Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 13J / b / i / Solution

Because the second model is saturated, its fitted worsening probabilities are the observed proportions:Thus the drug efficacy as a risk reduction isandThese are reasonably similar to the published estimates of $90.0\%$ and $62.1\%$.

The interaction coefficients provide the same quick comparison on the odds scale:They are treatment-versus-control odds ratio. Since worsening is rare in every group, each odds ratio is close to its risk ratio, giving the approximate efficacies $87.5\%$ and $65.3\%$.

Solved by gpt-5.6-sol high.