Some sophisticated techniques for meta-analysis exploit a statistical framework called hierarchical models, or multilevel models (Thompson 2001). This is because the information in a meta-analysis usually stems from two levels: studies at the higher level, and participants within studies at the lower level. Sometimes additional levels may be relevant, for example centres in a multicentre trial, or clusters in a cluster-randomized trial. A hierarchical framework is appropriate whether meta-analysis is of summary statistic information (for example, log odds ratios and their variances) or individual patient data (Turner 2000). Such a framework is particularly relevant when random effects are used to represent unexplained variation in effect estimates among studies (see Chapter 9, Section 9.5.4).
Hierarchical models rather than simpler methods of meta-analysis are useful in a number of contexts. For example, they can be used to:
allow for the imprecision of the variance estimates of treatment effects within studies;
allow for the imprecision in the estimated between-study variance estimate, tau-squared (see Chapter 9, Section 9.5.4);
provide methods that explicitly model binary outcome data (rather than summary statistics);
investigate the relationship between underlying risk and treatment benefit (see Chapter 9, Section 9.6.7); and
Hierarchical models are particularly relevant where individual patient data (IPD) on both outcomes and covariates are available (Higgins 2001). However even using such methods, care still needs to be exercised to ensure that within- and between-study relationships are not confused.
Implementing hierarchical models needs sophisticated software, either using a classical statistical approach (e.g. SAS proc mixed, or MlwiN) or a Bayesian approach (e.g. WinBUGS). Much current methodological research in meta-analysis uses hierarchical model methods, often in a Bayesian implementation.