Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 37 / 4 / d

After adjusting for location, adding the period effect reduces deviance by $9.750$ on one degree of freedom, giving the supplied likelihood-ratio test $p\simeq 0.002$. The adjusted incidence rate ratio isUnder this Poisson exposure model, the accident rate after installation is estimated to be about $54.2\%$ lower, with a statistically significant reduction. The remaining lack of fit merits residual checks and possibly a Quasi-Poisson model or a model allowing location-specific changes. This before-and-after observational study establishes an association under the fitted model; changes in traffic volume, broader trends, or regression to the mean at sites chosen for high prior counts could also contribute, so the estimated reduction is not by itself a causal treatment effect.