Abstract
BackgroundWhen 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 must be estimated from other reported summary statistics, such as the median, the minimum, the maximum, and quartiles.MethodsWe 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).ResultsIn the estimation of the standard deviation, our ABC method performs better than the other methods when data are generated from skewed or heavy-tailed distributions. The corresponding average relative error (ARE) approaches zero as sample size increases. In data generated from the normal distribution, our ABC performs well. However, the Wan et al. method is best for estimating standard deviation under normal distribution. In the estimation of the mean, our ABC method is best regardless of assumed distribution.ConclusionABC 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.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-015-0055-5) contains supplementary material, which is available to authorized users.
Highlights
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
Comparison of Hozo et al, Wan et al, and Approximate Bayesian Computation (ABC) in S1 for standard deviation estimation In Fig. 1 we show average relative error (ARE) in estimating standard deviation for the three methods as a function of sample size under simulated data from the selected five distributions
Under the normal distribution (Fig. 1b) in S1, while the Hozo et al method shows large average relative errors for sample size less than 300, the Wan et al method shows quite good performance over all sample sizes
Summary
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 must be estimated from other reported summary statistics, such as the median, the minimum, the maximum, and quartiles. When the outcome is continuous, in order to conduct meta-analysis, we need estimated means and the corresponding standard deviations (or equivalently, variances) from the selected studies. The sample median is often used as the estimate of the sample mean assuming symmetric distribution, and the sample standard deviation is commonly estimated by either range 4 or
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