Use of the Probability Integral Transformation to Fit Nonlinear Mixed-Effects Models With Nonnormal Random Effects

Nelson, Kerrie P.; Lipsitz, Stuart R.; Fitzmaurice, Garrett M.; Ibrahim, Joseph G.; Parzen, Michael; Strawderman, Robert L.

doi:10.1198/106186006x96854

Cited by 72 publications

(59 citation statements)

References 13 publications

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“…Depending on the choice for the bivariate frailty distribution, either an explicit expression can be given or numerical integration is required. In general, numerical integration with respect to the frailty, or random-effects, distribution is not straightforward but has become more accessible through the development of appropriate statistical software and reformulating non-normal random effects, as done by Nelson et al [15] and Liu and Yu [16]. In the following sections, we will focus on the gamma frailty distribution as the most often used frailty distribution because of its explicit solution for the unconditional survival function (see e.g.…”

Section: Methodsmentioning

confidence: 99%

The correlated and shared gamma frailty model for bivariate current status data: An illustration for cross‐sectional serological data

Hens

Wienke

Aerts

et al. 2009

Statistics in Medicine

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SUMMARYFrailty models are often used to study the individual heterogeneity in multivariate survival analysis. Whereas the shared frailty model is widely applied, the correlated frailty model has gained attention because it elevates the restriction of unobserved factors to act similar within clusters. Estimating frailty models is not straightforward due to various types of censoring. In this paper, we study the behavior of the bivariate-correlated gamma frailty model for type I interval-censored data, better known as current status data. We show that applying a shared rather than a correlated frailty model to cross-sectionally collected serological data on hepatitis A and B leads to biased estimates for the baseline hazard and variance parameters.

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Section: Methodsmentioning

confidence: 99%

The correlated and shared gamma frailty model for bivariate current status data: An illustration for cross‐sectional serological data

Hens

Wienke

Aerts

et al. 2009

Statistics in Medicine

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“…The numerical study below suggests that the joint use of the probability integral transformation and Gaussian-Hermite quadrature techniques performs well in practice. Nelson et al (2006) gives a detailed discussion about the probability integral transformation when the random effects or frailties follow non-normal distributions.…”

Section: Notation Assumptions and The Likelihood Functionmentioning

confidence: 99%

Regression Analysis of Multivariate Current Status Data with Semiparametric Transformation Frailty Models

Li¹,

Hu²,

Zhao³

et al. 2020

STAT SINICA

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This article investigates regression analysis of multivariate current status data with the use of a class of flexible semiparametric transformation frailty models. For the problem, the maximum likelihood estimation procedure is derived and in particular, a novel EM algorithm, which is quite stable and can be easily implemented, is developed. Also the asymptotic properties of the resulting estimators are established and the numerical study indicates that the proposed methodology works well in practical situations. An application is provided for the illustration of the presented method.

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“…We refer to Thiébaut 67 et al for an example in the context of linear mixed models. While most procedures require random effects to be normally distributed, appropriate reformulation of the model sometimes allows fitting models with other randomeffects distributions, see, e.g., Liu and Yu 68 and Nelson 69 et al for examples with the SAS procedure NLMIXED. Note that the general idea of joining separate mixed models by allowing their model-specific random effects to be correlated is applicable irrespective of the number of outcomes involved.…”

Section: Random-effects Modelsmentioning

confidence: 99%

The analysis of multivariate longitudinal data: A review

Verbeke

Fieuws

Molenberghs

et al. 2017

Stat Methods Med Res

105

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Longitudinal experiments often involve multiple outcomes measured repeatedly within a set of study participants. While many questions can be answered by modeling the various outcomes separately, some questions can only be answered in a joint analysis of all of them. In this paper, we will present a review of the many approaches proposed in the statistical literature. Four main model families will be presented, discussed and compared. Focus will be on presenting advantages and disadvantages of the different models rather than on the mathematical or computational details.

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Use of the Probability Integral Transformation to Fit Nonlinear Mixed-Effects Models With Nonnormal Random Effects

Cited by 72 publications

References 13 publications

The correlated and shared gamma frailty model for bivariate current status data: An illustration for cross‐sectional serological data

The correlated and shared gamma frailty model for bivariate current status data: An illustration for cross‐sectional serological data

Regression Analysis of Multivariate Current Status Data with Semiparametric Transformation Frailty Models

The analysis of multivariate longitudinal data: A review

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