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Table 4 Sample size estimation

From: Quetiapine versus aripiprazole in children and adolescents with psychosis - protocol for the randomised, blinded clinical Tolerability and Efficacy of Antipsychotics (TEA) trial

  β SD MIREDIF Effect size Calculations: N = 4 * (zα/2 + zβ)2 * (SD1/MIREDIF)2 # N
TEA original 0.10 7.4 3.5 0.47 N = 42 * (7.4 / 3.5) 2 188
TEA smaller MIREDIF 0.10 7.4 2.0 0.27 N = 42 * (7.4 / 2.0)2 575
TEA larger MIREDIF 0.10 7.4 5.0 0.67 N = 42 * (7.4 / 5.0)2 92
TEA larger SD 0.10 10.0 3.5 0.35 N = 42 * (10.0 / 3.5)2 343
TEA smaller SD 0.10 5.7 3.5 0.61 N = 42 * (5.7 / 3.5)2 111
TEA larger β 0.20 7.4 3.5 0.47 N = 31 * (7.4 / 3.5)2 139
TEA updated larger β, smaller SD, smaller MIREDIF 0.20 5.7 3.0 0.53 N = 31 * (5.7 / 3.0) 2 112
  1. The original and the updated TEA calculations and examples of different values of MERIDIF (minimally relevant difference), SD (standard deviation) and β (risk of type II error) are shown. As can be seen, the larger the MIREDIF you wish/expect to be able to detect or the smaller the estimated SD of the outcome measures or the larger the β, the smaller the sample size needed. In these calculations we used a two-sided α (risk of type I error) = 0.05 and we assumed SD1 = SD2. Effects sizes depend on MIREDIF and SD. Compared to the original calculation, the updated sample size calculation is balanced by allowing for a larger β, expecting a zsmaller SD and lowering the detectable MIREDIF. z = fractiles in normal distribution. #N = 2 * (SD12 + SD22) * (zα/2 + zβ)/MIREDIF2 N = 4 * (zα/2 + zβ)2 * (SD1/MIREDIF)2. The product 4 * (zα/2 + zβ)2 is rounded up to whole figures in the equations.