Trial sequential methods for meta-analysis

Statistical methods for sequential meta-analysis have applications also for the design of new trials. Existing methods are based on group sequential methods developed for single trials and start with the calculation of a required information size. This works satisfactorily within the framework of fixed effects meta-analysis, but conceptual difficulties arise in the random effects model. One approach applying sequential meta-analysis to design is 'trial sequential analysis', developed by Wetterslev, Thorlund, Brok, Gluud and others from the Copenhagen Trial Unit. In trial sequential analysis, information size is based on the required sample size of a single new trial, which, in the random effects model, is obtained by simply inflating it in comparison with fixed effects meta-analysis. However, this is not sufficient as, depending on the amount of heterogeneity, a minimum of several new trials may be indicated, and the total number of new patients needed may be substantially reduced by planning an even larger number of small trials. We provide explicit formulae to determine the requisite minimum number of trials and their sample sizes within this framework, which also exemplify the conceptual difficulties referred to. We illustrate all these points with two practical examples, including the well-known meta-analysis of magnesium for myocardial infarction.