A serially correlated gamma frailty model for longitudinal count data

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Abstract
A Poisson‐gamma model is introduced to account for between‐subjects heterogeneity and within‐subjects serial correlation occurring in longitudinal count data. The model extends the usual time‐constant shared frailty approach to allow time‐varying serially correlated gamma frailty whilst retaining standard marginal assumptions. A composite likelihood approach to estimation and testing for serial correlation is proposed. The work is motivated by a clinical trial on patient‐controlled analgesia where the number of analgesic doses taken by hospital patients in successive time intervals following abdominal surgery is recorded.

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