Small sample estimation properties of longitudinal count models

Motivated by the need to validly analyse data from small longitudinal designs with count outcomes, we carried out a simulation study with a two-group longitudinal design with as few as five subjects per group and three measurements per subject. Various correlation structures related to auto regression and/or subject heterogeneity were used to simulate, most of which did not correspond to any of the methods being assessed and so induced some model misspecification. We evaluated validity (Type I error rate) and efficiency (power) for the interaction effect using several methods based on generalized linear mixed models (GLMM) or generalized estimating equations (GEE). Conclusions included that Type I error rates were too high for GEE using sandwich standard errors, and too low for GLMM. Generally, Type I error rate was improved with more subjects but not with more measurements per subjects, and both improved power. Many of our results differ from corresponding results in other cases (e.g. logistic models), emphasizing a diversity of behaviour for various non-normal outcomes.