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Table 2 Bias, mean square error, empirical type I error and power in cluster randomized trials according to several types of imbalance in cluster size – Effect size = 0.50

From: Planning a cluster randomized trial with unequal cluster sizes: practical issues involving continuous outcomes

Simulation parameters1 Type of imbalance Bias Mean Square Error Empirical type I error2 Empirical power2
Intraclass correlation coefficient (ρ) Number of clusters in each arm (g) Total number of subjects in each arm (N) Type of imbalance     
0.005 5 89 None 0.0025 0.0238 0.0190 0.7648
    Moderate 0.0010 0.0243 0.0204 0.7622
    Poisson 0.0014 0.0243 0.0214 0.7596
    Pareto -0.0064 0.0393 0.0256 0.6250
0.005 10 73 None -0.0011 0.0288 0.0328 0.7660
    Moderate -0.0015 0.0290 0.0322 0.7718
    Poisson -0.0007 0.0298 0.0318 0.7662
    Pareto -0.0005 0.0344 0.0352 0.7090
0.005 20 67 None -0.0011 0.0303 0.0384 0.7764
    Moderate -0.0038 0.0296 0.0318 0.7700
    Poisson -0.0012 0.0301 0.0382 0.7664
    Pareto -0.0004 0.0323 0.0334 0.7322
0.005 40 65 None 0.0005 0.0310 0.0446 0.7986
    Moderate 0.0021 0.0322 0.0478 0.7896
    Poisson 0.0028 0.0305 0.0396 0.7860
    Pareto -0.0007 0.0320 0.0382 0.7518
0.020 5 119 None 0.0025 0.0238 0.0190 0.7648
    Moderate -0.0011 0.0248 0.0310 0.7856
    Poisson -0.0021 0.0250 0.0306 0.7786
    Pareto 0.0009 0.0413 0.0674 0.6262
0.020 10 81 None -0.0031 0.0273 0.0320 0.7798
    Moderate 0.0006 0.0282 0.0364 0.7772
    Poisson -0.0003 0.0288 0.0378 0.7778
    Pareto 0.0078 0.0394 0.0550 0.6910
0.020 20 70 None 0.0026 0.0312 0.0476 0.7838
    Moderate 0.0026 0.0312 0.0476 0.7838
    Poisson 0.0032 0.0306 0.0436 0.7894
    Pareto 0.0003 0.0362 0.0460 0.7056
0.020 40 66 None -0.0026 0.0314 0.0498 0.7878
    Moderate 0.0026 0.0312 0.0476 0.7838
    Poisson 0.0049 0.0326 0.0476 0.7828
    Pareto -0.0007 0.0337 0.0422 0.7328
0.050 5 423 None 0.0015 0.0246 0.0482 0.7980
    Moderate -0.0001 0.0240 0.0460 0.8004
    Poisson -0.0005 0.0237 0.0478 0.7988
    Pareto 0.0026 0.0337 0.0768 0.6808
0.050 10 103 None -0.0006 0.0280 0.0426 0.7964
    Moderate 0.0012 0.0286 0.0446 0.7952
    Poisson -0.0017 0.0293 0.0440 0.7754
    Pareto -0.0022 0.0466 0.0770 0.6342
0.050 20 76 None 0.0027 0.0298 0.0436 0.8020
    Moderate -0.0018 0.0308 0.0452 0.7784
    Poisson -0.0016 0.0323 0.0526 0.7672
    Pareto -0.0056 0.0396 0.0528 0.6620
0.050 40 67 None -0.0019 0.0313 0.0468 0.7880
    Moderate -0.0012 0.0294 0.0516 0.7740
    Poisson 0.0000 0.0335 0.0504 0.7712
    Pareto 0.0022 0.0376 0.0516 0.7026
0.100 10 213 None 0.0006 0.0263 0.0426 0.8056
    Moderate 0.0015 0.0289 0.0530 0.7940
    Poisson -0.0007 0.0287 0.0538 0.8004
    Pareto -0.0027 0.0438 0.0730 0.6394
0.100 20 89 None -0.0029 0.0303 0.0470 0.7888
    Moderate -0.0020 0.0324 0.0530 0.7760
    Poisson -0.0004 0.0316 0.0488 0.7744
    Pareto 0.0064 0.0492 0.0674 0.6276
0.100 40 70 None 0.0038 0.0331 0.0510 0.7890
    Moderate 0.0031 0.0337 0.0506 0.7738
    Poisson 0.0020 0.0332 0.0456 0.7658
    Pareto 0.0019 0.0433 0.0536 0.6641
  1. 1N is the number of subjects per intervention arm, calculated under the assumption of constant cluster size
  2. 2 The nominal values for type I and type II error rates were fixed at 0.05 and 0.20, respectively.