Abstract
This manuscript implements a maximum likelihood based approach that is appropriate for equally spaced longitudinal count data with over-dispersion, so that the variance of the outcome variable is larger than expected for the assumed Poisson distribution. We implement the proposed method in the analysis of seizure data and a subset of German Socio-Economic Panel data. To demonstrate the importance of correctly modeling the over-dispersion, we make comparisons with the semi-parametric generalized estimating equations approach that incorrectly ignores any over-dispersion in the data. Our simulations demonstrate that accounting for over-dispersion results in improved small-sample efficiency and appropriate coverage probabilities. We also provide code in R so that readers can implement our approach in their own analyses.
Highlights
Longitudinal count data are often encountered in scientific studies
Simulation studies In the previous section we identified significant treatment effects for the proposed ML approach that were not observed for generalized estimating equations (GEE)
The percent bias was similar for ML and GEE; the mean square error (MSE) was slightly smaller for ML than for GEE
Summary
Longitudinal count data are often encountered in scientific studies. For example, Thall and Vail (1990) analyzed repeated seizure counts on subjects in a clinical trial. In this paper we implement a maximum-likelihood based method for the analysis of longitudinal count data with over-dispersion induced by the serial correlation of measurements. We conduct simulations for moderately sized samples to demonstrate that when the likelihood is correctly specified, we have improved efficiency in estimation of the regression and correlation parameters for our approach relative to GEE that incorrectly ignores the over-dispersion. Another model for longitudinal count data is the class of generalized linear mixedeffects models that incorporate random effects in the linear predictor.
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