Methods for Estimating the Decision Rules in Dynamic

Treatment Regimes

S.A. Murphy

Univ. of Michigan

IBC/ASC: July, 2004

Dynamic Treatment Regimes

Dynamic Treatment Regimes are individually tailored treatments, with treatment type and dosage changing with ongoing subject information. Mimic Clinical Practice.

•Brooner et al. (2002) Treatment of Opioid Addiction

•Breslin et al. (1999) Treatment of Alcohol Addiction

•Prokaska et al. (2001) Treatment of Tobacco Addiction

•Rush et al. (2003) Treatment of Depression

EXAMPLE: Treatment of alcohol dependency. Primary outcome is a summary of heavy drinking scores over time.

Treatment of Alcohol Dependency

Initial Txt Intermediate Outcome Secondary Txt

Monitor +Responder counseling

Monitor

Med B

Med ANonresponder

EM + Med B+ Psychosocial

Intensive OutpatientProgram

Responder Monitor +counseling

Monitor

Med A + Psychosocial Med B

Nonresponder

EM +Med B+Psychosocial

Sequential Multiple Assignments

Initial Txt Intermediate Outcome Secondary Txt

Monitor +

Responder R counseling

Monitor

Med B

Med A

Nonresponder REM + Med B+ Psychosocial

R

Responder Monitor +

R counseling

Monitor

Med A + Psychosocial Med B

Nonresponder R

EM +Med B+Psychosocial

Examples of sequential multiple assignment randomized trials:

•CATIE (2001) Treatment of Psychosis in Alzheimer’s Patients

•CATIE (2001) Treatment of Psychosis in Schizophrenia

•STAR*D (2003) Treatment of Depression

•Thall et al. (2000) Treatment of Prostate Cancer

k Decisions

Observations made prior to jth decision

Action at jth decision

Primary Outcome:

for a known function f

A dynamic treatment regime is a vector of decision rules, one per decision

If the regime is implemented then

Methods for Estimating Decision Rules

Three Methods for Estimating Decision Rules

• Q-Learning (Watkins, 1989)

---regression

• A-Learning (Murphy, Robins, 2003)

---regression on a mean zero space.

• Weighting (Murphy, van der Laan & Robins, 2002)

---weighted mean

One decision only!

Data:

is randomized with probability

Goal

Choose to maximize:

Q-Learning

Minimize

A-Learning

Minimize

Weighting

Discussion

Discussion

• Consistency of Parameterization

---problems for Q-Learning

• Model Space

---bias

---variance

Q-Learning

Minimize

Minimize

Discussion

• Consistency of Parameterization

---problems for Q-Learning

• Model Space

---bias

---variance

Points to keep in mind• The sequential multiple assignment randomized trial

is a trial for developing powerful dynamic treatment regimes; it is not a confirmatory trial.

• Focus on MSE recognizing that due to the high dimensionality of X, the model parameterization is likely incorrect.

Goal

Given a restricted set of functional forms for the

decision rules, say , find

Discussion

• Mismatch in Goals

---problems for Q-Learning & A-Learning

Suppose our sample is infinite. Then in general

neither

or

is close to

Open Problems

• How might we “guide” Q-Learning or A-Learning so as to more closely achieve our goal?

• Dealing with high dimensional X-- feature extraction---feature selection.

This seminar can be found at:

http://www.stat.lsa.umich.edu/~samurphy/seminars/

ibc_asc_0704.ppt

My email address:samurphy@umich.edu