Longitudinal Joint Modelling of Ordinal and Overdispersed Count Outcomes: A Bridge Distribution for the Ordinal Random Intercept
Open Access
- 3 March 2021
- journal article
- research article
- Published by Hindawi Limited in Computational and Mathematical Methods in Medicine
- Vol. 2021, 1-13
- https://doi.org/10.1155/2021/5521881
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.Keywords
This publication has 29 references indexed in Scilit:
- Time-varying copula models for longitudinal dataStatistics and Its Interface, 2018
- Joint longitudinal data analysis in detecting determinants of CD4 cell count change and adherence to highly active antiretroviral therapy at Felege Hiwot Teaching and Specialized Hospital, North-west Ethiopia (Amhara Region)AIDS Research and Therapy, 2017
- Marginalized multilevel hurdle and zero‐inflated models for overdispersed and correlated count data with excess zerosStatistics in Medicine, 2014
- Gaussian Copula Mixed Models for Clustered Mixed Outcomes, With Application in Developmental ToxicologyJournal of Agricultural, Biological and Environmental Statistics, 2013
- A joint model for hierarchical continuous and zero-inflated overdispersed count dataJournal of Statistical Computation and Simulation, 2013
- Modeling Longitudinal Data Using a Pair-Copula Decomposition of Serial DependenceJournal of the American Statistical Association, 2010
- Joint Regression Analysis of Correlated Data Using Gaussian CopulasBiometrics, 2009
- Multilevel zero-inflated negative binomial regression modeling for over-dispersed count data with extra zerosJournal of Applied Statistics, 2008
- Longitudinal Data AnalysisPublished by Taylor & Francis Ltd ,2008
- Multivariate Dispersion Models Generated From Gaussian CopulaScandinavian Journal of Statistics, 2000