Augmented Beta rectangular regression models: A Bayesian perspective.
Mixed effects Beta regression models based on Beta distributions have been widely used to analyze longitudinal percentage or proportional data ranging between zero and one. However, Beta distributions are not flexible to extreme outliers or excessive events around tail areas, and they do not account for the presence of the boundary values zeros and ones because these values are not in the support of the Beta distributions. To address these issues, we propose a mixed effects model using Beta rectangular distribution and augment it with the probabilities of zero and one. We conduct extensive simulation studies to assess the performance of mixed effects models based on both the Beta and Beta rectangular distributions under various scenarios. The simulation studies suggest that the regression models based on Beta rectangular distributions improve the accuracy of parameter estimates in the presence of outliers and heavy tails. The proposed models are applied to the motivating Neuroprotection Exploratory Trials in Parkinson's Disease (PD) Long-term Study-1 (LS-1 study, n = 1741), developed by The National Institute of Neurological Disorders and Stroke Exploratory Trials in Parkinson's Disease (NINDS NET-PD) network.
Department of Biostatistics, The University of Texas Health Science Center at Houston, 1200 Pressler St, Houston, TX, 77030, USA.
Jue
J
Wang
Department of Biostatistics, The University of Texas Health Science Center at Houston, 1200 Pressler St, Houston, TX, 77030, USA.
Sheng
S
Luo
D001499:Bayes Theorem; D002986:Clinical Trials as Topic; D006801:Humans; D008390:Markov Chains; D015233:Models, Statistical; D009010:Monte Carlo Method; D010300:Parkinson Disease; D012044:Regression Analysis
Augmented Beta; Beta rectangular distribution; GAMLSS family; Longitudinal data; Markov chain Monte Carlo; Proportional data