Modeling of Bounded Outcome Scores with Data on the Boundaries: Application to Disability Assessment for Dementia Scores in Alzheimer’s Disease

Abstract

Abstract. Mixed-effects beta regression (BR), boundary-inflated beta regression (ZOI), and coarsening model (CO) were investigated for analyzing bounded outcome scores with data at the boundaries in the context of Alzheimer's disease. Monte Carlo simulations were conducted to simulate disability assessment for dementia (DAD) scores using these three models, and each set of simulated data were analyzed by the original simulation model. One thousand trials were simulated, and each trial contained 250 subjects. For each subject, DAD scores were simulated at baseline, 13, 26, 39, 52, 65, and 78 weeks. The simulation-reestimation exercise showed that all the three models could reasonably recover their true parameter values. The bias of the parameter estimates of the ZOI model was generally less than 1%, while the bias of the CO model was mainly within 5%. The bias of the BR model was slightly higher, i.e., less than or in the order of 20%. In the application to real-world DAD data from clinical studies, examination of prediction error and visual predictive check (VPC) plots suggested that both BR and ZOI models had similar predictive performance and described the longitudinal progression of DAD slightly better than the CO model. In conclusion, the investigated three modeling approaches may be sensible choices for bounded outcome scores with data on the edges. Prediction error and VPC plots can be used to identify the model with best predictive performance.

Development of a Disease Progression Model for Leucine‐Rich Repeat Kinase 2 in Parkinson's Disease to Inform Clinical Trial Designs

“…The residual variability was assumed to be beta distributed to account for the bounded nature of MDS-UPDRS 23 . 20 Beta regression (i.e., combination of logistic model and beta-distributed residual variability) has been previously used to characterize disease progression in Alzheimer's disease [10][11][12][13][14] and rheumatoid arthritis. 21 Herein, we have applied for the first time beta regression to characterize the longitudinal progression of MDS-UPDRS in PD patients.…”

“…Therefore, ignoring the bounded nature of UPDRS score could cause bias in appropriately quantifying the disease progression. Xu et al . pioneered the implementation of beta regression models in the context of Nonlinear Mixed Effect Model (NONMEM) to characterize longitudinal progression of Alzheimer's Disease Assessment Scale–cognitive subscale in Alzheimer's disease patients.…”

“…Therefore, ignoring the bounded nature of UPDRS score could cause bias in appropriately quantifying the disease progression. Xu et al 11,12 pioneered the implementation of beta regression models in the context of Nonlinear Mixed Effect Model (NONMEM) to characterize longitudinal progression of Alzheimer's Disease Assessment Scale-cognitive subscale in Alzheimer's disease patients. Conrado et al 13 extended the implementation of beta-regression within NONMEM by including third-level random effect (i.e., between-study, between-subject, and residual variability).…”

A generalized partially linear mean-covariance regression model for longitudinal proportional data, with applications to the analysis of quality of life data from cancer clinical trials

“…Simulation studies were performed by Molas and Lesaffre and Xu et al. to evaluate the performances for some of these procedures. All of these approaches require parametric assumptions on the density of the response and also the probability of boundary values, which may be difficult to justify in practice.…”

Is It Time for Going Beyond the P‐Value Paradigm With the Estimation of the Probability of Clinical Benefit as a Criterion for Assessing the Outcomes of a Clinical Trial? A Case Study in Patients With Major Depressive Disorder

“…19 Among them, β-regression has been shown to perform better due to its flexibility to account for various skewed unimodal and bimodal distributions, particularly when normalizing transformations fail to work. 20,21 In addition to the bounded variable issues, the placebo response level at study end has been shown to represent a confounding factor for the assessment of treatment effect in major depressive disorders because the level of placebo response affects the probability of detecting the treatment effect. [22][23][24] The data from 3 clinical trials (studies 810, 926, and 927 from clinical trial register http://ctr.gsk.…”