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Table 2 Validation of the approximate design effect formula.

From: Design effect in multicenter studies: gain or loss of power?

ICC = 0.01
N subjects 100 200 500
N centers 5 10 20 5 10 20 50 5 10 20 50 100
S1 Deff 0.9969 0.9938 0.9921 0.9966 0.9936 0.9922 0.9911 0.9965 0.9933 0.9919 0.9913 0.9908
rdiff 0.0065 0.0032 0.0016 0.0065 0.0032 0.0016 0.0006 0.0065 0.0032 0.0016 0.0006 0.0003
S2 Deff 0.9972 0.9949 0.9928 0.9972 0.9956 0.9938 0.9917 0.9980 0.9989 0.9956 0.9931 0.9918
rdiff 0.0065 0.0032 0.0014 0.0065 0.0032 0.0016 0.0005 0.0065 0.0033 0.0016 0.0006 0.0003
S3 Deff 1.0102 1.0306 1.0147 1.0217 1.0622 1.0431 1.0132 1.0575 1.1788 1.1143 1.0487 1.0204
rdiff 0.0066 0.0035 0.0016 0.0066 0.0036 0.0018 0.0006 0.0066 0.0036 0.0019 0.0007 0.0003
S4 Deff 1.1038 1.0323 1.0285 1.2026 1.0538 1.0604 1.0184 1.4788 1.1290 1.1588 1.0559 1.0186
rdiff 0.0077 0.0051 0.0027 0.0077 0.0052 0.0030 0.0011 0.0077 0.0053 0.0030 0.0013 0.0006
ICC = 0.10
N subjects 100 200 500
N centers 5 10 20 5 10 20 50 5 10 20 50 100
S1 Deff 0.9655 0.9356 0.9197 0.9642 0.9337 0.9209 0.9105 0.9631 0.9313 0.9177 0.9124 0.9076
rdiff 0.0643 0.0318 0.0155 0.0649 0.0320 0.0160 0.0061 0.0649 0.0324 0.0161 0.0063 0.0031
S2 Deff 0.9709 0.9469 0.9269 0.9696 0.9547 0.9359 0.9171 0.9793 0.9827 0.9549 0.9300 0.9174
rdiff 0.0656 0.0318 0.0142 0.0648 0.0323 0.0157 0.0053 0.0651 0.0325 0.0161 0.0063 0.0028
S3 Deff 1.1101 1.3018 1.1721 1.2095 1.6471 1.4256 1.1337 1.6662 2.7175 2.1685 1.4965 1.2049
rdiff 0.0654 0.0349 0.0166 0.0659 0.0354 0.0182 0.0063 0.0662 0.0358 0.0185 0.0074 0.0034
S4 Deff 2.0718 1.3360 1.2725 3.1669 1.5750 1.6252 1.1934 6.2708 2.5759 2.5886 1.5687 1.2017
rdiff 0.0768 0.0507 0.0272 0.0770 0.0517 0.0299 0.0110 0.0771 0.0513 0.0299 0.0126 0.0059
  1. ICC: Intraclass Correlation Coefficient
  2. Simulations are conducted with varying center sizes: 20% of centers recruit 80% of subjects. Average exact design effect estimate (Deff) and average relative difference (rdiff) between exact and approximate design effect formula are given for 4 situations (Si, i = 1,2,3,4), two ICC values, and obtained for 1000 simulations.
  3. S1: Equal group sizes. In each center, the probability, for a subject, to be in group 1 is 1/2
  4. S2: Slight variations in group 1 proportions among centers. The ratio between the sizes of group 1 and group 2 varies uniformly between 0.8 and 1.25 among centers
  5. S3: Important variations in group 1 proportions among centers. The ratio between the sizes of group 1 and group 2 varies uniformly between 0.1 and 10 among centers
  6. S4: "Cluster design". The center is nested within the group and the probability, for each center, to be in group 1 is 1/2