Transcript unc1103 - Statistics

An Experimental Paradigm for
Developing Adaptive Treatment
Strategies
S.A. Murphy
Univ. of Michigan
UNC: November, 2003
Adaptive Treatment Strategies
Setting: Management of chronic, relapsing disorders
such as alcohol, cocaine addiction and mental illness
Characteristics:
•May need a sequence of treatments prior to
improvement
•Improvement marred by relapse
•Intervals during which more intense treatment is
required alternate with intervals in which less treatment
is sufficient
Adaptive Treatment Strategies are individually tailored
treatments, with treatment type and dosage changing
with ongoing subject need. 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
•Unützer et al. (2001) Treatment of Depression
GOAL: Provide experimental methods for developing
treatment assignment, i.e. decision, rules.
k Decisions
Observations made prior to jth decision
Action at jth decision
Summary Response:
for a known function u
An adaptive treatment strategy is a vector of decision
rules, one per decision
If the strategy is implemented then
for j=1,…., k.
EXAMPLE: Treatment of alcohol dependency.
Response is a summary of heavy drinking scores over
time
GOAL: How do we design trials so as to develop
decision rules that minimize the mean response, mean
of summarized drinking score?
Treatment of Alcohol Dependency
Initial T xt
Intermediate Outcome
Responder
Secondary T xt
Monitor +
counseling
Monitor
Med B
Med A
Nonresponder
EM +
Med B+
Psychosocial
Intensive Outpatient
Program
Responder
Monitor +
counseling
Monitor
Med A +
Psychosocial
Med B
Nonresponder
EM +
Med B+
Psychosocial
Treatment of Alcohol Dependency
Initial T xt
Intermediate Outcome
Responder
Secondary T xt
Monitor +
counseling
Monitor
Med B
Med A
Nonresponder
EM +
Med B+
Psychosocial
Intensive Outpatient
Program
Responder
Monitor +
counseling
Monitor
Med A +
Psychosocial
Med B
Nonresponder
EM +
Med B+
Psychosocial
Challenges
Two Challenges
•Delayed Effects
---sequential within-person randomization
•Adaptive Treatment Strategies are High Dimensional
Multi-component Treatments
---series of randomized developmental
trials prior to confirmatory trial.
Delayed Effects
Or, why choosing the best initial treatment on the basis
of a randomized trial of initial treatments and
choosing the best secondary treatment on the basis of
a randomized trial of secondary treatments will not
provide the best adaptive treatment strategy.
Treatment of Alcohol Dependency
Initial T xt
Intermediate Outcome
Responder
Secondary T xt
Monitor +
counseling
Monitor
Med B
Med A
Nonresponder
EM +
Med B+
Psychosocial
Intensive Outpatient
Program
Responder
Monitor +
counseling
Monitor
Med A +
Psychosocial
Med B
Nonresponder
EM +
Med B+
Psychosocial
Treatment of Alcohol Dependency
Initial T xt
Intermediate Outcome
Responder
Secondary T xt
Monitor +
counseling
Monitor
Med B
Med A
Nonresponder
EM +
Med B+
Psychosocial
Intensive Outpatient
Program
Responder
Monitor +
counseling
Monitor
Med A +
Psychosocial
Med B
Nonresponder
EM +
Med B+
Psychosocial
Summary:
Determining the best initial treatment requires that we
first calculate the mean responses of patients for each
combination of secondary treatment, intermediate
outcome and initial treatment.
The main point:
If the mean responses to secondary treatment vary by
initial treatment then we need to use sequential withinperson randomization.
When would the mean response to each
combination of secondary treatment,
intermediate outcome and initial treatment vary
by initial treatment?
Causal Effects of Initial Txt
Unmeasured
Common Causes
Initial Txt
intermediate
outcome
Secondary
Txt
Response
Noncausal Correlations
Unmeasured
Common Causes
Initial Txt
intermediate
outcome
Secondary
Txt
Response
Delayed Effects: The Bottom Line
•Are there unobserved but potentially important
common causes of the response and intermediate
outcome?
•Are there unobserved but potentially important causal
pathways from initial treatment to final response?
If yes to either of the above then use sequentially
within-person randomized trials to develop good
adaptive treatment strategies.
Adaptive Treatment Strategies are High
Dimensional Multi-Component
Treatments
•when to start treatment?
•which treatment to start?
•when to step-up treatment?
•which step-up treatment?
•when to step down treatment to
maintenance/monitoring?
•which maintenance/monitoring treatment?
•what information to use to make each of the above
decisions?
Meeting the Challenges
Delayed Effects: Sequential within-person
randomization: Randomize at each decision point.
High Dimensionality: Series of developmental
randomized trials prior to a confirmatory trial (Box,
Hunter and Hunter,1978, pg. 303).
Examples of sequentially within-person randomized
trials:
•CATIE (2001) Treatment of Psychosis in Alzheimer’s
Patients
•CATIE (2001) Treatment of Psychosis in
Schizophrenia
•STAR*D (2001) Treatment of Depression
•Thall et al. (2001) Treatment of Prostate Cancer
Principles in Designing a Sequentially
Within-Person Randomized Trial
Principles in Designing a Sequentially
Within-Person Randomized Trial
•At each decision point, restrict class of treatments only
by ethical, feasibility or strong scientific considerations.
Use a low dimension summary (responder status)
instead of all intermediate outcomes (time until
nonresponse, adherence, burden, stress level, etc.) to
restrict class of treatments.
•Collect intermediate outcomes that might be useful in
ascertaining for whom each treatment works best;
information that might enter into the decision rules.
Principles in Designing a Sequentially
Within-Person Randomized Trial
•Choose a primary hypothesis that is both scientifically
interesting and aids in developing the adaptive treatment
strategy.
•Choose secondary hypotheses that further develop the
adaptive treatment strategy and use the randomization
to eliminate confounding.
Test Statistic and Sample Size
Formula for Primary Analysis
Proposal
• Primary analysis in developmental trial is to
discriminate between strategies with different initial
treatments.
• In primary analysis consider adaptive treatment
strategies with decision rules depending only on
summaries of Xj’s (say Sj’s)
• In secondary analyses consider adaptive treatment
strategies with decision rules depending on the Xj’s.
• Choose randomization probabilities to equalize the
sample size across possible strategies.
Analyses that do not aid in the
development of adaptive treatment
strategies!
1) Decide whether initial treatment A is better than
initial treatment B by comparing intermediate
outcomes (responder status).
2) Decide whether initial treatment A is better than
initial treatment B by comparing mean response
ignoring the secondary treatments.
Proposal
Estimate the mean of Y when the decision rules,
are followed:
The variance of the estimator is used to construct a
sample size formula.
Randomization probability of treatment
Aj=aj given past:
Estimating Function:
Solve,
We obtain:
Primary Analysis: Test statistic to compare two
strategies with different initial treatments:
See Murphy, van der Laan and Robins (2001) for technical details.
Calculating Sample Sizes:
Treatment of Alcohol Dependency
Initial T xt
Intermediate Outcome
Responder
Secondary T xt
Monitor +
counseling
Monitor
Med B
Med A
Nonresponder
EM +
Med B+
Psychosocial
Intensive Outpatient
Program
Responder
Monitor +
counseling
Monitor
Med A +
Psychosocial
Med B
Nonresponder
EM +
Med B+
Psychosocial
In this example:
Balanced design hence choosing the randomization
probabilities to equalize the sample size across all
possible strategies yields uniform randomization
probabilities.
An estimator of the mean of Y under the decision rules
is the average response of individuals whose
treatment pattern is consistent with the rules:
The average response for
individuals whose treatment pattern
is consistent with the rules:
is the number of treatment
alternatives at decision j
is response variance under
treatment strategy
Sample Size Formula:
where
is the Type I error and
is the power of the test to detect a difference in
the mean response between strategies.
In our simple example:
Secondary Hypotheses
•Compare adaptive treatment strategies that begin with
the same treatment; in this example, compare response
to secondary treatments by levels of the summary
intermediate outcome.
•Use an analysis that tests if other intermediate
outcomes differentiate for whom each secondary
treatment is best and if any pretreatment information
differentiates for whom each initial treatment is best.
(Murphy, 2003; Robins, 2003)
Discussion
• Simulations indicate that sample size formula is
accurate for balanced designs.
• Secondary analyses can only explore adaptive
treatment strategies that comply with the restrictions
imposed by the experimental design.
• Trial design and analyses targeted at scientific goal.
Open Problems
• This setting requires development/generalization of
Box's experimentation approach of several
developmental trials, all based on randomization prior
to a confirmatory trial.
• How could one use working assumptions on the form
of delayed effects to speed up the developmental
process? Use working assumptions to pool
information. What kinds of working assumptions
make sense? How do you detect potential violations
of the working assumptions?
Open Problems
• What is the impact of decisions being made at
different times?
• Choosing randomization probabilities in
unbalanced designs.
• Dealing with high dimensional X-- feature
extraction--in secondary analyses.
This seminar can be found at
http://www.stat.lsa.umich.edu/~samurphy/seminars/unc1103.p
pt
The paper can be found at
http://www.stat.lsa.umich.edu/~samurphy/papers/Experiment
alEvidence.pdf