  Comparative binary outcome data are of fundamental interest in statistics and
are often pooled in meta-analyses. Here we examine the simplest case where for
each study there are two patient groups and a binary event of interest, giving
rise to a series of $2 \times 2$ tables. A variety of measures of treatment
effect are then available and are conventionally used in meta-analyses, such as
the odds ratio, the risk ratio and the risk difference. Here we propose a new
type of measure of treatment effect for this type of data that is very easily
interpretable by lay audiences. We give the rationale for the new measure and
we present three contrasting methods for computing its within-study variance so
that it can be used in conventional meta-analyses. We then develop three
alternative methods for random-effects meta-analysis that use our measure and
we apply our methodolgy to some real examples. We conclude that our new measure
is a fully viable alternative to existing measures. It has the advantage that
its interpretation is especially simple and direct, so that its meaning can be
more readily understood by those with little or no formal statistical training.
This may be especially valuable when presenting `plain language summaries',
such as those used by Cochrane.
