A method to aggregate results of trials with heterogeneous treatment modalities: a rheumatology example

Boers M., Felson D. T., Kessels A. G. H. and Anderson J. J. Depts of Rheumatology, Epidemiology, University of Limburg, The Netherlands.

Introduction: Meta-analysis of antirheumatic therapy has been hampered by the fact that many different drugs have been tested in placebo or head-to-head comparisons, but too few trials are available for any given comparison to perform quantitative analysis with confidence. A previous meta-analysis constructed cohorts of patients by aggregating data from trial arms. With this approach, the balance of prognostic factors ideally obtained by randomization may be lost.
Objective: We suggest a method to compare effect sizes across 2-group trials that allows ranking of individual drugs without sacrificing this balance.
Discussion: The method entails the following steps:

1. Assuming one endpoint variable, each trial yields an effect X, defined as the mean difference on the variable between treatment groups.
2. All trials of the same comparison, or contrast, are pooled in the traditional manner. Given j trials of the same contrast, the effect of the i-th trial Xi is weighted through division by its variance: Wi = 1 / var(Xi). The pooled effect size E of all j trials is calculated by S[(wi - Xi] / S wi, with a variance of var(E) = 1 /S wi.
3. Extra information on all possible contrasts, including those that have not been tested directly in trials, is obtained by subtracting contrasts that have been tested directly: Eab = Ea - Eb, with variance var(Eab) = Var(Ea) + var(Eb).
4. For each contrast, the results of steps 2 and 3 are pooled. This process is repeated for each possible contrast, to obtain a final rank-ordering of all the drugs tested.

An application of this method to the data of a recent meta-analysis of anitrheumatic therapy (Felson and colleagues) will be shown.

Hamilton 1994 P17