cluster-level adaptive interventions and sequential ...tnecamp/slide show_ibc_2016_2464158.pdf ·...

Cluster-level adaptive interventions and sequential, multiple assignment,

randomized trials: Estimation and sample size considerations

Tim NeCampUniversity of Michigan

Joint work with Amy Kilbourne and Daniel Almirall

JITAIs

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Overview

• Cluster level Adaptive Interventions• Trial Design to Develop Cluster-level

Adaptive Interventions• Sample Size Formula and Simulation Results

Cluster-level Interventions

• Often times, interventions are delivered at the cluster level, e.g.:– A new curriculum for 8th grade math classes– Family therapy sessions– Intervention designed to increase the adoption

of an evidence based practice (EBP) in routine clinical settings

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Towards Cluster-level AdaptiveInterventions

• However, due heterogeneity in clusters…– Within cluster heterogeneity– Between cluster heterogeneity

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it is often necessary to use an adaptiveapproach to intervention

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Adaptive Implementation of Effective Programs Trial (ADEPT) (Kilbourne et al., 2014)

REP+EF

Month 6 Month 240 Month 12

Third-stageSecond-stageFirst-stage

Add IF (REP+EF+IF)

REP

REP

Discontinue EF (REP)

A clinic is “not responding” at months 6 and 12 if < 50% of the pre-specified patients identified have received ≥3 Life Goals sessions

REP

An Example of a Cluster-Level Adaptive Intervention

6Adaptive Implementation of Effective Programs Trial (ADEPT) (Kilbourne et al., 2014)

REP+EF



Add IF (REP+EF+IF)

REP

REP


REP

Questions when developing an adaptive intervention?

Timing: Why don’t we reevaluate sooner at month 3, or wait longer?

7Adaptive Implementation of Effective Programs Trial (ADEPT) (Kilbourne et al., 2014)

REP+EF



Add IF (REP+EF+IF)

REP

REP


REP

Questions when developing an adaptive intervention?

Sequence:Why don’t we start with REP+EF?

Why do we stop giving EF to second stage responders?

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Sequential Multiple Assignment Randomized Trials (SMARTs)

• Sequential multiple assignment randomized trials (SMARTs) are trial designs used to build high-quality adaptive interventions.

• Here we consider cluster randomized SMARTs, where the unit of randomization is a cluster and the outcomes are measured at the patient level.

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ADEPT: SMART trial design

REP+EF Continue REP+EF


Continue REP+EF+IF

Discontinue EF+IF (REP )

REF+EF+IF

Month 6 Month 24

A

B

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0 Month 12

CellsThird-stageSecond-stage

Non-‐responding sites after 6 months of REPenter the study

First-stage

R

R Add IF (REP+EF+IF)


Comparison of Embedded Adaptive Interventions in a SMART

• Common primary aim in a SMART

• Can be conceptualized as:– Comparing two pre-specified embedded

adaptive interventions

– Select the best embedded adaptive intervention

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Oetting et al. (2010)

Ghosh et al. (2015); Li Z and Murphy SA (2011)

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Adaptive intervention 1



Continue REP+EF+IF


REF+EF+IF

Month 6 Month 24

A

B

C

D

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0 Month 12



First-stage

R



12




Continue REP+EF+IF


REF+EF+IF

Month 6 Month 24

A

B

C

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0 Month 12



First-stage

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13




Continue REP+EF+IF


REF+EF+IF

Month 6 Month 24

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First-stage

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Methodology to Compare Embedded Adaptive Interventions

• By design, clusters could have different probabilities of receiving a particular sequence of interventions.

• We extended the use of inverse probability weighted(IPW) regression estimators for cluster-randomized SMART data.

• The regression methodology allows for estimation of adaptive intervention effects conditional on baseline covariates.

14Orellana et al. (2010); Murphy et al. (2001); Robins et al. (2000); Hernan et al. (2000); Robins (1999)

Sample Size Formula(for comparing 2 adaptive interventions with different first stage

treatment)

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Regular Constants

Variance Inflation Factor

SMART Specific Constants

2 arm RCT

Without Covariates

Variance Deflation Factor

Deflated ICC

With a single cluster-wide covariate

Sample Size Formulae Are Robust to Working Assumptions

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Future Work

• Extensions of formula to allow for individual level covariates

• Combining cluster-randomized and individual-randomized SMARTs

• Develop random effects methodology for cluster-randomized SMARTs

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Thank you!

• Collaborators: – Daniel Almirall– Amy Kilbourne

• Funding– NIH grants: R01MH099898, P50DA039838,

R01HD073975, R01DA039901

18Questions?

Citations• Kilbourne AM, Almirall D, Eisenberg D, Waxmonsky J, Goodrich DE, Fortney JC, Kirchner JE,

Solberg LI, Main D, Bauer MS et al. (2014) Protocol: Adaptive implementation of effective programs trial (adept): cluster randomized smart trial comparing a standard versus enhanced implementation strategy to improve outcomes of a mood disorders program. Implement Science 9: 132

• Ghosh P, Cheung Y and Chakraborty B (2015) Sample size calculations for clustered smart designs. In: Kosorok MR and Moodie EE (eds.) Adaptive Treatment Strategies in Practice: Planning Trials and Analyzing Data for Personalized Medicine, chapter 5. Alexandria, Virginia: SIAM, pp. 55–70.

• Li Z and Murphy SA (2011) Sample size formulae for two-stage randomized trials with survival outcomes. Biometrika 98(3): 503–518.

• Oetting A, Levy J, Weiss R and Murphy S (2011) Statistical methodology for a smart design in the development of adaptive treatment strategies. In: Shrout P, Keyes K and Ornstein K (eds.) Causality and psychopathology: Finding the determinants of disorders and their cures. Arlington, VA: Oxford University Press, pp. 179–205.

• Orellana L, Rotnitzky A and Robins J (2010) Dynamic regime marginal structural mean models for estimating optimal dynamic treatment regimes, part i: Main content. International Journal of Biostatistics 6(2): Article 8.

• Murphy SA, van der Laan MJ, Robins JM and CPPRG (2001) Marginal mean models for dynamic regimes. Journal of the American Statistical Association 96: 1410–1423. 19

More Citations• Herna ́n M, Brumback B and Robins J (2000) Marginal structural models to estimate the causal effect

of zidovudine on the survival of hiv-positive men. Epidemiology 11(561-70).

• Robins JM (1999) Association, causation, and marginal structural models. Synthese 121: 151– 179. • Robins JM, Hernan M and Brumback B (2000) Marginal structural models and causal inference.

Epidemiology 11(5): 550–560.

• Lu, X., Nahum-Shani, I., Kasari, C., Lynch, K. G., Oslin, D. W., Pelham, W. E., et al. (2015). Comparing dynamic treatment regimes using repeated-measures outcomes: modeling considerations in SMART studies. Stat Med. doi:10.1002/sim.6819

• Nahum-Shani I, Qian M, Almirall D, Pelham W, Gnagy B, Fabiano G, Waxmonsky J, Yu J and Murphy S (2012) Experimental design and primary data analysis methods for comparing adaptive interventions. Psychological Methods 17: 457–477.

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Extra Slides

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Methodology• We developed an inverse probability weighted

(IPW) regression approach in order to obtain estimates of the intervention effects

• We parameterize the mean as:

22Orellana et al. (2010); Murphy et al. (2001); Robins et al. (2000); Hernan et al. (2000); Robins (1999)

Methodology

• The estimates are obtain by solving:

•

• I here is an indicator function which is 1 if you are consistent with adaptive intervention (a1,a2)

• W is the known inverse probability weight.• V is the working correlation matrix

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Orellana et al. (2010); Nahum-Shani et al. (2012); Lu et al. (2015)

*

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Discontinue REP+EF

Continue REP+EF+IF

Discontinue REP+EF+IF

REF+EF+IF

Month 6 Month 24

A

B

C

D

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0 Month 12



First-stage

R


Using sample size formula with ADEPT

• In ADEPT we projected:– 16 patients per site (m = 16)– .01 is the estimated pre-trial ICC (ρ = .01)– .3 is the estimate response rate to first stage

intervention REP + EF (p1 = .3)With an effect size of .2, Type I error of .05, and desired power of 80% we would need

N = 77

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Extensions to the Prototypical SMART Study

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1st Treatment 1 (T11) 2nd Treatment 2 (T22)

2nd Treatment 1 (T21)

1st Treatment 2 (T12)

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CellsSecond-stageFirst-stage

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R2nd Treatment 3 (T23)



2nd Treatment 6 (T26)R

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