Joint modeling of longitudinal continuous, longitudinal ordinal, and time-to-event outcomes
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Joint modeling of longitudinal continuous, longitudinal ordinal, and time-to-event outcomes Khurshid Alam1 · Arnab Maity2 · Sanjoy K. Sinha3 · Dimitris Rizopoulos4 · Abdus Sattar1 Received: 28 October 2019 / Accepted: 7 November 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we propose an innovative method for jointly analyzing survival data and longitudinally measured continuous and ordinal data. We use a random effects accelerated failure time model for survival outcomes, a linear mixed model for continuous longitudinal outcomes and a proportional odds mixed model for ordinal longitudinal outcomes, where these outcome processes are linked through a set of association parameters. A primary objective of this study is to examine the effects of association parameters on the estimators of joint models. The model parameters are estimated by the method of maximum likelihood. The finite-sample properties of the estimators are studied using Monte Carlo simulations. The empirical study suggests that the degree of association among the outcome processes influences the bias, efficiency, and coverage probability of the estimators. Our proposed joint model estimators are approximately unbiased and produce smaller mean squared errors as compared to the estimators obtained from separate models. This work is motivated by a large multicenter study, referred to as the Genetic and Inflammatory Markers of Sepsis (GenIMS) study. We apply our proposed method to the GenIMS data analysis. Keywords Joint models · Association parameters · Frailty model · Linear mixed model · Proportional odds model
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Abdus Sattar [email protected]
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Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH 44106, USA
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Department of Statistics, NC State University, 2311 Stinson Drive, Raleigh, NC 27695, USA
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School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6, Canada
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Department of Biostatistics, Erasmus University Medical Center, Rotterdam, The Netherlands
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K. Alam et al.
1 Introduction Joint modeling of multiple outcomes is an active area of biostatistical research. It is common to find joint models for analyzing two outcomes by addressing a wide range of complex issues (Sattar and Sinha 2017; Rizopoulos et al. 2008; Rizopoulos 2011; Li et al. 2010). Joint modeling of similar multivariate longitudinal outcomes and survival outcomes is also available in the literature (Diggle et al. 2009; Kim and Albert 2016; Li and Luo 2019; Rizopoulos 2011; Hughes et al. 2017). However, less work has been done in the context of joint models for three or more heterogeneous outcomes. In fact, using listed keywords, the Scopus search engine resulted only one article (Ivanova et al. 2016). Using two case studies (examples), Ivanova et al. (2016) presented joint models for binary and ordinal longitudinal data. The two discrete outcomes were linked via random effects, and parameters of the joint models were estimated by the method of maximum likelihood. Li et al. (2010) devel
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