Meta-analyses involving cross-over trials: methodological issues

We would like to make a correction to the description of the Becker–Balagtas method found in the 2002 International Journal of Epidemiology article by Elbourne et al.1 The article describes methods of combining parallel and cross-over trials for the purposes of meta-analysis. In the following summary, we will provide a revised description of the Becker–Balagtas approach with an example of how to implement it. The Becker–Balagtas approach is an estimation method used in the meta-analysis of cross-over trials with binary outcomes.1 It is considered a marginal method because it relies on the marginal probabilities of the outcome to estimate the odds ratio (OR).2 Typically, a conditional approach, such as the Mantel–Haenszel odds ratio (of the discordant pairs), is the usual effect estimate for cross-over trials.3 However, when summarizing results across study designs the Becker–Balagtas approach is the preferred method.3 To compute the Becker–Balagtas estimates, we first define the observed cell quantities from a cross-over trial. In the cross-over design, all subjects participate in all treatments in successive periods where the sequence of treatments is determined by randomization.1 For example, some subjects are randomized to receive placebo for the first period followed by the active treatment in the second period, others are randomized to receive the active treatment in the first period followed by the placebo in the second period. Each subject contributes two results for the active and placebo treatment periods. Binary outcomes from a cross-over trial may be summarized as displayed in Table 1. Here, the outcome from the trial is either success or failure and the treatment is either active or placebo. Let s be the number of subjects that had a success with both treatments. Let v be the number of subjects that experienced failure with both treatments. Let t and u represent the number of subjects that had a success with one treatment, but failed with the other. Let a and c represent the row totals, b and d the column totals and n the total number of subjects.1 2 × 2 table for a cross-over trial 2 × 2 table for a cross-over trial The Becker–Balagtas estimation method is applied when combining data from different designs in a meta-analysis.1 For example, consider a meta-analysis of two trials of the effect of brand name and generic anti-epileptic drugs on seizure outcomes. The first trial has a parallel design (independent outcomes) and the second trial has a cross-over design (correlated outcomes). Our objective is to combine the results of these two trials into a single summary estimate of the odds ratio of uncontrolled seizures for generic anti-epileptic drugs compared with brand-name anti-epileptic drugs. Table 2 presents results from a trial with a parallel design.4 A total of 60 newly diagnosed patients were randomized to either a brand name or generic anti-epileptic drug. Of the 45 patients randomized to generic anti-epileptic drugs, 6 had uncontrolled seizures as did 5 of the 15 allocated to brand-name drugs.4 Results from Kishore et al. (parallel design) Results from Kishore et al. (parallel design) Table 3 presents results from a different trial with a cross-over design.5 In this case, all 20 participants received both treatments and the order of treatment was randomly assigned. Of the 20 participants, 2 experienced uncontrolled seizures with both the generic and brand-name anti-epileptic drugs.5 Results from Oles et al. (cross-over design) Results from Oles et al. (cross-over design) Correct application of the Becker–Balagtas method is important to ensure accurate estimation of summary estimates for meta-analysis. When including various trial designs in a meta-analysis, it is best to select a common measurement that does not favour one design over the other.1 Of the currently available methods, the marginal approach (or Becker–Balagtas method2) introduces the least bias when the meta-analysis combines cross-over trials with parallel trials.3