such as aminogiycoside antibiotics, digoxin, theophylline,

Improving Drug Dosing In Hospitalzed Patients:
Automated Modeling of Phannacoldnetics for Individualization of Drug Dosage Regmens
Leslie Lenert M.D., Lewis Sheiner M.D., and Terrence Blaschke M.D.
Many clinically useful drugs have a narrow range of
blood concentrations which are both safe and efficacious.
Inter-individual and intra-individual variation in drug
disposition are important factors causing blood
concentrations of drug to fall outside of the therapeutic
range. Modeling of the pharmacokinetics of the individual
offers an effective approach to this problem. Previous
approaches for the modeling of individual pharmacokinetics
have required either extensive computations or access to
computer software and hardware in the clinical
environment, and special expertise to interpret the results.
As part of the MENTOR therapeutic monitoring system,
we have developed software which can, in an automated
fashion, monitor drug dosing and recommend changes
which may be needed to obtain blood concentrations in the
therapeutic range. The software can also detect changes in
drug disposition in particular patients which will lead to
concentrations outside of the therapeutic range, identify
potentially erroneous drug concentration measurements,
and assess the need for further measurements. The
recommendations of the program are delivered to
physicians in a timely fashion through issuance of
MENTOR advisories. A prototype version of this program
has been implemented for aminoglycoside antibiotics.
Expansion to other drugs is planned.
Introduction
For a number of clinically useful drugs, efficacy and
toxicity are correlated with concentrations of drug in
plasma. Achieving therapeutic concentrations, that is,
concentrations likely to result in efficacy with minimal
toxicity, is often difficult. Inter-individual variation can
result in large differences in plasma concentrations in
patients given the same dose per kdlogram. This variability
creates significant difficulties when the therapeutic range,
the interval between a miimum effective concentration
and a maximum safe concentration, is small. For agents
such as aminogiycoside antibiotics, digoxin, theophylline,
lidocaine and cyclosporine, periodic monitoring of
concentrations in blood and individual adjustment in dosage
is imperative for safe and efficacious drug therapy.
Examples of the importance and difficulty of
individualization of a dosing regimen are common. Digoxin
0195-4210/88/0000/0308$01.00 X 1988 SCAMC, Inc.
Divisions of Clinical Pharmacology
Stanford University and University of California San Francisco
308
administration is associated with a high rate (5-23%) of
drug toxicity due to excessive dosage. There is also a high
rate of ineffective dosing: 11-36% of patients do not
achieve concentrations in the therapeutic range(1). Interindividual
variation may be an important cause of this
problem. We observed similar problems with gentamicin
administration at Stanford Medical Center. 365 consecutive
gentamicin concentrations in 117 patients between 1/7/88
and 2/7/88 were reviewed retrospectively. Concentrations
had been identified by nursing staff as either peak or
trough prior to submission to the laboratory.
Concentrations were then classified into therapeutic peak
concentrations, >5.0 mg/L and < 12.0 mg/L, therapeutic
trough concentrations, < 2.0 mg/L, and non-therapeutic
concentrations of both types. Non-therapeutic
concentrations were more common than therapeutic ones.
Twelve percent of patients had peak or trough
concentrations above the therapeutic range and more than
60 percent never achieved a therapeutic peak
concentration. When confronted with the well known
toxicities of digoxin and gentamicin, physician dosing
strategies were conservative, usually sacrificing efficacy to
prevent toxicity. Nonetheless, there is sufficient interindividual
variation that supra-therapeutic concentrations
are frequent despite the tendency to under dose.
Intra-individual variation, change in drug disposition in
an individual over time, is another problem. Progression or
remission of disease, or the addition of other drugs can
alter pharmacokinetics, resulting in drug concentrations
outside the therapeutic range. Examples include decreased
aminoglycoside clearance with renal failure and increased
digoxin concentration due to co-therapy with quinidine or
verapamil. Changes in pharmacoldnetics may also appear
without a recognized cause. Intra-individual variation is
often apparently spontaneous and unpredictable in
magnitude or timing. It is usually detected by unexpected
drug concentrations seen during therapeutic monitoring
done for that purpose or performed routinely.
Because of wide inter-individual and intra-individual
variation, adjustments in dosing often are calculated by
using a computer model of an individual's
pharmacokinetics. Bayesian forecasting is an approach that
allows the estimation of individual pharmacoldnetic model
parameters from one or two drug concentrations and an
accurate history of drug administration (2). For several
drugs, dosing assisted by Bayesian forecasting has been

shown to be a faster and more accurate means of achieving
desired drug concentrations than unassisted dosing (3,4).
Routine use of Bayesian forecasting programs in the clinical
setting, however, has been limited by inaccessibility of
hardware and software in the clinical setting, time required
for data collection, and knowledge required for use and
interpretation of the results of Bayesian analysis.
While there are practical difficulties in applying this
technology, the data required for individual model
formulation using Bayesian forecasting is available for most
patients in routine laboratory and drug administration
records. As part of a general therapeutic monitoring
system which captures and analyzes data from hospital
information systems, MENTOR (5), we are developing a
computer program that can automatically model individual
pharmacokinetics for selected drugs using Bayesian
forecasting. Drugs to be included are aminoglycoside
antibiotics, theophylline, lidocaine, digoxin, cyclosporine,
phenytoin, and warfarin. The estimated pharmacokinetic
parameters for each individual will be used to predict drug
concentrations for a given regimen (to assess efficacy and
safety), to generate advice for adjustments in dosage if
necessary, and to warn physicians of changes in an
individual's pharmacokinetics or suspected erroneous drug
concentration measurements. In addition, the program will
also be able to analyze the pattern of blood sampling in a
patient and make recommendations for future sampling.
The program's conclusions will be passed to a linked
symbolic expert system for further analysis. Final
recommendations will be communicated to the physician in
the form of MENTOR advisories (5). We have
implemented a prototype of this program for
aminogiycoside antibiotics. The remainder of this paper
will discuss the design and performance of that prototype.
Overview
Plrogram Desigg
The automatic pharmacokinetic monitoring module will
be an integral part of the MENTOR system of programs.
The link between MENTOR and PKMonitor is shown in
figure 1. Data from the H.I.S. of interest to MENTOR is
written into the Data Base and placed in a queue for
processing. If the data is of interest to PK Monitor, a
controller activates PKMonitorwhich reads the patient data
base and estimates individual pharmacokinetic parameters
for the patient. If data from the H.I.S. concerns drug
concentrations, the program determines whether the
concentration is expected or unexpected in a manner to be
described later, and in the face of an unexpected
concentration, attempts to determine if this reflects a true
change in the patient or 'bad data." Information about
changes in physiology (serum creatinine measurements for
example) cause PK Monitor to re-estimate the
pharmacokinetic model parameters for the patient and
determine if important changes in drug concentration are
imminent. Data about drug dose changes cause PKMonitor
to predict the effect of the new regimen on the drug
concentration using that individual's pharmacokinetic
parameters. Doses that would result in concentrations
309
b
I
-ro
tk I
Figure 1. Operation of PK Mnitor wih MENTOR.
m VAXb
outside the therapeutic range are identified. These data
are written back into the patient data base for later access
by the Inference Engine using rules and frames in the
Knowledge Base. Advisories on this data are issued in the
same fashion as other MENTOR advisories, through the
Advisory module.
Bayesian forecasting balances prior knowledge of the
population mean and variance of the pharmacokinetic
parameters of a drug and observations of the drug
concentrations in an individual to find the parameters for
an individual (posterior mode). Many programs have been
written using this technique to estimate drug dosage, and
some of these programs have been validated in clinical
trials. However, all of these programs operate in a
consultative mode. They are applied at a given point in the
course of a patient's therapy to formulate a dose
recommendation. We are modifying this technology to
work in a monitoring mode, following a patient's course
and learning more about the patient as the number of
relevant observations increase.
In a monitoring mode the program must be able,
independent of an expert, to suggest appropriate doses for
a patient using historical information, detect changes in the
patient and revise estimates of model parameters. The
program must also have an understanding of the validity of
its recommendations, or sel kn.wle to prevent poor
wording of advisories in the absence of data. Because
spurious results can occur from time to time in the clinical
environment, independent operation in a monitoring mode
requires identification and minimition of their impact.
Further, the capability to detect change, assess selfknowledge,
and identify spurious drug concentration results
allows PK Monitor to feed back to physicians through
MENTOR advisories new kinds of information. First, it
can inform physicians of changes in drug pharmacokinetics
and "bad data" and prevent toxicity and inappropriate
w
Xeo 1166 bad prorm

decisions based on erroneous data. Second, the program
can evaluate the pattern of blood sampling It can then
intervene through advisories to maintain adequate
pharmacokinetic knowledge of the patient and to prevent
unnecessary samphng.
Change Over lime
Fundamental to the ability to monitor a patient is the
ability to deal with change in that patient over time. PK
Monitor has two methods for dealing with changes in
pharmacokinetics over time. One method is used for
alterations in physiology or drug interactions which are
known to cause changes in pharmacokinetics. Such events
categorize an individual as a member of a special subpopulation.
For example, the sub-population of patients
receiving theophylline and cimetidine have theophylline
clearances with a mean 40% less than the general
population. The program manages this type of change by
allowing the patient to move from one sub-population to
another at discrete intervals. These discrete intervals are
the times when drug doses are administered. The patient
is then assumed to stay in the same sub-population until the
next dose. This method of managing anticipated change is
standard for consultative Bayesian forecasting programs
(2,3,4,6).
Other changes are unantcipated that is, PKMonitor has
no knowledge of the patient that suggests a possible cause
of the change. The approach for this type of change
assumes the patient is homeostatic, but tests each new
concentration for evidence of change. The program
operates with the following postulate: change has occurred
when model parameters that once were predictive of
incoming drug concentrations in an individual are no longer
predictive. Therefore PK Monitor tests for change in an
individual by determining whether a new observed drug
concentration can be predicted from prior patient data. By
definition a new drug concentration is predicted by the
previous data, if it falls within the predictive interval. The
predictive interval is defined as:
prediction ± 2 x . VFPF
where V(P) = variance of prediction
The variance of prediction is the sum of the variance due
to lack of knowledge of the exact values of the individual's
unique shift(s) of the parameter(s) from the sub-population
mean value, (called corectabl uncertainty) and the variance
due to error in the timing and measurement of the drug
concentration (called uncorrectable uncertainty). As more
concentrations are observed (assuming no parameter
changes), the program calculates progressively better
estimates of the parameter shifts, and both the correctable
uncertainty and the predictive interval become smaller.
When enough data are available (e.g., 4 or 5 drug
concentrations), the predictive interval asymptotes to its
lower bound, the variance due to error in timing or drug
measurement, the uncorrectable uncertainty. If no further
data on the patient are forthcoming, PKMonitor allows the
predictive interval to enlarge by assuming the correctable
310
model: constant l.v. Infusion
decay of
uneXpectod knowldge of
to popublan
drug tbap~
cone. p; redi tiv
time
Figure 2. Change In the predictive Interval with
blood concentration measurement and time
uncertainty increases back to the naive (population) value
over a period of time approximately equal to the tempo of
change in the individual (figure 2.)
When an observed concentration is outside the
predictive intervaL PK Monitor labels this concentration
unexpected, because neither uncertainty in parameters nor
drug concentration measurement error accounts for this
observation. Unewected concentrations could be due either
to change in the patient since the last observation or an
erroneous measurement (bad data). Without additional
data not normally available to the program, it is not
possible to determine which is the most likely etiology.
Physicians are advised about unexpected data and a repeat
concentration measurement is recommended. If the repeat
(or next) concentration is within the old predictive intervaL
(that is, the predictive interval before the unexpected
observation), then the hypothesis of no change in the
patient is confirmed and the unexpected concentration is
identified as bad data. An advisory to this effect will be
sent to the physician to prevent inadvertent action on
erroneous data. The effect of the erroneous data on future
prediction is minimized by a technique for dealing with
outliers in data, known as robust estimation (7).
If, however, the second concentration is also outside the
old predictive intervaL then the type of change suggested by
both concentrations is analyzed. The program applies the
Bayesian estimaion technique to each concentration
separately and determines the most likely change in
parameters which account for each concentration. If there
is internal consistency between the two concentrations (that
is, calculated confidence intervals for the parameter
estimates overlap) then the hypothesis of change is
confirmed (figure 2).
After unanticipated change is identified, blood
concentration data and parameter estimates from before
that change are discarded. Only blood concentrations after
the change are used for model parameter estimation. If
there is no internal consistency between the concentrations
(i.e., the parameter estimates calculated from each
concentration are widely disparate), then robust estimation
is used to estimate model parameters using all available

data. The observation "widely varying inconsistent data" is
noted and labeled noisy da.
Self-knowIedge
Automatic monitoring with expert proficiency requires
that a program be able to provide some measure of the
validity of its recommendations and be able to anticipate
the loss of the validity of its predictions. We call this Self
Knowlee. Assuming the model accurately represents the
sub-population to which a patient belong, uncertainty in
prediction has two sources (as discussed above): that due
to uncertainty in true parameter values (correctable
uncertainty) and that due to uncertainty due to error in
timing of and measurement of drug concentrations
(uncorrectable uncertainty). These two combine to produce
the forecasting error and the predictive interval. The ratio
of correctable to uncorrectable uncertainty is an estimate
of PK Monitor's knowledge of the model for future
observations in a patient We call this the Knowledge Index
(Figure 3.)
The knowledge index is applied in two ways. It is used
to suppress issuance of advisories on unexpected
concentrations when PKMonitor's knowledge of the patient
is inadequate. This reduces the number of "false positive"
advisories about unexpected concentrations. The
knowledge index is also used to evaluate the adequacy of
pharmacokinetic monitoring. When the knowledge index
is small (small amount of correctable uncertainty compared
to uncorrectable uncertainty), further concentration
measurements will not meaningfully improve predictive
performance and may not be indicated (unless the physician
suspects change in the patient). The program can issue
advisories in this setting to reduce the number of
unnecessary drug concentration measurements. When the
knowledge index is large, it indicates that further data are
needed to allow accurate dosing and additional
measurements of drug blood concentration can be
recommended. The Knwwledge Index decays to the
population value with the predictive interval.
Imglementation
A prototype version of this software for aminoglycoside
antibiotics (gentamicin, tobramycin, and amikacin) has been
implemented in PASCAL on a VAX 11/750 computer. This
prototype is being modified to link with a symbolic software
implemented in Interlisp D on a Xerox 1186 workstation
Knowledge Base under development as part of the
MENTOR system The conclusions of PK Monitor are
passed as primitives for further reasoning by this symbolic
software.
Results
Clinical evaluation of the program will be conducted as
part of the validation of the MENTOR therapeutic
monitoring system. As a preliminary test of the prototype
program, Monte Carlo simulations were performed to
311
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estimate the sensitivity and specificity of the program for
diagnosing change. Normally distributed random error was
introduced into simulated drug concentration measurements
(s.d. error 10%), creatinine measurements (s.d. error 7%)
and drug administration times (s.d. 12 minutes). Two peak
and two trough drug concentrations were used for
information to evaluate a fifth concentration to determine
if significant change had occurred. A 30% reduction in
clearance between the fourth and the fifth concentrations
was identified by the program as a significant change in
pharmacokinetics 92% of the time. The program identified
significant change when there was none only 8% of the
time. These results suggest that, given adequate amounts
of data, the program can detect change without an unduly
high false positive rate.
Discussion
PKMonitor is the mathematical component of an expert
system for pharmacoldnetic monitoring of drug dosing. The
program formulates a model of drug disposition for an
individual patient for subsequent analysis by a symbolic
expert system. A mathematical model of the individual, as
opposed to a hierarchical or heuristic model, has many
advantages. It expresses the course of drug concentrations
in the individual over time and is well suited the task of
prediction. Mathematical models for drug disposition have
been well studied and validated. Uncertainty can be
expressed in explicit mathematical terms as probability
distributions of the parameters and a predictive interval.
Finally, relationships of model parameters such as
clearance and volume of distribution to physiology and
pathophysiology allow mapping between the model and
disease states.
However, independent monitoring of therapy by PK
Monitor requires "common sense" concepts such as change
and self knowledge to maintain predictive performance.
These concepts are difficult to express with mathematical
models. We have developed an approach to the expression
of these concepts by joining model outputs and expert
derived heuristics.

One type of conceptual link uses rules about model
outputs to determine the program's actions. The
identification and management of unanticipated change is
an example of such a link An individual-specific model
and rules about model outputs allow identification of the
failure of the model to be predictive. A repeat blood
concentration allows the program to determine if the
failure is due to change or bad data. Change is dealt with
by preventng data obtained before the change from
influencng estimates of model parameters used for further
prediction after the change. The diagnosis and
management of change in PKMonitor is a heuristic which
imitates how a skilled operator of Bayesian
pharmacokinetic forecasting program would deal with
probable change in patient pharmacokinetics. Formal
methods of modeling change in parameters over time are
complicated and warrant further study (8). PK Monitor's
method will allow the program to warn the physician of
potential change and to track change, but does not
anticipate the magnitude or acceleration of change in a
patient. Because of PKMonitor's goals are to monitor and
provide recommendations about the dosing aspects of
therapy, with additional interpretation in a timely way by
the patient's physician, we believe this will be adequate.
A second type of connection between model outputs
and expert heuristics concerns model outputs which are
modified to represent a heuristic concept. PK Monitor
represents its self knowledge as a numeric function, the
knowledge index This function integrates uncertainty in
the knowledge of the parameters, dosing history and the
time from the last measured plasma concentration in order
to express the program's overall confidence in the
predictions of the model. Rules in the linked symbolic
system apply the knowledge index to prevent false positive
advisories due to lack of knowledge of the patient. Further
the concept of "cost effective" knowledge of the patient,
Referene
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312
knowledge which allows accurate dosing without
unnecessary blood sampling, is represented in the "target"
knowledge index value. Rules can then compare the
current value of the knowledge index with the target value
to give advice for further blood sampling.
While our intent has been to develop software which
allows the application of Bayesian modeling techniques for
monitoring drug dosing, the above described techniques
could be incorporated into "consultative style" Bayesian
forecasting programs to provide intelligent assistance with
data analysis and editing.
Smmay
We have developed a prototype computer program for
automatic modeling of individual pharmacokinetics using
data from a hospital information system. The program
links the model of the individual with schema to detect
change and measure self knowledge to allow accurate
independent operation. This program is an integral part of
the MENTOR therapeutic monitoring system. Through
application of the model of the individual the program
performs dosage monitoring, formulates dosing advice,
identifies change, or bad data, and formulates
recommendations for further monitoring of drug
concentrations. The recommendations of the program are
issued to the physician in a timely manner through
MENTOR advisory notices. The program awaits
evaluation along with the rest of the MENTOR system, but
preliminary simulations suggest reasonable sensitivity and
specificity in monitoring change.
This work was supported by N.I.H. Training grant number
GM07065 and N.C.H.S.R. grant number HS05263.
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D.C.: IEEE, 1987.
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