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Table 2 Test statistics

From: A simulation study for comparing testing statistics in response-adaptive randomization

Log-relative-risk T Risk = (log(f 2 n 1/f 1 n 2))2/(r 1/n 1 f 1 + r 2/n 2 f 2)
Log-odds-ratio T Odds = (log(f 2 r 1 /f 1 r 2))2/(1/f 1 + 1/f 2 + 1/r 1 + 1/r2)
Wald-type Z
Chi-square T Chisq = (n - 1) (r 1 f 2 - r 2 f 1)2/rfn 1 n 2
Log-likelihood-ratio T LLR = 2·(r 1 log r 1 + r 2 log r 2 + f 1 log f 1 + f 2 log f 2 - r log r- f log f - n 1 log n 1 - n 2 log n 2 + n log n)
Gart's correction to T Odds [29] T MO = (log (f' 2 n' 1/f' 1 n' 2))2/(r' 1/n' 1 f' 1 + r' 2/n' 2 f' 2)
Agresti's correction to T Wald
Cook's correction to T Chisq T MC = (n - 1)(|r 1 f 2 - r 2 f 1|- 0.5)2/rfn 1 n 2
William's correction to T LLR [31] T ML = [1 + (n 2 - rf)(n 2 - n 1 n 2)/6rfn 1 n 2 n]-1·T LLR
  1. r' 1 = r 1 + 0.5, r' 2 = r 2 + 0.5, f' 1 = f 1 + 0.5, f' 2 = f 2 + 0.5, r' = r + 1, f' + 1, n' 1 = n 1 + 1, n' 2 = n 2 + 1, n' = n + 2 r" 1 = r 1 + 1, r" 2 = r 2 + 1, f" 1 = f 1 + 1, f" 2 = f 2 + 1, r" = r + 2, f" = f + 2, n" 1 = n 1 + 2, n" 2 = n 2 + 2, n" = n+ 4