Comparison of methods for the analysis of longitudinal interval count data

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Abstract
Longitudinal studies are often concerned with estimating the recurrence rate of a non‐fatal event. In many cases, only the total number of events occurring during successive time intervals is known. We compared a mixed Poisson‐gamma regression method proposed by Thall and a quasi‐likelihood method proposed by Zeger and Liang for the analysis of such data, in the case where the mean was correctly specified, using simulation techniques with large samples. Both methods produced similar standard errors in most situations, except in the case of time‐dependent covariates with non‐Poisson‐gamma data where they were seriously underestimated by the Thall method. A simple method for discriminating between the variance forms of the two methods is described. The findings are applied to the analyses of clinical trials of non‐melanoma skin cancer and familial polyposis. This study extends the findings of Breslow concerning variance misspecification in overdispersed Poisson and quasi‐likelihood models to the longitudinal setting.

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