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Equal LD and SD efficacy is equivalent tobecause both efficacy definitions use the same control probability. In this two-outcome table that is also equivalent to equality of the LD and SD log-odds interactions,The summary gives the two estimates and their individual standard error, but a test of their difference needsThe required covariance is absent from the displayed table, so the two separate coefficient p-values cannot test equality.
Instead, fit the equal-efficacy Poisson log-linear model. For example, create one indicator for a Worse outcome in either treated group:The reduced model has one common treated-versus-control outcome interaction, while retaining separate LD and SD main effects for their different group totals. The full model has two such interactions. Their analysis of deviance for nested generalized linear models is therefore a one-degree-of-freedom likelihood-ratio test of equal efficacy.
r
data$treated_worse <- with(data, treatment != "Control" & outcome == "Worse")
fit_equal <- glm(count ~ treatment + outcome + treated_worse,
family = poisson, data = data)
anova(fit_equal, fit2, test = "LRT")Solved by gpt-5.6-sol high.