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{\LARGE \bf Representing Health Outcomes for Automated
Decision Formulation}\\[1cm]
Michael P. Wellman\\[.5cm]
MIT Laboratory for Computer Science\\
545 Technology Square, room 373\\
Cambridge, MA  02139\\
Tel: (617) 253-5839\\
Net: {\tt MPW@MIT-MC} \\[5mm]
In MEDINFO 86\\[1.5cm]

{\Large \bf Abstract}\\[1.2cm]
\end{center}

Knowledge-based programs for medical decision making generally do not have
explicit representations for the possible outcomes of their recommendations or
their preferences for these outcomes.  A general framework for
representing health outcomes is presented, designed expressly to
facilitate expressions of preference over them.  The concept of a health
outcome knowledge base is developed, with examples illustrating its 
possible contents and uses of the knowledge for medical decision
formulation.

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\section{\bf Introduction}

Two judgments underly every decision made in the care of a patient.  The
{\it prognosis} is a forecast of the patient's
response to each action considered.  The
{\it evaluation} compares the desirability of each action's prognosis.
Computer programs designed to aid 
medical practitioners in the decision-making process could be more
useful if they shared the central concepts needed for these
judgments---those of health {\it outcomes} and {\it preferences} over
them.  While some programs have elements which may seem to
correspond to these concepts, none have provided a general
representation facility.

Knowledge-based systems often make therapy recommendations without
considering the outcome of the treatment directly.
Clancey~\cite{Clancey83} relates an example from {\sc
mycin}: the rule that eliminates tetracycline from
consideration when the patient is a young child.  Tetracycline is
avoided because it sometimes has the side-effect of
discoloring developing teeth.  However, neither this
outcome nor its undesirability is encoded in
the expert system.  Clancey argues that this kind of
knowledge could improve the explainability of the program.
It is indispensable for formulating and resolving
tradeoffs that arise in more complex decision
situations.

Preferences are invariably implicit in knowledge-based
systems when selection of actions is associated directly
with conditions or situations.  This style of
reasoning---pervasive in rule-based systems---completely
bypasses the two judgments noted above.  Thus, it is
impossible to determine the ``value'' that the program
attaches to particular health outcomes or even which
final outcomes are taken into account.  Furthermore, a program
can never accommodate
variations in preferences among patients without these explicit
concepts.  Such variations are commonplace in medical
situations and often have significant impact on
decisions~\cite{Kassirer83,McNeil-Pauker}.

Decision analysis tools allow for specification of preferences via
utilities associated with the terminal nodes of a
decision tree.  However, a utility expression does not encode
``what actually
happens to the patient'' along that tree path.
Explicit outcomes would provide the analyst with ``risk
profiles'' directly indicating the effects on the patient of
each choice.  As in knowledge-based systems, this would facilitate
explanation and justification of the results of the analysis.
Moreover, separating outcomes from utilities would make it easier to explore
alternate utility structures.

The approach to outcome representation taken here is motivated
primarily by the need for reasoning about preferences to resolve the
tradeoffs that arise in medical decisions.  Once suitable
attributes for health outcomes are chosen, preferences can be
expressed in the language provided by the {\it U}\/tility {\it
R}\/easoning {\it P}\/ackage ({\sc urp})~\cite{WellmanSM}.
Knowledge-based applications programs can use 
{\sc urp} {\it preference models} for making decisions in their specific
domains.

The following section contains a discussion of the general issues and
requirements for a health outcome representation.  Section~\ref{scheme}
outlines a general framework for such representations.  Decision
formulation under this framework is described in
Section~\ref{formulation}.  The concluding section reviews
the main contributions of this work, focusing on viewpoints and
observations underlying the proposed scheme.

\typeout{ -2. }
\section{\bf Representing Health Outcomes}

\typeout{ -2.1. }
\subsection{Issues in Outcome Representation}

In formulating a medical decision problem for analysis by computer,
the choice of a representation for the outcome is
crucial.  Despite its importance, no programs are able to
choose measurement scales automatically.  Hence, systems using any
explicit outcome
measure at all have that measure built into their design.
Consequently, the same scales and representations are applied to each
problem instance.

Decision-making programs designed for even narrow application
domains must be able to customize their outcome representations for
specific patients and problems.  No general outcome
representation can capture every conceivable criterion
without being cumbersome for use in specific instances.  We require,
therefore, a {\it framework} for
outcome description mechanisms that covers the imaginable criteria
without being committed to the inclusion of particular
attributes.  The framework must provide structure to assist
generation of appropriate representations, and mechanisms
to interpret and relate the various outcome measures.

Note also that we want to represent outcomes at the
``health status'' level, where descriptors are direct
indicators of the patient's general state of health or well-being.
Physiological parameters are
important indicators of the patient's medical condition,
yet cannot be interpreted in terms of health status without substantial context
information.  Assigning
preferences to these kinds of parameters (called ``proxy attributes''
by Keeney~\cite{Keeney81a}) would be an  indirect and therefore more
complicated means of specifying the desirability of health outcomes.
Significant disparity between the measurement scale and the ``true
objective'' results in difficult-to-model
interdependencies among attributes and inconvenient (nonlinear or even
non-analytical) representations for utility
measures~\cite{Keeney81b}.  Outcomes described at the health status
level more closely convey how the patient feels and functions and are
therefore more simply related to preferences.

Numerous instruments for measuring health status have been developed for
retrospective evaluation of health programs.
Unfortunately, health status indexes alone are
inadequate for use by decision-making programs.  Measurement
scales designed for evaluation may be inconvenient 
to estimate before the fact.  And for prospective examination,
we must consider sets of {\it possible}
outcomes.  Ideally, we would associate a
probability distribution over outcomes, or {\it
prospect}, with each strategy.

The indexes are also deficient because
they only measure {\it instantaneous} health states: snapshots 
of a patient's situation at a particular point in time.
In general, we are concerned with a prognosis that extends to
the relevant future for the decision---often the patient's entire lifetime.

Descriptions of instantaneous health states, however, are indispensable
as the building blocks of more complete outcome representations.
Consider a stream of such health states, composed of a sequence of
``snapshots'' of the patient's health state in each time period.
The precision of the representation increases with the density of the
snapshots and the completeness of the instantaneous descriptions.  In
the limit, time streams of this sort are the most general kind of
health-status outcome representation possible.

Markov models of prognosis used for decision analysis~\cite{Beck-Pauker83}
in effect use health-state streams as their basic outcome structure.
The quality-adjusted life-year (QALY) utility model~\cite{Pliskin}
assigns values directly to streams of health states.  But
straightforward use of time streams becomes
cumbersome as the instantaneous measures become more detailed and the
time periods more numerous.  Direct analysis of probability
distributions over 
nontrivial time streams (time stream {\it prospects}\/) is
pragmatically unthinkable; it entails enumerating each possible
future sequence of health states.  Indeed, 
the Markov analyses and commonly used QALY models consider only {\it
expected} time within each state. 
Thus, the most general description is an impractical
one.

\typeout{ -2.2. }
\subsection{Structured Outcome Knowledge}\label{structured-knowledge}

A library of useful outcome measures would include attributes like
lifespan, hospitalization time, presence of 
chronic morbidities, discolored teeth, short-term morbidities due to a
surgical procedure, and perhaps some particular health status 
indexes, such as one developed by 
Torrance and associates~\cite{Torrance-Boyle}.
A formulation program might customize representations
for particular decision problems
by selection from this library based on features of the
outcome descriptors and problem instance.  Clearly,
any selection procedure must have considerable information about what
the outcome descriptor denotes and how it is measured.  A specification
of the nature and organization of this information constitutes a
knowledge base design.

As a starting point, notice that the sample outcome measures listed
above are highly related concepts.  For
example, patients undergoing surgical procedures are necessarily
hospitalized, and discolored teeth are a kind of chronic morbidity.
Health status indexes overlap each other and include
many other outcome measures as components.  Any useful knowledge organization
must reflect these kinds of interrelationships so that the selection
criteria may evaluate the relative expressive power of the candidate
representations.

To remedy the problem of {\sc mycin}'s tetracycline rule, Clancey's
{\sc neomycin}~\cite{Clancey83} classifies
discoloration of teeth as a kind of ``undesirable body change.''
In generating a justification for rejecting tetracycline, the
program uses its higher-level knowledge that ``undesirable body
changes'' are to be avoided.  Organizing the outcomes in this fashion
facilitates the encoding of knowledge about {\it classes} of outcome
types.  In this case, of course, the classification is not sufficient
for decision making because we do not know how undesirable the body
change is.  Loss of hair and loss of limb are both ``undesirable body
changes.''

At this point we have two criteria for the structure of knowledge about
outcomes: that important interrelationships can be captured and that knowledge
about classes of outcomes can be represented.  These criteria suggest
the use of hierarchies of outcome descriptors.  In a hierarchy, classes
and subclasses are prominent, and relationships can be derived
from relative position in the taxonomies along various dimensions.
For this reason,
taxonomies of concepts are central structures in several knowledge
representation languages designed by AI
researchers~\cite{Brachman-Schmolze}.

Taxonomic reasoning plays a particularly important role in the
``hybrid representation languages''~\cite{Vilain85} developed in recent
years.  The {\it terminological component} of a hybrid system manages
the lattice of concepts, computing properties of the concepts and
relations among them from the taxonomic structure.  The reasoner is
called ``terminological'' because the structure encodes {\it
definitions} of the concepts in terms of related concepts.  Examples of
taxonomies and their use in a terminological reasoner are presented below.

\typeout{ -3. }
\section{\bf A Scheme for Representing Outcomes}\label{scheme}

\subsection{Health-State Time Streams}

Despite the acknowledged infeasibility of the direct use of time
streams, they form the basis for the outcome representation scheme
proposed here.  The idea is to use the {\it concept} of time streams as
an underlying structure for building more convenient outcome measures.
The intractability of enumerating possible time streams is irrelevant
because the individual streams are never instantiated by the program.
The program reasons about {\it properties} of time stream
classes in deriving relations among outcome descriptors.

If health-state time streams are the most general form of
health outcome description, then there is some sense in which these
streams subsume any other description.  Indeed, any
property of a patient's health status outcome can be defined in terms of
necessary and sufficient conditions on time streams reflecting that
property.  For example, the property  ``${\rm lifespan}=x$'' is true of
exactly those patients whose characteristic time stream has length $x$
(total duration of the time periods).  Similarly, the property
``discolored teeth'' indicates that the patient's teeth are
discolored in all of the time periods after some reference point (or, in
an alternate representation, that the patient suffered a ``tooth
discoloration event'' in one time period).  Any health status
outcome we can imagine would be reflected 
in a sufficiently detailed health-state time stream.

To understand how a taxonomic knowledge base can capture the
relationship between time streams and other health outcome descriptors,
it helps to examine a fragment of the structure used to represent these
concepts.  The representation language used is {\sc
nikl}~\cite{Vilain85}, a successor of {\sc
kl-one}~\cite{Brachman-Schmolze}.

Figure~\ref{nikl-time-stream} depicts part of the {\sc nikl} structure
relating health-state time streams ({\tt HS-stream}) to
instantaneous health states ({\tt inst-HS}).  The ellipses in the
diagram are {\sc nikl} {\it concepts}, representing classes of
individual objects---in our case, usually outcome
descriptors.  Wide arrows denote specialization
links, which indicate subset relationships among classes.  An {\tt
inst-HS}, for example, is (among other things) an outcome description
({\tt outcome-desc}).

\begin{figure}[htbp]
\vspace{5cm}
\caption{Relation between {\tt HS-stream} and {\tt inst-HS} }
\label{nikl-time-stream}
\end{figure}

Concepts can have {\it roles}, which are shown in the diagram as small
circles with single arrows.  For example, an {\tt HS-stream}
has at least one {\tt period} role, which are all filled by
health-status time periods ({\tt HS-period}).  An {\tt HS-period} is a
{\tt time-period} (not shown) with exactly one {\tt health-state},
which is an {\tt inst-HS}.  Conceptually, each {\tt HS-period} is a
length of time over which the patient's health state is
constant, and
an {\tt HS-stream} is a sequence of these intervals.  The path
through these two roles (the periods
of the time stream and the state associated with each) links
health-state time streams to instantaneous health states.

A concept is {\it defined} by the knowledge base if its position in the
lattice expresses necessary and sufficient conditions for individual
membership.  For example, an {\tt HS-stream} can be defined as ``a
{\tt time-stream} in which every {\tt time-period} is an {\tt HS-period}.''
Any time stream with that property---and nothing else---is a
health-status time stream.  For {\it primitive} concepts, such as {\tt
inst-HS} in the figure, the lattice expresses
necessary but not sufficient conditions.  Thus, every instantaneous
health state must be an outcome description, but the converse does not
generally hold.  Employing these semantics, relations between more
specific outcome
descriptors may be derived from 
their positions in the lattice beneath {\tt HS-stream} and {\tt
inst-HS}.

\typeout{ -3.2. }
\subsection{Summary Health Measures}

Note that the two main categories of outcome description presented so far
were judged above to be unsuitable for practical outcome representation.
Instantaneous descriptions only cover single time points, and time
streams are intractable.  We need a category, it seems, to cover the
genuinely useful measures that were earlier contemplated for our
library.  Because these measures are
summaries of information that can in principle be encoded
in the complete time streams, each of these is termed an
{\tt HS-summary}.

Definitions of some general subtypes of
summary measures are valuable as organizing concepts.  A {\tt
total-time} is an outcome description that measures the total amount of time
spent by the patient in a 
particular {\tt inst-HS}.  For instance, the summary
measure {\tt lifespan} can be defined as a {\tt
total-time} where the {\tt inst-HS} is ``alive'' (in essence,
any instantaneous health state, since
all are subconcepts of ``alive'').  And
{\tt hospitalization} is a {\tt total-time} linked to an
{\tt inst-HS} for the property of being in a hospital ({\tt in-hospital}).

A second category of {\tt HS-summary} is the {\tt
episode-count}.  These are conceptually similar to
measures of total time, but record the number
of periods in which a particular episode occurred, rather than summing
the duration of those periods.  A 
common special case is the {\tt episode-occurrence} which
only measures whether the episode happened at least
once.  Subclasses of summary measures like these represent the
correspondence between the measures themselves and the
conceptual time
streams---that is, they indicate the method of examining the time stream
to derive the measured value.

Concepts grouped under {\tt HS-stream}, {\tt inst-HS}, and {\tt
HS-summary} to a large degree form parallel taxonomic structures.  The
{\tt total-time} measure {\tt hospitalization} is
linked to the instantaneous health state {\tt in-hospital}, and
a value of $x$ for {\tt hospitalization} corresponds
to the set of time streams where the durations of {\tt in-hospital} states
sum to $x$.  Any summary measure will have
correspondences like these in the other two taxonomies.

It may appear that we are encoding redundant
information, but in practice we do not need to generate the complete
taxonomies for each category.  The value of this structure is that a
separate reasoning program can use the knowledge structures to derive
relationships among concepts that are not mentioned in the
existing taxonomies.  For example, suppose that a knowledge base has the
{\tt inst-HS} concept {\tt in-hospital} but not the summary measure
{\tt hospitalization}.  A decision
formulation program might choose to represent the total time a
patient is confined to a hospital, based on criteria described in the
next section.  The automated formulator can
synthesize the summary measure at run-time by instantiating a {\tt
total-time} concept linked to {\tt in-hospital}.  The knowledge
representation system would then automatically determine the appropriate
position for the new concept in the {\tt HS-summary} taxonomy, based on
the location of {\tt in-hospital} in the {\tt inst-HS} lattice.  This
operation (called {\it classification}\/) is a major feature of terminological
knowledge representation languages~\cite{Brachman-Schmolze}.

The ability to automatically classify concepts reduces the
number of outcome descriptions we need to specify explicitly.  A
detailed lattice of instantaneous health states together with a rich
assortment of summary classes provides a set of basic building blocks
for constructing a great variety of more complex outcome descriptors.
The two lattices encode distinct types of knowledge.  Knowledge about
instantaneous health states is
organized around health-specific properties, while the summary-measure
lattice stratifies descriptors according to characteristics of measures in
general.  Both types are crucial for intelligent decision
formulation, but are applied in an orthogonal fashion.

Summarizing the proposed outcome representation scheme:
\begin{itemize}
\item All health outcome descriptors are defined in terms of their relation to
health-state time streams.  These time streams are never instantiated,
but serve as underlying concepts for organizing the practical outcome measures.
\item Classes of health-state time streams can be organized by the
characteristics of instantaneous health states describing the individual
time periods.  Parallel taxonomies are related by inferences of a
terminological reasoner.
\item The outcome measures practical for knowledge-based decision making
are summaries of time streams.  They can be classified according to the
manner in which they are related to the underlying time streams.
\item Specific outcome measures are defined by the health properties
they refer to and the means of abstracting them from time streams,
reflected by their position in the two lattices.  Relations between
different outcome measures can be deduced by their characteristics along
each of these dimensions.
\end{itemize}

\typeout{ -4. }
\section{\bf Decision Formulation}\label{formulation}

The test of a knowledge base lies in its support of the objectives
of application programs.  The applications we
have in mind are medical decision problems, and the objective of a
program using the knowledge base is to formulate the decision for
analysis.  This consists of selecting outcome descriptors and
constructing models around them.  The knowledge base can support
formulation by providing information about the outcome descriptors that
is related to the selection and modeling criteria.
To determine the value of this representation scheme for automated
formulation, we must
examine the sort of criteria that can be used for selecting attributes
and constructing decision models.  Such criteria may be divided into
several categories: 

{\it Domain-specific}.  A knowledge-based system uses knowledge
about the medical problem to choose the health issues to
be considered.  This will not usually be in the form of
particular outcome descriptors, because there may be more than
one set of representations covering the necessary features.  The
knowledge base provides the ability to reference classes of
descriptors corresponding to particular issues.  For example,
many measures of pain, mobility,
and functional levels singly or in combination address the
issue of ``angina severity.''

{\it Data availability}.  The choice of representations is often
limited to forms for which the applications program has data,
models, or other access.

{\it Types of measurement scales}.  I have already mentioned Keeney's
classification~\cite{Keeney81a} of attributes as proxy or direct
according to how 
closely they correspond to the real objectives underlying decisions.
Keeney also distinguishes scales constructed for 
the narrow purpose at hand from ``naturally occurring''
measures (directly measurable parameters or general-purpose
scales in common use).  Most health status indexes, for example,
would be considered constructed scales.  Choice of a natural scale may
provide more modeling flexibility, because they are usually composed of
fewer primitive
elements.  It is difficult to identify preference judgments implicit in
complex aggregate scales.

{\it Preferences}.  Some outcome descriptors are more
convenient for building preference models.  Perhaps information is
available regarding patient's preferences for particular attributes or
convenient model structures are known for certain combinations
of attributes.  This kind of knowledge could be derived from a
health {\it preference} knowledge base containing {\sc
urp} preference assertions~\cite[chapter 8]{WellmanSM}.

At the very least, a health outcome knowledge base would indicate
the standing of every candidate representation with respect to
each of these criteria.  Of greater significance, however, is the role
of the knowledge base in resolving conflicts among them.  These
conflicts are resolved not only by 
compromise but through knowledge-directed transformations whenever
possible.

The most satisfying solutions are obtained when attributes dictated by
one criterion can be transformed to attributes optimizing other
criteria.  Sometimes these transformations can be easily
synthesized through analysis of the relation between the
attributes in the knowledge base.  For example, an {\tt
episode-count} measure can always be translated to an {\tt
episode-occurrence} for the same {\tt inst-HS} by simply mapping
nonzero counts to ``true.''

Other transformations are more complex, requiring auxiliary
models or knowledge.  Suppose that the only
available data for a strategy under consideration is in
the form of five-year survival
rates, while preference information relates to the entire
lifespan.  Although there is no general transformation that
is valid in all situations, adding some reasonable
assumptions (chosen based on
problem characteristics) yields a functional relationship between
the measures.  In a similar fashion, the DEALE
model~\cite{Beck-Kassirer} provides a link between excess
mortality rates and life expectancy.

Knowledge in the taxonomies or from the application program can
also bring outcome descriptions closer to the ``health status''
level.  Morbidity due to a surgical procedure (exclusive of complications),
for example, may
be translated to pain levels and hospitalization time.
High-level knowledge indicates that this sort of transformation may
be applicable for any surgical procedures; details of the
translation are domain-dependent.

Substantial advantages also accrue when applying transformations
for the construction of preference models.  Preference assertions
referencing particular outcomes can be translated to their
corresponding implications for the measures selected.  Or
assertions may be couched in terms of abstract classes of
measures, then applied to individuals.  For
example, a general expression of {\it time preference} can be
used to indicate that the patient places greater importance on
events in the short-term than the distant future.  Consequently,
``good events'' are desired as soon as possible, and it is
preferred that ``bad'' ones be delayed.  A preference
modeler can use time preference to determine an ordering for
measures which index events by time of occurrence (another class
of summary measures).  In addition, time preference influences risk
attitude (a qualitative property expressible in {\sc urp}) for all {\tt
total-time} measures.  

Describing preferences becomes much more convenient when it is
possible to fit outcome measures to existing multiattribute
utility models, such as the QALY model~\cite{Pliskin} mentioned
above.  To generate a QALY model, knowledge about the outcome measures
is used to separate 
the lifespan measures from quality-of-life measures and specify
the latter in the appropriate form.  In this case, all health
status descriptors are transformed to {\tt total-time}
measures. 

Transformations are sometimes
implicit in the knowledge base; at other times extra models or
procedures must be specified.  Even in the latter case, the
knowledge base provides a structure in which to organize the
transformation procedures.  The relation of measures to
underlying time streams is valuable here because many of the
transformations are strictly in terms of that relationship.

\typeout{ -5. }
\section{\bf Conclusions}

Key features of the framework for outcome representation developed are
influenced by particular 
viewpoints and observations on automated medical decision making.  The
first is an emphasis on modeling preferences.  The idea of a health
outcome knowledge base was motivated by the need for including
preferences in decision-making programs, and preference considerations
have clearly influenced the design of the outcome representation.

The second viewpoint concerns the premise that ``decision modules''
combined with medical
consultation programs cannot employ the same preconceived outcome descriptors
for every decision problem.  Because advance manual identification of
appropriate health measures for every decision situation is not
feasible, expert decision makers must also be competent decision
formulators.  Without minimizing the difficulties of
automatic decision formulation, I would claim that the kind
of knowledge structures described here can provide substantial support to
this task.  Less elaborate mechanisms for providing the building blocks
of decision models, such as the library of descriptors suggested in
section~\ref{structured-knowledge}, will never be sufficient for
nontrivial formulation.

The design of the knowledge base is heavily influenced by a view of the
formulation process as controlled transformation of outcome
descriptors.  While it is only one component of the attribute selection task,
a transformation capability greatly enhances the flexibility of the
formulator, reducing the dependence on single criteria such as data
availability.

The main contribution of the scheme itself is in the observation that it
is possible to realize the organizational benefits of general
health-state time streams without incurring the computational cost of
time-stream data structures.  The concept of outcome attributes as
summary measures provides a valuable structural principle for
designing a health outcome knowledge base.

\subsection*{\bf Acknowledgment}

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This research was supported (in part) by National Institutes of
Health Grant No.\ R01~LM04493 from the National Library of Medicine and
National Institutes of Health Grant No.\ R24~RR01320 from the
Division of Research Resources.  Suggestions from Mark Eckman, Zak Kohane,
Ramesh Patil, Elisha Sacks, and Kathe Unrath contributed to
the content and presentation of this paper.

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