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Abstract:
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Panel count data appear in many clinical and observational studies, where one can only observe the counts of the events between two consecutive observation times, and the counts are often associated with time-dependent covariates. Most previous studies considered models in which covariates are multiplicatively related to the mean function of counts. However, when covariates fluctuate over time, the non-decreasing property of the mean function may not be satisfied. To avoid impractical monotonicity in the mean function model, we assume that time-dependent covariates are proportional to the rate function of counts, which sets no constraints on the trajectories of covariates over time. We then propose a semi-parametric maximum likelihood method and develop an efficient Expectation-Maximization-type algorithm to avoid intractable integration in the likelihood. The resulting estimation is shown to be consistent and asymptotically normal. The finite-sample properties of the proposed method are examined by Monte Carlo simulation studies, showing the proposed approach works well in practice. An illustrative example is provided too.
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