From: Lewis B Sheiner <lewis@c255.ucsf.edu>
Subject: FYI - MEM for binary response with one obs/individual
Date: Sat, 15 Sep 2001 10:22:40 -0700
So, perhaps it can be done after all, but Stuart is not sanguine ...\
Quoted reply history
-------- Original Message --------
Date: Sat, 15 Sep 2001 04:21:02 -0700 (PDT)
From: stuart@c255b.ucsf.edu
To: dennis.fisher@durect.com, lewis@c255b.ucsf.edu
>I'm basing my "can't be done" on the idea that the omega is unidentifable:
>if you have 1 success, and 1 failure, how can you
>know if the success will be a success the next time with p>.5
>(=> omega > 0) or with p=.5 (=> omega = 0)?
>
> Lewis
The highly nonlinear nature of the logistic-type model often allows
the inter-
and intra-individual variability to be separated. In one example I
just
ran, I got legitimate estimates 90% of the time. However, as we have
learned since the time of the Bailey-Gregg article in 1997, and as
we
report in our JPP article in last month's issue: When the amount of
data
per individual is very small, the estimates are not
as good as those obtained when interindividual variability is omitted
from the model. In the example I just ran, the estimates are indeed
quite poor, so poor in fact as to suggest that it would be ill-advised
to include interindividual-variability in the model.
Stu
From: LSheiner <lewis@c255.ucsf.edu>
Subject: 1 binary response/person
Date: Mon, 17 Sep 2001 11:29:23 -0700
All -
There's been an exchange recently about whether one can estimate
a hierarchical model given only a single binary response from each
individual. I claimed it couldn't be done, by which I meant that
OMEGA would be meaningless. Stu Beal, in a personal
reply to me (which I shared with nmusers) pointed out that my
claim that it couldn't be done was not strictly true, in the sense
that
NONMEM will not necessarily terminate in rounding errors.
But he did not claim that the estimate of the structural
parameters (theta's) would be good, and he made no claim
whatever about OMEGA.
Perhaps there are circumstances in which taking a MEM
view of single binary response per person data is helpful,
but experience to date indicates that if such
circumstances exist, they are hard to find. All my experience to date
suggests that estimates of those parameters that
are common to both the hierarchical and non-hierarchical formulations
are actually more precisely estimated under the latter,
and estimates of the parameters unique to the hierarchical formulation,
namely OMEGA, are meaningless.
LBS.
--
_/ _/ _/_/ _/_/_/ _/_/_/ 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: Nick HolfordDate: September 17, 2001technical
From: Nick Holford <n.holford@auckland.ac.nz>
Subject: Re: 1 binary response/person
Date: Tue, 18 Sep 2001 07:19:57 +1200
Lewis,
Would you please confirm that your comments about OMEGA being meaningless
are restricted to the single binary response per person case? How exactly
do you know they are meaningless? Is your assertion that they are meaningless
based on theoretical considerations or on the results of simulation?
Are your comments about the precision of estimates from hierarchical
vs non-hierarchical methods based on (misguided) attempts to estimate OMEGA
or in the case where OMEGA is fixed to zero?
What is your opinion/experience of the meaningfulness of OMEGA estimates
for repeated measures binary responses?
I am not familiar with other non-hierarchical methods for logistic
regression. Do they exist for repeated measures?
The key advantages of using NONMEM for binary and other categorical
responses is that one is not restricted to estimating parameters of linear
(or linearized) models and one can perform joint estimation of PK parameters
with the PK predictions driving the model for the binary response. And
of course given a hammer everything looks like a nail.
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: LSheiner <lewis@c255.ucsf.edu>
Subject: Re: 1 binary response/person
Date: Mon, 17 Sep 2001 17:08:46 -0700
Nick Holford wrote:
>
> Lewis,
>
> Would you please confirm that your comments about OMEGA being meaningless
are restricted to the single binary response per person case? How exactly
do you know they are meaningless? Is your assertion that they are meaningless
based on theoretical considerations or on the results of simulation?
I am talking about a single binary response per person. It actually
applies more widely.
Ikuko Yano, Stu and I have a paper in press in JPP ("The need for mixed
effect modeling with population
dichotomous data") which deals with the matter more extensively.
Despite the title, it also p makes some points about continuous
1-observation/person data.
>
> Are your comments about the precision of estimates from hierarchical
vs non hierarchical methods based on (misguided) attempts to estimate OMEGA
or in the case where OMEGA is fixed to zero?
When OMEGA is set to zero, and there is 1 binary obs/person, then NONMEM
does exactly the same thing as standard logistic regression.
>
> What is your opinion/experience of the meaningfulness of OMEGA estimates
for repeated measures binary responses?
> I am not familiar with other non-hierarchical methods for logistic
regression. Do they exist for repeated measures?
If there are repeated measures, then at least in theory, it makes sense
to try to estimate a hierarchical model. The to-appear paper I referred
to
above indicates that even with several observations per person which
truly arise from a MEM, a MEM analysis may still not be better than
a NPD
analysis (i.e. essentially viewing all
of the binary observations as independent).
>
> The key advantages of using NONMEM for binary and other categorical
responses is that one is not restricted to estimating parameters of linear
(or linearized) models and one can perform joint estimation of PK parameters
with the PK predictions driving the model for the binary response. And
of course given a hammer everything looks like a nail.
This is a feature of NONMEM and not of ML for binary data. As I said
above, if you
set OMEGA = 0 then NONMEM does what standard logistic regression would
do,
and, as you point out, makes it more convenient to implement non-linear
models
for the logistic model parameters.
--
_/ _/ _/_/ _/_/_/ _/_/_/ 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: 1 binary response/person
Date: Tue, 18 Sep 2001 10:22:05 +0200
Even if OMEGA is not fixed to zero and the random effect is at the level
of
logit [e.g., LOGIT = INT + SLOPE * LOG(CONC) + ETA(1)] the program
converges
to a negligible value of OMEGA in case of a single binary observation
per
individual.
If more than one observation are available and they are independent,
the
following control works fine:
$PROB dichotomous response: mutiple obs per individual
$DATA nmd.ssc
$INPUT ID CONC DV
$PRED
EC50 = THETA(1)*EXP(ETA(1))
SLOPE = THETA(2)*EXP(ETA(2))
INT = -LOG(EC50) * SLOPE
LOGIT = INT + SLOPE * LOG(CONC)
A=EXP(LOGIT)
P=A/(1+A)
IF (DV.EQ.1) THEN
Y=P
ELSE
Y=1-P
ENDIF
$THETA (0,200,300) (.5,2,15)
$OMEGA .1 .1
$EST METHOD=COND LAPLACE LIKE MAX=500 PRINT=10
$COV
The number of observations/individual should be substantial. I tested
it
with 10 obs/individual and 50 individuals, and it was fine. I presume
if the
number of obs/individual is relatively small, the IIV in SLOPE (which
corresponds to Hill coeff) cannot be estimated, although it has not
been
tested.
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