[PDF] Bayesian Nonparametric And Semi Parametric Methods For Incomplete Longitudinal Data eBook

Author : Chenguang Wang
Publisher :
Page : pages
File Size : 42,64 MB
Release : 2010
Category :
ISBN :

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In Chapter 4, we discuss pattern mixture models. Pattern mixture modeling is a popular approach for handling incomplete longitudinal data. Such models are not identifiable by construction. Identifying restrictions are one approach to mixture model identification (Daniels and Hogan, 2008; Kenward et al., 2003; Little, 1995; Little and Wang, 1996; Thijs et al., 2002) and are a natural starting point for missing not at random sensitivity analysis (Daniels and Hogan, 2008; Thijs et al., 2002). However, when the pattern specific models are multivariate normal (MVN), identifying restrictions corresponding to missing at random may not exist. Furthermore, identification strategies can be problematic in models with covariates (e.g. baseline covariates with time-invariant coefficients). In this paper, we explore conditions necessary for identifying restrictions that result in missing at random (MAR) to exist under a multivariate normality assumption and strategies for identifying sensitivity parameters for sensitivity analysis or for a fully Bayesian analysis with informative priors. A longitudinal clinical trial is used for illustration of sensitivity analysis. Problems caused by baseline covariates with time-invariant coefficients are investigated and an alternative identifying restriction based on residuals is proposed as a solution.

Author : Michael J. Daniels
Publisher : CRC Press
Page : 324 pages
File Size : 37,9 MB
Release : 2008-03-11
Category : Mathematics
ISBN : 1420011189

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Drawing from the authors' own work and from the most recent developments in the field, Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis describes a comprehensive Bayesian approach for drawing inference from incomplete data in longitudinal studies. To illustrate these methods, the authors employ

Author : Garrett Fitzmaurice
Publisher : CRC Press
Page : 633 pages
File Size : 16,10 MB
Release : 2008-08-11
Category : Mathematics
ISBN : 142001157X

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Although many books currently available describe statistical models and methods for analyzing longitudinal data, they do not highlight connections between various research threads in the statistical literature. Responding to this void, Longitudinal Data Analysis provides a clear, comprehensive, and unified overview of state-of-the-art theory

Author : Yuzhu Yang
Publisher :
Page : 288 pages
File Size : 29,73 MB
Release : 2018
Category :
ISBN :

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This dissertation consists of two studies that introduce and investigate two Bayesian non/semi-parametric estimation methods for latent growth mixture modeling (LGMM). LGMM is a useful statistical tool for modeling latent classes or unobserved subgroups in longitudinal data analysis. One of the major challenges of fitting an LGMM is deciding on the number of latent classes that exist in the population from which data were collected. In this dissertation, I introduce two non/semi-parametric estimation methods, that is Reversible jump Markov chain Monte Carlo (RJMCMC) and Dirichlet process modeling (DP) for LGMM. Specifically, I examined the estimation performance of these two non/semi-parametric methods along with traditional estimation methods, such as maximum likelihood (ML) and the Bayesian estimation framework. I also investigated some commonly discussed topics within the LGMM context, such as class enumeration and the impact of class separation. In particular, Study 1 examines the ability of RJMCMC, DP, and ML to recover the model parameters, especially the number of classes and class sizes via a simulation study. Simulation results showed that RJMCMC and DP performed comparable to ML and even better under some conditions for some parameters. An empirical example is included in Study 1 as an illustration of how to apply RJMCMC and DP; the example uses an education-related data set and covers how to interpret the results. In Study 2, the investigation is focused on the impact of class separation on class enumeration and model parameter recovery. Specifically, different degrees of class separation and several separation conditions were investigated. The performance of RJMCMC, DP and two Bayesian estimation methods with different prior specifications were examined for the LGMM via a simulation study. Results of Study 2 showed that RJMCMC and DP performed comparable to the Bayesian estimators under different degrees of class separation. Findings of the two studies suggested that RJMCMC and DP can be used as alternatives to traditional ML and Bayesian estimation methods in accurately recovering the number of latent classes for LGMM under most conditions. However, there are added benefits to the use of RJMCMC and DP over the other approaches. Other implications, suggestions for applied researchers, limitations, and future directions are also discussed.

Author : Peter Müller
Publisher : Springer
Page : 203 pages
File Size : 38,92 MB
Release : 2015-06-17
Category : Mathematics
ISBN : 3319189689

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This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in online software pages.

Author : Lang Wu
Publisher : CRC Press
Page : 431 pages
File Size : 48,14 MB
Release : 2009-11-11
Category : Mathematics
ISBN : 9781420074086

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Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.