Preparing for a meta-analysis of rates: extracting effect sizes and standard errors from studies of count outcomes with person-time denominators.

Background: Formulas for the extraction of continuous and binary effect sizes that are entered into a meta-analysis are readily available. Only some formulas for the extraction of count outcomes have been presented previously. The purpose of this methodological article is to present formulas for extracting effect sizes and their standard errors for studies of count outcomes with person-time denominators.

Methods: Formulas for the calculation of the number of events in a study and the corresponding person time in which these events occurred are presented. These formulas are then used to estimate the relevant effect sizes and standard errors of interest. These effect sizes are rates, rate ratios and rate differences for a two-group comparison and rate ratios and rate differences for a difference-in-difference design.

Results: Two studies from the field of suicide prevention are used to demonstrate the extraction of the information required to estimate effect sizes and standard errors. In the first example, the rate ratio for a two-group comparison was 0.957 (standard error of the log rate ratio, 0.035), and the rate difference was -0.56 per 100,000 person years (standard error 0.44). In the second example, the rate ratio for a difference-in-difference analysis was 0.975 (standard error of the log rate ratio 0.036) and the rate difference was -0.30 per 100,000 person years (standard error 0.42).

Conclusions: The application of these formulas enables the calculation of effect sizes that may not have been presented in the original study. This reduces the need to exclude otherwise eligible studies from a meta-analysis, potentially reducing one source of bias.