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A strategy for residual error modeling incorporating scedasticity of variance and distribution shape.

ABSTRACT: Nonlinear mixed effects models parameters are commonly estimated using maximum likelihood. The properties of these estimators depend on the assumption that residual errors are independent and normally distributed with mean zero and correctly defined variance. Violations of this assumption can cause bias in parameter estimates, invalidate the likelihood ratio test and preclude simulation of real-life like data. The choice of error model is mostly done on a case-by-case basis from a limited set of commonly used models. In this work, two strategies are proposed to extend and unify residual error modeling: a dynamic transform-both-sides approach combined with a power error model (dTBS) capable of handling skewed and/or heteroscedastic residuals, and a t-distributed residual error model allowing for symmetric heavy tails. Ten published pharmacokinetic and pharmacodynamic models as well as stochastic simulation and estimation were used to evaluate the two approaches. dTBS always led to significant improvements in objective function value, with most examples displaying some degree of right-skewness and variances proportional to predictions raised to powers between 0 and 1. The t-distribution led to significant improvement for 5 out of 10 models with degrees of freedom between 3 and 9. Six models were most improved by the t-distribution while four models benefited more from dTBS. Changes in other model parameter estimates were observed. In conclusion, the use of dTBS and/or t-distribution models provides a flexible and easy-to-use framework capable of characterizing all commonly encountered residual error distributions.

SUBMITTER: Dosne AG

PROVIDER: S-EPMC4791481 | biostudies-literature | 2016 Apr

REPOSITORIES: biostudies-literature

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A strategy for residual error modeling incorporating scedasticity of variance and distribution shape.

Dosne Anne-Gaëlle AG Bergstrand Martin M Karlsson Mats O MO

Journal of pharmacokinetics and pharmacodynamics 20151217 2

Nonlinear mixed effects models parameters are commonly estimated using maximum likelihood. The properties of these estimators depend on the assumption that residual errors are independent and normally distributed with mean zero and correctly defined variance. Violations of this assumption can cause bias in parameter estimates, invalidate the likelihood ratio test and preclude simulation of real-life like data. The choice of error model is mostly done on a case-by-case basis from a limited set of ...[more]

PMID: 26679003

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Project description:Paeonia (Paeoniaceae), a culturally and economically important plant genus, has an isolated taxonomy while the evolution of this genus is unclear. A plant species endemic to southwest China, Paeonia mairei is precious germplasm for evolution-related research and cultivar improvement, and its conservation is urgent. However, little is known about its patterns of habitat distribution and responses to climate change. Using 98 occurrence sites and data of 19 bioclimatic variables, we conducted principal component analysis and hierarchical cluster analysis to delineate different climatic populations. Maximum entropy algorithm (MaxEnt) was applied to each population to evaluate the importance of environmental variables in shaping their distribution, and to identify distribution shifts under different climate change scenarios. We also applied MaxEnt to all of the P. mairei presence sites (P_Whole) to evaluate the need to construct separate species distribution models for separate populations rather than a common approach by treating them as a whole. Our results show that local adaptation exists within the distribution range of P. mairei and that all presence sites were clustered into a western population (P_West) and an eastern population (P_East). Two variables (precipitation of the driest month and temperature seasonality) are important when shaping the distribution of P_West, and another two variables (mean diurnal range and mean temperature of the wettest quarter) are important for P_East. Both populations are likely to shift upward under climate change, while P_East may lose most current suitable areas while P_West may not. P_Whole produced a narrower area compared to the combination of P_West and P_East but a suitable area (south Chongqing) may have been missed in the prediction. Accordingly, a population-based approach in constructing a species distribution model is needed to provide a detailed appreciation of the distribution of P. mairei, allowing for a population-based conservation strategy. In this case, it could include assisted migration to new and suitable distribution areas for P_West and in situ conservation in high elevation regions for P_East. The results of our study could be a useful reference for implementing the long-term conservation and further research of P. mairei.

Dataset Information

A strategy for residual error modeling incorporating scedasticity of variance and distribution shape.

Publications

A strategy for residual error modeling incorporating scedasticity of variance and distribution shape.

Similar Datasets

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