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Table 3 Summary of observations from the two-treatment case

From: Investigating the relationship between predictability and imbalance in minimisation: a simulation study

  Predictability at P= 1.0, % Na Recommended P- value Predictability at this P- value, % Reduction in predictability, % P-value at which imbalance occurs
One variable
Two categories 50.0 <90 0.8b 45.0 to 48.8 1.2 to 5.0 0.7
   90 to <200 0.7b 49.0 1.0 0.6
   ≥200 0.7b 49.5 to 49.9 <1.0 0.5
Two categories - unequal prevalence   < 80 0.9b 45.0 to 48.8 1.4 to 5.0 0.8
   80 to <200 0.8b 49.0 <1.0 0.7
   ≥200 0.7b 49.0 to 49.9 <1.0 0.5
Three categories   <90 0.9b 45.0 to 48.8 1.2 to 5.0 0.8
   90 to <200 0.8b 49.0 1.0 to 1.1 0.7
   200 and <300 0.7b 49.0 1.0 0.6
   ≥300 0.7b 49.3 to 49.6 <1.0 0.5
Four categories   ≤100 0.9b 40.0 to 49.0 1.0 to 5.0 0.8
   200 and <400 0.7b 49.0 to 49.3 0.7 to 1.0 0.6
   ≥400 0.7b 49.5 to 49.6 <1.0 0.5
Two variables
Both with 2 categories 72.0 100 0.8 63.0 9.0 0.7
   200 0.7 60.0 12.0 0.6
   ≥300 0.7 60.0 12.0 0.5
Both with 2 categories - unequal prevalence   <100 1.0 - - 0.9
   100 0.9 68.0 4.0 0.8
   200 0.7 60.0 12.0 0.6
   ≥300 0.7 60.0 12.0 0.5
One with 2 categories, one with 3 categories   100 0.9 68.0 4.0 0.8
   200 to 300 0.7 60.0 12.0 0.6
   ≥400 0.7 60.0 12.0 0.5
Both with 3 categories   ≤100 1.0 - - 0.9
   200 to 300 0.7 60.0 12.0 0.6
   ≥400 0.7 60.0 12.0 0.5
Both with 4 categories 70.0 ≤100 1.0 - - 0.9
   200 0.8 64.0 6.0 0.7
   300 to 400 0.7 60.0 10.0 0.6
   500 0.7 60.0 10.0 0.5
Three variables
All with 2 categories - equal prevalence 80.0 100 0.8 68.0 12.0 0.7
   200 to 300 0.7 63.0 17.0 0.6
   ≥400 0.7 63.0 17.0 0.5
All with 2 categories - unequal prevalence   100 0.9 74.0 6.0 0.8
   200 0.8 69.0 11.0 0.7
   300 0.7 63.0 17.0 0.6
   ≥400 0.7 63.0 17.0 0.5
Four variables
All with 2 categories- equal prevalence 85.0 100 0.9 78.0 7.0 0.8
   200 0.8 72.0 13.0 0.7
   300 to 400 0.7 65.0 20.0 0.6
   ≥500 0.7 65.0 20.0 0.5
All with 2 categories- unequal prevalence   100 1.0 - - 0.9
   200 0.8 72.0 13.0 0.7
   300 to 400 0.7 65.0 20.0 0.6
   ≥500 0.7 65.0 20.0 0.5
  1. aThe categories of N are dependent upon the point at which imbalance is observed (the value of probability of assignment P). bFor one prognostic variable the reduction in predictability is so small as the probability of assignment P is reduced that the recommended P- value is 1.0.