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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:[email protected]
