Research synthesis methods
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Conventional meta-analysis estimators are weighted means of study measures, meant to estimate an overall population measure. For measures such as means, mean differences and risk differences, a weighted arithmetic mean is the conventional estimator. When the measures are ratios, such as odds ratios, logarithms of the study measures are most frequently used, and the back-transform is a weighted geometric mean, rather than the arithmetic mean. ⋯ However, when the weights are the usual reciprocal variance estimates, the inequalities go in the opposite direction. The use of reciprocal variance weights is therefore questioned as perhaps having a fundamental flaw. An example is shown of a meta-analysis of frequencies of two classes of drug-resistant HIV-1 mutations.