Abstract
Associated longitudinal response variables are faced with variations caused by repeated measurements over time along with the association between the responses. To model a longitudinal ordinal outcome using generalized linear mixed models, integrating over a normally distributed random intercept in the proportional odds ordinal logistic regression does not yield a closed form. In this paper, we combined a longitudinal count and an ordinal response variable with Bridge distribution for the random intercept in the ordinal logistic regression submodel. We compared the results to that of a normal distribution. The two associated response variables are combined using correlated random intercepts. The random intercept in the count outcome submodel follows a normal distribution. The random intercept in the ordinal outcome submodel follows Bridge distribution. The estimations were carried out using a likelihood-based approach in direct and conditional joint modelling approaches. To illustrate the performance of the model, a simulation study was conducted. Based on the simulation results, assuming a Bridge distribution for the random intercept of ordinal logistic regression results in accurate estimation even if the random intercept is normally distributed. Moreover, considering the association between longitudinal count and ordinal responses resulted in estimation with lower standard error in comparison to univariate analysis. In addition to the same interpretation for the parameter in marginal and conditional estimates thanks to the assumption of a Bridge distribution for the random intercept of ordinal logistic regression, more efficient estimates were found compared to that of normal distribution.
Highlights
Many longitudinal studies are designed so that more than one response variable is recorded for the same subject
Likelihood ratio test confirmed the use of random intercepts in the model
A significant association was found between the random effects which confirms the use of a joint modeling approach
Summary
Many longitudinal studies are designed so that more than one response variable is recorded for the same subject. Various methods have been developed for jointly modeling longitudinal and survival data [6]. Kassahun et al used generalized linear mixed models to model two longitudinal outcomes simultaneously. They considered weight and days of illness as the continuous and overdispersed count responses, respectively, [7]. Seyoum et al considered the determinants of CD4 cell count change and adherence to highly active antiretroviral therapy among HIV adult patients, and they utilized a generalized linear mixed model to determine joint predictors of two longitudinal response variables over time. In addition to several approaches for jointly modeling two longitudinal responses, the association among the repeated measurements and between the two longitudinal processes can be considered via correlated random effects [9]
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