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Wald's, the likelihood ratio (LR) and Rao's score tests andtheir corresponding confidence intervals (CIs), are the three most commonestimators of parameters of Generalized Linear Models. On finite samples, theseestimators are biased. The objective of this work is to analyze the coverageerrors of the CI estimators in small samples for the log-Poisson model (i.e.estimation of incidence rate ratio) with innovative evaluation criteria, takingin account the overestimation/underestimation unbalance of coverage errors andthe variable inclusion rate and follow-up in epidemiological studies.  METHODS: Exact calculations equivalent to Monte Carlo simulations with aninfinite number of simulations have been used. Underestimation errors (due tothe upper bound of the CI) and overestimation coverage errors (due to the lowerbound of the CI) have been split. The level of confidence has been analyzedfrom $0.95$ to $1-10^{-6}$, allowing the interpretation of P-values below$10^{-6}$ for hypothesis tests.  RESULTS: The LR bias was small (actual coverage errors less than 1.5 timesthe nominal errors) when the expected number of events in both groups was above1, even when unbalanced (e.g. 10 events in one group vs 1 in the other). For95% CI, Wald's and the Score estimators showed high bias even when the numberof events was large ($\geq 20$ in both groups) when groups were unbalanced. Forsmall P-values ($<10^{-6}$), the LR kept acceptable bias while Wald's and thescore P-values had severely inflated errors ($\times 100$).  CONCLUSION: The LR test and LR CI should be used.

Best estimator for bivariate Poisson regression