Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘Table 3. A fixed-effects model (the Woolf method) for computing a pooled odds ratio (OR) estimateand its 95% CI based on 2 × 2 tables.Data structure:Suppose there are k studies, each having data in theform of a 2 × 2 table:EventTotalYes NoTreatment A a ib ia i+ b iTreatment B c id ic i+ d iTotal a i+ c ib i+ d in iAssumptions:ORs are identical and fixed across all studies,and differences in the ORs are only due towithin-study variationComputing steps:(1) Calculate natural logarithm of the ORfor the i th study:aIn(OR i) = Ini× d ib i× c( )i(2) Calculate the standard error (SE) of ln(OR i):SE i=1 1 1 1+ + +a ib ic i(3) Compute the weighting for each study:d i(4) Calculate the pooled logarithm of the fixed-effectsOR:In(OR i) =(5) Calculate the standard error for In(OR F):SE F=∑ ik1(6) Do an antilogarithm conversion to obtain theestimate of the pooled OR:OR F= exp(In(OR F))=1w iIn(OR i)k∑ iw=1 ik∑ iw=1 i(7) Calculate the 95% CI for OR F:exp(In(OR F) ± 1.96SE F)Interpretation:(1) OR Frepresents the combined treatment effect(2) The 95% CI (exp(In(OR R) ± 1.96SE R)) gives thepossible range of the true treatment effect. If the CIdoes not include the value I, then the average effectof treatment B is different from that of treatment A.If this is not the case, there is no evidence that theeffects are differentw i=12SE iWhat is the appropriate statistical method?Two types of models are commonly used to conduct a meta-analysis: the fixedeffectsmodel and the random-effects model. These are each used under differentcircumstances, but both create a combined estimate of treatment effect.The fixed-effects modelThe fixed-effects model assumes that the meta-analysis is trying to estimate oneoverall treatment effect for all the studies included in the analysis. This impliesthat the researcher believes that there is a common ‘true’ treatment effect underlyingthe studies and that the results of these studies will vary randomly about this trueeffect. This model can be used when considering studies that match closely indesign and methodology. Table 3 demonstrates the computing procedures of oneof the fixed-effects models (the Woolf method) [9]. By applying this model to thedata in Table 1, the results generated for the estimated pooled OR and its 95% CI445