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Piloting and Sizing Sequential Multiple Assignment Randomized Trials in Dynamic Treatment Regime Development

Advances in Interdisciplinary Statistics and Combinatorics October 6, 2012—University of North Carolina Greensboro Daniel Almirall & Susan A. Murphy

Outline

• Dynamic Treatment Regimes
• Sequential Multiple Assignment

Randomized Trial (SMART)

• External Pilots

– Tailoring Variables – Transition to Next Stage – Assessment Schedule – Sizing a Pilot SMART

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Dynamic treatment regimes are individually tailored sequences of treatments, with treatment type and dosage changing according to patient

• utcomes. Operationalizes clinical practice.

k Stages for one individual

Patient information available at jth stage Action at jth stage (usually a treatment)

Dynamic Treatment Regimes

• A dynamic treatment regime (DTR) is a

sequence of decision rules, one per treatment stage.

• Each decision rule inputs one or more tailoring

variables and outputs a treatment action.

• The tailoring variables are (summaries of)

patient information (possible time-varying) available at each stage.

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Example of a Dynamic Treatment Regime (DTR)

• Adaptive Drug Court Program for drug

abusing offenders.

• Goal is to minimize recidivism and drug

use.

• Marlowe et al. (2008, 2009)

6 non-responsive As-needed court hearings As-needed court hearings low risk + standard counseling + ICM non-compliant high risk non-responsive Bi-weekly court hearings Bi-weekly court hearings + standard counseling + ICM non-compliant Court-determined disposition

Adaptive Drug Court Program

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Sequential, Multiple Assignment, Randomized Trial (SMART)

At each stage subjects are randomized among alternative options. For k=2, data on each subject is of form: Aj is a randomized treatment action with known randomization probability.

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• Usually the treatment options for A2 are

restricted by the values of one or more summaries of (X1, A1, X2)

• These summaries are embedded

tailoring variables; they are embedded in the experimental design.

• The embedded tailoring variable(s)

restrict the class of DTRs that can be investigated using data from the SMART.

Pelham ADHD Study

Begin low dose Med 8 weeks Assess- Adequate response? Continue, reassess monthly; randomize if deteriorate Med ++ Random assignment: BMOD + Med No Yes Begin low-intensity BMOD 8 weeks Assess- Adequate response? Continue, reassess monthly; randomize if deteriorate BMOD + Med Random assignment: BMOD++ Yes No Random assignment:

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ADHD: Embedded Tailoring Variable

• Early response is determined by two teacher-

rated instruments, ITB and IRS.

• Binary embedded tailoring variable
• R=0 if ITB<.75 and one or more subscales of

IRS >3; otherwise R=1.

• R is the embedded tailoring variable.

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External Pilot Studies

• Goal is to examine feasibility of full-scale trial.

– Can investigator execute the trial design? – Will participants tolerate treatment? – Do co-investigators buy-in to study protocol? – To manualize treatment(s) – To devise trial protocol quality control measures

• Goal is not to obtain preliminary evidence

about efficacy of treatment/strategy.

– Rather, in the design of the full-scale SMART, the

• min. detectable effect size comes from the science.

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Embedded Tailoring Variable

• Don’t use an embedded tailoring variable

unless the science demands it.

• If you have an embedded tailoring variable

make it simple (e.g. binary measure of (non-) response)

– Non-responders likely to fail if continue on current treatment OR responders unlikely to gain much benefit if they stay on current treatment. – Usually need to use analyses of existing data to justify the use of the tailoring variable

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Jones’ Study for Drug-Addicted Pregnant Women

rRBT 2 wks Response Continue on same Continue on same Random assignment: Increase scope/intensity Nonresponse tRBT Random assignment: Random assignment: Random assignment: Decrease scope/intensity 2 wks Response Random assignment: Increase scope/intensity Continue on same Continue on same Decrease scope/intensity Nonresponse

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Missing Tailoring Variable

• How to manage missingness in the

embedded tailoring variable for purposes

• f randomizing/assigning subsequent

treatment?

– VERY different from handling missing data in a statistical analysis. – Tailoring variable is part of the definition of the treatment and experimental design.

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Missing Tailoring Variable

• Need to formulate a fixed, pre-specified

rule to determine subsequent treatment if tailoring variable is missing.

– Unexcused visit==non-response – Use a rule that depends on all observed data, including the data collected when the subject again shows up at a clinic visit. – Try out the rule in pilot.

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Assessment Schedule

• How often should the tailoring variable be

measured?

• Example: Alcoholism study with weekly

assessments of days of heavy drinking.

– Weekly assessments were insufficient and likely a pilot study would have detected this.

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Oslin’s ExTENd Study

Nonresponse if HDD>4 8 wks Response TDM + Naltrexone CBI Random assignment: CBI +Naltrexone Nonresponse Nonresponse if HDD >1 Random assignment: Random assignment: Random assignment: Naltrexone 8 wks Response Random assignment: CBI +Naltrexone CBI TDM + Naltrexone Naltrexone Nonresponse

Outcome Assessment versus Tailoring Variable Assessment

• Keep these separate.

– Tailoring variable assessment done at clinic visit by clinical staff or clinical lab or participant. Outcome assessment done at research visit by independent evaluator or independent lab or participant.

• Autism & Adolescent Depression Examples
• Try out in Pilot Study

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Transition Between Stages

• Clinical staff disagree with when 2nd stage

treatment is introduced.

• Non-responding subject refuses 2nd stage

treatment.

– This may be VERY important scientifically – Cocaine/Alcoholism Example

• Test in Pilot

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Sample Size for a SMART Pilot

• Primary feasibility aim is to ensure

investigative team has opportunity to implement protocol from start to finish with sufficient numbers

– If investigator has good evidence to guess the response rate: Choose pilot sample size so that with probability q, at least m participants fall into the sub-groups (the “small cells”) – If little to no evidence concerning response rate, size the study to estimate the response rate with a given confidence interval width.

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Pelham ADHD Study

Begin low dose Med 8 weeks Assess- Adequate response? Continue, reassess monthly; randomize if deteriorate Med ++ Random assignment: BMOD + Med No Yes Begin low-intensity BMOD 8 weeks Assess- Adequate response? Continue, reassess monthly; randomize if deteriorate BMOD + Med Random assignment: BMOD++ Yes No Random assignment:

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Sample Size for a SMART Pilot

• There are 2 treatment actions in stage 1, kR

treatments for responders, kNR treatments for non-responders. Investigator chooses q (say 80%) and m (say 3), and assumes overall non- response rate pNR (say 50%).

• Solve
• for N, the total sample size, where
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Discussion

• SMART clinical trial designs are of

growing interest in the clinical sciences.

• Because these designs are very new, they

require a great deal of leadership on the part of the statistical community.

• The payoff for the statistician is

– Inform clinical science in a novel manner – Unusual and novel trial data for methodological development

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This seminar can be found at: http://www-personal.umich.edu/~dalmiral/ slides/almirall_AISC_2012.pdf Reference:

Almirall D, Compton SN, Gunlicks-Stoessel M, Duan N, Murphy SA. (2012) “Designing a Pilot SMART for Developing an Adaptive Treatment Strategy.” Statistics in Medicine, July 31(17), pp1887-1902.