Mixed-effects beta regression for modeling continuous bounded outcome scores using NONMEM when data are not on the boundaries

Model-Based Drug Development, Janssen Research & Development, 920 Route 202, Raritan, NJ, USA, .
Journal of Pharmacokinetics and Pharmacodynamics (Impact Factor: 1.86). 05/2013; 40(4). DOI: 10.1007/s10928-013-9318-0


Beta regression models have been recommended for continuous bounded outcome scores that are often collected in clinical studies. Implementing beta regression in NONMEM presents difficulties since it does not provide gamma functions required by the beta distribution density function. The objective of the study was to implement mixed-effects beta regression models in NONMEM using Nemes’ approximation to the gamma function and to evaluate the performance of the NONMEM implementation of mixed-effects beta regression in comparison to the commonly used SAS approach. Monte Carlo simulations were conducted to simulate continuous outcomes within an interval of (0, 70) based on a beta regression model in the context of Alzheimer’s disease. Six samples per subject over a 3 years period were simulated at 0, 0.5, 1, 1.5, 2, and 3 years. One thousand trials were simulated and each trial had 250 subjects. The simulation–reestimation exercise indicated that the NONMEM implementation using Laplace and Nemes’ approximations provided only slightly higher bias and relative RMSE (RRMSE) compared to the commonly used SAS approach with adaptive Gaussian quadrature and built-in gamma functions, i.e., the difference in bias and RRMSE for fixed-effect parameters, random effects on intercept, and the precision parameter were <1–3 %, while the difference in the random effects on the slope was <3–7 % under the studied simulation conditions. The mixed-effect beta regression model described the disease progression for the cognitive component of the Alzheimer’s disease assessment scale from the Alzheimer’s Disease Neuroimaging Initiative study. In conclusion, with Nemes’ approximation of the gamma function, NONMEM provided comparable estimates to those from SAS for both fixed and random-effect parameters. In addition, the NONMEM run time for the mixed beta regression models appeared to be much shorter compared to SAS, i.e., 1–2 versus 20–40 s for the model and data used in the manuscript.

1 Follower
68 Reads
  • [Show abstract] [Hide abstract]
    ABSTRACT: Introduction: Population pharmacokinetic and pharmacodynamic (PK/PD) modeling is a critical component of drug development. Quantitative PK/PD models are used in drug development to improve both the design and interpretation of clinical trials across therapeutic areas. Areas covered: In this review, the authors provide an overview of PK/PD modeling approaches and their applications in the management of acute and chronic pain as well as drug assessment. The advantages and limitations of these modeling approaches with regard to handling different end points of pain assessment in monotherapy and combination therapy are highlighted. Expert opinion: New modeling approaches suitable for analgesics used in treatment of acute and chronic pain have started to emerge during the past few years. The application of the clinical utility index is limited but highly encouraged in pain drug assessment as it may inform the optimal window for treatment of pain to attain the best benefit:risk ratio. Owing to the restricted range of pain scores, beta regression models and coarsening models may be more appropriate modeling approaches for the bounded outcome data, rather than regular nonlinear/linear models that assume normal or lognormal error distribution. Additionally, modeling of exposure-response in flexible chronic pain studies remains challenging, and further investigations are needed.
    Expert Opinion on Drug Metabolism &amp Toxicology 02/2014; 10(2):229-48. DOI:10.1517/17425255.2014.864636 · 2.83 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Background The objective of this analysis was to develop a nonlinear disease progression model, using an expanded set of covariates that captures the longitudinal Clinical Dementia Rating Scale–Sum of Boxes (CDR–SB) scores. These were derived from the Alzheimer’s Disease Neuroimaging Initiative ADNI-1 study, of 301 Alzheimer’s disease and mild cognitive impairment patients who were followed for 2–3 years. Methods The model describes progression rate and baseline disease score as a function of covariates. The covariates that were tested fell into five groups: a) hippocampal volume; b) serum and cerebrospinal fluid (CSF) biomarkers; c) demographics and apolipoprotein Epsilon 4 (ApoE4) allele status; d) baseline cognitive tests; and e) disease state and comedications. Results Covariates associated with baseline disease severity were disease state, hippocampal volume, and comedication use. Disease progression rate was influenced by baseline CSF biomarkers, Trail-Making Test part A score, delayed logical memory test score, and current level of impairment as measured by CDR–SB. The rate of disease progression was dependent on disease severity, with intermediate scores around the inflection point score of 10 exhibiting high disease progression rate. The CDR–SB disease progression rate in a typical patient, with late mild cognitive impairment and mild Alzheimer’s disease, was estimated to be approximately 0.5 and 1.4 points/year, respectively. Conclusions In conclusion, this model describes disease progression in terms of CDR–SB changes in patients and its dependency on novel covariates. The CSF biomarkers included in the model discriminate mild cognitive impairment subjects as progressors and nonprogressors. Therefore, the model may be utilized for optimizing study designs, through patient population enrichment and clinical trial simulations.
    Neuropsychiatric Disease and Treatment 05/2014; 10:929-52. DOI:10.2147/NDT.S62323 · 1.74 Impact Factor
  • Source
    [Show abstract] [Hide 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.
    The AAPS Journal 08/2014; 16(6). DOI:10.1208/s12248-014-9655-y · 3.80 Impact Factor
Show more