Applying
Decision Science and
Game Theory to
Suicidal Behaviors
Decision-Making Models of Functional
Psychopathology
Lawrence Amsel, MD, MPH
Director of Dissemination Research for
Trauma Studies and Services
Collaborators / Co-authors
Avital Pilpel
Randall Marshall
Applying Decision Science to
Clinical Psychiatry
• Examples of application of models and concepts
from decision science to clinical psychiatry
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•
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Modeling Ambivalent Suicide Attempts
Effecting Change in Clinicians Behavior
Modeling Addictions with Discounting
Deconstructing “Impulsivity”
Decision Deficits in OCD
Decision Deficits in Pathological Gambling
Social Phobia and Ultimatum Game
Conjectures on the Nature of the Anxiety-Avoidance
Relationship
Outline of Talk I
I Introduction: Suicidal Behaviors, Ideation and
Decisions
II Mathematical Modeling, Translational Research, and
Transdisciplinary Research
– Comparing animal models to mathematical models
– Why Decision Science should care about suicide ( and other
aspects of psychopathology).
– Why Psychiatrists should care about Decision Science
III The Research Agenda of the Neurobiology of Suicide
IV Towards a decisional (formal) model of suicidal
behaviors
A. Mixed Strategy Model of Suicide Behavior
B. Adding Inter-temporal Choice and Future Discounting – a Markov
Model
C. Signaling Game Model – Modeling the Relationship Aspects of
Some Suicidal Behaviors
Outline of Talk II
V Lessons from Suicide Modeling
• Theoretical Framework for suicidology
• Alternative frame for analyzing existing data
• Source of alternative operationalizations of key concepts and risk
factors in suicidology and Other aspects of Psychological
Dysfunction
VII Taking Decision Making and Decision Science
Seriously
VII Future Directions
– With Peter Jensen – Applying Decision Science to Dissemination of
guidelines
– With Randall Marshall – Applying Decision Science to
Dissemination of CBT for PTSD Personal Journey
– With Robert Rogers, Randall Marshall, Frank Schneier, Blair
Simpson – Risk Perception and Decision Tasks in Anxiety Disorders
Suicidal Behviors
• Completed Suicide: Rates about 3/100,000/ Year in US =
30,000/Year
• Suicide Attempt 10-100 times more common than
Completed – The ER Nightmare –Major Source of
Mortality in Psychiatric Practice
• Suicidal Preparation (Hoarding Pills): Rates Unknown
• Suicidal Intent w/o Preparation: Rates Unknown
• Suicidal Ideation – Quite Common, some estimates are
20% of young adults
• The vast majority of suicides have seen a clinician within
the months preceding the suicide
• Yet, despite extensive research programs, predicting
suicidal behavior has been an elusive goal
Risk Factors for Suicide I
• Suicidal Thoughts and Behaviors
– Suicidal Ideas, Plans, Attempts (current or past)
– Suicidal Intent
– Lethality of Plans or Attempt
• Psychiatric Diagnosis
• Physical Illness
• Psychosocial features
–
–
–
–
–
–
Loss of Social Support
Unemployment ( Recent Loss of Job)
Drop in Socioeconomic Status
Poor Family Ties
Domestic Violence
Other Life Stressors
Risk Factors for Suicide II
• Childhood Trauma
– Sexual or Physical or Psychological Abuse
• Genetic Familial Factors
– Family History of Suicide ( see Hemingways)
– Family History of Mental Illness
• Psychological Features
–
–
–
–
–
–
–
–
–
–
–
Hopelessness
Psychic Pain
Severe Anxiety
Panic Attacks
Shame or Humiliation
Psychological Turmoil
Loss of Self Esteem
Narcissistic Vulnerability
Agitation
Impulsivity
Aggression
Risk Factors for Suicide III
• Cognitive Features
–
–
–
–
Executive Function Impairments
Thought Constriction ( Tunnel Vision)
Polarized Thinking Style
Closed Mindedness
• Demographic Features
– Male Gender ( But see New York City Police)
– Widowed, Divorced or Single ( Especially for men)
– Adolescents are group with highest number of suicides (Third Leading Cause of Death
In 15-19 Year-olds, After Accidents and Homicides., 7.4 /1000,000/Yr, = 1,500 Deaths per
year in US
– White Race ( BUT See Police)
– Gay, Lesbian, or Bisexual Orientation
• Other Features
– Access to Firearms
– Intoxication
– Substance Abuse
• Protective Features
–
–
–
–
–
–
–
Children in Home or Responsibility to Family ( Except for Post Partum MDD)
Pregnancy ( Except post-partum depression/psychosis)
Religiosity
Life Satisfaction
Reality Testing
Positive Coping Skills / Problem Solving Ability
Social Support
–
Therapeutic Relationship / SOMATIC ANXIETY
The Prediction Problem - I
Non Suicide
Ideator
p1
p10
Suicide
Ideator
p9
p81
High
Lethality
Attempter
p2
Low Lethality
Attempter
p3
p5
p4
p6
p7
Suicide
Completer
The Prediction Problem -II
• Clinicians deal with ideators and attempters and need to
predict probability of transition to attempter status or
completer status in future.
• Only a small fraction of ideators actually make an attempt.
P2 <<< 1 and P9 <<< 1. Only a fraction of attempters
complete suicide. P7 < 1 and P4 << 1.
• Perhaps only high-lethality attempters are at high risk for
completion – accidents excepted.
• The risk relationships between these behaviors is not that
clear BECAUSE THERE IS NO BEHVIORAL THEORY
TO GUIDE RESEARCH
Translational Research and
Mathematical Modeling
Translational Research and Mathematical Modeling
Analogous
Animal Behavior
Human Behavior
Empirical
Study
(Evolutionary Preservation)
Isomorphic?
Basic Mechanism
(Dopamine Cell Function)
Mathematical Model
?
Human Behavior
Logical
Deduction
Complex Mechanism
(Game Theory Solution Set)
Human Mechanism
(Dopamine Cell Function?)
(Rationality Assumption? )
?
Human Mechanism
Why Psychiatric Suicidologists Should Care
to Study Rational Choice Models
• Decision making requires integrating basic capacities into
an organized cognition/behavior – a decision (recall your
mental experiences in the ultimatum game)
• Yet decision making appears to be below the complexity
level of clinical phenomena and thus a potential
explanation for them e.g. a deficit in discounting may
underlie addictive behaviors
• Decision-making is at a complexity level between clinical
phenomenon and basic neuro-bio-psychological
functional modules.
Why Psychiatric Suicidologists Should Care
to Study Rational Choice Models
• Because of its unique place in the hierarchy of behavioral
complexity – more complex that most basic neuropsych
functionalities we usually measure but less complex than clinical
symptoms- decision making involves interactions of simpler
systems , anatomical, neurochemical, and psychological
• As the following talks will show decision making concepts appear
to map nicely onto the interaction of these anatomical,
pharmacological as well as cognitive structures allowing for
experimental work in imaging, pharmacologic manipulation of
behavior, and contextual manipulation of cognitive processes
• In other words its good way to use our currently available research
toys… tools.
Why Psychiatric Suicidologists Should Care
to Study Rational Choice Models
• The work of Kahneman and Tversky on judgment and decision
anomalies (among normals) was only possible once a highly
developed normative theory was in place against which to test
human behavior
• Similarly with emotional components of decision making which are
now being incorporated into decision science.
• These aren’t failures but serial successes of the research program
• It is also important to note that rational choice axioms don’t
preclude seemingly irrational behavior once there are two people
involved as in the Prisoners Dilemma.
• Rational choice need not lead to intuitively ‘sensible’ behaviors- In
humans even the (axiomatically) rational s irrational
Why Decision Science Should Study
Suicide and its Models
• Important Public Health Problem in Its Own Right
• End of Life Decisions – Health Care policy
– Healthcare doesn’t work in America
• Costs of Cars’ steel vs. Healthcare and outsourcing
• End of Life Costs a Major Factor
• End of Life Decisions – Bioethics
– Wedge Issue Similar to Abortion
– Life Boundary Issues – Beginning, End, Ownership and Right
Why Decision Science Should Care to Study
Suicide and Its Modeling
• Rational Choice Modeling of Suicide and Related
Questions of Determining a Utility Function for Life
Itself
• One’s most Valued Commodity
• Greatest Liability
• Capital Asset
– Production Function
• Individual Marketplace
• Integrated Discounted Consumption Basket
• Meaning/Signal Based Value Assessment
– Contextual Specific Signal / Values / License
– Moral High ground
– License to Kill
Why Decision Science Should Care to
Study Suicide and Its Modeling
– The Dynamics of Spending or Risking Life in
Political Marketplace
– Almost Never see this in Economic
Marketplace Exception: Life insurance,
Suicide
– When does one spend Life, or appear to, and
what does it buy (Castro in the Mountains)
– Willingness to die as a license to kill
Why Decision Scientists Should Care to
Study Suicide and its Models
• Meaning / Signal Based / Licensing and Value
Assessment
•
•
•
•
Contextually Specific Values
Moral Currency Not Quite the High ground
Is a Uniform a License to Kill
Is willingness to die without uniform a license to kill
– Uniformed vs. Clandestine ( when is uniform advantageous)
– Target Civilian vs. Combatant vs. Both
– Risky Missions vs Suicide ( do S justify lack of uniform /civilian target?)
» Symmetric Information vs. Asymmetric
» Relate to Notion of Asymmetric War and Asssymetry of material forces
» For Whom is The Signal ( Signals) Intended
– Communal Induction of Strategic Emotion
– Community as Suicides antitheses reversal for suicide bombers
Research Agenda for Neurobiology
of Suicidal Behaviors
Suicidal Behaviors
Biological Factors
Neuro-chemical
Anatomical
Etc
Operationalized
(Psychometric)
Behavior and cognitions
related to suicidal risk
Beck Depression Scale
Impulsivity Scale
Hopelessness Scale
etc.
Basic Modular Neuropsychological Functions
Role of Decision Science for
Neurobiology of Suicidal Behaviors
Suicidal Behaviors
Biological Factors
Neuro-chemical
Anatomical
Etc
Rational
Choice Models
“neuroeconomics”
Behavior and
cognitions related
to suicidal risk
Beck depression
Impulsivity
Hopelessness
etc.
Basic Neuropsychological Functions
Expanded Stress Diathesis Model:
Incorporating a Decisional Axis
Non-Decisional Factors Decision Deficits
“Motivation”
(Judgment”)
Diathesis
Trait
Chronic
Stress
State
Acute
Beck Depression
Hopelessness
(Beck- Hamilton Gap)
Aggression
Impulsivity
Hx Head Injury
Hamilton
Life Events
Psychosis
Intoxication
Manic irritability
HPA –NE effects
What Decision Science has to Offer:
Decision Modeling
• Formal Modeling offers a framework for
conceptualizing an area of behavior as well as a
‘normative” model, both of which generate
empirically testable questions: Rational Choice
Models have made the Study of Bias, Heuristics,
and Emotions Possible
• Formal Modeling suggests alternative operationalization of key cognitive concepts and behavioral
tendencies
• Formal Modeling offers alternative approaches to
analyzing existing data
Decision Theory Modeling
• This study aimed at developing models
based on Game Theory that would
incorporate what is known about suicidal
risks and behaviors
• Explanatory
• Unifying
• Predictive
• Hypothesis Generating
“Economic” Modeling of Suicide
•
•
•
•
•
•
•
The real definition of originality
Darwinian model (deCatanzaro, 1986)
Cost-Benefit analysis (Yeh et al, 1987)
Demand Supply model (Yang et al, 1996)
Labor Force model (opportunity set?) (Huang, 1991)
Investment under uncertainty (Dixit et al, 1994)
Game theory model – suicide as signaling behaviors
(Rosenthal, 1993)
• Strategic Suicide (Norberg et al, 2000)
Naïve Expected Utility Model
U (Status quo)
Decision
U (Death)
Where U(X ) = The subjective Utility of a state
Mixed Strategies Model
• Nash equilibrium based on need for Mixed Decision
Strategies
• The idea of mixed strategies is that sometimes the
only good response to uncertainty is even more
uncertainty, deliberate uncertainty.
• Examples Menu Coalitions, Balanced portfolio,
Coin toss
• Key insight: The real decision is whether to make
an attempt. This is a decision under uncertainty.
Mixed Strategy Model
No
Attempt
U(Status Quo)
U(New Status)
Decision
Attempt
p(Death) ~ f (Attempt lethality,
and /or Intent)
U(Death)
Mixed Equilibrium Model
• The “solution” is a mixed strategy in which dying
and surviving are both seen as possible outcomes
with varying probabilities.
• In formal terms this is high stakes lottery.
• FORMAL MODEL OF AMBIVALENCE
• The decision maker (DM) chooses an attempt with a
particular probability parameter – namely the
lethality of the attempt.
• “Nature-Chance” then dictates the actual outcome -state of affairs.
• For now we assume that the utilities are independent
of the probability.
Mixed Equilibrium Model
No
Attempt
U(Status Quo)
U(New Status)
Decision
Attempt
p(Death) ~ f (attempt lethality)
U(Death)
Mixed Equilibrium Model
• The utility of not attempting suicide is U(SQ).
• The Expected Utility (EU) of attempting suicide
with lethality p is weighted average of surviving
and dying EU = pU(d)+(1-p)U(NS)
• The DM will attempt suicide when
the probability of Death p0 is such that
U(SQ) < p0U(D)+(1-p0)U(NS)
• The question is, when will that be the case?
Implications of the Model I
• While the naïve model allows for only two cases
• U(D) < U(SQ) or U(SQ) < U(D)
• The current model implies six cases
• Three for U(D) < U(SQ) – “No Death Wish”
– U(D) < U(NS) < U(SQ) -- Normal -- Not an attempter
– U(NS) < U(D) < U(SQ) -- Samurai -- Not an attempter
– U(D) < U(SQ) < U(NS) -- “manipulative” -- Only low
lethality
Implications of the Model II
• Three for U(SQ) < U(D) - “Death Wish”
• U(SQ) < U(D) < U(NS) -- Desperation -- Prefers Low
lethal
• U(NS) < U(SQ) < U(D) --Cautious Terminal -Only
high lethal
• U(SQ) < U(NS) < U(D) --Hopeless --Prefers high
lethal
Implications of the Model III
• Consider U(D) < U(SQ) < U(NS): --“the
manipulative gesture”
• The indifference point p0 is given by:
p0= [U(NS) - U(SQ)] / [U(NS)- U(D)]
• [U(NS) - U(SQ)] is the potential utility gained
from surviving an attempt. Call this the Gain,
which is a positive quantity
• [U(NS)- U(D)] = {[U(NS) – U(SQ)] + [U(SQ) –
U(D)]}
• [U(SQ) – U(D)] is the current perceived Value of
Living (VoL) which is positive.
Implications of the Model IV
• Thus to “take the gamble”
• p0 <=
Gain______
Gain + VoL
• The quantity above depends on the relative
perceived worth of Gains compared to current
VoL.
• In general this DM makes only low lethality
attempts.
• But depression (decrease in VoL) or neediness
(increase in Gains) will increase acceptable
lethality .
Implications of the Model V
• The difference U(SQ) – U(D) is not by itself predictive of
attempt. The literature bears this out as severity of
depression does not correlate well with attempter status
• Risk of an attempt depends on U(NS) a factor rarely
elicited in suicide risk assessment
• The lethality level chosen depends on U(NS). The model
predicts that the availability of a method ( of a particular
lethal potential) is extremely important in determining if
an attempt occurs, as borne out in the literature.
• FORMAL MODEL OF LETHALTY INTENT LEVEL
• Thus, prevention strategy is type dependant -- e.g.
removing firearms -- may not help for the wrong type
Implications of the Model VI
• This DM prefers status quo to death but is willing
to risk death at some level to arrive at a desired
post attempt state. (like Army volunteers). This
could be a change in status in family relations in
financial or legal situation it could be a desired
hospitalization.
• In this case the attempt will be limited to low
lethality methods, as is found in certain
adolescents who make dramatic but low lethal
attempts in order to influence a situation about
which they feel they are helpless to change in any
other way.
Implications of the Model VII
• Risk assessment is often done on basis of
estimates of patients wish to die instead of
their willingness to make an attempt.
• Yet this model indicates that some of the
truly suicidal will not make an attempt unless
the correct lethality level is available.
• Similarly, some non-suicidal will make an
attempt under right conditions.
Implications of the Model VIII
Model predicts that one could reduce risk in
“manipulative” type by reducing U(NS) this is
consistent with Kernberg's contracting of the
therapeutic frame in which specific disincentives
are part of the therapy for this specific patient type.
This may be the basis for clinical practice of
“contracting for safety” with suicidal patients
Markov Model
• This previous model assumes that the Status
Quo is permanent.
• A more realistic model must include the fact
that patients status changes, and they have
some expectation of the possibility of this
change—
• Hope and its opposite Hopelessness
The Markov Model
P(r)
P(s)
Depressed
State
Recovery
P(w)
P(t)
The Markov Model
Depressed
Recovered
Depressed
P(s)
0.8
Recovered
P(r)
0.2
P(w)
0.1
P(t)
0.9
Markov Model
• This introduces three new parameters, the first is
p(R) perceived probability of recovery -• The second is the degree of expected recovery
reflected in the Utility of recovery.
• Third is discount rate on future well being
• Taken together these may correspond to
measurements of hopelessness that strongly
correlate with suicidal status …
• FORMAL MODEL OF HOPLESSNESS
Markov Model
U(R)
Recovery
Recovery
p(R)
No
Attempt
SQ
{
U(NS)
Attempt
p(D)
U(D)
{<<}
n
}
Markov Model
• The third parameter relates to when one
expects to recover.
• How long will it take?
• Can I hold on?
• This introduces a discounting factor which
may relate to degree of impulsivity in
suicidal behavior – (a well established risk
factor).
• FORMAL MODEL OF IMPULSIVITY
Markov Model
• Closely related to this is an unexpected
bonus that fell out of this model, namely the
protective effect of future potential attempts.
• “Suicidal thoughts have gotten me through
some bad nights” Nietzsche
• The only thing that keeps me from
attempting suicide is that I could do it
tomorrow –and I hold on one day at a time
(Patient comment).
• Suicide attempt are “at the margin”.
Signaling Game Model
• Question –In the case of a “manipulative’ attempt (we
don’t like this word) doesn’t the DM have to take into
account the reaction of others?
• Might That reaction not depend on the nature and
lethality of the attempt?
• Signaling games are a class of games that have been
studied that precisely model this attempt situation
• As a benefit it help us get rid of the word
‘manipulative’
• Unless you want to grant that all signaling games
including dressing well for an interview are also
‘manipulative’.
Signaling Game Model
Signaling Game
Nature
Copy of Game Tree for another type
Player 1
No Attempt
SQ
Status Quo
Markov Chain
Recover
Attempt Low Lethality
Survive
PLayer 2
Empathy
Anger
Don't Survive
Attempt High Lethality
Don't Survive
Survive
Player 2
Empathy
Anger
Signaling Game Model
L. Amsel, 2001
Recovery
U(R)
{<<}
{
Recovery
U(NS-H)
Attempt Low
pL (D)
U(D)
Attempt High
pH
(copy of above for another type)
}
U(NS-L)
Status Quo
(Nature)
n
(D)
U(NS-L)
U(NS-H)
Signaling Game Model
• As in all signaling games there is asymmetric information.
• The ‘first player’ ie the suicidal patient knows his intentions and
thus his real ‘type’ the ‘second’ player e.g. The clinician or family
member does not.
• The first player chooses a strategy to signal the second player as
to type namely that U(D)> U(SQ).
• There is a cost to this signaling, which is a higher risk of death
than the first player intrinsically wants, which is the dangerous
part. Thus the lethality level chosen depends not only on the
acceptable risk level given the potential outcomes, it also depends
on the first player’s belief about the other’s reaction to different
lethality levels.
• There may be cultural conventions that prescribe intensive
responses at low levels of attempt and are thus protective.
Signaling Game Model
• FORMAL MODEL OF MANIPULATION
• Behavior (not verbalization) that signals that an
individual belongs to one type when in fact they belong
to another type is a model of manipulation and may be
the basis of countertransferential anger elicited by
certain character pathologies –
• Not playing by the Rules of The Game
Signaling Game Model
• Because it’s a signaling game we assume that
U(NSQ-H) > U(NSQ-L)
• In the discrete case with only choices of High and
Low lethality this leads to twelve possible types –
( the orderings on four outcomes divided by 2
because U(NSQ-H) > U(NSQ-L))
• These types react in characteristic ways based on
preference structures among U(D), U(SQ), U(NSL), U(NS-H)
• Thus we would need to know these Utilities to
predict suicide risk – this needs testing!
Formal (Mathematical) Modeling Forces the Clarification of
Psychiatric Concepts
Difference between Concept Modeling and Operationalzing
• Ambivalence – Mixed Nash Equilibrium
• Lethality Intension - probability distribution of above
• Hopelessness –
•
•
•
•
•
Probability of recovery
Estimate of extent of recovery
Discounting of Recovery
Attenuated processing of gain or loss cues
Loss frame mis-contextualization
• Manipulation – Signaling Game Solution
Formal (Mathematical) Modeling Forces the Clarification of
Psychiatric Concepts
Difference between Concept Modeling and Operationalzing
• Impulsivity –
•
•
•
•
•
•
•
Utility ( Reward loss Cues)
Discounting rate -- time to reward
Reduced time to decision
Risk Seeking
Decreased harm avoidance
Poor assessment of risk probabilities
Meta-cognitive deficit – poor “deciding” about how to decide –inappropriate
cognitive tool choice
• Aggressivity
• Overconfidence in Judgment
• Non-Impulsive High Risk Bias ( In loss frame only?)
• Decision-Implementation linkage
• Reasons for Living Scale (Gap with life events)
• Subjective Experience of Depression (Gap with Hamilton)
• Attenuated processing of gain or loss cues
Summary I
• We Have shown that the Suicide Prediction
problem incorporates a number of Operationalized
but not well modeled psychiatric Concepts
• With the aid of decision science we have shown
how formal modeling can sharpen these concepts
and lead to further empirical testing via
operationalzing the model components
Summary II
• Decision Theoretic models of suicidal behavior are consistent with
the published phenomenology, and may lead to an improved ability
to predict and prevent suicidal behaviors.
• Decision theoretic models may help explain certain suicidal
behaviors that appear anomalous as well as generating testable
hypothesis about these behaviors
• Thus suicidal behaviors might best understood by using Normative
Decisional perspective as well as incorporating deviations from this,
as in theories of Bounded Rationality
• This perspective is part of a larger intellectual convergence within
Mathematical Psychology/Psychiatry between Decision Theory and
Behaviorism - which are two approaches divided by differing
terminologies