Formal criteria for establishing equivalence in meta-analysis Of randomized clinical trials

Article type
Authors
Prins M, de HR
Abstract
Abstract: The demonstration of 'equivalence' is an increasingly important issue in clinical research, since new treatments and diagnostic strategies are becoming available, which instead of being better, are less expensive or more convenient. Consequently, equivalence has to be addressed, not only in the relevant randomized clinical trials but also in meta-analyses. The usual statistical calculations available for the summary statistics in systematic reviews are designed to test superiority on relative terms, but also allow for the calculation of confidence intervals around the summary effect estimates. For a single randomized controlled trial a conventional approach to demonstrate equivalence is to set a threshold of a percentage increase of a poor outcome, which would be clinically acceptable as equivalent. The usual approach is to demonstrate that at least a large proportion (e.g. 75%) of the efficacy of the active 'standard' comparator is maintained. For example, if drug A were to reduce the complication rate with no or placebo treatment from 15 to 7%, a result that excludes an increase of more than 2 % with 95% confidence would be accepted as demonstration of clinical equivalence when comparing a new drug B with the standard drug A. A statistical approach designed to test for this threshold and to calculate confidence intervals on difference of proportions over strata is available1. However, comparable frequencies in all strata are assumed. A problem with this approach in meta-analysis is the intrinsic variability in expected frequencies in the arms of the different randomized trials that are included, due to the heterogeneity in both duration of follow-up and baseline characteristics of the populations in these trials. Assuming a fairly comparable relative risk reduction or odds ratio, which is an underlying assumption when trying to calculate the usual summary statistics, a comparable strategy can be adopted. This strategy should take into account the change in comparator from placebo to active drug. If RRR is the relative risk reduction expressed as a proportion achieved with drug A versus placebo, and PEM is the proportion of the effect to be maintained to indicate clinical equivalence, the formula -(1-PEM)*((1/(1-RRR))-1) can be used to calculate the limit of the 95% or 99% confidence interval to be regarded as acceptable for indicating equivalence. The confidence intervals can then be calculated using the traditional formulas available. For odds ratios a similar formula can be developed. 1. Yanagawa T, Tango T, Hiejema Y. Mantel-Haenszel-Type Test for Testing Equivalence or More Than Equivalence in Comparative Clinical Trials. Biometrics 1994; 50: 859-863.