  The era of big data is coming, and evidence-based medicine is attracting
increasing attention to improve decision making in medical practice via
integrating evidence from well designed and conducted clinical research.
Meta-analysis is a statistical technique widely used in evidence-based medicine
for analytically combining the findings from independent clinical trials to
provide an overall estimation of a treatment effectiveness. The sample mean and
standard deviation are two commonly used statistics in meta-analysis but some
trials use the median, the minimum and maximum values, or sometimes the first
and third quartiles to report the results. Thus, to pool results in a
consistent format, researchers need to transform those information back to the
sample mean and standard deviation. In this paper, we investigate the optimal
estimation of the sample mean for meta-analysis from both theoretical and
empirical perspectives. A major drawback in the literature is that the sample
size, needless to say its importance, is either ignored or used in a stepwise
but somewhat arbitrary manner, e.g., the famous method proposed by Hozo et al.
We solve this issue by incorporating the sample size in a smoothly changing
weight in the estimators to reach the optimal estimation. Our proposed
estimators not only improve the existing ones significantly but also share the
same virtue of the simplicity. The real data application indicates that our
proposed estimators are capable to serve as "rules of thumb" and will be widely
applied in evidence-based medicine.
