 Solution

The additional estimate points in the same direction as the pooled effect: its odds ratio is about $1.90$, compared with the original pooled value about $2.34$. Its standard error is relatively large, and the approximate two-standard-error interval for its log odds ratio is $0.64\pm 1.14=(-0.50,1.78)$, or about $(0.61,5.93)$ on the odds-ratio scale. This interval includes both no effect and the existing pooled effect. Thus it supplies compatible but imprecise evidence and would tend to pull the pooled estimate somewhat toward one while adding information. A change in the main conclusion is unlikely.

For scale, a conventional inverse-variance common-effect fit to the six rounded tabulated estimates can be updated by ${\hat{\delta }}_{\mathrm{new}}=(W\hat{\delta }+wy)/(W+w)$, with new weight $w=0.57^{-2}$. This gives the new study roughly eleven percent of the combined weight, a modest effect on the estimate. An exact update of the supplied Mantel–Haenszel pooled odds ratio needs the new two-by-two table, which the reported log ratio and standard error do not uniquely specify. The qualitative compatibility conclusion does not depend on pretending that the supplied plot used inverse-variance weights.