Keunbaik Lee

Flexible marginalized models for bivariate longitudinal ordinal data

Random effects models are commonly used to analyze longitudinal categorical data. Marginalized random effects models are a class of models that permit direct estimation of marginal mean parameters and characterize serial correlation for longitudinal categorical data via random effects (Heagerty, 1999). Marginally specified logistic-normal models for longitudinal binary data. Biometrics 55, 688-698; Lee and Daniels, 2008. Marginalized models for longitudinal ordinal data with application to quality of life studies. Statistics in Medicine 27, 4359-4380). In this paper, we propose a Kronecker product (KP) covariance structure to capture the correlation between processes at a given time and the correlation within a process over time (serial correlation) for bivariate longitudinal ordinal data. For the latter, we consider a more general class of models than standard (first-order) autoregressive correlation models, by re-parameterizing the correlation matrix using partial autocorrelations (Daniels and Pourahmadi, 2009). Modeling covariance matrices via partial autocorrelations. Journal of Multivariate Analysis 100, 2352-2363). We assess the reasonableness of the KP structure with a score test. A maximum marginal likelihood estimation method is proposed utilizing a quasi-Newton algorithm with quasi-Monte Carlo integration of the random effects. We examine the effects of demographic factors on metabolic syndrome and C-reactive protein using the proposed models.

Modeling the random effects covariance matrix for generalized linear mixed models

Generalized linear mixed models (GLMMs) are commonly used to analyze longitudinal categorical data. In these models, we typically assume that the random effects covariance matrix is constant across the subject and is restricted because of its high dimensionality and its positive definiteness. However, the covariance matrix may differ by measured covariates in many situations, and ignoring this heterogeneity can result in biased estimates of the fixed effects. In this paper, we propose a heterogenous random effects covariance matrix, which depends on covariates, obtained using the modified Cholesky decomposition. This decomposition results in parameters that can be easily modeled without concern that the resulting estimator will not be positive definite. The parameters have a sensible interpretation. We analyze metabolic syndrome data from a Korean Genomic Epidemiology Study using our proposed model.

Bayesian Cholesky factor models in random effects covariance matrix for generalized linear mixed models

Random effects in generalized linear mixed models (GLMM) are used to explain the serial correlation of the longitudinal categorical data. Because the covariance matrix is high dimensional and should be positive definite, its structure is assumed to be constant over subjects and to be restricted such as AR(1) structure. However, these assumptions are too strong and can result in biased estimates of the fixed effects. In this paper we propose a Bayesian modeling for the GLMM with regression models for parameters of the random effects covariance matrix using a moving average Cholesky decomposition which factors the covariance matrix into moving average (MA) parameters and IVs. We analyze lung cancer data using our proposed model.

Bayesian Modeling of Random Effects Covariance Matrix for Generalized Linear Mixed Models

Generalized linear mixed models(GLMMs) are frequently used for the analysis of longitudinal categorical data when the subject-specific effects is of interest. In GLMMs, the structure of the random effects covariance matrix is important for the estimation of fixed effects and to explain subject and time variations. The estimation of the matrix is not simple because of the high dimension and the positive definiteness; subsequently, we practically use the simple structure of the covariance matrix such as AR(1). However, this strong assumption can result in biased estimates of the fixed effects. In this paper, we introduce Bayesian modeling approaches for the random effects covariance matrix using a modified Cholesky decomposition. The modified Cholesky decomposition approach has been used to explain a heterogenous random effects covariance matrix and the subsequent estimated covariance matrix will be positive definite. We analyze metabolic syndrome data from a Korean Genomic Epidemiology Study using these methods.

Autoregressive Cholesky Factor Modeling for Marginalized Random Effects Models

Marginalized random effects models (MREM) are commonly used to analyze longitudinal categorical data when the population-averaged effects is of interest. In these models, random effects are used to explain both subject and time variations. The estimation of the random effects covariance matrix is not simple in MREM because of the high dimension and the positive definiteness. A relatively simple structure for the correlation is assumed such as a homogeneous AR(1) structure; however, it is too strong of an assumption. In consequence, the estimates of the fixed effects can be biased. To avoid this problem, we introduce one approach to explain a heterogenous random effects covariance matrix using a modified Cholesky decomposition. The approach results in parameters that can be easily modeled without concern that the resulting estimator will not be positive definite. The interpretation of the parameters is sensible. We analyze metabolic syndrome data from a Korean Genomic Epidemiology Study using this method.

ARMA Cholesky factor models for the covariance matrix of linear models

In longitudinal studies, serial dependence of repeated outcomes must be taken into account to make correct inferences on covariate effects. As such, care must be taken in modeling the covariance matrix. However, estimation of the covariance matrix is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcomes these limitations, two Cholesky decomposition approaches have been proposed: modified Cholesky decomposition for autoregressive (AR) structure and moving average Cholesky decomposition for moving average (MA) structure, respectively. However, the correlations of repeated outcomes are often not captured parsimoniously using either approach separately. In this paper, we propose a class of flexible, nonstationary, heteroscedastic models that exploits the structure allowed by combining the AR and MA modeling of the covariance matrix that we denote as ARMACD. We analyze a recent lung cancer study to illustrate the power of our proposed methods.

Bayesian Pattern Mixture Model for Longitudinal Binary Data with Nonignorable Missingness

In longitudinal studies missing data are common and require a complicated analysis. There are two popular modeling frameworks, pattern mixture model (PMM) and selection models (SM) to analyze the missing data. We focus on the PMM and we also propose Bayesian pattern mixture models using generalized linear mixed models (GLMMs) for longitudinal binary data. Sensitivity analysis is used under the missing not at random assumption.

Marginalized transition shared random effects models for longitudinal binary data with nonignorable dropout

In longitudinal studies investigators frequently have to assess and address potential biases introduced by missing data. New methods are proposed for modeling longitudinal categorical data with nonignorable dropout using marginalized transition models and shared random effects models. Random effects are introduced for both serial dependence of outcomes and nonignorable missingness. Fisher-scoring and Quasi-Newton algorithms are developed for parameter estimation. Methods are illustrated with a real dataset.

Dimension test approach of heteroscedasticity in the linear model

ABSTRACT Heteroscedasticity testing has a long history and is still an important matter in the linear model. There exist many types of tests, but they are limited in use to their own specific cases and sensitive to normality. Here, we propose a dimension test approach to heteroscedasticity. The proposed test overcomes the shortcomings of the existing methods, so that it is robust to normality and is unified in sense that it is applicable in the linear model with multi-dimensional response. Numerical studies confirm that the proposed test is favorable over the existing tests with moderate sample sizes, and real data analysis is presented.

Analysis of long series of longitudinal ordinal data using marginalized models

Marginalized models (Heagerty, 1999, 2002) are often used for short longitudinal series when population averaged effects are of interest. Lee and Daniels (2007, 2008) proposed marginalized models for the analysis of longitudinal ordinal data to permit likelihood-based estimation of marginal mean parameters. In this paper, we extend their work to accommodate the response dependence that we have seen with long series of response data (the functional form of response dependence has both serial and long-range components). Maximum likelihood estimation is proposed utilizing the Quasi-Newton algorithm with a Quasi Monte Carlo method for integration of the random effects. The methods are illustrated on quality of life data from a recent lung cancer clinical trial.