Transcript How are we Doing? Developing Performance Indicators

A Bayesian, Meta Cost-Benefit
Model
John Roman, Ph.D.
P. Mitchell Downey
District of Columbia
Crime Policy Institute
Partnership for Greater
Washington Research
The Brookings Institution
June 30, 2010
The Urban Institute
The Brookings Institution
The views expressed are those of the authors and should not be
attributed to The Urban Institute, its trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Presentation Overview
• Background
–
–
–
–
Existing Models
DCPI
Drug Courts
Meta-Analysis
• Proposed Model
• Analytic Strategy
• Results
• Next Steps
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
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Justice Policy Center
General Approach
Estimate:
• Costs of drug court in DC;
• Benefits of reduced crime (general);
• Expected benefits for a DC drug court
population;
• Effect of drug court on criminal behavior;
• Translate effects into benefits, difference the
costs.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Presentation Overview
• Background
– Existing Models
– DCPI
– Drug Courts
– Meta-Analysis
• Proposed Model
• Analytic Strategy
• Results
• Next Steps
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
The Origins of DCPI
Funded by the Justice Grants Administration (JGA) in the
Washington, D.C. Mayor’s office using Recovery Act
funds.
Key goal was to create an entity similar to the Washington
State Institute of Public Policy (WSIPP).
• WSIPP is a non-partisan, non-profit that provides
evidence to support the Legislature;
• Created in the late 1980s, WSIPP (under the leadership
of Steve Aos and Roxanne Lieb) conducted research
funded by the legislature to inform decision-making.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
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The Origins of DCPI
In 1998, WSIPP researchers create a meta, cost-benefit
model (often called the Aos model).
• Performs meta analysis across a range of policies and
programs;
• Links to Washington state specific costs of operations;
• Monetizes outcomes;
• Prioritizes policy choices and makes recommendations to
the legislature.
In 2008, recommended funding several cost-effective
initiatives. Savings from those programs allowed plans to
build two new prisons to be shelved. Passed by the
Legislature.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
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How Can Existing Models be Improved?
The WSIPP model embodies a quantum leap is evidencebased policymaking. However, there are two (intractable)
problems with the model:
• First, general problem in meta analysis that if the
underlying studies are not identified, no aggregate causal
relationship can be established;
• Second, the model does not account for uncertainty in
several steps of the estimation process, nor does it
account for uncertainty in combining multiple estimates;
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
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Identification Issues in the Existing Model
Consider the question of whether DC should
implement an Adult Drug Court in Washington.
In order to believe that there is a causal
relationship between drug court participation
and successful outcomes (Y) must believe:
YT > YC and, that assignment is exogenous, such
that in the absence of drug court YT = YC
If assignment is not exogenous and YT ≠ YC then
no causal attribution is possible. Problem gets
worse with aggregation.
We have not solved this identification problem.
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trustees, or its funders.
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Integrating Uncertainty into the Model
If model is not identified, and causal attribution is not
possible, must include all sources of uncertainty into the
model. Two types of uncertainty:
• Estimation. Each step in the process should yield both a
point estimate and a distribution.
• Aggregation. Final results should integrate uncertainty
from each estimate.
WSIPP model produces a single point estimate with no
confidence interval. Cannot determine probabilistically
whether expected outcomes will occur.
Problem akin to comparison of fingerprints and DNA
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trustees, or its funders.
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Integrating Uncertainty into the Model, con’t
Why isn’t uncertainty included in the WSIPP
model?
The problem was intractable using classical
techniques at the time the model was conceived
due to limitations in computing power.
Also, difficult to revisit estimates in a policy
environment.
Solution: Bayesian inference allows distributions
rather than ‘moments’ to be aggregated,
maximizing how much uncertainty is included in
the model.
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trustees, or its funders.
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Donald Rumsfeld on the Importance of
Incorporating Uncertainty
"Reports that say that something hasn't
happened are always interesting to me,
because as we know, there are known knowns;
there are things we know we know. We also
know there are known unknowns; that is to say
we know there are some things we do not
know. But there are also unknown unknowns -the ones we don't know we don't know.“
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
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Other Benefits of a Bayesian, Meta, Cost-Benefit
Analysis
• The model is designed to be replicable;
• Does not requires abundant reputational capital
with stakeholders, because;
– It allows for stakeholder input;
– Can be adjusted in real-time to test different
assumptions;
– All assumptions are transparent.
• Reduces the number of stages of estimation.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Presentation Overview
• Background
– Existing Models
– DCPI
– Drug Courts
– Meta-Analysis
• Proposed Model
• Analytic Strategy
• Results
• Next Steps
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
What is the District of Columbia Crime Policy
Institute (DCPI)?
A nonpartisan, public policy research organization
focused on crime and justice policy in Washington, DC.
DCPI’s mission is to support improvements in the
administration of justice and public safety policies,
through evidence-based research.
Collaboration of UI and Brookings researchers to inform
long-term strategic and short-term operations research
on juvenile and criminal justice mattres.
Goal is timely, practitioner-oriented research to develop
and implement evidence-based crime policy in DC.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
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What will DCPI Do?
Year 1 DCPI activities include:
• Develop a cost-benefit model to identify cost-effective DC
based interventions;
• Develop a research library (DCCrimePolicy.org);
• Conduct independent research:
– An Evaluation of the Mayor’s Focused Improvement
Area Initiative;
– A Study of Promising Practices at the Metropolitan
Police Department;
– A Study to Understand the Impact of Pre-Trial
Detention on Defendants and its Implications for
Evidence-Based Practice
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Presentation Overview
• Background
– Existing Models
– DCPI
– Drug Courts
– Meta-Analysis
• Proposed Model
• Analytic Strategy
• Results
• Next Steps
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
What are Drug Courts?
Drug courts use court-based treatment as an alternative to
incarceration.
• Begun in Miami in 1989, drug courts are specialized
dockets that process drug-involved offenders.
• Client behavior closely monitored by a judge.
Key premises:
• Drug involved offenders would commit fewer crimes if
they desisted from drug use.
• Relapse is part of recovery.
• Treatment participation can be encouraged (coerced?).
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
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Do Drug Courts Work?
Yes? Can’t randomly assign courts to have a drug
court or not. So next best studies find client
outcomes are moderately better using;
• RCTs in a single site;
• Meta-analyses of many studies with varying
designs;
• Simulation studies using population data.
Generally, recidivism is reduced 10-15 percent.
Potential for large net social benefits.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Presentation Overview
• Background
– Existing Models
– DCPI
– Drug Courts
– Meta-Analysis
• Proposed Model
• Analytic Strategy
• Results
• Next Steps
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
What is Meta Analysis?
Policymakers seem most convinced by metaanalysis as it uses evidence from many settings.
Steps in meta analysis are to:
•
Calculate an effect size (standardized mean
effect size comparing T and C);
•
Sum across studies (weighting by the inverse of
the variance of each effect size);
•
Account for heterogeneity;
•
Apply ad hoc weights.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
What is Meta, Cost Analysis?
Translate effect size into net benefits to account for:
•
Savings to law enforcement - reducing new crime;
•
Savings to courts – not prosecuting new offenders
•
Savings to corrections - not locking those people up;
•
Savings to those who are not victimized;
Add in costs of new policies and programs.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Presentation Overview
• Background
–
–
–
–
Existing Models
DCPI
Drug Courts
Meta-Analysis
• Proposed Model
• Analytic Strategy
• Results
• Next Steps
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
What is Meta, Cost Analysis (Again)?
What are the criticisms?
•
Garbage in, garbage out (identification);
•
No uncertainty in these estimates.
Can’t solve identification issues at this time;
Can introduce additional uncertainty.
How? Use Bayesian inference rather than classical
(inferential, repeated sample) statistics.
Analogous to measuring using the metric system.
Represents the same fact, but standardized Base
10 can be more efficient than Base Whatever.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Why go Bayesian (Statistically)
Accounts for uncertainty in the presence of
common problems:
• Multi-stage model.
– Output of one stage is next stage’s input.
– Bayesian inference takes a weighted average of
all output (weighted by the probability) versus
just using the mode (frequentist).
• Non-symmetric distributions. Default is ‘mode’
in frequentist inference.
• Presence of Missing Data. Again, uses
distribution rather than MI or listwise deletion.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Why Should DCPI Go Bayesian?
• Policy Buy-In.
– Presents data more intuitively (e.g. weather forecaster
does not predict an expected mean precipitation of 0.5
inches with a standard deviation of .25).
– Allow Policymaker input. (e.g. can provide information
about prior beliefs that can improve model
performance (effect of policy changes on various
problems, changes in crime patterns in DC,
demographic changes, etc.).
• Flexibility. Can adapt to all manner of common problems
in inference (missing data, etc.);
• Can’t combine multiple estimates with uncertainty
without going Bayes. Replaces sensitivity analyses.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Presentation Overview
• Background
–
–
–
–
Existing Models
DCPI
Drug Courts
Meta-Analysis
• Proposed Model
• Analytic Strategy
• Results
• Next Steps
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Analytic Strategy: General
Estimate:
• Costs of drug court in DC;
• Benefits of reduced crime (general);
• Expected benefits for a DC drug court
population;
• Effect of drug court on criminal behavior;
• Translate effects into benefits, difference the
costs.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Analytic Strategy: Costs
• Taken from a prior study of a DC drug court
(Harrell, et al. 1998)
• Inflation adjusted to get present day per
participant costs of drug court operations
• Estimates $11,500 per participant (for entire
process)
• Limitations:
– Based on FY 1995 costs – could have changed
– Assumes same size drug court (returns to scale)
• Advantages:
– DC specific
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
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Analytic Strategy: Valuing Benefits of Reduced
Crime
The cost of crime is the product of the price of crime (P)
and the quantity of crime (Q), so:
Costi= Pi*Qi
Where i’s are the categories of crime costs.
• Law enforcement costs of investigating crime;
• Court costs of processing crime;
• Corrections costs of supervision;
• Victims costs of being victimized.
Main source of uncertainty: price of crime to victims.
Extant estimates produce point estimates, Roman
(2009) includes distribution of prices.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Analytic Strategy: Estimates of the Price of
Crime to Victims
Mean
Median
Standard Deviation
$1,445,463
$1,380,246
$771,395
Rape
149,542
23,143
355,583
Robbery
279,085
88,915
452,485
Assault
134,770
66,644
212,510
Burglary
4,444
814
384,591
Motor Vehicle Theft
15,175
6,174
76,477
Theft
1,996
192
459,817
Crime Type
Murder/Non-negligent
Manslaughter
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trustees, or its funders.
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Analytic Strategy: Calculating Benefits
The goal of this analysis is to create an estimate
of the distribution of net harms averted.
Calculate reduced crime (impact)
• From large scale, multi-site evaluation of drug
courts find:
– the rate of re-arrest among comparison group
(not participating in drug court);
– the distribution of crimes committed by those
comparisons who were re-arrested;
– the proportion of arrests that led to
incarceration.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
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Analytic Strategy: Benefits (cont.)
In the next step, we will estimate how many
crimes are prevented by drug court.
• For each arrest prevented, estimate what the
crime would have been by sampling from the
distribution of crimes committed by controls;
• Estimate the price of that crime by sampling
from Roman (2009);
• Find the probability that would have led to
incarceration (calculate costs of incarceration);
• These last two prices are the benefits of
preventing one crime.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Analytic Strategy: Impact Estimates
• Meta-analysis
• Data:
– From Shaffer (2006)
– Coded typical meta-data (effect size, research
design, length of follow-up, sample size, etc.)
– Called drug courts which had been evaluated
and interviewed about policies and practices
• Our approach:
– Bayesian linear regression of estimated effect
size (correlation between re-arrest and drug
court participation)
– Condition effect size on court and study
characteristics
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
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Analytic Strategy: Impact Estimates
• Variable selection (court traits):
– Preliminary regressions of effect size on
theoretically meaningful characteristics
(treatment type, program design, response to
graduation/failure, eligibility, etc.)
– Selected those which were significant: violent
offenders eligible and motivation required for
enrollment
• Variable selection (study traits):
– Length of follow-up;
– Methodology (random trial, matching, etc.);
– Similarity between treatment and control groups
(race, age, gender, prior criminal history);
– Composition of control group (dropouts,
ineligible, etc.).
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
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Analytic Strategy: Final Comments
• Missing data
• Sample size
• Pearson’s Correlation Coefficient
(unconditional/zero-order correlation)
• Follow-up time
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Presentation Overview
• Background
–
–
–
–
Existing Models
DCPI
Drug Courts
Meta-Analysis
• Proposed Model
• Analytic Strategy
• Results
• Next Steps
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
0.6
Does not
Require
Motivation
0.4
Requires
Motivation
0.2
Probability
0.8
1.0
Results: Effect Sizes, Tests Eligibility Rules
0.0
Allows
Violent
Offenders
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
Effect Size
Good
Effects
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trustees, or its funders.
0.05
Bad Effects
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0.6
Does not
Require
Motivation
0.4
Requires
Motivation
0.2
Probability
0.8
1.0
Results: Effect Sizes, Probability of a Large
Effect
0.0
Allows
Violent
Offenders
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
Effect Size
Good
Effects
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
0.05
Bad Effects
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0.00
0.05
Allows
Violent
Offenders
-0.05
Does not
Require
Motivation
-0.10
Mean Effect Size
0.10
0.15
Results: Effect Size Over Time
-0.15
Requires
Motivation
0
5
10
15
20
25
30
35
Months of Follow-Up
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trustees, or its funders.
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0.0 0.5 1.0 1.5 2.0 2.5 3.0
Density
Densities of Change in Rearrest
-0.6
-0.4
-0.2
0.0
0.2
0.4
Percent Change in Rearrests
Reduction in Rearrest
|
Increase in Rearrest
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trustees, or its funders.
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0.20
0.15
0.10
0.05
-0.05
0.00
Averted Arrests per Participant
0.25
0.30
Results: Averted Arrests
0
100
200
300
400
500
Number of Participants
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trustees, or its funders.
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0.2
0.1
0.0
-0.1
Observed Reduction (true = 15%)
0.3
Why Effect Size is Misleading
0
500
1000
1500
2000
N
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trustees, or its funders.
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0.6
0.4
0.0
0.2
Probability
0.8
1.0
Results: Averted Arrests
-20
0
20
40
60
80
Averted Arrests
n:2500 m:0
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trustees, or its funders.
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0.6
0.4
0.0
0.2
Proportion Greater Than
0.8
1.0
Results: Distribution of Net Benefits
-10000
0
10000
20000
30000
40000
50000
Net Benefits per Participant
n:2500 m:0
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trustees, or its funders.
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0.6
0.4
0.0
0.2
Proportion Less Than
0.8
1.0
Costs Per Crime
0
5000
10000
15000
Cost per Crime
n:77104 m:0
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
Presentation Overview
• Background
–
–
–
–
Existing Models
DCPI
Drug Courts
Meta-Analysis
• Proposed Model
• Analytic Strategy
• Results
• Next Steps
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
The Last Word
• Finalize the estimates of costs of drug court in
DC;
• Code other alternatives to incarceration
strategies;
• Code other interventions;
• Rank policy priorities;
• Link to fiscal policy.
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center
The Last Word
"I would not say that the future is necessarily
less predictable than the past. I think the past
was not predictable when it started."
- Donald Rumsfeld
“All models are wrong, some are useful."
- George E.P. Box and Norman Draper
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
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Full Analytic Strategy
• Distribution of possible Effect Sizes
• Distribution of possible recidivism rates
• Difference between control recid. rate and
estimate recid. rate is effect of drug court
• Distribution of crimes prevented
• Distribution of prices of those crimes (and
associated incarceration)
• Benefits of drug court are P*Q
• Subtract costs of participation to get net
benefits of drug court
The views expressed are those of the authors and should not be attributed to the Urban Institute, its
trustees, or its funders.
URBAN INSTITUTE
Justice Policy Center