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Formal comparisons of intervention effects according to risk of bias can be done using meta-regression (see Chapter 9, Section 9.6.4). For studies with dichotomous outcomes, results of meta-regression analyses are most usefully expressed as ratios of odds ratios (or risk ratios) comparing results of studies at high or unclear risk of bias with those of studies at low risk of bias.

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Alternatively, separate comparisons of high versus low and unclear versus low can be made. For studies with continuous outcomes (e.g. blood pressure), intervention effects are expressed as mean differences between intervention groups, and results of meta-regression analyses correspond to differences of mean differences.

If the estimated effect of the intervention is the same in studies at high and unclear risk of bias as in studies at low risk of bias then the ratio of odds ratios (or risk ratios) equals 1, while the difference between mean differences will equal zero. As explained in Section 8.2.3, empirical evidence from collections of meta-analyses assembled in meta-epidemiological studies suggests that, on average, intervention effect estimates tend to be exaggerated in studies at high or unclear risk of bias compared with studies at low risk of bias.

When a meta-analysis includes many studies, meta-regression analyses can include more than one domain (e.g. both allocation concealment and blinding).

Results of meta-regression analyses include a confidence interval for the ratio of odds ratios, and a P value for the null hypothesis that there is no difference between the results of studies at high or unclear and low risk of bias. Because meta-analyses usually contain a small number of studies, the ratio of odds ratios is usually imprecisely estimated. It is therefore important not to conclude, on the basis of a non-significant P value, that there is no difference between the results of studies at high or unclear and low risk of bias, and therefore no impact of bias on the results. Examining the confidence interval will often show that the difference between studies at high or unclear and low risk of bias is consistent with both no bias and a substantial effect of bias.

A test for differences across subgroups provides an alternative to meta-regression for examination of a single entry (e.g. comparing studies with adequate versus inadequate allocation concealment). Within a fixed-effect meta-analysis framework, such tests are available in RevMan 5. However, such P values are of limited use without corresponding confidence intervals, and they will in any case be too small in the presence of heterogeneity, either within or between subgroups.