Likelihood ratio test (LRT)
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One final option is to perform a likelihood ratio test. The method works as follows:The unconstrained maximum likelihood estimates of the control and experimental arm risk are estimated (with the observed event risks), and the associated likelihood is calculated;The constrained maximum likelihood estimates are estimated, forcing the estimates to lie on the SAFE frontier, i.e. assuming inferiority, and finding the maxima with Newton-Raphson optimisation [The test statistic is then calculated as minus twice the difference of the unconstrained and constrained log-likelihoods. Under the null hypothesis of the experimental arm being inferior to the control, this should follow a chi-square distribution.Given this test, one can then build a test-based confidence interval, by providing the confidence interval for the risk difference that would correspond to the same p-value.