Bayesian Nonparametric Regression Analysis of Data with Random Effects Covariates from Longitudinal Measurements

Ryu, Dongseok; Li, Erning; Mallick, Bani K.

doi:10.1111/j.1541-0420.2010.01489.x

Cited by 13 publications

(12 citation statements)

References 34 publications

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“…The central idea of the streamlined approach requires permuting the previous matrix into an approximate block-diagonal form for decomposition, as shown in (15). The matrices U, V i , and W −1 i are usually of general forms with small dimension (Appendix of [21]); each can be easily derived via straightforward matrix manipulation.…”

Section: Factor-by-curve Interactionsmentioning

confidence: 99%

“…Their proposed covariance matrix for the random basis coefficients was modeled parametrically with independence assumptions. Chen and Wang [14] and Ryu, Li, and Mallick [15] extended this work by allowing a more general covariance matrix structure for the random basis coefficients, although the former was confined to functional data analysis. When the dimension of the spline basis functions and the number of groups become large, many of the aforementioned approaches become too slow, or even computationally infeasible.…”

Section: Introductionmentioning

confidence: 99%

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Variational methods for fitting complex Bayesian mixed effects models to health data

Lee

Wand

2015

Statistics in Medicine

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We consider approximate inference methods for Bayesian inference to longitudinal and multilevel data within the context of health science studies. The complexity of these grouped data often necessitates the use of sophisticated statistical models. However, the large size of these data can pose significant challenges for model fitting in terms of computational speed and memory storage. Our methodology is motivated by a study that examines trends in cesarean section rates in the largest state of Australia, New South Wales, between 1994 and 2010. We propose a group-specific curve model that encapsulates the complex nonlinear features of the overall and hospital-specific trends in cesarean section rates while taking into account hospital variability over time. We use penalized spline-based smooth functions that represent trends and implement a fully mean field variational Bayes approach to model fitting. Our mean field variational Bayes algorithms allow a fast (up to the order of thousands) and streamlined analytical approximate inference for complex mixed effects models, with minor degradation in accuracy compared with the standard Markov chain Monte Carlo methods.

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Section: Factor-by-curve Interactionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Variational methods for fitting complex Bayesian mixed effects models to health data

Lee

Wand

2015

Statistics in Medicine

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“…Now, to remedy the computational difficulty of sampling

β

, we use the latent variables such that

W_{j} = x_{j} β + V_{j}

j = 1, \dots, n

, where

V_{j} \overset{iid}{\sim} N false(0, σ_{v}^{2} false)

. The full conditional distribution of

W_{j}^{*} = e^{- σ W_{j}}

j = 1, \dots, n

, is given by

\begin{matrix} right & center & left W_{j}^{*} | \cdot \overset{italiciid}{\propto} ([], {W_{j}^{*}}^{2} exp \{- (λ_{1} + λ_{2} - λ_{2}^{'}) W_{j}^{*} t_{1 j}^{*} σ - (λ_{0} + λ_{2}^{'}) W_{j}^{*} {t_{2 j}^{*}}^{σ}\}) I {j \in G_{1}} \\ right & center & left \times ([], {W_{j}^{*}}^{2} exp \{- (λ_{0} + λ_{1}^{'}) W_{j}^{*} {t_{1 j}^{*}}^{σ} - (λ_{1} + λ_{2} - λ_{1}^{'}) W_{j}^{*} {t_{2 j}^{*}}^{σ}\}) I {j \in G_{2}} \\ right & center & left \times ([], W_{j}^{*} exp \{- (λ_{0} + λ_{1} + λ_{2}) W_{j}^{*}\}) \end{matrix}

…”

Section: Model Formulation and Bayesian Inferencementioning

confidence: 99%

Bayesian Framework for Parametric Bivariate Accelerated Lifetime Modeling and Its Application to Hospital Acquired Infections

et al. 2015

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Infectious diseases that can be spread directly or indirectly from one person to another are caused by pathogenic microorganisms such as bacteria, viruses, parasites, or fungi. Infectious diseases remain one of the greatest threats to human health and the analysis of infectious disease data is among the most important application of statistics. In this article, we develop Bayesian methodology using parametric bivariate accelerated lifetime model to study dependency between the colonization and infection times for Acinetobacter baumannii bacteria which is leading cause of infection among the hospital infection agents. We also study their associations with covariates such as age, gender, apache score, antibiotics use 3 months before admission and invasive mechanical ventilation use. To account for singularity, we use Singular Bivariate Extreme Value distribution to model residuals in Bivariate Accelerated lifetime model under the fully Bayesian framework. We analyze a censored data related to the colonization and infection collected in five major hospitals in Turkey using our methodology. The data analysis done in this article is for illustration of our proposed method and can be applied to any situation that our model can be used.

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“…Among them, for instance: (Wong and Kohn, 1996;Li, 2000;Smith et al, 2000;Kandala et al, 2001;Panagiotelis and Smith, 2008;Ryu et al, 2011) were those who use regression spline with Bayesian approach, while (Lang and Brezger, 2004;Jerak and Wagner, 2006;Nott, 2006;Costa, 2008;Marley and Wand, 2010;Shen, 2011) were those who use p-spline with Bayesian approach. Wang (2011) used a smoothing spline in semiparametric regression model whose parametric components are linear patterned with Bayesian approach.…”

Section: That Comparesmentioning

confidence: 99%

Smoothing Spline in Semiparametric Additive Regression Model With Bayesian Approach

Diana¹,

Budiantara²,

Purhadi³

et al. 2013

Journal of Mathematics and Statistics

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Semiparametric additive regression model is a combination of parametric and nonparametric regression models. The parametric components are not linear but following a polynomial pattern, while the nonparametric components are unknown pattern and assumed to be contained in the Sobolev space. The nonparametric components can be approximated by smoothing spline functions. In the development of smoothing spline, the classical statistical approach cannot be applied for solving the inference problem such as constructing confidence intervals for the regression curve. To construct confidence interval of smoothing spline curve in the semiparametric additive regression model, we propose to use Bayesian approach, by assuming improper Gaussian distribution for prior distribution in nonparametric components and multivariate normal distribution for parametric components. In this study, we obtain parameter estimators for parametric component and smoothing spline estimators for the nonparametric component in semiparametric additive regression model. Moreover, we also develop a smoothing parameters selection method simultaneously using Generalized Maximum Likelihood (GML) and confidence intervals for the parameters of the parametric component and the smoothing spline functions of the nonparametric component using Bayesian approach. By computing each posterior mean and posterior variance of parametric component parameters and smoothing spline functions, confidence intervals can be constructed for the parametric component parameters and confidence interval smoothing spline functions for nonparametric components in semiparametric additive regression models. We create R-code to implement estimation model and inference procedure. Our simulation studies reveal estimation and inference method perform reasonably well.

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Bayesian Nonparametric Regression Analysis of Data with Random Effects Covariates from Longitudinal Measurements

Cited by 13 publications

References 34 publications

Variational methods for fitting complex Bayesian mixed effects models to health data

Variational methods for fitting complex Bayesian mixed effects models to health data

Bayesian Framework for Parametric Bivariate Accelerated Lifetime Modeling and Its Application to Hospital Acquired Infections

Smoothing Spline in Semiparametric Additive Regression Model With Bayesian Approach

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