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Nonlinear mixed-effects models with misspecified random-effects distribution.

Drikvandi, Reza (2020) 'Nonlinear mixed-effects models with misspecified random-effects distribution.', Pharmaceutical statistics., 19 (3). pp. 187-201.


Nonlinear mixed‐effects models are being widely used for the analysis of longitudinal data, especially from pharmaceutical research. They use random effects which are latent and unobservable variables so the random‐effects distribution is subject to misspecification in practice. In this paper, we first study the consequences of misspecifying the random‐effects distribution in nonlinear mixed‐effects models. Our study is focused on Gauss‐Hermite quadrature, which is now the routine method for calculation of the marginal likelihood in mixed models. We then present a formal diagnostic test to check the appropriateness of the assumed random‐effects distribution in nonlinear mixed‐effects models, which is very useful for real data analysis. Our findings show that the estimates of fixed‐effects parameters in nonlinear mixed‐effects models are generally robust to deviations from normality of the random‐effects distribution, but the estimates of variance components are very sensitive to the distributional assumption of random effects. Furthermore, a misspecified random‐effects distribution will either overestimate or underestimate the predictions of random effects. We illustrate the results using a real data application from an intensive pharmacokinetic study.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Publisher statement:This is the peer reviewed version of the following article: Drikvandi, Reza (2020). Nonlinear mixed-effects models with misspecified random-effects distribution. Pharmaceutical Statistics 19(3): 187-201 which has been published in final form at This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
Date accepted:08 October 2019
Date deposited:02 November 2020
Date of first online publication:28 October 2019
Date first made open access:02 November 2020

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