Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘Table 4. A random-effects model (the DerSimonian–Laird method) for computing a pooled odds ratio (OR)estimate and its 95% CI based on 2 × 2 tables.Data structure:Same as in Table 1Assumptions:ORs are different across studies. Differences in ORsare not only due to within-study variation but also tobetween-study variationComputing steps:(1) Calculate the heterogeneity test statistic, Q a :Null hypothesis: the k underlying ORs are equalkTest statistic: Q = ∑ w (OR – OR )i =1 i i FDefinitions of w i, OR i, OR Fare the same as in Table 3.(2) Calculate the between-study variability:τ = max 0,(Q – (k – 1)( ))∑ ikw – =1 i w =1 i(3) Calculate the weighting for each study:1*w i=1+ τw i∑ k w 2i =1 i∑ ik(4) Calculate the pooled logarithm of therandom-effects OR estimate:k∑ w *iIn(OR=1 ii)In(OR R) =(5) Calculate the standard error (SE) for In(OR R):1SE R=*k∑ w i =1 i(6) Do an antilogarithm conversion to obtainan estimate of the pooled OR:OR R= exp(In(OR R))k∑ w *i =1 i(7) Calculate the 95% CI for OR R:exp(In(OR R) ± 1.96SE R)Interpretation:(1) If Q ≥ k – 1, then there is evidence of statisticalheterogeneity, ie, the ORs are different acrossthe studies a . Otherwise, ther is no evidence thatthe ORs are different(2) OR Rgives the combined treatment effect:exp(In(OR R) ± 1.96SE R) gives the possible range ofthe true treatment effect and, if the 95% CI doesnot include the value 1, then the pooled effect oftreatment B is different from that of treatment AaFor the formal statistical test, please refer to reference 3.populations included, do not fully match the other studies. These different effectsare amalgamated and the meta-analysis is used to estimate an overall effect.Therefore, a random-effects model gives more weight to smaller studies and itsoverall estimate has a wider confidence interval [2,3,5,9]. Some authors regardthis approach to be conceptually problematic because one of the fundamentalassumptions inherent in this model is that the studies included are a randomsample from a hypothetical population of studies [3].The procedures for using the DerSimonian–Laird random-effects model aredescribed in Table 4, where they are applied to the data from Table 1. A test forheterogeneity (the difference in beta-blocker effect on mortality between studies)for this meta-analysis was performed. The value of the heterogeneity test statistic(Q) was 8.44, and, since k – 1 = 13, Q < k – 1, which indicates that the includedstudies are very similar (there is no evidence of statistically significantheterogeneity; see Table 4). The pooled estimate of the effect of beta-blockertreatment on mortality using the random-effects model is: OR R= 0.65, 95% CI447