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Dynamic Treatment Regimes

S.A. MurphyCASBS

November 2, 2007

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Outline

– Three apparently dissimilar problems– Myopic decision making– Constructing strategies– Challenges

• Unknown, unobserved causes• Small, expensive data sets

– Discussion

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Three Apparently Dissimilar Problems

– Artificial Intelligence: Autonomous Helicopter Flight

– Management of Substance Abuse/Mental Illness

– Management of a Welfare Program

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Artificial Intelligence

• Autonomous Helicopter Flight– Observations: characteristics of the helicopter (position,

orientation, velocity, angular velocity, ….), characteristics of the environment (wind speed, wind angle, turbulence….)

– Actions/treatments: cyclic pitch (causes forward/backward and sideways acceleration), tilt angle of main rotor blades (direction), tail rotor pitch control (turning)

– Rewards: Closeness of helicopter’s flight path to the desired path; avoidance of crashes(!)

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Andrew Ng’s Helicopter: http://ai.stanford.edu/~ang/

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The Management of Substance Abuse/Mental Illness

• Treating Patients with Opioid Dependence (heroin)– Observations: individual characteristics (withdrawal

symptoms, craving, attendance at counseling sessions, results of urine tests….), characteristics of the environment (housing, employment.…)

– Actions/treatments: methadone dose, amount of weekly group counseling sessions, daily dosing time of methadone, individual counseling sessions, methadone taper

– Rewards: minimize opioid use and maximize health/functionality, minimize cost

7http://www.nida.nih.gov/perspectives/vol1no1.html

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Management of a Welfare Program

• “Jobs First” Program in Connecticut– Observations: individual characteristics (assets,

income, age, health, employment), characteristics of the environment (domestic violence, incapacitated family member, # children, living arrangements…)

– Actions/treatments: child care, job search skills training, amount of cash benefit, medical assistance, education

– Rewards: maximize employment/independence.

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The Common Thread: Multi-Stage Decision Making

• Observation, action, observation, action, observation, action,…………………….

• A strategy tells us how to use the observations to choose the actions.

• We’d like to develop strategies that maximize the rewards.

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Role of the Statistician

• What kinds of data are most useful for developing strategies?

• How do we use limited and expensive data to construct good strategies?

• How do we evaluate strategies using the limited data?

(A strategy tells us how to use the observations to choose the actions.)

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Outline

– Three apparently dissimilar problems– Myopic decision making– Constructing strategies– Challenges

• Unknown, unobserved causes• Small, expensive data sets

– Discussion

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Myopic Decision Making

• In myopic decision making, decision makers use strategies that seek to maximize immediate rewards. Problems:

– Ignore longer term consequences of present actions.– Ignore the range of feasible future actions/treatments– Ignore the fact that immediate responses to present actions

may yield information that pinpoints best future actions

• (A strategy tells us how to use the observations to choose the actions.)

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Autonomous Helicopter FlightThe helicopter has veered from flight plan.

• Myopic action: Choose an acceleration and direction that will ASAP bring us back to the flight plan.

• The result: The myopic action results in the helicopter overshooting the planned flight path and in drastic situations may lead to the helicopter cycling out of control.

• The mistake: We did not consider the range of actions we can take following the initial action. The ability to slow down is mechanically limited.

• The message: Use an acceleration that will not return us as quickly to the planned flight path but will take into account the ability of the helicopter to slow down and reduce the overshoot.

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Treatment of Psychosis

• Myopic action: Offer patients a treatment that reduces psychosis for as many people as possible.

• The result: Some patients are not helped and/or experience abnormal movements of the voluntary muscles (TDs). The class of subsequent medications is greatly reduced.

• The mistake: We should have taken into account the variety of treatments available to those for whom the first treatment is ineffective.

• The message: Use an initial medication that may not have as large a success rate but that will be less likely to cause TDs.

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Treatment of Opioid Dependence• Myopic action: Choose an intensive multi-component

treatment (methadone + counseling + behavioral contingencies) that immediately reduces opioid use for as many people as possible.

• The result: Behavioral contingencies are burdensome/expensive to implement and many people may not need the contingencies to improve.

• The mistake: We should allow the patient to exhibit poor adherence prior to implementing the behavioral contingencies.

• The message: Use an initial treatment that may not have as large an immediate success rate but carefully monitor patient adherence to ascertain if behavioral contingencies are required.

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Outline

– Three apparently dissimilar problems– Myopic decision making– Constructing strategies– Challenges

• Unknown, unobserved causes• Small, expensive data sets

– Discussion

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Treatment Treatment

Observations (Action) Observations (Action) RewardTime 1 Time 2

Time 2 Time 3

Basic Idea for Constructing a Strategy: Move Backwards Through Time.

(Pretend you are “All-Knowing”)

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Outline

– Three apparently dissimilar problems– Myopic decision making– Constructing strategies– Challenges

• Unknown, unobserved causes (e.g. how data might mislead you)

• Small, expensive data sets– Discussion

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Artificial Intelligence

• Scientists who construct strategies in autonomous helicopter flight use mechanistic theory (physical laws: momentum=m*v, W=F*d*cos(θ)…) to model the interrelationships between observations and how the actions might impact .– Scientists know many (most?) of the causes of the

observations and know how the observations relate to one another.

• Scientists can quickly evaluate strategies for selecting the actions (within a matter of months).

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Comparatively Less Known Mechanistic Models in

Behavioral/Social/Medical Sciences

• Scientists who want to use data on individuals to construct strategies must confront the fact that non-causal “associations” occur due to the unknown causes of the observations.

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Unknown UnknownCauses Causes

Observations Treatment Observations Treatment RewardTime 1 Time 2

Time 2 Time 3

Conceptual Structure in the Behavioral/Social/Medical Sciences

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Unknown, Unobserved Causes(Incomplete Mechanistic Models)

Maturity/Unknown DecisionCauses to join "Adult"

Society

+

+

Binge Drinking Treatment Binge Drinking Counseling Functionality Time 1 Time 2

Time 2 Time 3

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Unknown, Unobserved Causes (Incomplete Mechanistic Models)

• Problem: Non-causal associations between treatment (here counseling) and rewards are likely.

• Solution: Construct strategies using data sets in which randomization is used to assign treatments to students. This breaks the non-causal associations yet permits causal associations.

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Maturity/

Unknown DecisionCauses to join "Adult"

Society

"+"

Observations Treatment Binge Drinking Counseling FunctionalityTime 1 Time 2

Time 2 Time 3

Unknown, Unobserved Causes(Incomplete Mechanistic Models)

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Maturity/

Unknown DecisionCauses to join "Adult"

Society

+ -

Binge Drinking Counseling on - Binge Drinking Sanctions FunctionalityYes Health Yes/No + counseling

Consequences Time 2 Yes/No Time 3 Yes/No

Unknown, Unobserved Causes (Incomplete Mechanistic Models)

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Unknown High SATCauses Scores

+

+

Observations Student + Student Treatment Gradesis a superior admitted to Time 2athlete University

Unknown, Unobserved Causes (Incomplete Mechanistic Models)

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• The problem: Even when treatments are randomized, non-causal associations occur in the data.

• The solution: Statistical methods for constructing strategies must be conducted in stages as opposed to “all-at-once.” Statistical methods should appropriately “average” over the non-causal associations between treatment and reward.

Unknown, Unobserved Causes (Incomplete Mechanistic Models)

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Maturity/

Unknown DecisionCauses to join "Adult"

Society

+ -

Binge Drinking Counseling on - Binge Drinking Sanctions FunctionalityYes Health Yes/No + counseling

Consequences Time 2 Yes/No Time 3 Yes/No

Unknown, Unobserved Causes (Incomplete Mechanistic Models)

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Summary of Solutions To Causal Problems

• Experiments should randomize treatments (e.g. actions).

• Develop statistical methods that avoid being influenced by non-causal associations yet help you construct the strategy.

• Subjects in your data should be representative of population of subjects.

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Outline

– Three apparently dissimilar problems– Myopic decision making– Constructing strategies– Challenges

• Unknown, unobserved causes• Small, expensive data sets

– Discussion

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Expensive Data on a Limited Number of Individuals

• Scientists who want to use data on individuals to construct treatment strategies must provide measures of confidence and also evaluations of alternative treatment strategies.

• Above is challenging because methods for constructing strategies are non-smooth.

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Observations Treatment Observations Treatment Reward

Time 1 Time 2Time 2 Time 3

Basic Idea for Constructing a Strategy: Move Backwards Through Time.

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Expensive, Limited Data on Individuals

• In order to provide measures of confidence and comparisons of strategies, the statistical methods for constructing strategies must be regularized.

• A number of theoreticians are working hard on this open question.

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Outline

– Three apparently dissimilar problems– Myopic decision making– Constructing strategies– Challenges

• Unknown, unobserved causes• Small, expensive data sets

– Experiments & Discussion

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ExTENd

• Ongoing study at U. Pennsylvania (D. Oslin)

• Goal is to learn how best to help alcohol dependent individuals reduce alcohol consumption.

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Oslin ExTENd

Late Trigger forNonresponse

8 wks Response

TDM + Naltrexone

CBIRandom

assignment:

CBI +Naltrexone

Nonresponse

Early Trigger for Nonresponse

Randomassignment:

Randomassignment:

Randomassignment:

Naltrexone

8 wks Response

Randomassignment:

CBI +Naltrexone

CBI

TDM + Naltrexone

Naltrexone

Nonresponse

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Adaptive Treatment for ADHD

• Ongoing study at the State U. of NY at Buffalo (B. Pelham)

• Goal is to learn how best to help children with ADHD improve functioning at home and school.

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ADHD Study

B. Begin low dosemedication

8 weeks

Assess-Adequate response?

B1. Continue, reassess monthly; randomize if deteriorate

B2. Increase dose of medication with monthly changes

as neededRandomassignment:

B3. Add behavioral treatment; medication dose remains stable but intensity

of bemod may increase with adaptive modifications

based on impairment

No

A. Begin low-intensity behavior modification

8 weeks

Assess-Adequate response?

A1. Continue, reassess monthly;randomize if deteriorate

A2. Add medication;bemod remains stable butmedication dose may vary

Randomassignment:

A3. Increase intensity of bemod with adaptive modifi-

cations based on impairment

Yes

No

Randomassignment:

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Studies under review

• H. Jones study of drug-addicted pregnant women (goal is to reduce cocaine/heroin use during pregnancy and thereby improve neonatal outcomes)

• J. Sacks study of parolees with substance abuse disorders (goal is reduce recidivism and substance use)

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Jones’ Study for Drug-Addicted Pregnant Women

rRBT

2 wks Response

rRBT

tRBTRandom

assignment:

rRBT

Nonresponse

tRBT

Randomassignment:

Randomassignment:

Randomassignment:

aRBT

2 wks Response

Randomassignment:

eRBT

tRBT

tRBT

rRBT

Nonresponse

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Sack’s Study of Adaptive Transitional Case Management

Standard Services

Standard TCM

Randomassignment:

Randomassignment:

4 wks Response

Standard TCM

Augmented TCM

Standard TCM

Nonresponse

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Discussion• The best management of chronic disorders

(poverty, mental illness, other medical conditions) requires multi-stage decision making.

• Avoid myopic decision making!– Allow for longer term effects of the treatment– When comparing treatment options take into account

the effect of future treatments– Appreciate the value of observing patients outcomes

such as adherence• Basic experimental designs and statistical methods

are available.

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This seminar can be found at:http://www.stat.lsa.umich.edu/~samurphy/seminars/CASBS07.ppt

Email me with questions or if you would like a copy:

samurphy@umich.edu

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Unknown, Unobserved Causes

Unknown UnknownCauses Causes

Observations Treatment Observations Treatment RewardTime 1 Time 2

Time 2 Time 3

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Unknown, Unobserved Causes

Unknown MaturityCauses of Student

+ -

Binge Drinking Treatment Frequent Drinking Treatment GradeTime 1 Binge Drinking Time 2

Time 2 Time 3

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Unknown, Unobserved Causes

• Problem: We recruit students via flyers posted in dormitories. Associations between observations and rewards are highly likely to be (due to the unknown causes) non-representative.

• Solution: Sample a representative group of college students.

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STAR*D

• This trial is over and the data is being analyzed (PI: J. Rush).

• One goal of the trial is construct good treatment sequences for patients suffering from treatment resistant depression.

www.star-d.org

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