Stepped wedge with three treatments
Stepped-wedge like designs
to compare active implementation strategies
with natural development in absence of active
implementation
Steven Teerenstra
biostatistics, Radboud Instituted for Health Sciences
joint work with
Hilly Calsbeek, Hub Wollersheim from IQ Healthcare
Nijmegen, NL
The
SO HIP study
(Margriet Pol, Gerben ter Riet)
how to calculate sample size
simulation, theory (design matrix,
known random effects)
1. How to calculate sample size for SW with 3 trt?
2. If stepped wedge possible, does it compare
favourable to other designs?
2
1. How to sample size for SW with 3 trt
 Cross-sectional
• equal cluster size, equal number of clusters per
group
 Systematic effects; T+, T, C
– two intervention effects: θT+, T > 0, θT, C > 0
 Model of Hussey and Hughes
– Fixed effects for trt and time, random for cluster
– Yijk = μ + βi + θT+, T + θT, C + υj + eijk if T+ at i,j
– Yijk = μ + βi +
– Yijk = μ + βi +
θT, C + υj + eijk
+ υj + eijk
if T
if C
at i,j
at i,j
1. How to sample size for SW with 3 trt
 WLS (like H&H)
– Z design matrix for time effects and two treatment
effects
– V Covariance matrix of cluster means
1
1
– Covariance matrix of fixed effects is
( ZV Z )
 Simulation (e.g. SAS macro)
2. If stepped wedge possible,
does it compare favourable to other
designs?
What other designs?
time
T1
C
T
Group 1
2
Time
T1 T2
group
1
2
C
C
C
T
time
T1 T2 T3
gr
p 1 C
C
T
2 C
T
T
Building blocks
post-test
Preposttest
(simplest)
stepped
wedge
Some possible designs
built from these
posttest
2( 2   2 )
var( T ,C ) 
n
2( 2   2 )
var( T  ,T ) 
n
hybrid pre-posttest
2( 2   2 )
var( T  ,T ) 
n
2( 2   2 )
var(T ,C ) 
n
Parallel overlapping pre-posttest
2 2  ( 2  2 2 )
var(T ,C ) 
n   2  2

2 

2 2  ( 2  2 2 )
var( T  ,T ) 
n   2   2 
within - cluster variance
,  2  between - cluster variance
cluster size
Sequential double
pre-posttest
2 2  ( 2  3 2 )
2 2  ( 2  3 2 )
var( T ,C ) 
var( T  ,T ) 
n   2  2 2 
n   2  2 2 
sequential hybrid double
pre-posttest
2 2  ( 2  2 2 )
var( T ,C ) 
n   2   2 
2 2  ( 2  2 2 )
var( T  ,T ) 
n   2   2 
Sequential double stepped wedge
2   2  ( 2  4 2 )
var( T ,C ) 
n   2  3 2 
2   2  ( 2  4 2 )
var( T  ,T ) 
n   2  3 2


Sequential hybrid double
stepped wedge
2 2  ( 2  3 2 )
var( T ,C ) 
n   2  2 2 
2 2  ( 2  3 2 )
var( T  ,T ) 
n   2  2 2


parallel double pre-posttest
3( 2  2 2 )   2  ( 2  2 )
var(T ,C ) 
n   5 4  8 2 2  2 4 
(7 2  3 2 )   2  ( 2  2 2 )
var(T ,T ) 
n   5 4  8 2 2  2 4 
parallel hybrid double pre-posttest
6( 2  2 2 )   2  ( 2   2 )
var( T ,C ) 
n  7 4  14 2 2  3 4


6(2 2   2 )   2  ( 2  2 2 )
var(T  ,T ) 
n  7 4  14 2 2  3 4


parallel double stepped wedge
10( 2  3 2 )   2  (5 2  7 2 )
var( T ,C ) 
n  9 2  20 2 )  (11 2  8 2


10( 2  3 2 )   2  (5 2  7 2 )
var( T  ,T ) 
n  9 2  20 2 )  (11 2  8 2


parallel hybrid double stepped wedge
( 2  3 2 )   2  (7 2  10 2 )
var( T ,C ) 
2n  2 2   2 )  (3 2  8 2


( 2  3 2 )   2  (7 2  10 2 )
var( T  ,T ) 
2n  2 2   2 )  (3 2  8 2


many others possible…
Different goals / constraints
 Small number of clusters
– e.g. limited number of memory clinics
 Small number of measurements
– e.g. trial has to finish in 2 years due to grant
obligation
 Small number of total subjects
– #clusters * cluster size * #measurements
(because design is cross-sectional)
 Small costs
– Optimalization of power given cost function
– Given cost per cluster, per subj., per measurement
Different goals / constraints
 Small number of clusters
– e.g. limited number of memory clinics
 Small number of measurements
– e.g. trial has to finish in 2 years due to grant
obligation
 Small number of total subjects
– #clusters * cluster size * #measurements
(because design is cross-sectional)
 Small costs
– Optimalization of power given cost function
– Given cost per cluster, per subject, per
measurement
Small clusters (size =5 per step)
Moderate cluster (size 50 per step)
Conclusion
 Smallest number of clusters
• double SW (parallel or sequential)
– If n=5: parallel double SW fewest clusters
– If n=50: sequential double SW fewest
clusters
• seq. pre-post-post, seq.double pre-post,
seq.double hybrid SW
 Yes, ‘SW’ favorably for comparing 3 trt
Discussion
 Not exhaustive list of ‘all’ designs …other?
 Order of ‘best’ designs may be different when
minimizing cost / total sample size
 Designs (including SW) more sensitive to ICC
(<0.15) if cluster size (per step) is large
 If cluster size (per step) or icc is large,
difference between designs becomes less
 ..
Thanks for your attention
Back up slides
 Two interventions in context to placebo
– Implementation strategy T, enhanced T+
– What if no active strategy was applied: C
– T+ superior to T+
• (descriptive) comparison T vs C, T+ vs C
 Golden standard non-inferiority trial
– placebo P, active control AC, test T
– T non-inferior to AC,
– AC (and/or T) superior to P (assay sens.)
 Equal interest in 3 interventions
– A vs B, A vs C, B vs C
21
Observations
 SW designs are less influenced by ICC
than (pre)post test designs
 Impact of ICC increases with cluster size
Sample size
1. calculate sample size per group as
usual
•
for a individual randomized posttest design
2. multiply by (1+(n-1)*ICC)
•
•
to account for clustering of subjects in clusters
n=cluster size
3. multiply by appropriate design effect
•
gives the sample size per group
4. multiply by #groups for sample size per
time
•
So divide by cluster size to get total number of clusters
23
Total number of clusters ..