# Power and sample size calculation for meta-epidemiological studies

Meta-epidemiological studies are used to compare treatment effect estimates between randomized clinical trials with and without a characteristic of interest. In this method, one identifies a number of meta-analyses that included at least one trial with and without the characteristic, concerning a variety of medical conditions and interventions. For each meta-analysis, treatment effect estimates are compared between trials with and without the characteristic (eg by estimating a ratio of odds ratios or a difference in standardized mean differences). The mean impact of the characteristic is then estimated across all meta-analyses.

## Power and sample size formula

We derived a closed-form power function and sample size formula to detect a mean impact of the characteristic on treatment effect estimates. In doing so, we considered a hierarchical model which allows for variation in the impact of the characteristic between trials within a meta-analysis and between meta-analyses. We assumed that trials have equal weights within and between meta-anamysis.

The formula requires that you input values for the following variables :

- β : mean impact of the characteristic on treatment effect estimates (log ratio of odds ratios or difference in standardized mean differences)
- φ²: variability of the impact between meta-analyses
- κ²: variability of the impact between trials within a meta-analysis
- τ²: variability of treatment effect between trials within a meta-analysis (assumed constant)
- σ² : sampling variance of the estimated effect size (assumed constant)
- n+ : the mean number of trials with the characteristic of interest
- n- : the mean number of trials without the characteristic of interest
- α : type I error rate

Test more scenarios

Reinitialize

If φ² = 0.04, κ² = 0.16, τ² = 0.28, σ² = 0.5, n+ = 5 and n- = 0.5 then M=26 meta-analyses are required to have 80% power to detect a mean difference β = -0.29 with type I error risk α = 0.05.

## Simulation approach

We also developed a simulation-based approach to sample size calculation. We provide two propgrams to implement it using R (and WinBUGS).

References :

Giraudeau B, Higgins JP, Tavernier E, Trinquart L. Sample size calculation for meta-epidemiological studies. Stat Med. 2015. doi: 10.1002/sim.6627. [Epub ahead of print]

Contacts : bruno.giraudeau*AT*univ-tours.fr, julian.higgins*AT*bristol.ac.uk, elsa.tavernier*AT*univ-tours.fr, ludovic.trinquart*AT*htd.aphp.fr