  Meta-analysis is an important tool for combining results from multiple
studies and has been widely used in evidence-based medicine for several
decades. This paper reports, for the first time, an interesting and valuable
paradox in random-effects meta-analysis that is likely to occur when the number
of studies is small and/or the heterogeneity is large. With the incredible
paradox, we hence advocate meta-analysts to be extremely cautious when
interpreting the final results from the random-effects meta-analysis. And more
importantly, with the unexpected dilemma in making decisions, the new paradox
has raised an open question whether the current random-effects model is
reasonable and tenable for meta-analysis, or it needs to be abandoned or
further improved to some extent.
