Bayesian joint modeling of patient-reported longitudinal data on frequency and duration of migraine

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.