This type of analysis is increasingly used to combine results from several clinical trials which assess the same treatments in order to provide a more precise overall estimate of the treatment effects. When the original data are available, an identical hierarchical structure to the multi-centre trial arises, with trials replacing centres. The implications of fitting trial and trial-treatment effects as fixed or random are then the same as in multi-centre analyses (see Section 5.2).
If treatment estimates are to relate only to the trials included, then local treatment estimates are obtained by fitting trial and treatment-trial effects as fixed (although in practice the trial-treatment interaction is usually removed if non-significant). If they are to relate more widely to the circumstances and locations sampled by the trials, global estimates can be obtained by fitting trial and treatment-trial effects as random. When this is done the standard errors of treatment estimates are increased to reflect the heterogeneity across trials. Trial-treatment variance components are often larger than centre-treatment variance components, because different protocols are used by the different trials. Thus, there are often more noticeable increases in the treatment standard errors in meta-analyses than in multi-centre trials.
As with multi-centre trials, taking trial effects as random has the advantage of increasing the accuracy of treatment estimates. This is because information from the trial error stratum is used in addition to that from the residual stratum. Sometimes there are factors that differ at the trial level that can help to explain differences in results between trials. For example, race or type of clinic may affect the treatment effect size. These variables can be included as covariates in a mixed model and may reduce the trial-treatment variability (and hence lead to more precise treatment estimates).
Outlying trials can be checked for, using the shrunken estimates of trial and trial-treatment effects. Since shrinkage is greater when there are fewer observations per trial, spurious outlying estimates caused by random variation are less likely to occur. However, this would not be the case in a fixed effects model where there is no shrinkage of the trial and trial-treatment estimates. Often, the estimates of treatment effects from individual trials are themselves of interest. The shrunken estimates which utilise information from all trials are more robust than estimates from a fixed effects model, although it has to be recognised that there may be difficulty in conveying the concept of shrunken estimates to a medical researcher!
Meta-analysis tends to be carried out most frequently with binomial data and most published work has related to this. Commonly, this is based on frequencies for the main outcome variable(s) as individual data is commonly unavailable. Although meta-analysis can be used with normal data, in practice individual trials are often adequate to achieve the desired power whereas this is not always the case with binary outcomes. Achieving adequate power is therefore less of a motivation with normal data. However, in a pharmaceutical company it may still be advantageous to undertake a meta-analysis on normal data arising from a series of trials in the same drug programme. Also, systematic reviews are being conducted increasingly commonly for an expanding number of treatments and outcome variables. Readers wishing to learn more about meta-analysis are advised to consult Whitehead (2002).
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