  Background: We proposed approximate Bayesian computation with single
distribution selection (ABC-SD) for estimating mean and standard deviation from
other reported summary statistics. The ABC-SD generates pseudo data from a
single parametric distribution thought to be the true distribution of
underlying study data. This single distribution is either an educated guess, or
it is selected via model selection using posterior probability criterion for
testing two or more candidate distributions. Further analysis indicated that
when model selection is used, posterior model probabilities are sensitive to
the prior distribution(s) for parameter(s) and dependable on the type of
reported summary statistics. Method: We propose ABC with Bayesian model
averaging (ABC-BMA) methodology to estimate mean and standard deviation based
on various sets of other summary statistics reported in published studies. We
conduct a Monte Carlo simulation study to compare the new proposed ABC-BMA
method with our previous ABC-SD method. Results: In the estimation of standard
deviation, ABC-BMA has smaller average relative errors (AREs) than that of
ABC-SD for normal, lognormal, beta, and exponential distributions. For Weibull
distribution, ARE of ABC-BMA is larger than that of ABC-SD but <0.05 in small
sample sizes and moves toward zero as sample size increases. When underlying
distribution is highly skewed and available summary statistics are only
quartiles and sample size, ABC-BMA is recommended but it should be used with
caution. Comparison of mean estimation between ABC-BMA and ABC-SD shows similar
patterns of results as for standard deviation estimation. Conclusion: ABC-BMA
is easy to implement and it performs even better than our previous ABC-SD
method for estimation of mean and standard deviation.
