U-M Personal World Wide Web Server - A Look Under the ...dalmiral/slides/ALMIRALL-NYU-11...Myths or Misconceptions about Adaptive Interventions and SMARTs Almirall and many friends

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

Almirall and many friends Adaptive Interventions April 2016 1 / 66

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...


Outline

Adaptive Interventions

Sequential Multiple Assignment Randomized Trials (SMART)

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


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


Adaptive Interventions


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.


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;


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;


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.


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


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


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)


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.


Sequential Multiple Assignment Randomized Trials (SMART)


What is a Sequential Multiple Assignment RandomizedTrial (SMART)?

A type of multi-stage randomized trial design.

At each stage, subjects randomized to a set of feasible/ethicaltreatment options.

Treatment options at latter stages may be restricted by response toearlier treatments.

SMARTs were developed explicitly for the purpose of building ahigh-quality Adaptive Intervention.


What is a Sequential Multiple Assignment RandomizedTrial (SMART)?

A type of multi-stage randomized trial design.

At each stage, subjects randomized to a set of feasible/ethicaltreatment options.

Treatment options at latter stages may be restricted by response toearlier treatments.

SMARTs were developed explicitly for the purpose of building ahigh-quality Adaptive Intervention.


Example of a SMART in Autism Research

The population of interest:

Children with autism spectrum disorder

Age: 5-8

Minimally verbal: <20 spontaneous words in a 20-min. language test

History of treatment: ≥2 years of prior intervention

Functioning: ≥2 year-old on non-verbal intelligence tests


Example of a SMART in Autism Research (N = 61)PI: Kasari (UCLA).


There are 3 AIs Embedded in this Example Autism SMART

(JASP,JASP+)

Subgroups A+C

(JASP,AAC)

Subgroups A+B

(AAC,AAC+)

Subgroups D+E


SMARTs permit scientists to answer many interestingquestions for building a high-quality adaptive intervention.

Primary Aim: What is the best first-stage treatment in terms ofspoken communication at week 24: JASP alone vs JASP+AAC?

Secondary Aim: Which is the best of the three adaptiveinterventions embedded in this SMART?

I will show you results for the Secondary Aim:Compare 3 adaptive interventions based on a longitudinal outcome.


SMARTs permit scientists to answer many interestingquestions for building a high-quality adaptive intervention.

Primary Aim: What is the best first-stage treatment in terms ofspoken communication at week 24: JASP alone vs JASP+AAC?

Secondary Aim: Which is the best of the three adaptiveinterventions embedded in this SMART?

I will show you results for the Secondary Aim:Compare 3 adaptive interventions based on a longitudinal outcome.


There are 3 AIs Embedded in this Example Autism SMART

(JASP,JASP+)

Subgroups A+C

(JASP,AAC)

Subgroups A+B

(AAC,AAC+)

Subgroups D+E


Longitudinal Analyses


Longitudinal Outcomes in the Autism SMART

Outcomes collected at baseline, and weeks 12, 24 and 36

Primary outcome (verbal): from 20-minute “natural language sample”:

Total spontaneous communicative utterances (TSCU)

Secondary outcome (non-linguistic):

Initiating joint attention (IJA; e.g., pointing; JASP mechanism)


Results

Adaptive (a) TSCU (b) IJAIntervention AUC 95% CI AUC 95%CI

(AAC,AAC+) 51.7 [43, 60] 9.5 [7.2,11.8](JASP,AAC) 36.0 [28, 44] 7.2 [5.6,8.8]

(JASP,JASP+) 33.1 [25, 42] 6.6 [5,8.2]No diff null p < 0.01 p < 0.05


Looking Under the Hood of Various SMART Case Studies


SMART Case Study #1:

Adaptive Interventions for Minimally Verbal Children with ASD(AIM-ASD)


Interventions for Minimally Verbal Children with AutismPIs: Kasari(UCLA), Almirall(Mich), Kaiser(Vanderbilt), Smith(Rochester), Lord(Cornell)

What the original study did not aim to examine?But in post-funding conversations, there was great interest in the effect of JASP+DTT!

Interventions for Minimally Verbal Children with AutismPIs: Kasari(UCLA), Almirall(Mich), Kaiser(Vanderbilt), Smith(Rochester), Lord(Cornell)

!

!

!!

!

!

Subgroup!

A!

B!

C!

D!

E!

Non0Responders!(Parent!training!no!feasible)!

JASP!(joint!attention!and!social!play)! Continue!JASP!

JASP!+!Parent!Training!R!

DTT!(discrete!trials!training)!

Continue!DTT!

DTT!+!Parent!Training!

Responders!(Blended!txt!unnecessary)!

R!

Non0Responders!(Parent!training!not!feasible)!

Responders!(Blended!txt!unnecessary)!

R!

JASP!+!DTT!

Continue!JASP!R!

JASP!+!DTT!

Continue!DTT!R!

F!

G!

H!

Primary and Secondary Aims

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!]



Adaptive Implementation of Effective Programs (ADEPT) in MoodDisorders


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.)


ExTEnd Study in Adult Alcoholism


Extending Treatment Effectiveness in Alcohol DependencePIs: David Oslin (N = 302)


Treatment for Pregnant Women with Heroine Dependence


Extending Treatment Effectiveness in Alcohol DependencePIs: Hendree Jones (N = 300)


Getting SMART about Social and Academic Engagement in ElementaryAged Children with ASD


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.


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


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


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!)


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

Topics: Over 10 papers covering anxiety, depression, autism,prevention, ADHD, child obesity

Discussion: Dr. Joel Sherrill, NIMH Division of Services andInterventions Research, NIMH


Thank you! [email protected], http://www-personal.umich.edu/∼dalmiral/

Funding for Methods Development

NIMH: R03-MH09795401 (PI: Almirall)NIDA: R01-DA039901 (Co-PIs: Almirall and Nahum-Shani)NIDA: P50-DA10075 (PI: Murphy; Co-I: Almirall)

Funding for some of the SMARTs Presented

Autism Speaks: Grant 5666 (PI: Kasari; Co-I: Almirall)NICHD: R01-HD073975 (PI: Kasari; Co-I: Almirall)IES (PI: Kasari; Co-I: Almirall)NIMH: R01-MH099898 (PI: Kilbourne; Co-I: Almirall)


Extra, Back-pocket Slides; Slightly More Technical


Challenges in the Conduct of this Initial Autism SMART

Slow responder rate, while based on prior data, was lower thananticipated during the design of the trial.

Responder/Slow-responder measure could be improved to make moreuseful in actual practice.

There was some disconnect with the definition of slow-response statusand the therapist’s clinical judgment.


A Simple Regression Model for Comparing the EmbeddedAIs

Y (a1, a2) denotes SCU at Wk 24 under AI (a1, a2). X ’s are mean-centeredbaseline (pre-txt) covariates. Consider the following marginal model:

E [Y (a1, a2)|X ] = β0 + ηTX + β1a1 + β2I (a1 = 1)a2

E [Y (1, 1)] = β0 + β1 + β2 = (JASP,JASP+)

E [Y (1,−1)] = β0 + β1 − β2 = (JASP,AAC)

E [Y (−1, .)] = β0 − β1 = (AAC,AAC+)





E [Y (1, 1)] = β0 + β1 + β2 = (JASP,JASP+)

E [Y (1,−1)] = β0 + β1 − β2 = (JASP,AAC)

E [Y (−1, .)] = β0 − β1 = (AAC,AAC+)





−2β1 + β2 = (AAC,AAC+) vs (JASP,JASP+)

−2β1 − β2 = (AAC,AAC+) vs (JASP,AAC)

−2β2 = (JASP,AAC) vs (JASP,JASP+)


How Do We Estimate this Marginal Model?


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!


Before Weighting-and-Replicating


After Weighting-and-Replicating


Weighted-and-Replicated Regression Estimator (WRR)

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.


Weighted-and-Replicated Regression Estimator (WRR)

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).


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.


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+) 60.5 5.8 < 0.01 61.0 6.0 < 0.01(JASP,AAC) 42.6 4.9 < 0.01 38.2 6.9 < 0.01

(JASP,JASP+) 36.3 5.0 < 0.01 40.0 8.0 < 0.01(AAC,AAC+) vs (JASP,JASP+) 24.3 7.9 < 0.01 21.0 10.2 0.04

(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...


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 !




















Sim: Relative RMSE for (AAC,AAC+) vs (JASP,JASP+)


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

(JASP,JASP+) 36.3 5.0 < 0.01 35.4 4.4 < 0.01(AAC,AAC+) vs (JASP,JASP+) 24.3 7.9 < 0.01 24.9 7.4 < 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.


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.


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


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:

E [Yt(a1, a2)|X ] = β0 + ηTX + 1t≤12{β1t + β2ta1}+ 1t>12{12β1 + 12β2a1 + β3(t − 12) + β4(t − 12)a1 + β5(t − 12)a1a2}

where X ’s are mean-centered baseline covariates.


Modeling Considerations

Regime (-1,0): (AAC, AAC+)

12 24 36 t0

Y

•

•

•

•

β0

••

••

•

slope =

β1 − β2

slope = β3 − β4



Regime (1,1): (JASP, JASP+)

12 24 36 t0

Y

•

•

•

•

••

••

•

slope =

β1 + β2slope = β3 + β4 + β5



Regime (1,-1): (JASP, AAC)

12 24 36 t0

Y

•

•

•

•

••

•

•

•

•

slope =

β1 + β2

slope = β3 + β4 − β5


Implications of New Modeling Considerations forSummarizing each AI

Potential Solution: Summarize each AI by the area under the curve(during an interval chosen by the investigator)

Clinical advantage: AUC is easy to understand clinically; it is theaverage of the primary outcome over a specific interval of time

Statistical inference is easy: AUC is linear function of parameters(β’s) in marginal model


Statistical: WRR Estimator for Longitudinal Outcomes

We use the following estimating equation to estimate marginal model forlongitudinal outcomes:

0 =1

M

M∑i=1

Di (Xi , Ai )Vi−1Wi (Yi − µi (Xi , Ai ;β, η)),

where

Yi : a vector of longitudinal outcomes, i.e. (Yi ,0,Yi ,12,Yi ,24,Yi ,36)T ;µi a vector of corresponding conditional means;

Di : the design matrix, i.e.(∂µi (Xi ,Ai ;β,η)

∂βT , ∂µi (Xi ,Ai ;β,η)∂ηT

)T;

Wi : a diagonal matrix containing inverse probability of following theoffered treatment sequence at each time point;

Vi : working covariance matrix for Yi .


Child Attention Deficit Hyperactivity Disorder (ADHD)PI: Pelham (FIU) (N = 153; ages 6-12; 8 month study; monthly non-response based ontwo teacher ratings (ITB < 0.75 and IRS > 1 domain)


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


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.)

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U-M Personal World Wide Web Server - A Look Under the ...dalmiral/slides/ALMIRALL-NYU-11...Myths or Misconceptions about Adaptive Interventions and SMARTs Almirall and many friends