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1.  Flexible marginalized models for bivariate longitudinal ordinal data 
Biostatistics (Oxford, England)  2013;14(3):462-476.
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.
doi:10.1093/biostatistics/kxs058
PMCID: PMC3677737  PMID: 23365416
Kronecker product; Metabolic syndrome; Partial autocorrelation
2.  CAUSAL EFFECTS OF TREATMENTS FOR INFORMATIVE MISSING DATA DUE TO PROGRESSION/DEATH 
SUMMARY
In longitudinal clinical trials, when outcome variables at later time points are only defined for patients who survive to those times, the evaluation of the causal effect of treatment is complicated. In this paper, we describe an approach that can be used to obtain the causal effect of three treatment arms with ordinal outcomes in the presence of death using a principal stratification approach. We introduce a set of flexible assumptions to identify the causal effect and implement a sensitivity analysis for non-identifiable assumptions which we parameterize parsimoniously. Methods are illustrated on quality of life data from a recent colorectal cancer clinical trial.
doi:10.1198/jasa.2010.ap08739.
PMCID: PMC3035160  PMID: 21318119
Principal stratification; QOL; Ordinal data; Sensitivity analysis
3.  Marginalized models for longitudinal ordinal data with application to quality of life studies 
Statistics in medicine  2008;27(21):4359-4380.
SUMMARY
Random effects are often used in generalized linear models to explain the serial dependence for longitudinal categorical data. Marginalized random effects models (MREMs) for the analysis of longitudinal binary data have been proposed to permit likelihood-based estimation of marginal regression parameters. In this paper, we introduce an extension of the MREM to accommodate longitudinal ordinal data. Maximum marginal likelihood estimation is implemented utilizing quasi-Newton algorithms with Monte Carlo integration of the random effects. Our approach is applied to analyze the quality of life data from a recent colorectal cancer clinical trial. Dropout occurs at a high rate and is often due to tumor progression or death. To deal with progression/death, we use a mixture model for the joint distribution of longitudinal measures and progression/death times and principal stratification to draw causal inferences about survivors.
doi:10.1002/sim.3352
PMCID: PMC2858760  PMID: 18613246
marginalized likelihood-based models; ordinal data models; dropout
4.  A Class of Markov Models for Longitudinal Ordinal Data 
Biometrics  2007;63(4):1060-1067.
Summary
Generalized linear models with serial dependence are often used for short longitudinal series. Heagerty (2002, Biometrics 58, 342–351) has proposed marginalized transition models for the analysis of longitudinal binary data. In this article, we extend this work to accommodate longitudinal ordinal data. Fisher-scoring algorithms are developed for estimation. Methods are illustrated on quality-of-life data from a recent colorectal cancer clinical trial.
doi:10.1111/j.1541-0420.2007.00800.x
PMCID: PMC2766273  PMID: 18078479
Fisher scoring; Generalized linear models; QOL

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