Modeling Concordance Correlation Coefficient for Longitudinal Study Data

et al. 2013

Psychometrika

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Mediation analysis constitutes an important part of treatment study to identify the mechanisms by which an intervention achieves its effect. Structural equation model (SEM) is a popular framework for modeling such causal relationship. However, current methods impose various restrictions on the study designs and data distributions, limiting the utility of the information they provide in real study applications. In particular, in longitudinal studies missing data is commonly addressed under the assumption of missing at random (MAR), where current methods are unable to handle such missing data if parametric assumptions are violated. In this paper, we propose a new, robust approach to address the limitations of current SEM within the context of longitudinal mediation analysis by utilizing a class of functional response models (FRM). Being distribution-free, the FRM-based approach does not impose any parametric assumption on data distributions. In addition, by extending the inverse probability weighted (IPW) estimates to the current context, the FRM-based SEM provides valid inference for longitudinal mediation analysis under the two most popular missing data mechanisms; missing completely at random (MCAR) and missing at random (MAR). We illustrate the approach with both real and simulated data.

Section: Functional Response Modelsmentioning

confidence: 99%

A Class of Distribution-Free Models for Longitudinal Mediation Analysis

Gunzler

et al. 2013

Psychometrika

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“…For example, by setting q = 1, we immediately obtain from (8) the class of distribution-free GLMs for longitudinal data with m assessments. With FRM, we can express a broader class of problems under a regression-like framework(25; 36; 37; 38; 39; 40). Below, we focus on the application of FRM within our setting for modeling count responses.…”

Section: Functional Response Models For Count Responsementioning

confidence: 99%

Distribution‐free models for longitudinal count responses with overdispersion and structural zeros

Chen

et al. 2012

Statistics in Medicine

Summary Overdispersion and structural zeros are two major manifestations of departure from the Poisson assumption when modeling count responses using Poisson loglinear regression. As noted in a large body of literature, ignoring such departures could yield bias and lead to wrong conclusions. Different approaches have been developed to tackle these two major problems. In this paper, we review available methods for dealing with overdispersion and structural zeros within a longitudinal data setting and propose a distribution-free modeling approach to address the limitations of these methods by utilizing a new class of functional response models (FRM). We illustrate our approach with both simulated and real study data.

“…Given an estimate \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\widehat{\boldsymbol{\theta}}$\end{document} of θ , we can estimate ρ CCC by \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\widehat{\boldsymbol{\rho}}_{\mathrm{CCC}}=\boldsymbol{\phi}( \widehat{\boldsymbol{\theta}}) $\end{document} and compute the asymptotic distribution of \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\widehat{\boldsymbol{\rho }}_{\mathrm{CCC}}$\end{document} using the Delta method. Within our context, we used Fieller's method to further improve the approximation to the asymptotic distribution of the ratio statistics \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\widehat{\boldsymbol{\rho}}_{\mathrm{CCC}}$\end{document} by the Delta method 25,26…”

Section: Real Study Applicationsmentioning

confidence: 99%

“…(26), and the asymptotic variance Σ of \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\widehat{\boldsymbol{\theta}}$\end{document} using Eq. (27) 26…”

Section: Real Study Applicationsmentioning

confidence: 99%

Multivariate U‐statistics: a tutorial with applications

WIREs Computational Stats

Kowalski³

et al. 2011

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U‐statistics represent an important class of statistics arising from modeling quantities of interest defined by multi‐subject responses such as the classic Mann–Whitney–Wilcoxon rank tests. However, classic applications of U‐statistics are largely limited to univariate outcomes within a cross‐sectional data setting. As longitudinal study designs become increasingly popular in today's research, it is imperative to generalize the classic theory of U‐statistics to such a study setting to meet the challenges of modern clinical and translational research. In this article, we focus on applications of U‐statistics to longitudinal study data. We first give a brief overview of U‐statistics and then discuss how to apply this powerful class of statistics to model quantities of interest with a longitudinal data setting. In addition to generalizing U‐statistics and associated inference theory to longitudinal data analysis, we also discuss a class of function response models (FRM) to bring the power of U‐statistics to uncharted territory. We illustrate applications of generalized U‐statistics and FRM with data from some real longitudinal studies. WIREs Comp Stat 2011 3 457–471 DOI: 10.1002/wics.178 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis