  Background: When conducting a meta-analysis of a continuous outcome,
estimated means and standard deviations from the selected studies are required
in order to obtain an overall estimate of the mean effect and its confidence
interval. If these quantities are not directly reported in the publications,
they need to must be estimated from other reported summary statistics, such as
the median, the minimum, the maximum, and quartiles. Methods: We propose a
simulation-based estimation approach using the Approximate Bayesian Computation
(ABC) technique for estimating mean and standard deviation based on various
sets of summary statistics found in published studies. We conduct a simulation
study to compare the proposed ABC method with the existing methods of Hozo et
al. (2005), Bland (2015), and Wan et al. (2014). Results: In the estimation of
the standard deviation, our ABC method performs best in skewed or heavy-tailed
distributions. The average relative error (ARE) approaches zero as sample size
increases. In the normal distribution, our ABC performs well. However, the Wan
et al. method is best since it is based on the normal distribution assumption.
When the distribution is skewed or heavy-tailed, the ARE of Wan et al. moves
away from zero even as sample size increases. In the estimation of the mean,
our ABC method is best since the AREs converge to zero. Conclusion: ABC is a
flexible method for estimating the study-specific mean and standard deviation
for meta-analysis, especially with underlying skewed or heavy-tailed
distributions. The ABC method can be applied using other reported summary
statistics such as the posterior mean and 95% credible interval when Bayesian
analysis has been employed.
