The impact of missing data in a generalized integer-valued autoregression model for count data.

The impact of the missing data mechanism on estimates of model parameters for continuous data has been extensively investigated in the literature. In comparison, minimal research has been carried out for the impact of missing count data. The focus of this article is to investigate the impact of missing data on a transition model, termed the generalized autoregressive model of order 1 for longitudinal count data. The model has several features, including modeling dependence and accounting for overdispersion in the data, that make it appealing for the clinical trial setting. Furthermore, the model can be viewed as a natural extension of the commonly used log-linear model. Following introduction of the model and discussion of its estimation we investigate the impact of different missing data mechanisms on estimates of the model parameters through a simulation experiment. The findings of the simulation experiment show that, as in the case of normally distributed data, estimates under the missing completely at random (MCAR) and missing at random (MAR) mechanisms are close to their analogue for the full dataset and that the missing not at random (MNAR) mechanism has the greatest bias. Furthermore, estimates based on imputing the last observed value carried forward (LOCF) for missing data under the MAR assumption are similar to those of the MAR. This latter finding might be attributed to the Markov property underlying the model and to the high level of dependence among successive observations used in the simulation experiment. Finally, we consider an application of the generalized autoregressive model to a longitudinal epilepsy dataset analyzed in the literature.