Eran Bendavid

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When Rationality Falters Limitations and
Extensions of Decision Analysis
Eran Bendavid
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Experiment Part 1

• Assume that the United States is preparing for
  the outbreak of an unusual Icelandic disease,
  which is expected to kill 600 people in the
  absence of intervention.
• Two alternative programs to combat the disease
  have been proposed. Assume that the exact
  estimates of the programs are as follows

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Experiment 1

• If program A is adopted, 200 people will be
  saved.
• If program B is adopted, there is 1/3 chance that
  600 people will be saved and 2/3 probability that
  no people will be saved.

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Experiment 1 Switch Groups

• If program A is adopted, 400 people will die.
• If program B is adopted, there is a 1/3 chance
  that nobody will die, and 2/3 chance that 600
  people will die.

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Experiment 2 Everyone

• Imagine yourself 3000 richer than you are right
  now. You have to choose between (a) a sure gain
  of 1000, (b) a 50 chance of gaining 2000 and
  50 of gaining nothing.
• Imagine yourself 5000 richer than you are right
  now. You have to choose between (a) a sure loss
  of 1000, (b) a 50 chance of losing nothing and
  50 chance of losing 2000.

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Cartoon
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Three Topics

• Frames
• Equity
• Economic epidemiology

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Normative Problem Formulation

• Classical decision theory axioms
• Ordering of preference
• Transitivity of preference
• Quantification of judgment
• Comparison of alternatives
• Substitution
• Cost benefit rationale

Risky prospects arecharacterized by their
possible outcomes and by the probabilities of
these outcomes. The same option, however, can
be framed or described in different ways. --
Tversky Kahneman, 1981
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Formulation Effects

• Positive formulation
• Keep the status quo
• Risk averse
• Negative formulation
• Gamble to achieve a better result
• Risk seeking

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Mental Accounting

• You set off to buy an iPod shuffle at what you
  believe to be the cheapest store in your
  neighborhood. When you arrive, you discover that
  the price of the Shuffle is 75, a price you
  believe is consistent with low estimates of the
  retail price.
• A friend walks into the store and tells you a
  store 10 minutes away sells Shuffles for 55.
• Do you go to the other store?
• Now suppose you are buying a MacBook Pro for
  1960, and a friend tells you it sells for 1940
  in a store 10 minutes away. Do you go?

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Different Frames

• Real versus Hypothetical
• Experiment 1 What do you think?
• Experiment 2 Framing with hypothetical payoffs
• Experiment 3 Framing with real payoffs
• Framing the choice to the civil jury can greatly
  affect the award
• Framing the choice to the criminal jury
• Can help decide guilt or innocence
• Can affect the sentencing of the guilty

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Framing Effects in Medical Decision-Making
Treatments

• When framed positively (i.e. survival vs.
  mortality)
• Respondents 1.5 x more likely to choose surgery
  over other treatments (i.e. radiotherapy)
• Respondents demonstrated increased preference for
  invasive/toxic treatments
• No framing effect noted in hypothetical vs. real
  life treatment decisions
• Medicine use intention higher when results
  presented as RRR vs. ARR or NNT

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RRR, ARR, and NNT

• RRR Relative Risk Reduction
• ARR Absolute Risk Reduction
• NNT Numbers Needed to Treat
• Dead Alive
• Meds 404 921
• CABG 350 974
• Risk of death (from having CABG) 350/1324
  0.264
• Relative risk of death 0.264/0.305 0.87 87
• RRR Amt of risk of death is reduced by surgery
  100 - 87 13
• ARR Absolute amt of risk surgery reduces death
  30.5 - 25.4 4.1
• NNT pts needing surgery to prevent 1 death
  1/ARR 24
• Source http//www.ebm.worcestervts.co.uk/trial_re
  sults.htm

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Conclusions on Frames

• Humans are inconsistent.
• Framing is effective
• Framing can be manipulated to achieve desired
  outcomes
• Awareness of framing effects can make you a
  better decision maker
• Crucial in understanding discrepancies and
  inconsistencies in individual preferences.

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Implications for Cost-Effectiveness Analysis

• Important when considering perspective for
  analysis.
• Preferences are dependent on framing and point of
  reference.
• Individual preferences vs. community preferences
• Preferences at time of illness or during recovery
• Availability of alternative treatments

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Three Topics

• Frames
• Equity
• Economic epidemiology

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Equity

• Efficiency and Equity
• Both important for health care resource
  allocation decisions
• Few guidelines for measuring or incorporating
  equity
• Equity Values
• How can equity concerns be incorporated in
  cost-effectiveness analyses?

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What is equity?

• An equal and fair distribution
• Are treatments fairly allocated? Or Are benefits
  fairly distributed?
• Canadian Common Drug Review Pharmacoeconomic
  Review Template
• What equity assumptions were made in the
  analysis?
• No guidance on how to assess

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Vertical Equity

• Principle of vertical equity allocation linked
  to need
• Greater care is given to people with greater
  health needs
• Sicker patients ? first priority for funding
• Goal is to create equity in eventual health
  status

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Neglecting Vertical Equity

• Implies all health outcomes are valued equally
• Regardless of to whom they accrue
• Conversely, paying attention to equity
• Could make some relatively inefficient
  technologies more attractive
• If benefits groups with greater claim to
  treatment
• Or could make efficient options less attractive

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NICE (UK) Decisions, 1999 to 2002
Cost per QALY, Accepted Restricted Rejected
lt20,000 14 3 1
20,00030,000 0 4 0
gt30,000 1 4 3
Sculpher, M.The use of quality-adjusted
life-years in cost-effectiveness
studies.Allergy 61 (5), 527-530.
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Controversy

• Vertical equity may be controversial
• If your definition of need is different than
  mine
• Assume we accept vertical equity
• What characterizes equity?
• How should it measured?

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Review of Efficiency

• The Incremental Cost-Effectiveness Ratio
• Comparing treatments A and B
• The cost of obtaining one extra unit of health
  effect
• Cost-effectiveness analysis
• A measure of efficiency
• Tradeoff between made explicit between
• scarce resources
• potential changes in health

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QALYs as a Measure of Health

• Quality Adjusted Life Year
• Life expectancy 10 years
• Quality adjusted LE 6.45 QALYs

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Are All QALYs Gains Equivalent?
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E '
Each associated with a gain of 3 QALYs!
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E
B '
B
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A
Life Expectancy
C '
10
D '
7 QALYs
A
5
4 QALYs
C
D
1 QALY
0
0
0.2
0.4
0.6
0.8
1
Quality of Life
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Steps in Applying Equity to CEA

• Define groups which should receive priority to
  advance equity
• Derive equity weights
• Determine how equity weights can be applied to
  results of cost-effectiveness analyses (CEA)
• Apply equity weighting to CEA results as a form
  of sensitivity analysis

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Some Possible Equity Factors
Baseline life expectancy
Baseline quality of life
Improvement in or final life expectancy
Improvement in or final quality of life
Duration of health benefits
Direction of health benefits
Distribution of benefits (number of people)
Health care endowment (prior expenditure)
Age
Personal behaviours
Relation to others
Social status
Lifetime health
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Steps in Applying Equity to CEA

1. Define groups which should receive priority to
   advance equity
2. Derive equity weights
3. Determine how equity weights can be applied to
   results of cost-effectiveness analyses (CEA)
4. Apply equity weighting to CEA results as a form
   of sensitivity analysis

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Attribute Levels
Baseline quality of life (0 to 100) 30 60 85
Gain in quality of life (0 to 100) 0 5 15
Baseline life expectancy (years) 2 10
Gain in life expectancy (years) 1 2 10
Number of beneficiaries 100 10,000 1,000,000
Pre-program financial resources allocated to treat the condition () 0 5,000 50,000
Age (years) 15 45 75
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Survey to Understand Equity

• Pilot in elected officials, municipal and
  provincial public clerks.
• Participants recruited from waiting rooms at
  major Toronto downtown teaching hospital.
• Asked to imagine they were voting in a referendum
  between 2 programs.

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An Example
Attributes Scenario Scenario
Attributes A B
Baseline QOL 30 30
Gain in QOL 0 15
Baseline LE 10 10
Gain in LE 10 2
N 10,000 100
Prior Allocation 50,000 5,000
Age 75 15
Number Selecting () 79 (29) 191 (71)

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Solve the problem of equity?

• Personal circumstances made such decision making
  challenging.
• Several disliked the conceptual basis of the
  study,
• Fairness factors arent measurable
• Trade-offs between attributes too complex
• Individual or group values should dominate over
  centralized decision making

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More Comments

• 7 interesting and thought-provoking
• 14 challenging (3 both interesting and
  challenging)
• 5 wanted equal option to indicate that they
  considered some scenarios equivalent
• Some felt that any rationing was objectionable
• Everyone should have a chance to be treated. It
  is up to the patient and his doctor to decide
  whether it is worthwhile.
• Choices are best left in the hands of God

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Significant factors in equity

• Consistent with prioritization for those with
  poorer health
• Less prior resource allocation viewed as having
  priority
• Equal priority two groups alike except
• 1st had a quality of life that was 50 points
  worse
• 2nd had an expected 10 year increase in life
  expectancy
• Equal priority two groups alike except
• 1st 10 years younger
• 2nd had received about 13,000 less in prior
  resources

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Some Factors Not Significant

• Number of people expected to benefit
• Potential improvement in quality of life
• Could have important implications for resource
  allocation models
• Distributional aspects (how many benefit?) may
  be less important than the characteristics of
  individuals (who benefits?)

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Steps in Applying Equity to CEA

• Define groups which should receive priority to
  advance equity
• Derive equity weights
• Determine how equity weights can be applied to
  results of cost-effectiveness analyses (CEA)
• Apply equity weighting to CEA results as a form
  of sensitivity analysis

37
Equity-Weighted QALYs

• Vertical equity
• Implies society values some health gains more
  than others
• For example
• A QALY gain a sick person more valuable than a
  QALY gain for a well person
• Cancer drug vs. lifestyle drug
• One often proposed solution is to adjust QALYs
• QALYs transformed into eQALYs equity-weighted
  QALYs

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An alternative to focusing on QALYs

• Rather than focusing on health outcome
• Focus on resource allocation decision
• Reframe vertical equity as more willing to pay
  for some health outcomes than others
• i.e., a higher (or lower) willingness to pay
  threshold
• Advantage
• Policy implications more transparent
• Accommodated by current CEA methods
• Disadvantage
• Measurement more difficult
• Knee-jerk rejections more common?

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Limitations of eQALYs

• QALYs already controversial
• Construct is artificial, somewhat foreign
• Measurement issues
• Already conflate survival, quality of life
• Putting equity in might confuse more than it
  illuminates
• And exacerbate concerns about subjectivity,
  values
• i.e. eQALY components
• Survival Objective
• Quality of life (preference) Subjective
• Equity weight Subjective and value-laden

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The Net Benefit Approach

• Consider an ICER
• ? C / ? E
• Decision favorable if
• ICER lt societys willingness to pay for an extra
  unit of E (?)
• ? C / ? E lt ?
• Define Net Monetary Benefit (NMB) as
• NMB ? ? E- ? C
• Decision favorable if NMBgt0

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Equity-weighted NMB

• Assume an intervention
• We want to assign an equity weight to the health
  effect
• Call the equity weighting function f()
• Equity-weighted health effect is f(? E,q)
• Where q is a vector of equity factors
• So equity-weighted NMB is
• NMB ? f(? E,q)- ? C

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Steps in Applying Equity to CEA

• Define groups which should receive priority to
  advance equity
• Derive equity weights
• Determine how equity weights can be applied to
  results of cost-effectiveness analyses (CEA)
• Apply equity weighting to CEA results as a form
  of sensitivity analysis

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Conclusions

• Equity weighting the willingness to pay threshold
  is algebraically equivalent to equity adjusting
  QALYs
• A form of sensitivity analysis, offers
  transparency, reproducibility
• Focus on methods to estimate the relative
  attractiveness of allocating to different groups
• Doesnt obviate need for determining societal
  willingness to pay threshold

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Equity Considerations

• Fairness in process
• Accountability for reasonableness
• Fairness in outcomes
• A decision that is
• Transparent
• Principled
• Defensible

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Three Topics

• Frames
• Equity
• Economic epidemiology

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Traditional View of Epidemics

• How is an epidemic started?
• Index case
• The first case to start an epidemic
• Not necessarily the first case of the disease
• Epidemic is an interaction of the disease, the
  host, and the susceptible population

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Finding the Index Case

• Detective work to find Patient Zero
• Gaëtan Dugas
• the French-Canadian gay flight attendant reputed
  to introduce HIV to the US.
• Made famous by the book And the Band Played On
• The research used for that study was later
  repudiated
• Introduction probably through Haiti rather than
  Africa
• Typhoid Mary
• The SARS outbreak
• On Feb 21, 2003, a 65-year-old medical doctor
  from Guangdong checks into the 9th floor of the
  Metropole hotel in Hong Kong

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The importance of a susceptible population and
hosts
Index case from Guangdong
Hospital 2 Hong Kong 4 HCW 2
Canada 12 HCW 4
Hospital 3 Hong Kong 3 HCW
F
Ireland
G
156 close contacts of HCW and patients
Hotel M Hong Kong
A
K
H
I
Hospital 1 Hong Kong 99 HCW
E
USA
D
J
C
B
Viet Nam 37 HCW ?
Hospital 4 Hong Kong
Germany HCW 2
Singapore 34 HCW 37
New York
Bangkok HCW
4 other Hong Kong hospitals 28 HCW
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SARS 8,445 probable cases, 790 deaths
Europe 10 countries (38)
Russian Fed. (1)
Canada (238)
Mongolia (9)
Mongolia (9)
China (5328)
USA (70)
Kuwait (1)
Hong Kong (1755)
India (3)
Colombia (1)
Viet Nam (63)
Singapore (206)
Brazil (3)
South Africa (1)
South Africa (1)
Australia (5)
New Zealand (1)
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Epidemic Models

• S-I-R Models

POPULATION
Susceptible
Infected
Removed

• Have no immunity
• Never had the disease
• Have not been immunized

• Recovered and immune
• Dead

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S-I-R Models simple setup

• dS/dt-?S dI/dt?S-?I dR/dt-?I
• N S I R

POPULATION
Susceptible
Infected
Removed
?
?
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S-I-R Models more realistic

• dS/dt?N-?S-?S dI/dt?S-?I-?I dR/dt-?I-?R
• N S I R

?
?
?
?
Susceptible
Infected
Removed
?
?
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What determines infection (?)?

• The prevalence of infection in the population
• How frequently a susceptible individual comes in
  contact with an infected individual
• The probability of transmission from infected to
  uninfected per contact

Susceptible
Infected
?
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What determines the rate of removal (?)?

• The duration of infection
• The diseases case-fatality rate (of the people
  who get infected, how many die)

Infected
Removed
?
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What does an epidemic look like?
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R0

• Called the basic reproduction number
• The average number of secondary cases a typical
  infectious individual will cause in a completely
  susceptible population

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R0

• R0gt1
• R0lt1

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Examples of R0
Disease Transmission R0
Measles Airborne 12-18
Pertussis Airborne droplet 12-17
Diphtheria Saliva 6-7
Smallpox Social contact 6-7
Polio Fecal-oral route 5-7
Rubella Airborne droplet 5-7
Mumps Airborne droplet 4-7
HIV/AIDS Sexual contact 2-5
SARS Airborne droplet 2-5
Influenza (1918 pandemic strain) Airborne droplet 2-3
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How does an epidemic propagate?

• R0 only describes the initial epidemic dynamics,
  and will tell you whether an epidemic is likely
  to take hold in a population
• To find out what will happen to the epidemic,
  need to look at the effective reproductive rate
• Re(t) R0 S(t)
• It is the number of new infections by a typical
  individual at a particular time

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Other reproduction numbers

• Eventually, insufficient susceptibles to
  maintain chains of transmission
• When each infectious person infects less than 1
  other (on average), epidemic dies out

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Historical example
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Implications

• What is the effective reproductive rate for an
  endemic disease?
• Re(t)1
• Implications for preventing epidemics
• Re(t)1R0S(t)
• As long as S(t) stays below 1/R0, the epidemic
  cannot propagate in a population!

63
1/R0 is the susceptibility threshold

• If R0 is 2, then keeping 50 of the population
  protected will prevent an epidemic
• If R0 is 10, then keeping 10 of the population
  susceptible (90 protected) will prevent an
  epidemic
• What are the implications for vaccines?
• Measles (R0 is 17)?
• Seasonal influenza (R0 is 2)?
• This is the elimination criteria for epidemics

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Vaccine coverage and disease
1-1/Ro
rubella
measles
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Traditional view of epidemics

• Preventive efforts ? reduction in disease
  transmission
• Reduced contact (abstinence)
• Reduced chance of transmission per contact
  (gloves)
• Reduced disease transmission ? reduced prevalence
• Reduced prevalence ? further reduction in
  transmission
• Risk of infection is directly proportional to
  prevalence. Therefore controlling prevalence
  is highest priority.
• Preventive efforts are a public health imperative

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Behavioral view of epidemics

• Economists view prevention and prevalence
  affect each other
• High prevalence disease ? people increase
  personal preventive measures
• Low prevalence disease ? people increase risky
  behaviors

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Economic Epidemiology

• Mathematical conceptualization of the interplay
  between economics, human behavior and disease to
  improve our understanding of
• the emergence, persistence and spread of
  infectious agents
• optimal strategies and policies to control their
  spread
• Prevalence response elasticity
• Hazard rate into infection of susceptibles is a
  decreasing function of prevalence (opposite of
  epidemiological model predictions)
• Application to HIV
• Application to Measles

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Empirical evidence?
Geoffard and Philipson, Int. Econ. Rev., 1996
69
Implications of behavioral view

• Any highly prevalent epidemic is self-limiting
  because of preventive measures taken by
  individuals
• Any campaign to eradicate a disease will run into
  trouble when after prevalence decreases
• HIV in USA

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• Attached to SPH
• Research center across the university
• Multidisciplinary PH research group
• Staff of 70 people
• Faculty of 20-30 people
• Based on campus in Zambia, Kenya, SA
• Activities in Africa, a little in Latin America
• Clinicians, economists, epidemiologists,
• ID or child survival
• ID HIV, malaria, ARI
• Interest in urban health and mental health
• Soft funding
• Teaching paid by university, core U
• Some US govt
• Applied economics group
• Impact assessment in Africa
• Expand set of activities
• Evaluation of interventions, economic and epi
• Hope for long-term future