When Zero Events Mislead: Evidential Fragility in Rare-Event Epidemiology

Rare-event studies often generate strong claims based on the absence of observed outcomes. However, when expected event counts are small, evidential conclusions may depend on one or two cases. We define evidential fragility as the sensitivity of inferential conclusions to minimal changes in observed data. We examine this phenomenon using the hypothesis that early blindness protects against psychosis as an illustrative example.

Using aggregate data from a Danish nationwide registry, we evaluated how evidential support changes as observed case counts vary from zero to a few events. A Bayesian comparison of protection versus no protection was conducted, and the impact of borrowing information from prior Australian data was assessed using a discounted (power prior) approach to account for cross-study heterogeneity. Detailed mathematical derivations are provided in the Supporting Material.

When zero cases were observed among individuals with early blindness, evidence for protection ranged from anecdotal to strong depending on the outcome definition. However, the observation of a single case markedly attenuated support, and two cases reversed the evidential balance toward no protective effect. Borrowing external prior information increased apparent support when no cases were observed, but this influence diminished rapidly once minimal events accumulated.

Rare-event epidemiologic claims can be structurally fragile. Even minimal changes in observed counts may reverse conclusions. This work provides a conceptual demonstration of how Bayesian stress-testing can be used to evaluate the robustness of such findings before they inform clinical interpretation or policy decisions.