An obvious extension to the methods described above is to consider a measure of study size (for example the standard error of the effect estimate) as one of a number of different possible explanations for between-study heterogeneity in a multivariable 'meta-regression' model (see also Chapters 8 to 10 for a discussion of the use of regression models in meta-analysis).

For example, the effects of study size, adequacy of randomisation and type of blinding might be examined simultaneously. Thompson and Sharp46 recently reviewed different methods for meta-regression. These have been implemented in Stata (see Chapter 18).

Three notes of caution are necessary. Users of standard regression models know that it is unwise to include large numbers of covariates, particularly if the sample size is small. In meta-regression the number of data points corresponds to the number of studies, which is usually less than 50 and often less than 10.44 Thus tests for association between treatment effect and large numbers of study characteristics may lead to "overfitting" and spurious claims of association. Secondly, all associations observed in such analyses are observational, and may therefore be confounded by other unknown or unmeasured factors. Thirdly, regression analyses using averages of patient characteristics from each trial (such as the mean age of all the patients) can give a misleading impression of the relation for individual patients. As discussed in Chapter 9, there is potential for the so-called ecological fallacy,47 whereby the relation with treatment benefit may be different across trials as compared to within trials.

Meta-regression could be used to examine associations between clinical outcomes and markers of adherence to treatment or of the biological effects of treatment, weighting appropriately for study size. As discussed above, the intercept (coefficient of the constant term) should be zero if there is no biological effect so a non-zero intercept may be evidence of bias, or of a treatment effect which is not mediated via the marker. Unless the error in estimating the effect of treatment on the marker is small, this error must be incorporated in models of the association between the treatment effect and the change in the surrogate marker. Daniels and Hughes48 discuss this issue and propose a Bayesian estimation procedure. This method has been applied in a study of CD4 cell count as a surrogate endpoint in HIV clinical trials.49

The case study illustrates the use of some of the methods described in this chapter, using the example of a widely cited meta-analysis of placebo-controlled trials of homoeopathy.

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