Download - Experiments and Dynamic Treatment Regimes S.A. Murphy Univ. of Michigan JSM: August, 2005
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• Joint work with– Derek Bingham (Simon Fraser)– Linda Collins (PennState)
• And informed by discussions with– Vijay Nair (U. Michigan)– Bibhas Chakraborty (U. Michigan)– Vic Strecher (U. Michigan)
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Outline
• Dynamic Treatment Regimes
• Challenges in Experimentation
• Defining Effects
• Estimating Effects
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Dynamic treatment regimes are individually tailored treatments, with treatment type and dosage changing with ongoing subject need. Mimic Clinical Practice.
•High variability across patients in response to any one treatment
•Relapse is likely without either continuous or intermittent treatment for a large proportion of people.
•What works now may not work later
•Exacerbations in disorder may occur if there are no alterations in treatment
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The Big Questions
•What is the best sequencing of treatments?
•What is the best timings of alterations in treatments?
•What information do we use to make these decisions?
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k Decisions on one individual
Observation made prior to jth decision point
Treatment at jth decision point
Primary outcome Y is a specified summary of decisions and observations
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An dynamic treatment regime is a vector of decision rules, one per decision
where each decision rule
inputs the available information
and outputs a recommended treatment decision.
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Long Term Goal: Construct decision rules that lead to a maximal mean Y.
An example of a decision rule is:
stop treatment if
otherwise maintain on current treatment.
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Challenges in Experimentation
1) Dynamic Treatment Regimes are multi-component treatments• Multiple decision points through time• Different kinds of decisions• Decision options for improving patients are often
different from decision options for non-improving patients
• Delivery mechanisms, encouragement-to-adhere training of staff…….
2) Constructing decision rules is a multi-stage decision problem
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Challenges in Experimentation
• Dynamic Treatment Regimes are High Dimensional Multi-component Treatments
•series of screening/refining, randomized trials prior to confirmatory trial (MOST)--- à la G. Box!
• Multistage Decisions
•sequential multiple assignment randomized trials (SMART): randomize at each decision point— à la full factorial.
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Challenges in Experimentation
3) In the screening experiment, resources are scarce relative to the number of interesting treatment components/factors. Implementing many cells of a full factorial is very expensive.
Consider designs that are similar to balanced fractional factorials. To do this you must define the effects.
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Treatment of Alcohol Dependency
T1 Intermediate Outcome T2
TDM +Responder counseling
TDM
Med B
Med ANonresponder
EM + Med B+ Psychosocial
Intensive OutpatientProgram
Responder TDM +counseling
TDM
Med B
Med A
Nonresponder
EM +Med A +Psychosocial
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Defining the stage 2 effects
Two decisions (two stages):
Define effects involving T2 in an ANOVA decomposition of
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Defining the stage 1 effects
Define
Define effects involving only T1 in an ANOVA decomposition of
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Why uniform?Define effects involving only T1 in an ANOVA
decomposition of
1) The defined effects are causal; they are total effects.
2) The defined effects are marginal -- consistent with tradition in experimental design for screening.
– The main effect for one treatment factor is defined by marginalizing over the remaining treatment factors using an uniform distribution.
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Why uniform?2) The defined effects are marginal consistent with
tradition in experimental design for screening.– The main effect for one treatment factor is defined by
marginalizing over the remaining factors using an uniform distribution.
When there is no R the main effect for treatment T1 is
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Why uniform?
3) If R were always equal to 1 then the proposal is equivalent to defining both stage 2 and stage 1 effects in an ANOVA decomposition of
T2 denotes the treatment options when R=1.
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An Aside: Ideally you’d like to replace
by
(X2 is a vector of intermediate outcomes)
in defining the effects of T1.
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Stage 1 effects:
so the interesting stage 1 and stage 2 effects are contained in the same decomposition.
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To define effects of treatment factors at first and second stages use the ANOVA-like decomposition:
where
To design an experiment we make assumptions concerning the negligibility of these effects.
Summary
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Estimating the effects
Two decisions (two stages):
Four cells corresponding to (T1,T2)= (1,1), (1,-1), (-1,1), (-1,-1). For R=1, cells are unequal in size and similarly for R=0.
Proposal: Estimate stage 2 effects using cell means
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Proposal: Estimate stage 2 effects using cell means. This yields the same estimators as a weighted regression analysis in which an individual in the (i,j)th cell is weighted by
where pij is the proportion of responders (R=1) in the (i,j)th cell.
Estimating the stage 2 effects
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Proposal: Estimate stage 2 effects using weighted regression with Y as the outcome variable.
• The advantage is that the design matrix is orthogonal with respect to the weights. – The alias structure is easily determined using
standard design of experiments techniques. – The estimators of the stage 2 effects are the same
regardless of whether you include nuisance effects in the regression.
Estimating the stage 2 effects
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Proposal: Use a regression with outcome variable,
and regressors equal to the stage 1 treatment factors (here T1).
Why?
Estimating the stage 1 effects
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Proposal: Estimate stage 1 effects using the outcome
• The advantage is that the design matrix is orthogonal (if more than one first stage treatment). – The alias structure is easily determined using
standard design of experiments techniques. – The estimators of the stage 1 effects are the same
regardless of how many of these effects you choose to include in the regression.
Estimating the stage 1 effects
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Discussion
• In the screening experiment the goal is to ascertain which decisions (“factors”) need further investigation; these are not confirmatory experiments.
• Some fractional factorial experiments will result in aliasing between causal effects and the nuisance effects. Using these experiments requires assumptions based on design principles such as effect hierarchy and effect heredity.
• It is unclear what kinds of secondary analyses are possible if the experiment is a fractional factorial.
• This seminar can be found at: http:// www.stat. lsa.umich.edu/~samurphy/seminars/jsm0805.ppt