Nonlinear mixed-effects models for pharmacokinetic data analysis: assessment of the random-effects distribution

Drikvandi, Reza

doi:10.1007/s10928-017-9510-8

Cited by 14 publications

(15 citation statements)

References 25 publications

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“…In this case, the CPI model yields nearly the same fitted values as the MEM model, so we consider only the MEM model from this point. A variety of methods have been proposed to assess the assumption of independent normally distributed random effects . We use several of these methods to assess the assumption in this case; details are in Appendix S3.…”

Section: Resultsmentioning

confidence: 99%

Novel methods for the analysis of stepped wedge cluster randomized trials

Kennedy‐Shaffer

Gruttola

Lipsitch

2019

Statistics in Medicine

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Stepped wedge cluster randomized trials (SW‐CRTs) have become increasingly popular and are used for a variety of interventions and outcomes, often chosen for their feasibility advantages. SW‐CRTs must account for time trends in the outcome because of the staggered rollout of the intervention. Robust inference procedures and nonparametric analysis methods have recently been proposed to handle such trends without requiring strong parametric modeling assumptions, but these are less powerful than model‐based approaches. We propose several novel analysis methods that reduce reliance on modeling assumptions while preserving some of the increased power provided by the use of mixed effects models. In one method, we use the synthetic control approach to find the best matching clusters for a given intervention cluster. Another method makes use of within‐cluster crossover information to construct an overall estimator. We also consider methods that combine these approaches to further improve power. We test these methods on simulated SW‐CRTs, describing scenarios in which these methods have increased power compared with existing nonparametric methods while preserving nominal validity when mixed effects models are misspecified. We also demonstrate theoretical properties of these estimators with less restrictive assumptions than mixed effects models. Finally, we propose avenues for future research on the use of these methods; motivation for such research arises from their flexibility, which allows the identification of specific causal contrasts of interest, their robustness, and the potential for incorporating covariates to further increase power. Investigators conducting SW‐CRTs might well consider such methods when common modeling assumptions may not hold.

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Section: Resultsmentioning

confidence: 99%

Novel methods for the analysis of stepped wedge cluster randomized trials

Kennedy‐Shaffer

Gruttola

Lipsitch

2019

Statistics in Medicine

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“…Drikvandi et al. () have developed a diagnostic tool for assessing the random‐effects distribution that can be applied to mixed models with multiple random effects and correlated errors (see also Drikvandi, ).…”

Section: Discussionmentioning

confidence: 99%

“…It would be useful to check the normality assumption on random effects before applying the proposed test. Drikvandi et al (2017) have developed a diagnostic tool for assessing the random-effects distribution that can be applied to mixed models with multiple random effects and correlated errors (see also Drikvandi, 2017).…”

Section: Parametermentioning

confidence: 99%

Testing random effects in linear mixed‐effects models with serially correlated errors

Drikvandi

Noorian

2019

Biometrical J

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In linear mixed‐effects models, random effects are used to capture the heterogeneity and variability between individuals due to unmeasured covariates or unknown biological differences. Testing for the need of random effects is a nonstandard problem because it requires testing on the boundary of parameter space where the asymptotic chi‐squared distribution of the classical tests such as likelihood ratio and score tests is incorrect. In the literature several tests have been proposed to overcome this difficulty, however all of these tests rely on the restrictive assumption of i.i.d. measurement errors. The presence of correlated errors, which often happens in practice, makes testing random effects much more difficult. In this paper, we propose a permutation test for random effects in the presence of serially correlated errors. The proposed test not only avoids issues with the boundary of parameter space, but also can be used for testing multiple random effects and any subset of them. Our permutation procedure includes the permutation procedure in Drikvandi, Verbeke, Khodadadi, and Partovi Nia (2013) as a special case when errors are i.i.d., though the test statistics are different. We use simulations and a real data analysis to evaluate the performance of the proposed permutation test. We have found that random slopes for linear and quadratic time effects may not be significant when measurement errors are serially correlated.

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“…In this section, we describe Gauss-Hermite quadrature for approximating the marginal log-likelihood function (2). To avoid the numerical complexity with multiple integrals, one might change the variables of integration in (2) to independent standard normally distributed random effects z i , as suggested by Pinheiro and Bates.…”

Section: Gaussian Quadrature For Calculation Of the Marginal Log-likementioning

confidence: 99%

“…For example, in pharmacokinetics, often a nonlinear function for drug concentration is achieved over time after administration of a drug and the goal is to characterise drug disposition. 1,2 The term "mixed-effects" refers to the presence of both fixed effects and random effects in the model. Fixed effects are regression parameters constant across subjects, while random effects are subject-specific random variables incorporated to capture the inter-subject variability.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear mixed‐effects models with misspecified random‐effects distribution

Drikvandi

2019

Pharmaceutical Statistics

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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.

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Nonlinear mixed-effects models for pharmacokinetic data analysis: assessment of the random-effects distribution

Cited by 14 publications

References 25 publications

Novel methods for the analysis of stepped wedge cluster randomized trials

Novel methods for the analysis of stepped wedge cluster randomized trials

Testing random effects in linear mixed‐effects models with serially correlated errors

Nonlinear mixed‐effects models with misspecified random‐effects distribution

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