Nonlinear mixed-effects models with misspecified random-effects distribution

Drikvandi, Reza ORCID: https://orcid.org/0000-0002-7245-9713 (2019) Nonlinear mixed-effects models with misspecified random-effects distribution. Pharmaceutical Statistics, 19 (3). pp. 187-201. ISSN 1539-1604

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Abstract

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