Transcript Document

The BigWinPops and MM-USCPACK Programs, USC Laboratory
of Applied Pharmacokinetics (www.lapk.org)
Roger Jelliffe, MD, Alan Schumitzky, PhD, David Bayard, PhD, Michael Van Guilder, PhD, Andreas Botnen, M.S., Michael Neely, M D,
Alison Thomson, Ph.D, Maurice Khayat, B.S., and Aida Bustad, B. S., Laboratory of Applied Pharmacokinetics, USC Keck School of
Medicine, Los Angeles CA
•Get the entire ML distribution, a Discrete
Joint Density: one parameter set per
subject, + its probability.
•Shape of distribution not determined by
some equation, only by the data itself.
•Multiple individual models, up to one
model set per subject.
•Can discover, locate, unsuspected
subpopulations.
•Behavior is statistically consistent.
Study more subjects, guaranteed better
results.
•The multiple models permit multiple
predictions.
•Can optimize precision of goal
achievement by a MM dosage regimen.
•Use IIV +/or assay SD, stated ranges.
•Computes environmental noise.
•Bootstrap, for confidence limits,
significance tests.
EFFICIENCY AND
RELATIVE ERROR
Estimator Relative Efficiency % Relative
Error
Direct Observation
100
1.00
PEM
75.4
1.33
NPAG
61.4
1.63
NONMEM FOCE
29.0
IT2B FOCE
25.3
3.95
0.9
111.11
NONMEM FO
3.45
HYBRID BAYESIAN POSTERIOR UPDATING
Start with MAP Bayesian. It reaches out, but pop prior
holds it back.
Add new support points nearby, inside and outside, to
precondition the population model for the patient
data it will receive.
Then do MM Bayesian on ALL the support points.
We are implementing this now. Out soon.
16
14
histogram (white)
of PEM estimators
12
histogram (blue) of
NONMEM FO
estimators
10
8
6
4
BAYESIAN FOR VERY UNSTABLE PATIENTS:
INTERACTING MULTIPLE MODEL (IMM) UPDATING
2
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Multiple Model (MM)
Dosage Design
1)Use a prior with discrete multiple
models - an NPEM or NPAG model.
2)Give a candidate regimen to each
model.
3)Predict results with each model.
4)Compute weighted squared error
of failure to hit target goal at target
time.
5)Find the regimen hitting target with
minimal weighted squared error.
6)This is multiple model (MM)
dosage design – the IMPORTANT
clinical reason for using
nonparametric population PK
models.
Limitation of all other current Bayesian methods - find only the 1 set
of fixed parameter values which fit the data.
Sequential MAP or MM Bayesian = same as fitting all at once.
IMM - Relax this assumption. Let the “true patient” change during
data analysis if more likely to do so.
Lidocaine stepwise infusion regimen
based on Parameter MEANS:
Predicted response of full 81 point
lidocaine population model. Target =
3ug/ml
C o n c e n tr a tio n in c e n tr a l c o m p a r tm e n t [u g /m L ]
0
0.04
W g tA vg
10
9
8
4
7
6
5
5
4
2
3
6
2
3
1
1
8
7
9
10
0
0
100
200
300
400
T i m e [ h o u rs ]
500
600
700
SMM: only the first serum creatinine –
MM Bayesian updating – poor tracking
W g tA vg
1 2 .5
1 0 .0
7 .5
4
5
5 .0
2
2 .5
6
3
1
8
7
9
10
0 .0
0
100
200
300
400
T i m e [ h o u rs ]
500
600
700
RMM: all serum creatinines – changing renal function
richer data MM Bayesian updating – better tracking
W g tA vg
2 0 .0
1 7 .5
1 5 .0
1 2 .5
1 0 .0
4
7 .5
5
5 .0
2
6
2 .5
3
1
7
8
9
10
0 .0
0
MM maximally precise stepwise lido infusion
regimen: Predicted response of full 81 point
lidocaine population model. Most precise
regimen. Target = 3ug/ml
MULTIPLE MODEL (MM) BAYESIAN
POSTERIOR UPDATING.
Support point values don’t change.
Use Bayes’ theorem to compute the
Bayesian posterior probability of
each support point, given the
patient’s data.
Problem: will not reach out beyond
pop parameter ranges.
May miss unusual patient.
100
200
300
400
T i m e [ h o u rs ]
500
600
700
IMM: interacting sequential MM Bayesian
updating – best tracking
Plots of measured versus estimated gentamicin data from a
typical patient with unstable renal function, using (a) SMM, (b)
RMM and (c) IMM analysis. IMM tracks drug behavior best.
Unsigned PE
(means are indicated by solid circles)
25
Unsigned PE mg/L
NONPARAMETRIC
POPULATION MODELS
Approximate likelihoods can
destroy precision of estimation
C o n c e n tr a tio n in c e n tr a l c o m p a r tm e n t [u g /m L ]
modeling software
runs in XP. The user defines a
c
c
structural PK/PD model using the BOXES program.
This is compiled and linked transparently. The data
files are entered. along with the instructions. Routines
for checking data files and viewing results are
provided, similar to the older DOS version, but now in
XP. Likelihoods are exact, behavior is statistically
consistent, and parameter estimates are precise [1].
The software is available by license from the first
author for a nominal donation.
The MM-USCPACK clinical software [2] uses
NPAG population models, currently for a 3
compartment linear system. It computes the dosage
regimen to hit desired targets with minimum expected
weighted squared error, thus providing maximal
precision in dosage regimen design, a feature not
seen with other currently known clinical software.
Models for planning, monitoring, and adjusting therapy
with aminoglycosides, vancomycin (including
continuous IV vancomycin), digoxin, carbamazepine,
and valproate are available.
The interactive multiple model (IMM) Bayesian fitting
option [3] now allows parameter values to change if
needed during the period of data analysis, and
provides the most precise tracking of drugs in over
130 clinically unstable gentamicin and 130
vancomycin patients [4].
In all the software, creatinine clearance is
estimated based on one or two either stable or
changing serum creatinines, age, gender, height, and
weight [5].
1. Bustad A, Terziivanov D, Leary R, Port R,
Schumitzky A, and Jelliffe R: Parametric and
Nonparametric Population Methods: Their
Comparative Performance in Analysing a Clinical Data
Set and Two Monte Carlo Simulation Studies. Clin.
Pharmacokinet., 45: 365-383, 2006.
[2] Jelliffe R, Schumitzky A, Bayard D, Milman M, Van
Guilder M, Wang X, Jiang F, Barbaut X, and Maire P:
Model-Based, Goal-Oriented, Individualized Drug
Therapy: Linkage of Population Modeling, New
"Multiple Model" Dosage Design, Bayesian Feedback,
and Individualized Target Goals. Clin. Pharmacokinet.
34: 57-77, 1998.
[3]. Bayard D, and Jelliffe R: A Bayesian Approach to
Tracking Patients having Changing Pharmacokinetic
Parameters. J. Pharmacokin. Pharmacodyn. 31 (1):
75-107, 2004.
[4]. Macdonald I, Staatz C, Jelliffe R, and Thomson A:
Evaluation and Comparison of Simple Multiple Model,
Richer Data Multiple Model, and Sequential Interacting
Multiple Model (IMM) Bayesian Analyses of
Gentamicin and Vancomycin Data Collected From
Patients Undergoing Cardiothoracic Surgery. Ther.
Drug Monit. 30:67–74, 2008.
[5]. Jelliffe R: Estimation of Creatinine Clearance in
Patients with Unstable Renal Function, without a Urine
Specimen. Am. J. Nephrology, 22: 3200-324, 2002.
C o n c e n tr a tio n in c e n tr a l c o m p a r tm e n t [u g /m L ]
ABSTRACT The BIGWINPOPS
20
15
10
5
0
group
nmm
mm
0.0001
0.1
3
10
0.0001-50
Box and whisker plots of estimation errors from SMM, RMM, and
IMM analyses of gentamicin data from cardiothoracic surgery
patients at various initial % probabilities of change.