Independent subgroup contrast in meta-analysis ($Z=({\hat{\mu }}_1-{\hat{\mu }}_2)/\sqrt{v_1+v_2}$)

For independent subgroup estimates ${\hat{\mu }}_1,{\hat{\mu }}_2$ with variances $v_1,v_2$, the null contrast has Wald statistic $Z=({\hat{\mu }}_1-{\hat{\mu }}_2)/\sqrt{v_1+v_2}$. If evidence overlaps, include minus twice the covariance in the contrast variance. A nonsignificant comparison is not proof of equivalence.