= Solution
Zero observed events do not mean that the underlying event <probability> cannot be estimated. For independent observations having a common <Bernoulli distribution>, the <binomial likelihood> with no events is $(1-p)^{1515}$, maximized at $\widehat p=0$. A <zero-event binomial upper confidence bound> shows the remaining uncertainty: the one-sided 95% upper bound solves $(1-p_U)^{1515}=0.05$, giving
$$
\boxed{p_U=1-0.05^{1/1515}\simeq0.00198.}
$$
Thus the point estimate is zero, but a nonzero mortality risk is compatible with the observations. This bound is an illustration under independent equal-risk sampling; <clustered data> or unequal risks require their own uncertainty calculation.
The empirical unadjusted <odds ratio> is also defined:
$$
\boxed{\widehat{\mathrm{OR}}=\frac{0/1515}{53/75004}=0.}
$$
Its <log odds ratio> is $-\infty$, so the ordinary <normal approximation> for a log-odds <confidence interval> is unavailable. Exact likelihood-based limits can still describe uncertainty; a specified continuity correction would instead yield a finite, method-dependent point estimate.
In an unpenalized <logistic regression> with a separate coefficient for elective exposure, every exposed death outcome is zero. Decreasing that coefficient toward $-\infty$ increases the exposed observations' likelihood contributions and leaves the reference observations unchanged. This is <quasi-complete separation>: there is no finite ordinary <maximum-likelihood estimate> of the exposure coefficient, even after adding background predictors. It is reasonable to say that the usual finite adjusted coefficient could not be fitted; it is too strong to say that no risk estimate or statistical information is possible. A specified penalized likelihood or <Bayesian inference> with proper coefficient priors can provide a finite adjusted estimate, whose dependence on the regularization must be reported.
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