Abstract
In this methodological study, we address the joint modeling of longitudinal data on the frequency and duration migraine attacks collected from patients in a clinical study in which patients were repeatedly asked at each hospital visit to report the number of days of migraine attacks they had in the last $30$ days and the corresponding average duration of attacks. In our motivating data set, the migraine frequency outcome is a count variable inflated at multiples of $5$ and $10$ days, whereas the migraine duration outcome is reported entirely in discrete hours, including $0$ for non-migraine days and inflated at multiples of $12$ hours. In our study, we propose a joint modeling approach that models each migraine outcome by a multiple inflated negative binomial model with random effects and assumes a bivariate normal distribution for the random effects. We estimate the model parameters under Bayesian inference. We examine the performance of the proposed joint model using a Monte Carlo simulation study and compare its performance with a separate modeling approach in which each longitudinal count outcome is modeled separately. Finally, we present the results of the analysis of migraine data.
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