We conducted a simulation study to examine the performance of confidence intervals when multiplicative and additive rate (Poisson regression) models are fit to follow-up data, but the model form may be misspecified. Data were generated from over 129,000 different population structures that ranged from sub-additive to supra-multiplicative. When a multiplicative model was fit, all of the confidence intervals that we examined performed well as interval estimators of the asymptotic means of the point estimators, even when the correct model form was not multiplicative. When an additive model was fit, (1) only the likelihood ratio interval and the score interval with expected information consistently performed well, and they consistently performed better than any of the Wald intervals that we examined; (2) Wald intervals performed better when calculated with observed information rather than with expected information; and (3) Wald intervals with expected information performed better when the information matrix was evaluated at the restricted maximum likelihood estimate rather than the unrestricted maximum likelihood estimate.