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Table 3 Simulation Results

From: Accounting for confounding by time, early intervention adoption, and time-varying effect modification in the design and analysis of stepped-wedge designs: application to a proposed study design to reduce opioid-related mortality

  Time effects Scenario 1 Scenario 2.1 Scenario 2.2
Model Main Interaction Standard Confounding (+) Confounding (-)
index fixed random fixed random %bias SD SE cov pwr α %bias SD SE cov pwr α %bias SD SE cov pwr α
1 disc     0.1 0.09 0.08 0.94 1 0.05 -0.7 0.11 0.08 0.83 1 0.22 0.1 0.11 0.09 0.91 1 0.11
2 disc H/G    0.1 0.09 0.08 0.94 1 0.05 -0.8 0.11 0.09 0.92 1 0.08 0.1 0.11 0.1 0.93 1 0.07
3 disc UN    0.5 0.1 0.11 0.96 1 0.05 -0.2 0.12 0.12 0.95 0.99 0.06 1.3 0.13 0.12 0.94 0.98 0.05
4 disc lin    0.1 0.09 0.08 0.94 1 0.06 -0.3 0.11 0.08 0.82 1 0.22 0.1 0.11 0.09 0.89 1 0.11
5 disc H/G lin H/G 0.8 0.23 0.24 0.95 0.6 0.06 0.6 0.29 0.26 0.92 0.52 0.07 6.1 0.28 0.26 0.93 0.55 0.08
6 disc UN lin UN 0.3 0.27 0.31 0.97 0.38 0.03 0.7 0.32 0.33 0.95 0.34 0.05 8 0.33 0.35 0.97 0.35 0.04
7 disc lin lin lin 1.3 0.24 0.24 0.96 0.59 0.06 1.8 0.29 0.23 0.86 0.58 0.15 6.3 0.28 0.26 0.93 0.57 0.1
8 lin H/G lin H/G -0.7 0.14 0.14 0.95 0.95 0.05 -6.2 0.17 0.16 0.9 0.84 0.11 4.9 0.17 0.16 0.93 0.91 0.08
9 lin UN lin UN -1.6 0.16 0.17 0.97 0.84 0.04 -4.9 0.19 0.19 0.94 0.75 0.06 3.2 0.19 0.21 0.95 0.77 0.06
10 lin lin lin lin -1 0.14 0.14 0.94 0.95 0.06 -10.8 0.18 0.13 0.81 0.87 0.24 2.5 0.17 0.15 0.91 0.92 0.12
  Time effects Scenario 3 Scenario 4.1 Scenario 4.2
Model Main Interaction Early adoption Confounding (+)& Early adoption Confounding (-)& Early adoption
index fixed random fixed random %bias SD SE cov pwr α %bias SD SE cov pwr α %bias SD SE cov pwr α
1 disc     -33.9 0.09 0.09 0.48 0.96 0.04 -34 0.12 0.08 0.45 0.93 0.21 -33.3 0.12 0.09 0.52 0.92 0.1
2 disc H/G    -33.9 0.09 0.09 0.49 0.96 0.04 -34.3 0.11 0.1 0.57 0.89 0.1 -33.4 0.12 0.1 0.58 0.89 0.07
3 disc UN    -33.6 0.11 0.11 0.68 0.85 0.03 -33.1 0.12 0.12 0.71 0.77 0.07 -32 0.14 0.13 0.73 0.74 0.05
4 disc lin    -34.3 0.09 0.08 0.44 0.97 0.05 -34.1 0.12 0.08 0.45 0.94 0.21 -33.4 0.11 0.09 0.51 0.93 0.12
5 disc H/G lin H/G -3.4 0.26 0.24 0.93 0.53 0.06 -3.5 0.31 0.27 0.91 0.45 0.09 -0.9 0.3 0.27 0.93 0.47 0.08
6 disc UN lin UN 0.1 0.3 0.33 0.96 0.33 0.03 1.1 0.34 0.35 0.94 0.33 0.05 2.5 0.33 0.36 0.96 0.28 0.04
7 disc lin lin lin -2.1 0.27 0.25 0.93 0.54 0.06 -0.5 0.32 0.24 0.86 0.56 0.17 0 0.3 0.26 0.92 0.5 0.08
8 lin H/G lin H/G -1.3 0.14 0.14 0.95 0.94 0.06 -7.4 0.18 0.16 0.91 0.81 0.09 1.6 0.18 0.16 0.93 0.87 0.08
9 lin UN lin UN -0.5 0.16 0.18 0.96 0.84 0.04 -5.2 0.19 0.2 0.94 0.72 0.06 1.7 0.2 0.2 0.96 0.74 0.05
10 lin lin lin lin -1.2 0.14 0.14 0.94 0.95 0.05 -11.7 0.19 0.13 0.8 0.85 0.22 -0.7 0.18 0.15 0.9 0.9 0.11
  1. % bias \(\left (\frac {\widehat {\theta }-\theta }{\theta }\right)\), standard deviation (SD), estimated standard error (SE), coverage rate of 95% confidence interval (cov), power (pwr), and Type 1 error (α) of estimated intervention effect. Rows correspond to fitting models 1 through 10 under the scenarios described in Table 2; +/- imply positive/negative effect of confounding factors on outcome. Models include discrete (disc) or linear (lin) fixed time effects for all clusters (main effect) and/or control clusters (interaction effect). H/G, UN, and lin indicate Hooper/Girling, unstructured, and linear random effect structure for time effects