%-*- Mode: Latex; Default-character-style: (:SWISS :ROMAN :NORMAL) -*-
\documentstyle{article}
\input <ELAN>MARGINS.TEX

\begin{document}

\begin{titlepage}
\begin{center}
{\large Reasoning about Evidence in Causal Explanations}
\end{center}
\vspace{.2in}
\begin{center}
Phyllis Koton\\
MIT Laboratory for Computer Science\\
Clinical Decision Making Group\\
545 Technology Square, Room 371\\
Cambridge, MA 02139
\end{center}
\vspace{.5in}

\begin{center}
Abstract
\end{center}
\vspace{.1in}

Causal models can provide richly-detailed knowledge bases for producing
explanations about behaviors in many domains, a task often termed
interpretation or diagnosis.  However, producing a causal explanation from
the model can be time-consuming.  This paper describes a system that
solves a new problem by recalling a previous, similar problem and
modifying that problem's solution to fit the current problem. Because it is
unlikely that any new problem will exactly match a previous one, the
system evaluates differences between the problems using a set of
principles for reasoning about evidence in causal explanations.  These {\it
evidence principles} allow the system to reason about such concepts as
alternate lines of evidence, additional supporting evidence, and inconsistent
evidence.  If all differences between the new situation and the remembered
situation are found to be insignificant, {\it causal repair strategies} are
used to adapt the previous situation's causal explanation to the new case.
Although the evidence principles and repair strategies have thus far been
tested only for the domain of managing patients with heart disease, their
reasoning is domain-independent and should be generally applicable.

\vspace{.1in} 

The work reported here has been supported (in part) by National
Institutes of Health grants R01 LM 04493 from the National Library of
Medicine and R01 HL 33041 from the National Heart, Lung, and Blood Institute.

\end{titlepage}

\section{Explanation transfer}

Causal models are frequently proposed for knowledge-based systems
because they have a wide range of applicability, they are robust, and they
contain detailed information for providing explanations of their reasoning.
In practice they are not widely used because they are inefficient compared
to associational rules or other types of ``compiled'' knowledge.  This
inefficiency could be reduced by using a paradigm
such as Case-Based Reasoning \cite{Kolod85} or Memory-Based Reasoning
\cite{Stanfill}.   These methods use a memory of previously-solved
problems to avoid complex reasoning when presented with a new problem.
They recall a similar problem and adapt its solution to the new case.
However, the match between a new problem and a previously solved
problem usually is only partial.  This presents a difficulty when producing a
causal explanation.  Some feature of the previously-solved problem that
was used as evidence in the causal explanation may be absent from the new
problem.  Similarly, the new problem may exhibit features that are absent
from the previously-solved problem and which must be explained.  This
requires that the  program have a set of
principles for reasoning about dependencies between pieces of evidence and
the states that they support in the causal explanation, and about the
relationships (such as equivalence or incompatibility) between different
pieces of evidence.   The program can then determine whether a new
problem with a somewhat different set of features can still be explained by
a previous causal explanation.  I have developed and implemented such a
set of principles in a new system, CASEY.


\section{Overview of CASEY}

CASEY integrates case-based and causal reasoning techniques with a
model-based expert system for managing patients with cardiac disease, the
Heart Failure program \cite{LNCJ87}.  CASEY contains a self-organizing
memory system \cite{Kolo} for storing previously-seen problems (called
{\it cases}).  The memory contains descriptions of patients the program has
seen and generalizations derived from similarities between the patients.
The patient description is comprised of {\it features}.  These include both
input data, such as signs and symptoms, test results, history and current
therapy information, and solution data, such as the causal explanation for
the patient, the diagnosis, therapy recommendation and outcome
information.  A typical patient description in CASEY contains about 40 input
features. 
For example, Figure~\ref{descr} shows the patient description for Newman,  a
new patient presented to the system. 
\begin{figure}
{\tt 
\begin{verbatim}
(defpatient "Newman"
      history
      (age . 65)
      (sex male)
      (dyspnea on-exertion)
      (orthopnea absent)
      (chest-pain anginal)
      (anginal within-hours unstable)
      (syncope/near-syncope on-exertion)
      (palpitations none)
      (nausea/vomiting absent)
      (cough absent)
      (diaphoresis absent)
      (hemoptysis absent)
      (fatigue absent)
      (therapies none)
      vital-signs
      (blood-pressure 138 80)
      (heart-rate . 90)
      (arrhythmia-monitoring normal)
      (resp . 20)
      (temp . 98.4)
      physical-exam
      (appearance nad)
      (mental-status conscious)
      (jugular-pulse normal)
      (pulse slow-rise)
      (apex-impulse normal)
      (parasternal-impulse normal)
      (chest clear-to-auscultation-and-percussion)
      (abdomen normal-exam)
      (extremities normal-exam)
      laboratory-findings
      (ekg lvh normal-sinus)
      (cxr calcification)
      (calcification mitral aortic-valve))
\end{verbatim}
}
\caption{Patient description for Newman}
\label{descr}
\end{figure}


CASEY produces a causal explanation and therapy suggestions for a new
patient using a three-step process.  First, CASEY searches for a similar
case in its memory; second, it evaluates the significance of any differences
between the new case and the retrieved case; and finally, if none of the
differences rule out the match, it adapts the solution from the retrieved
case to fit the particulars of the new case.  If no acceptable previous case is
found, CASEY uses the Heart Failure program to produce a solution for the
case {\it de novo}.  This paper focuses on evaluating and adapting a
retrieved solution.   

The {\it new case} is the case that CASEY is currently trying to solve.  A
{\it retrieved case} is a case that has been retrieved from memory as a
result of matching against features of the new case.  CASEY will often
retrieve more than one case that matches the new case.  CASEY's method of
choosing among retrieved cases is described in \cite{Koton88}.  The {\it
precedent case} is a retrieved case in which all differences from the current
case have been judged insignificant and from which solution transfer will
occur.  The {\it precedent solution} is the solution associated with the
precedent case.  The {\it transferred solution} is a copy of the precedent
solution that is repaired to fit the new case.

A retrieved case for the patient Newman is a patient named David.  The cases
of David and Newman have many similarities.They also
have some differences, which are shown in Figure~\ref{diff-table}.
\begin{figure}
\begin{tabular}{lll}
Feature name  & Value for David & Value for Newman \\ \hline
age  &  72  & 65 \\
pulse-rate  &  96  & 90 \\
temperature  &  98.7 & 98.4 \\
orthostatic-change  &  absent &  unknown \\
angina & unstable &  within-hours \& unstable \\
mean-arterial-pressure  &  107  & 99.3 \\
syncope  &  none & on exertion \\
auscultation  &  murmur of AS  & unknown \\
pulse & normal & slow-rise \\
ekg & normal sinus \& lv strain & normal sinus \& lvh \\
calcification  &  none  &  mitral \& aortic 
\end{tabular}
\caption{Differences between patients David and Newman.}
\label{diff-table}
\end{figure}
CASEY must decide if these differences are serious enough to rule out
the match.    In this example, the first four differences are insignificant.
The remaining differences are important but the precedent solution can be
adapted to explain them.  This will be demonstrated in
section~\ref{evid-prin}. 

\section{The causal model and causal explanation}

CASEY reasons about the model of the cardiovascular system contained in
the Heart Failure system.  The building blocks of the Heart Failure model
are {\it measures}, {\it measure values}, {\it parameters}, and {\it
states}.  Measures correspond to observable features.  Measure values are
the allowed values of the measures, for example the patient's heart rate,
and are entered by the user.  Parameters are physiological parameters of
the patient, such as ``left atrial pressure.''  States represent specific
qualitative values of parameters, for example ``high left atrial pressure.''
The model also has information about the relationships between the entities:
for example, the probability of one state causing another, and the
probability of observing a particular measure given a particular state.
There are just over 100 measures and about 140 states defined in the
model.  Some states are distinguished as ``diagnosis'' states.  If a diagnosis
state established, the name of the state is added to the patient's diagnosis.
Others are defined as ``goal states''.   These are states
that can be treated.  If a goal state is established, the therapy associated
with the state is added to the list of therapy suggestions for the patient.

The Heart Failure program produces a causal explanation consisting of a set
of measures, states, and directed links.  The causal explanation describes
the relationship between physiological states and observable features.   A
link between two states, or a state and a measure, indicates that one
causes the other.  Only abnormal findings are explained, but the program
may not be able to explain all the abnormal findings.

A graphical representation of the Heart Failure program's causal explanation
for David's symptoms is shown in Figure~\ref{David-graph}. 
\begin{figure}
\vspace{2in}
\caption{Causal explanation produced by Heart Failure program for David.}
\label{David-graph}
\end{figure}
David was diagnosed as having aortic valve disease, specifically aortic
stenosis, and unstable angina.   Abnormal features in his patient description
accounted for by the causal explanation are: unstable anginal chest pain,
evidence of LV strain on EKG, a heart murmur, and dyspnea on exertion.
David's high heart rate, high respiration rate, and high blood pressure were
not explained.

CASEY translates its input into the Heart Failure program's representation
before it begins to use the causal model.  The causal explanation produced
by CASEY is in the same form as one produced by the Heart Failure
program.  CASEY translates the solution into its own representation before
storing it for future use.

\section{Principles for reasoning about evidence}
\label{evid-prin}

Most new cases will not exactly match any previous case in the memory.
To allow partial matches, differences between cases must be evaluated.
Two cases might have many similar features yet have one critical difference
that invalidates the match.  Alternatively, many differences may not affect
the validity of a match.   The feature involved may have no relation to the
solution of the case (the patient's name, for example) or the difference may
be explainable.  The module in CASEY that performs this evaluation is
called the {\it justifier} because it must justify using a retrieved case as a
precedent for the new case.  The justifier relies on a set of principles for
reasoning about evidence, termed {\it evidence principles}, that are
presented below.  The first evidence principle is used to determine whether
a state in the retrieved casual explanation is ruled out by evidence in the
new case.  The next four attempt to show that the difference in question is
insignificant or repairable, and the last three handle features which have
special values that are easy to reason about.  Other principles for
determining significance are being explored.

\begin{enumerate}
\item {\it Rule out}.  A state is ruled out from the transferred solution if
there is some feature in the new case which is incompatible with that state.
This is detected when the feature has zero probability for some state in the
retrieved solution.  For example, a heart rate of 40 beats per minute is
incompatible with the state {\sc high heart rate}.    
\item {\it Other evidence}.  This is used when a feature present in
the retrieved case is missing in the new case.  It tries to find a piece of
evidence in the new case which supports the state that the missing
feature supported.  
\item {\it Unrelated oldcase feature}.  This is used
when a feature is present only in the retrieved case.  If the feature was not
used in the causal  explanation, its absence has no effect on any states in
the explanation, so it can be ignored.
\item {\it  Supports existing state}.  This principle is used when a
feature is present in the new case but not in the retrieved case.  It tries
to attribute this feature to  a state in the retrieved causal explanation.
\item {\it  Unrelated newcase feature}.  This is also used when
a feature is present only in the new case.  If the feature is abnormal, but is
not evidence for any existing state and does not strongly suggest a new
state, then add it to the explanation as an unexplained feature.
\item {\it  Normal}.  Normal values are not explained by the Heart Failure
program, so a normal value in the new case does not need to be explained.
(Note that if a model did reason using normal values, this rule would be
eliminated).
\item {\it  No information}.  If there is no information given about a feature in one of
the cases and it is known to be absent in the other case, then assume
that it is also absent in the former case.
\item {\it  Same qualitative region}.   CASEY evaluates differences between
features with numerical values by translating them into qualitative value
regions.  For example, a blood pressure of 180/100 becomes ``high blood
pressure.''  Features whose values fall into the same qualitative region are
judged not to be significantly different.  The regions are determined using
range information for the corresponding measure in the Heart Failure model.
\end{enumerate}

CASEY can reject a match on either of two grounds:  a significant difference
could not be explained, or all the diagnosis states in the retrieved solution
were ruled out.  If all differences between the new case and the retrieved
case are insignificant or repairable, then the transfer of solutions from the
precedent to the current case proceeds.

CASEY makes the following inferences about the differences between
patients David and Newman:  
\begin{itemize}
\item David's age is judged to be insignificant by the
rule {\it unrelated oldcase feature}.  Newman's age is judged to be
insignificant by the rule {\it unrelated newcase feature}.
\item Both patients'
heart-rates are in the same qualitative region (moderately high heart rate)
so the difference is considered insignificant.  
\item Both temperatures are in the ``normal''
qualitative region so the difference is considered insignificant.
\item David's
mean arterial pressure is high, but Newman's is not.  However, this feature
was not accounted for by the causal explanation, so it is judged
insignificant by the rule {\it unrelated oldcase feature}.
Newman's mean arterial pressure is normal, so it does not have to be explained.  
\item Orthostatic change is absent in David,
but not specified for Newman, so the rule no-info concludes that it is also
absent in Newman.  
\item Newman's finding of angina within hours is additional
evidence for the state {\sc unstable angina}.
\item Syncope on exertion is additional evidence for the state  {\sc limited
cardiac output}.
\item Murmur of AS, which is absent in Newman, is
evidence for the state {\sc fixed high outflow resistance} in the precedent
solution, but this state has other evidence supporting it in the new case.
\item Newman's pulse has slow rise.  This is evidence for the existing state
{\sc slow ejection}.
\item LV strain on David's EKG is evidence for the state {\sc lv hypertrophy}.  Newman's
EKG shows LVH, which is evidence for the same state.  
\item Newman's finding of
aortic calcification is evidence for the existing state {\sc aortic valve
disease}.  
\item Newman's finding of mitral calcification has only one cause, {\sc
mitral valve disease}, so this state is added to the causal explanation.
{\sc mitral valve disease} has no causes in the model, so it remains unlinked,
forming a separate causal chain.
\end{itemize}
All the differences between David and Newman are insignificant or repairable, so the match
is  justified.

\section{The repair strategies}

CASEY uses {\it repair strategies} to adapt a previous solution (consisting
of causal explanation, diagnosis, and therapy) to a new case.  Causal
explanation repair strategies add or remove nodes and links to the
transferred causal explanation.\footnote{Diagnosis repairs add and remove
diseases from the transferred diagnosis.  Therapy repairs add and remove
therapy suggestions.  They are describe in \cite{Koton88}.}  
CASEY can make the following repairs:
\begin{enumerate}
\item {\it  Remove state}.   When  all evidence for a state has been
removed, or if the only cause of a state has been removed from the
transferred causal explanation, CASEY removes that state from the
explanation.  This also checks to see if states that this state caused have
to be removed.  This strategy is invoked by the {\it rule out} principle.
\item {\it  Remove evidence}.  When a piece of evidence  that was used in the
retrieved case is absent in the new case, this removes the feature and any
links to it.  It is invoked by the principles {\it other evidence} and {\it
unrelated oldcase feature}.
\item {\it  Add evidence}.  This repair adds a piece of evidence to the
causal explanation, and links it to the states for which it is evidence.  This
is invoked by {\it other evidence} and {\it supports existing state}.
\item {\it  Substitute evidence}.   When two numerical values have the
same qualitative value, this repair replaces the old value with the new as
evidence for some state.  It is invoked by the {\it same qualitative value}
principle.   
\item {\it  Add state}.  In one instance, it is very easy for
CASEY to add a state to the causal explanation. This is when the
evidence has only one possible cause.   This is invoked by the principle {\it
supports existing state}.\footnote{The fact that a feature has only
one cause is discovered while we are searching for existing states that cause
this feature.}  The state is added to the causal explanation,
and CASEY tries to link it to existing states and features in the causal
explanation (using {\it add link}).
\item {\it  Add link}.  This adds a causal link between two states.
\item {\it Add measure}.  This adds a feature which CASEY cannot link to the
causal explanation.  It is invoked by {\it unrelated newcase feature}.  
\end{enumerate}

In order to adapt the explanation
transferred from David to fit the data for Newman,
the following repair strategies are invoked by the justifier:
\begin{verbatim}
(substitute-evidence hr:90  hr:96)
(remove-evidence mean-arterial-pressure:107)
(add-evidence within-hours unstable-angina) 
(add-evidence syncope-on-exertion limited-cardiac-output)
(remove-evidence murmur-of-as)
(add-evidence slow-rise slow-ejection)
(remove-evidence lv-strain)
(add-evidence lvh lv-hypertrophy)
(add-evidence aortic-calcification aortic-valve-disease)
(add-state mitral-valve-disease)
(add-evidence mitral-calcification mitral-valve-disease)
\end{verbatim}

CASEY's causal explanation for Newman is shown in Figure~\ref{Newman-graph}.
\begin{figure}
\vspace{2in}
\caption{CASEY's causal explanation for Newman.}
\label{Newman-graph}
\end{figure}
It states Newman's diagnosis as aortic valve disease, aortic stenosis, mitral
valve disease, and unstable angina.  It does not explain his high heart rate
or his high respiration rate.  The causal explanation for Newman produced
by the Heart Failure program is identical.

The user has the option of rejecting CASEY's solution and running the Heart
Failure program on the data.  In either case, the patient description and
solution are saved  to be used for future problem-solving. 

\section{Discussion}
\label{disc}

\subsection{Related work}

SWALE \cite{swale} uses a memory of previously-solved problems to
create explanations.  It remembers prototype explanations, which it
attempts to modify to fit a new situation.   SWALE's process model is very
similar to CASEY's.  However, SWALE's explanations are very abstract, and
require a large amount of real-world knowledge to evaluate and repair
differences.  CASEY's explanations are very concrete.  In order to evaluate
or repair a difference, it needs only examine local information about states
and evidence.  CHEF \cite{Hammond86} also combines case-based
reasoning with a causal model.  It uses causal knowledge to explain plan
failures, so its causal reasoning consists of chaining rules backward from an
observed failure to the cause.  Also, the program does not save the
explanations and repair them to fit a new situation as CASEY and SWALE
do.  Recent work by Resnick and Davis \cite{ResnickDavis} uses a memory
of previously-solved problems and a causal model to explain hardware
faults.  It differs from CASEY in that it requires an exact match between the
descriptions of a new fault and a previous fault.

\subsection{Generalizing the results}

CASEY requires the following information for its reasoning:
\begin{itemize}
\item a set of features that can be used to describe some problem,
\item a set of states that can explain these observations,
\item specific information about features: 
\begin{itemize}
\item the set of possible values for this feature,
\item the set of states that use this feature as evidence,
\item the advisability of ignoring a particular feature.  This information is
used to determine if a match is invalid because it can't explain an important
feature.\footnote{The Heart
Failure program represents this information numerically, as the 
percentage of time a feature is explained by the model.  CASEY
determines this information experientially by examining the role the feature played in
similar past cases.    The same information could be 
represented and reasoned about qualitatively.} 
\end{itemize}
\item specific information about states:
\begin{itemize}
\item the set of features that are evidence for this state,
\item features that rule this state out,
\item  a list of states that cause this  state,
\item  a list of states that this state causes.
\end{itemize}
\end{itemize}

CASEY's reasoning does not depend on any knowledge specific
to the domain.  However, it accommodates certain assumptions of the
Heart Failure program, the most important being the assumption that there
is only limited interaction between states (for example, the Heart Failure
program  has no concept of two states jointly causing a third
state).  CASEY's evidence principles currently are being extended to handle
more complex interactions.

The criteria by which a match is
ruled out can be made more or less stringent.  For example, a match could
be ruled out if any state in a retrieved case was ruled out.   CASEY is very
accommodating of differences between new and retrieved cases because the
system currently does not have enough cases to allow very stringent
similarity requirements.  A more conservative criterion might be
implemented if the systems acquires a great many more cases.  This would
mean that CASEY would do less modification to a retrieved causal
explanation, but might also increase the number of times that it failed to
find an acceptable match.

The ability of the technique to produce a meaningful solution depends on
selecting a good precedent case.   Much research has been done in this area
(for example \cite{Kolod}, \cite{Simpson},
\cite{Stanfill}, \cite {swale}).   CASEY uses a novel matching algorithm
specifically designed for reasoning about causal explanations.  This algorithm
gives extra importance  to features that played a role in the causal
explanation of previous similar cases \cite{Koton88}.

\subsection{Limitations of the method}

CASEY's current implementation has  limitations.   Some problems
presented to the system have a large number of ``reasonable'' explanations.
CASEY does not use all the quantitative information available in the Heart
Failure model that would allow it to distinguish between statistically more-
and less-likely solutions.

For example, the program is parsimonious about adding additional states to
the causal explanation.   If a new feature could be attributed to two
different physiological states, one of which is already included in the
transferred explanation, CASEY will use the state that is already there
rather than add a new state.   It is possible that a feature has a higher
probability of being caused by the state not already in the explanation.
The model contains information that CASEY could use to discover this
circumstance.

CASEY works by modifying one particular solution, rather than by generating
a solution.  This makes it difficult to evaluate the likelihood of its solution
being correct compared to other possible explanations for the same data.
The Heart Failure program, on the other hand, calculates the probabilities of
all possible causal explanations that fit the data, and chooses the one with
the highest probability.  Again, the model contains information that could be
used to roughly determine whether or not CASEY is pursuing the most likely
explanation for the data.

For certain applications (e.g. \cite{Simmons87}), any explanation for the
input features is acceptable.  In the Heart Failure domain, the users require
the most likely explanation.  CASEY's justifier will soon be extended to
recognize when the solution it is creating is not the most likely one, in which
case it can reject the match.

\section{Conclusions}

CASEY demonstrates that combining a memory of past cases with causal
reasoning can have significant advantages over either method used alone.
CASEY's causal reasoning ability lets it produce a complete causal analysis
of the new case, not simply a reference to a previous solution.  CASEY can
produce a causal explanation even for problems that the Heart Failure
program cannot solve.  This is because a problem could lack sufficient
information for the Heart Failure program to calculate a solution, but still
have enough information for CASEY to find a matching case.  This also
suggests an interesting area for future work: using CASEY to integrate
several causal models developed for different domains, where no one model
could account for all the features in the problem.  CASEY can produce
causal explanations for common problems by recalling a similar problem
and adapting its solution through simple modifications.  It resorts to
detailed causal analysis when it lacks experience, then remembers its
solution for future use.


\subsection*{Acknowledgments}

Robert Jayes, MD kindly provided the example cases.   William
Long's Heart Failure program provided an excellent testbed for this work.
Thanks to Peter Szolovits, Ramesh Patil, and William Long for their
supervision of this research, and to Janet Kolodner, Michael Wellman, and
Paul Resnick for their helpful comments on this paper.

\bibliographystyle{plain}
\bibliography{bibcite:bibcite;abbrevs,bibcite:bibcite;bib}

\end{document}

