A Look Under the Hood of SMART Designs for Developing Adaptive Interventions Daniel Almirall, PhD Survey Research Center, Institute for Social Research University of Michigan April 11, 2016 Center for Drug Use and HIV Research New York, NY Almirall and many friends Adaptive Interventions April 2016 1 / 66
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A Look Under the Hood of SMART Designs forDeveloping Adaptive Interventions
Daniel Almirall, PhDSurvey Research Center, Institute for Social Research
University of Michigan
April 11, 2016Center for Drug Use and HIV Research
New York, NY
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I don’t do any of this research by myself.
Students
Xi Lu, Penn State
Colleagues
Billie Nahum-Shani, Univ Mich
Susan A. Murphy, Univ Mich
Connie Kasari, UCLA (autism)
Amy Kilbourne, Univ Mich (implementation science)
Kevin Lynch, Univ Penn
And many others...
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Longitudinal Analysis of a (first) SMART in Autism
5 SMART Case Studies (all in the field or in data analysis mode)
I Adaptive Interventions for Minimally Verbal Children (AIM-ASD)I Adaptive Implementation of Effective Programs (ADEPT, mood dx)I Extending Treatment Effectiveness in Adult Alcoholism (ExTEnD)I Treatment for Pregnant Women with Heroine Dependence (RBT)I Getting SMART about Social & Academic Engagement (ASD Schools)
Myths or Misconceptions about Adaptive Interventions and SMARTs
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Sequential, Individualized Treatment Often Needed inMental Health
Intervention often entails a sequential, individualized approachwhereby treatment is adapted and re-adapted over time in responseto the specific needs and evolving status of the individual.
This type of sequential decision-making is necessary when there ishigh level of individual heterogeneity in response to treatment.
I e.g., what works for one individual may not work for another
I e.g., what works now may not work later
I e.g., for some, what appears not to work in the short-run has positivelong-term consequences
Adaptive interventions help guide this type of individualized,sequential, treatment decision making
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Adaptive Interventions
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Definition of an Adaptive Intervention
Adaptive Interventions (AI) provide one way to operationalize thestrategies (e.g., continue, augment, switch, step-down) leading toindividualized sequences of treatment.
A sequence of decision rules that specify whether, how, when(timing), and based on which measures, to alter the dosage (duration,frequency or amount), type, or delivery of treatment(s) at decisionstages in the course of care.
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Example of an Adaptive Intervention in Alcoholism
Stage One NTX + MM + Monitor weekly for 2+ HDD/week;
Stage Two IF patient trigger’s a non-response in weeks 2-8I THEN Augment with Cognitive Behavioral Intervention (CBI);I ELSE IF continued responder until week 8
F THEN NTX + Phone Counseling to maintain response;
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Example of an Adaptive Intervention in Alcoholism
Stage One NTX + MM + Monitor weekly for 2+ HDD/week;
Stage Two IF patient trigger’s a non-response in weeks 2-8I THEN Augment with Cognitive Behavioral Intervention (CBI);I ELSE IF continued responder until week 8
F THEN NTX + Phone Counseling to maintain response;
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Many Unanswered Questions when Building a High-QualityAdaptive Intervention.
Why 2+ HDDs per week? Why not, instead, 5+ HDDs per week?
Why should responders transition at week 8 to maintenancetreatment?
For continued responders at week 8, what is the effect of providingPhone Counseling? Do we really need it?
Insufficient empirical evidence or theory to address such questions.
In the past: relied on expert opinion, clinical expertise, or piecingtogether an AI with separate RCTs (e.g., practice parameters)
Sequential Multiple Assignment Randomized Trials (SMARTs)address such questions empirically, using experimental design
principles.
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Example of an Adaptive Intervention in AutismFor minimally verbal children with autism spectrum disorder
Stage One JASP for 12 weeks;Stage Two At the end of week 12, determine early sign of response:
I IF slow responder: Augment JASP with AAC for 12 weeks;I ELSE IF responder: Maintain JASP for 12 weeks.
Continue: JASP Responders
JASP Augment: JASP + AAC Slow Responders
First‐stage Treatment
(Weeks 1‐12)
Second‐stageTreatment
(Weeks 13‐24)
End of Week 12 Responder Status
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Example of an Adaptive Intervention in AutismFor minimally verbal children with autism spectrum disorder
Stage One JASP for 12 weeks;Stage Two At the end of week 12, determine early sign of response:
I IF slow responder: Augment JASP with AAC for 12 weeks;I ELSE IF responder: Maintain JASP for 12 weeks.
Continue: JASP Responders
JASP Augment: JASP + AAC Slow Responders
First‐stage Treatment
(Weeks 1‐12)
Second‐stageTreatment
(Weeks 13‐24)
End of Week 12 Responder Status
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How was response/slow-response defined?
Percent change from baseline to week 12 was calculated for 7variables:
7 variables: socially communicative utterances (SCU), percent SCU,mean length utterance, total word roots, words per minute, totalcomments, unique word combinations
Fast Responder: if ≥25% change on 7 measures;
Slower Responder: otherwise (includes kids with no improvement)
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Many Unanswered Questions when Building a High-QualityAdaptive Intervention.
Is it better to provide AAC from the start?
Who benefits from initial AAC versus who benefits from delayed AAC?
For slow responders, what is the effect of providing the AAC vsintensifying JASP (not providing AAC)?
Insufficient empirical evidence or theory to address such questions.
In the past: relied on expert opinion, clinical expertise, or piecingtogether an AI with separate RCTs (e.g., practice parameters)
Sequential Multiple Assignment Randomized Trials (SMARTs)address such questions empirically, using experimental design
principles.
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Primary Aim: What is the best first-stage treatment in terms ofspoken communication at week 24: JASP vs DTT?
(Sized N = 192 for this aim; compares A+B+C+D vs E+F+G+H)
Secondary Aim 1: Determine whether adding a parent trainingprovides additional benefit among children who demonstrate apositive early response to either JASP or DTT (D+H vs C+G).
Secondary Aim 2: Determine whether adding JASP+DTT providesadditional benefit among children who demonstrate a slow earlyresponse to either JASP or DTT (A+E vs B+F).
Secondary Aim 3: Compare eight pre-specified adaptive interventions.[Note, we can now compare always JASP vs always DTT!]
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SMART Case Study #2:
Adaptive Implementation of Effective Programs (ADEPT) in MoodDisorders
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Adaptive Implementation Intervention in Mental HealthPI: Kilbourne; Co-I: Almirall (CO/AR/MI; Aim is to improve uptake of psychosocialintervention for mood disorders; primary aim compared initial REP+EF vs REP+EF+IF.)
SMART Case Study #3:
ExTEnd Study in Adult Alcoholism
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Extending Treatment Effectiveness in Alcohol DependencePIs: David Oslin (N = 302)
SMART Case Study #4:
Treatment for Pregnant Women with Heroine Dependence
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Extending Treatment Effectiveness in Alcohol DependencePIs: Hendree Jones (N = 300)
SMART Case Study #5:
Getting SMART about Social and Academic Engagement in ElementaryAged Children with ASD
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Academic & Social Engagement in School-Children w/ASDPIs: Kasari; Co-I: Almirall; IES-funded Pilot SMART
Primary and Secondary Aims of this Pilot SMART
Primary Aim: Address feasibility and acceptability concerns related tothe embedded adaptive interventions
I identifying children as early vs. slower responders by theparaprofessionals in the context of RR,
I transitioning children to Parent or Peer at wk12,
I providing augmented Peer+Parent to slower responders
I not providing augmented treatment to early responders at wk20
I satisfaction with txt sequences by children, parents, teachers,paraprofessionals & school champions
I teacher-rated measures of progress during CS for deciding Parent vsPeer
Secondary Aim: To obtain preliminary data to support afully-powered SMART.
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Myths and Misconceptions about Adaptive Interventions
Tailoring variables cannot differ based on previous intervention
An adaptive intervention must recommend a single interventioncomponent at each decision point
Adaptive interventions seek to replace clinical judgement
Adaptive interventions are only relevant in treatment settings
Adaptive interventions are non-standard because they involverandomization
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Myths and Misconceptions about SMART Studies
SMARTs require prohibitively large sample sizes
All SMARTs require Multiple-Comparisons Adjustments
All research on adaptive interventions requires a SMART
All SMARTs must include an embedded tailoring variable
All aspects of an embedded adaptive intervention must be randomized
SMARTs are a form of adaptive research design
SMARTs never include a control group
SMARTs require multiple consents
SMARTs are susceptible to high levels of study drop-out
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Current and Future Methodological WorkWhat am I most excited about lately?!
Current and future study design work: Major surge of interest latelyon the design of studies to inform cluster-level adaptive interventions(e.g., staged, multi-level prevention efforts)
Future collaborative work: Greater and greater emphasis on real-worldaspects of adaptive interventions (e.g., prime for nursing or healthservices type researchers)
Current and future statistical work: Dr. Nahum-Shani and I arecurrently developing linear mixed models for longitudinal andclustered SMART data. (Hard!)
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Special Issue inJournal of Clinical Child and Adolescent Psychology
Adaptive Interventions in Child and Adolescent Mental Health
Editors: Andrea Chronis-Tuscano and Daniel Almirall
Foreword: Adaptive interventions in CAMH, literature review,summarizing purpose of the special issue, and looking forward
The observed data is {Xi ,A1i ,Ri ,A2i ,Yi}, i = 1, . . . ,N.
Regressing Y on [1,X ,A1, I (A1 = 1)A2] often won’t work. Why?
By design, there is an imbalance in the types individuals followingAI#1 vs AI#3 (for example)? This imbalance is due to apost-randomization variable R. Adding R to this regression does notfix this and may make it worse!
How do we account for the fact that responders to JASP areconsistent with two of the embedded AIs?
We use something called weighted-and-replicated regression. It is easy!
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Before Weighting-and-Replicating
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After Weighting-and-Replicating
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Statistical foundation found in work by Orellana, Rotnitzky and Robins:
Robins JM, Orellana L, Rotnitzky A. Estimation and extrapolation inoptimal treatment and testing strategies. Statistics in Medicine. 2008Jul; 27:4678-4721.
Orellana L, Rotnitzky A, Robins JM. Dynamic Regime MarginalStructural Mean Models for Estimation of Optimal DynamicTreatment Regimes, Part I: Main Content. Int J Biostat. 2010; 6(2):Article No. 8.
(...ditto...), Part II: Proofs of Results. Int J Biostat. 2010;6(2):Article No. 9. 4678-4721.
Very nicely explained and implemented with SMART data in:
Nahum-Shani I, Qian M, Almirall D, et al. Experimental design andprimary data analysis methods for comparing adaptive interventions.Psychol Methods. 2012 Dec; 17(4): 457-77.
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Weighting (IPTW): By design, each individual/unit has a different
probability of following the sequence of treatment s/he was offered(weights account for this)
I e.g., W = 2I{A1 = 1,R = 1}+ 2I{A1 = −1}+ 4I{A1 = 1,R = 0}.
Replication: Some individuals may be consistent with multipleembedded regimes (replication takes advantage of this and permitspooling covariate information)
I e.g., Replicate (double) the responders to JASP: assign A2 = 1 to halfand A2 = −1 to the other half
I e.g., The new data set is of size M = N +∑
I{A1 = 1,R = 1}
Implementation is as easy as running a weighted least squares:
(η, β) = arg minη,β
1
M
M∑i=1
Wi (Yi − µ(Xi ,A1i ,A2i ; η, β))2.
SE’s: Use ASEs to account for weighting/replicating (or bootstrap).
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An Interesting Connection Between Estimators
Recall Robins’ G-Computation Estimator (not to be confused with theG-Estimator which is an entirely different thing!:)
E [Y (1, 1)] = E [Y |A]Pr [R = 1|JASP] + E [Y |C](1− Pr [R = 1|JASP])
E [Y (1,−1)] = E [Y |A]Pr [R = 1|JASP] + E [Y |B](1− Pr [R = 1|JASP])
E [Y (−1, .)] = E [Y |D]Pr [R = 1|AAC] + E [Y |E](1− Pr [R = 1|AAC])
This estimator is algebraically identical to fitting the WRREstimator with no covariates and sample-proportion estimated
weights (rather than the known true weights).
Comparing these two provides a way to compare the added-value ofadjusting for covariates in terms of statistical efficiency gains.
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Results from an Analysis of the Autism SMARTRecall: N = 61, and the primary outcome is SCU at Week 24 (SD=34.6).
WRR with no CovtsWRR with Covts and with SAMPLE
and Known Wt PROP Wt (G-Comp)ESTIMAND EST SE PVAL EST SE PVAL
(AAC,AAC+) vs (JASP,AAC) 17.9 8.2 0.03 22.8 9.4 0.02(JASP,AAC) vs (JASP,JASP+) 6.4 3.8 0.10 -1.8 7.7 0.82
What’s the lesson? The regression approach is more useful. (And, it is agood idea to adjust for baseline covariates!) Of course, this is well-known.
But the story gets even more interesting...
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Improving the Efficiency of the WRR by Estimating theKnown Weights with CovariatesBy design, we know the true weights. That is,
Since Pr(A1) = 1/2 and Pr(A2 = 1 | A1 = 1,R = 0) = 1/2,
then W = 4I{A1 = 1,R = 0}+ 2I{ everyone else }.
However, from work by Robins and colleagues (1995; also, Hirano et al(2003)), there are gains in statistical efficiency if using an WRR withweights that are estimated using auxiliary baseline (L1) and time-varying(L2) covariate information. Here’s how to do it with the autism SMART:
The observed data is now {L1i ,Xi ,A1i ,Ri , L2i ,A2i ,Yi}Use logistic regression to get p1 = Pr(A1 | L1,X )
Use logistic regression to get p2 = Pr(A2 | L1,X ,A1 = 1,R = 0, L2).
Use W = I{A1 = 1,R = 0}/(p1p2) + I{ everyone else }/p1.
The key is to choose Lt ’s that are highly correlated with Y !
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Improving the Efficiency of the WRR by Estimating theKnown Weights with CovariatesBy design, we know the true weights. That is,
Since Pr(A1) = 1/2 and Pr(A2 = 1 | A1 = 1,R = 0) = 1/2,
then W = 4I{A1 = 1,R = 0}+ 2I{ everyone else }.
However, from work by Robins and colleagues (1995; also, Hirano et al(2003)), there are gains in statistical efficiency if using an WRR withweights that are estimated using auxiliary baseline (L1) and time-varying(L2) covariate information. Here’s how to do it with the autism SMART:
The observed data is now {L1i ,Xi ,A1i ,Ri , L2i ,A2i ,Yi}Use logistic regression to get p1 = Pr(A1 | L1,X )
Use logistic regression to get p2 = Pr(A2 | L1,X ,A1 = 1,R = 0, L2).
Use W = I{A1 = 1,R = 0}/(p1p2) + I{ everyone else }/p1.
The key is to choose Lt ’s that are highly correlated with Y !
Almirall and many friends Adaptive Interventions April 2016 53 / 66
Improving the Efficiency of the WRR by Estimating theKnown Weights with CovariatesBy design, we know the true weights. That is,
Since Pr(A1) = 1/2 and Pr(A2 = 1 | A1 = 1,R = 0) = 1/2,
then W = 4I{A1 = 1,R = 0}+ 2I{ everyone else }.
However, from work by Robins and colleagues (1995; also, Hirano et al(2003)), there are gains in statistical efficiency if using an WRR withweights that are estimated using auxiliary baseline (L1) and time-varying(L2) covariate information. Here’s how to do it with the autism SMART:
The observed data is now {L1i ,Xi ,A1i ,Ri , L2i ,A2i ,Yi}Use logistic regression to get p1 = Pr(A1 | L1,X )
Use logistic regression to get p2 = Pr(A2 | L1,X ,A1 = 1,R = 0, L2).
Use W = I{A1 = 1,R = 0}/(p1p2) + I{ everyone else }/p1.
The key is to choose Lt ’s that are highly correlated with Y !
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Sim: Relative RMSE for (AAC,AAC+) vs (JASP,JASP+)
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Results from an Analysis of the Autism SMART
Recall: N = 61, and the primary outcome is SCU at Week 24 (SD=34.6).
WRR with Covts WRR with Covtsand Known Wt and Covt-Est Wt
ESTIMAND EST SE PVAL EST SE PVAL(AAC,AAC+) 60.5 5.8 < 0.01 60.2 5.6 < 0.01(JASP,AAC) 42.6 4.9 < 0.01 43.1 4.5 < 0.01
(AAC,AAC+) vs (JASP,AAC) 17.9 8.2 0.03 17.1 7.9 0.03(JASP,AAC) vs (JASP,JASP+) 6.4 3.8 0.10 7.7 3.0 0.01
The WRR implementation with covariates and covariate-estimated weightspermits us to obtain scientific information from a SMART with less uncertainty.
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Rule-of-thumb concerning which auxiliary variables to usein the WRR for comparing embedded of AIs in a SMART.
Key is to include in Lt variables which are (highly) correlated with Y , evenif not of scientific interest. A potentially useful rule-of-thumb (not dogma):
Include in L1, all variables that were used to stratify the initialrandomization.
Include in L2, all variables that were used to stratify the secondrandomization.
Let the science dictate which X ’s to include in the final regressionmodel.
I e.g., Investigator may be interested in whether baseline levels of spokencommunication moderate the effect of JASP vs JASP+AAC.
I Of course: It is possible for X = L1, but not possible for X to includeany post-A1 measures.
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Challenges to Address in Longitudinal Setting
Modeling Considerations: The intermixing of repeated measures andsequential randomizations requires new modeling considerations toaccount for the fact that embedded AIs will share paths/trajectoriesat different time points (this is non-trivial)
Implications for Interpreting Longitudinal Models: (1) Comparison ofslopes is no longer appropriate in many circumstances; (2) Need fornew, clinically relevant, easy-to-understand summary measures of themean trajectories over time
Statistical: Develop an estimator that takes advantage of the withinperson correlation in the outcome over time
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An Example Marginal Model for Longitudinal Outcomes
Yt : # Socially Communicative Utterances at week t. t = 0, 12, 24, 36
The comparison of embedded AIs with longitudinal data arising from aSMART will require longitudinal models that permit deflections intrajectories and respect the fact that some embedded AIs will sharepaths/trajectories up to the point of randomization.
An example is the following piece-wise linear model:
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Analysis of Longitudinal Outcomes in the ADHD SMART
Average classroom performanceover the school year for each AI
AI Estimate SE(BMD,BMD+) 21.4 0.91
(BMD,BMD+MED) 21.3 0.95(MED, MED+BMD) 19.2 0.96
(MED, MED+) 19.0 0.85
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Adaptive Implementation Intervention in Mental HealthPI: Kilbourne; Co-I: Almirall (CO/AR/MI; Aim is to improve uptake of psychosocialintervention for mood disorders; primary aim compared initial REP+EF vs REP+EF+IF.)