stepped wedge cluster randomized trials · crt references eldridges&kerrys.a practical guide to...

Stepped Wedge Cluster Randomized Trials

Nicole SolomonBIOS 790

December 14, 2015

Nicole SolomonBIOS 790 Stepped Wedge Cluster Randomized Trials

Cluster Randomized Trials

Groups (clusters) of individuals are randomizedMotivation:

logisticstatisticalfinancialethical

Primary use:evaluate effectiveness of delivery of (preventive) health services,especially intervention which previously demonstrated efficacy


Motivating example: GHIS

Gambia Hepatitis Intervention Study (GHIS)

large-scale study to evaluate effectiveness of HepB vaccine inliver disease preventionEpidemiological studies identified positive association betweenHepB and liver diseaseFollow-up on liver disease outcomes over 30-40 years (ongoing)Phased randomization was implemented by geographical regionRandomization intervals were 10-12 weeks apart


Motivating example: GHIS II

Design considerations:

Vaccine price and limited availabilityComparison groups available from the same time periodDesirable to have vaccine available nationwide with deliverysystem in place by study’s endSerious logistic difficulties for individual randomization:

large cohort (> 61,000 children)large number of immunization teamscomplicated vaccination: 4 doses per childquestionably ethical


CRTs

Experimental units (randomized): clustersObservational units (measured): individualsStatistical implications: correlated observations within clusters

inflated Type I errorbiased treatment effect

Design types:1. parallel2. crossover (stepped wedge)


CRT Designs I

Common features (between parallel and crossover):

2-arm studyRandomize 1x (order of treatment in crossover)2I clusters

Differences:

Parallel CrossoverDesign 1 trt both trt

Analysis (paired) t-testGEE, random effects paired t-test


CRT Designs II

ParallelTime

Cluster

11 12 13 04 0

CrossoverTime

Cluster

1 21 1 02 1 03 0 14 0 1


Crossover Implications

fewer clusters neededlonger trialdemands short follow-up period


Stepped Wedge Design

unidirectional crossover: control to treatmentcrossover occurs at different times for different clusterstiming of crossover is randomized

Stepped WedgeTime

Cluster

1 2 3 4 51 0 1 1 1 12 0 0 1 1 13 0 0 0 1 14 0 0 0 0 1


Strengths & Weaknesses of SWD

Strengths:Smaller fraction of clusters at a time [logistic]All clusters receive intervention [ethical]Intervention is never removed once implemented [ethical]Less sensitive to ICC

Weaknesses:same as crossover designs (longer trial length)cannot estimate treatment effect solely from within-clustercomparisons


SWD Assumptions

cross-sectional designN: number individuals sampled per cluster per time interval(k = 1, . . . ,N)I: number of clusters; assumed independent (i = 1, . . . , I)T = I + 1: number of time intervals (fixed) (j = 1, . . . ,T − 1)full treatment effect is realized in single time interval


SWD Notation

µij = µ+ αi + βj + Xijθ: expected response in cluster i at timejµ: overall meanαi ∼ N(0, τ2): random cluster effectβj : fixed time effect (βT = 0 for identifiability)Xij : indicator for administered treatment in cluster i at time jθ: treatment effect


SWD Model

Individual level responses:Yijk : response of individual k in cluster i at time jYijk = µij + eijk

eijkiid∼ N(0, σ2

e )V(Yijk) = τ2 + σ2

e

Cluster level responses:Yij = 1

N∑

k Yijk : mean response of cluster i at time jLinear Mixed Model (LMM):

Yij = µij + eij (1)

eij = 1N

∑k eijk

iid∼ N(0, σ2), σ2 = σ2e/N


Cluster Variability

Variance of the cluster-level response = sum of between andwithin cluster variability:

V(Yij) = τ2 + σ2

= τ2 + σ2e

N [1 + (N − 1)ρ]

= τ2

N1ρVIF

where ρ = τ2

τ2+σ2e

= ICC

Increase in V(Yij) due to clustering captured by:Variance Inflation Factor: VIF = 1 + (N − 1)ρCoefficient of Variation: CV = τ

µ


SWD Analysis Methods I

Fixed effects: η = (µ, β1, . . . , βT−1, θ)

1. τ2, σ2 known: use weighted least squares (WLS)η̂ = (Z′V−1Z)−1(Z′V−1Y)

whereZITx(T+1) is the design matrix corresponding to ηVITxIT block diagonal matrix where each TxT block describescorrelation structure between cluster means across timeV(η̂) = (Z′V−1Z)−1


SWD Analysis Methods II

2. τ2, σ2 unknown:a. Approximately equal cluster sizes (cluster level analysis):

empirical Bayes approach to estimate η and variance components(Laird & Ware, 1982)

b. Unequal cluster sizes (and non-normal responses):conduct individual level analysis w/GEE or GLMM


GLMM & GEE

GLMM is to LMM as GLM is to LMlink functionoutcome from exponential familyautomatically applies proper weights when cluster sizes vary

GEE can handle normal or non-normal datautilizes “sandwich" type variance estimatestends to be more robust to variance structure misspecificationautomatically adjusts for unequal cluster sizestends to give inflated α rates when I is small


SWD Analysis Comparison

LMM, GEE, and GLMM theories rely on asymptotics so caremust be taken when I, T is smallGEE, GLMM preferred for binary responseJackknife estimate of variance needed to maintain α rate forGEE, GLMM analysisComparisons:

Equal cluster sizes: LMM barely superior in power to GEEwhich in turn is superior to GLMMUnequal cluster sizes: GEE and GLMM dominate LMM


SWD Power

Test: H0 : θ = 0 vs H1 : θ = θA

power = Φ

θA√V(θ̂)

− Z1−α/2

where θ̂ = θ̂WLS


SWD Power Trends

Insensitive to variations in CVNonlinear relationship with ICC: (Hemming 2014)

smaller ICC values: power decreases with increasing ICClarger ICC values: power increases with increasing ICC

Fewer time intervals leads to reduced powerOptimal when each cluster randomized in a unique time interval

Sensitive to delayed treatment effectpartly recoverable if additional measurement intervals included


Cross-sectional vs Cohort Designs

Cross-sectional: different population at each time pointCohort: same population measured repeatedlyImplications of choosing a cohort design:

blinding of treatment allocation is not possible with individualrecruitment → selection biastwo-level hierarchical models may be modified to fit cohortdesign (Hemming 2015)


Recommendations

Ensure time intervals long enough to fully realize outcomeMaximize number time intervalsOnly use within-cluster analyses if no significant fluctuationsexpected over time (βj = 0)Use individual level analyses when cluster sizes varyconsiderablyUse jackknife variance estimate to maintain α rate with GEE,GLMM analyses


CRT ReferencesEldridge S & Kerry S. A Practical Guide to Cluster Randomised Trials inHealth Services Research. Wiley & Sons, 2nd ed, 2012.

Hemming K, Lilford R, & Girling A. (2014). Stepped-wedge clusterrandomised controlled trials: a generic framework including parallel andmultiple-level designs. Stat in Med, 34: 181-96.

Hemming K, Haines T, Chilton P, et al. (2015). The stepped wedgecluster randomised trial: rationale, design, analysis, and reporting. BMJ,350: h391.

Hussey M & Hughes J. (2007). Design and analysis of stepped wedgecluster randomized trials. Contemp Clin Trials, 28: 182-91.

Laird N & Ware J. (1982). Random-effects models for longitudinal data.Biometrics, 38: 963-74.

The Gambia Hepatitis Study Group. (1987). The Gambia HepatitisIntervention Study. Cancer Res, 47: 5782-7.

Torgerson D. (2001). Contamination in trials: is cluster randomisation theanswer? BMJ, 322: 355-7.


stepped wedge cluster randomized trials · crt references eldridges&kerrys.a practical guide to...

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