Inferential Statisticshard
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In a clinical trial with binary outcomes, a Wald-type interval for the log-odds ratio is constructed as β^±zα/2SE(β^)\hat{\beta} \pm z_{\alpha/2} \cdot SE(\hat{\beta}). If the sample size is small and the true probability of success is near 00, why does this Wald interval often fail to achieve its nominal coverage probability?