Clinical Trials

❘❙❚■ Chapter 38 | Meta-AnalysisTable 5. Meta-analysis of 10 hypothetical trials using the Woolf fixed-effects model and the DerSimonian–Lairdrandom effects model.Study Treated events/ Control events/ Odds ratio Fixed-effects Random-effectstotal events total events (95% CI) model weighting model weighting1 15/130 15/135 1.04 6.65 2.21(0.49, 2.23)2 21/400 17/135 0.38 8.51 2.39(0.20, 0.75)3 14/60 24/50 0.33 5.77 2.11(0.15, 0.75)4 6/40 18/40 0.22 3.37 1.67(0.07, 0.63)5 12/1010 35/760 0.25 8.75 2.41(0.13, 0.48)6 138/1400 175/765 0.37 64.73 3.16(0.29, 0.47)7 15/500 20/525 0.78 8.28 2.37(0.40, 1.54)8 6/110 2/105 2.97 1.46 1.01(0.59, 15.06)9 65/150 40/100 1.15 14.53 2.7(0.69, 1.92)10 5/70 2/35 1.27 1.34 0.96(0.23, 6.90)Combined OR 0.47 0.55(95% CI) (0.39, 0.55) (0.36, 0.85)The heterogeneity test (Q) for the random-effects model analysis was 34.66, and, since k – 1 = 9, Q > k – 1, whichindicates that the 10 studies are statistically heterogeneous. The fixed-effects model weights each study accordingto its sample size, so the largest trial has the most weight. On the other hand, the weightings generated by therandom-effects model are less varied, giving relatively more weight to smaller studies, yielding a wider confidenceinterval for the pooled odds ratio than occurs with the fixed-effects model.CI = confidence interval; OR = odds ratio.0.57, 0.74. For the data in Table 1, the between-study variability is zero (τ = 0; seeTable 4), therefore these results are identical to those from the fixed-effects model.Table 5 compares the meta-analysis of 10 hypothetically heterogeneous trials usingthe Woolf fixed-effects and DerSimonian–Laird random-effects models. Testingthe random-effects model for heterogeneity gives Q = 34.66, and, since k – 1 = 9,Q > k – 1, which indicates that the 10 studies are statistically heterogeneous. Theestimated between-study variability is 0.30 (τ = 0.30). The results from the metaanalysisshow that the random-effects model gives smaller studies more weightand yields a wider confidence interval for the pooled OR than occurs with thefixed-effects model.448