at another occasion. In other patients ALAG is not observable at any occasion. One more possibility: at both occasions ALAG is observable. This situation can be modelled as follows:

...

SUBP = MIXEST

SP1 = 0

SP2 = 0

SP3 = 0

SP4 = 0

IF (MIXNUM.EQ.1) SP1 = 1

IF (MIXNUM.EQ.2) SP2 = 1

IF (MIXNUM.EQ.3) SP3 = 1

IF (MIXNUM.EQ.4) SP4 = 1

ALG1 = (SP1*THETA(1) + SP2*THETA(2)) * EXP(ETA(1))

ALG2 = (SP3*THETA(3) + SP4*THETA(4)) * EXP(ETA(2))

ALAG1 = (2-OCC)*ALG1 * EXP(ETA(3)) + (OCC-1)*ALG2 * EXP(ETA(4))

; OCC is 1 or 2

...

$MIX

NSPOP = 4

P(1) = THETA(5)

P(2) = THETA(6)

P(3) = THETA(7)

P(4) = 1-P(1)-P(2)-P(3)

$THETA

(0 FIX) ; 1

(0 .5 1) ; 2

(0 FIX) ; 3

(0 1 2) ; 4

(0 .2 .3) ; 5

(0 .1 .2) ; 6

(0 .3 .4) ; 7

 

Finding proper boundaries for THETA(5) to THETA(7) can be a problem...

 

Best regards,

Vladimir

------------------------------------------------------------------------

Vladimir Piotrovsky, Ph.D.

Research Fellow

Global Clinical Pharmacokinetics and Clinical Pharmacology (ext. 5463)

Janssen Research Foundation

B-2340 Beerse

Belgium

Email: vpiotrov@janbe.jnj.com