Comparison of the Andersen–Gill model with poisson and negative binomial regression on recurrent event data

Many generalizations of the Cox proportional hazard method have been elaborated to analyse recurrent event data. The Andersen–Gill model was proposed to handle event data following Poisson processes. This method is compared with non-survival approaches, such as Poisson and negative binomial regression. The comparison is performed on data simulated according to various event-generating processes and differing in subject heterogeneity. When robust standard error estimates are applied, for Poisson processes the Andersen–Gill approach is comparable to a negative binomial regression, whereas the poisson regression has comparable coverage probabilities of confidence intervals, but increased type I error rates; however, none of the methods can generate unbiased parameter estimates with data violating the independent increment assumption. These findings are illustrated by data from a clinical trial of the efficacy of a new pneumococcal vaccine for prevention of otitis media.