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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 2

Dynamic treatment regimes are individually tailored sequences of treatments, with treatment type and dosage changing according to patient outcomes. Operationalizes clinical practice. k Stages for one individual Patient information available at j th stage Action at j th stage (usually a treatment) 3

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. 4

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) 5

Adaptive Drug Court Program 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 6

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: A j is a randomized treatment action with known randomization probability. 7

•Usually the treatment options for A 2 are restricted by the values of one or more summaries of ( X 1 , A 1 , X 2 ) • 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. 8

Pelham ADHD Study Continue, reassess monthly; randomize if deteriorate Yes 8 weeks Begin low-intensity Assess- BMOD BMOD + Med Adequate response? Random No assignment: BMOD ++ Random assignment: Continue, reassess monthly; randomize if deteriorate Yes 8 weeks Begin low dose Med ++ Med Assess- Random Adequate response? assignment: No BMOD + Med 9

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. 10

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. 11

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 12

Jones’ Study for Drug-Addicted Pregnant Women Decrease scope/intensity 2 wks Response Random Continue on same assignment: tRBT Continue on same Random assignment: Nonresponse Increase scope/intensity Random assignment: Decrease scope/intensity 2 wks Response Random assignment: Continue on same rRBT Random assignment: Continue on same Nonresponse Increase scope/intensity 13

Missing Tailoring Variable • How to manage missingness in the embedded tailoring variable for purposes of 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. 14

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. 15

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. 16

Oslin’s ExTENd Study Naltrexone 8 wks Response Random TDM + Naltrexone Nonresponse if assignment: HDD >1 CBI Random assignment: Nonresponse CBI +Naltrexone Random assignment: Naltrexone 8 wks Response Random assignment: TDM + Naltrexone Nonresponse if HDD>4 Random assignment: CBI Nonresponse CBI +Naltrexone 17

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 18

Transition Between Stages • Clinical staff disagree with when 2 nd stage treatment is introduced. • Non-responding subject refuses 2 nd stage treatment. – This may be VERY important scientifically – Cocaine/Alcoholism Example • Test in Pilot 19

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. 20

Pelham ADHD Study Continue, reassess monthly; randomize if deteriorate Yes 8 weeks Begin low-intensity Assess- BMOD BMOD + Med Adequate response? Random No assignment: BMOD ++ Random assignment: Continue, reassess monthly; randomize if deteriorate Yes 8 weeks Begin low dose Med ++ Med Assess- Random Adequate response? assignment: No BMOD + Med 21

Sample Size for a SMART Pilot • There are 2 treatment actions in stage 1, k R treatments for responders, k NR treatments for non-responders. Investigator chooses q (say 80%) and m (say 3), and assumes overall non- response rate p NR (say 50%). • Solve � � �� for N , the total sample size, where �� 22

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 23

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. 24 24