= Solution
The event and nonevent cell counts are $(a,b)=(30,60)$ and $(c,d)=(20,40)$. Thus the estimated <odds ratio> and <log odds ratio> are
$$
\widehat{\operatorname{OR}}=\frac{30/60}{20/40}=1,
\qquad \widehat\ell=\log1=0.
$$
For <independent> binomial groups, the <delta method> gives
$$
\widehat{\operatorname{Var}}(\widehat\ell)
=\frac1{30}+\frac1{60}+\frac1{20}+\frac1{40}
=\frac18=0.125,
\qquad \operatorname{SE}(\widehat\ell)=\sqrt{0.125}=0.353553\ldots.
$$
Using the permitted <normal approximation> quantile of 2, \b[the approximate 95% interval is]
$$
\boxed{\widehat\ell=0,\qquad \mathrm{CI}_{\log\mathrm{OR}}=(-0.7071,0.7071).}
$$
The observed odds of death are equal between groups. The <confidence interval> includes zero and allows appreciable effects in either direction; it does not demonstrate equivalence. Exponentiating gives an <odds ratio> interval approximately $(0.493,2.028)$, so the data are compatible with roughly half to twice the death odds for the first treatment relative to the second. The tabulated <standard error> is rounded.
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