Clinical Trials

❘❙❚■ Chapter 20 | Comparison of ProportionsTable 7. Summary of the statistical test methods described in this chapter.Statistical issues Tests or Null hypothesis Test statistics Confidence intervalsmeasurementsEstimate of the One-sample Z-test H 0: π 1= π 0p – π 1 0 p 1± Z α/2SE(p 1)population proportion π 1is the population proportion Z = p – π SE (p 1)for the drug group and π 0is 12112SE(p – p )= √p (1 – p )/n a fixed proportionComparison of Chi-squared test H 0: π 1= π 2 χ2= Σ (O – E)2 Not availabletwo proportions π 1and π 2are the population Eproportions for the active drug df = 1and placebo groups, respectivelyZ-test H 0: π 1= π 2Z =p 1– p 2(p 1– p 2) ± Z α/2SE(p 1– p 2)SE (p 1– p 2)SE(p 1– p 2)= √( p [1 – p][1/n 1+ 1/n 2])p =(a + b)(n 1+ n 2)Assessment of the size Risk difference H 0: π 1= π 2The same as in the Z-test, above The same as in the Z-test, aboveof treatment effectRisk ratio (RR) H 0: RR = 1Z =log RRp 1 95% CI(RR) = RR / EF to RR × EFSE (log RR) ,RR = p p 2EF = exp[1.96 × SE(log RR)]SE(log RR) = √1/a - 1/n 1+ 1/b - 1/n 2Odds ratio (OR) H 0: OR = 1Z =log OR 95% CI(OR) = OR / EF to RR × EFa/c SE (log OR) ,OR =b/d EF = exp[1.96 × SE(log OR)]SE(log OR) = √1/a + 1/b + 1/c + 1/d2 (O – E)2 Not availableComparison Chi-squared test H 0: percentage distributions areof r × c table the same among different groups χ 2 = Σ (O – E)2 , df = (r – 1)(c –1)E232