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Choi J, Cai J, Zeng D, et al. Joint Analysis of Survival Time and Longitudinal Categorical Outcomes. Stat Biosci. 2015;7(1):19-47doi: 10.1007/s12561-013-9091-z.
Choi, J., Cai, J., Zeng, D., & Olshan, A. F. (2015). Joint Analysis of Survival Time and Longitudinal Categorical Outcomes. Statistics in biosciences, 7(1), 19-47. https://doi.org/10.1007/s12561-013-9091-z
Choi, Jaeun, et al. "Joint Analysis of Survival Time and Longitudinal Categorical Outcomes." Statistics in biosciences vol. 7,1 (2015): 19-47. doi: https://doi.org/10.1007/s12561-013-9091-z
Choi J, Cai J, Zeng D, Olshan AF. Joint Analysis of Survival Time and Longitudinal Categorical Outcomes. Stat Biosci. 2015 May;7(1):19-47. doi: 10.1007/s12561-013-9091-z. PMID: 26052353; PMCID: PMC4454429.
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Stat Biosci. 2015 May;7(1):19-47. doi: 10.1007/s12561-013-9091-z.

Joint Analysis of Survival Time and Longitudinal Categorical Outcomes.

Statistics in biosciences

Jaeun Choi, Jianwen Cai, Donglin Zeng, Andrew F Olshan

Affiliations

  1. Department of Health Care Policy, Harvard Medical School 180 Longwood Avenue, Boston, MA 02115, USA Tel.: +617-432-0183, [email protected].
  2. Department of Biostatistics, University of North Carolina at Chapel Hill McGavran-Greenberg Hl, 135 Dauer Drive, CB 7420, Chapel Hill, NC 27599, USA [email protected].
  3. Department of Biostatistics, University of North Carolina at Chapel Hill McGavran-Greenberg Hl, 135 Dauer Drive, CB 7420, Chapel Hill, NC 27599, USA [email protected].
  4. Department of Epidemiology, University of North Carolina at Chapel Hill McGavran-Greenberg Hl, 135 Dauer Drive, CB 7435, Chapel Hill, NC 27599, USA [email protected].

PMID: 26052353 PMCID: PMC4454429 DOI: 10.1007/s12561-013-9091-z

Abstract

In biomedical or public health research, it is common for both survival time and longitudinal categorical outcomes to be collected for a subject, along with the subject's characteristics or risk factors. Investigators are often interested in finding important variables for predicting both survival time and longitudinal outcomes which could be correlated within the same subject. Existing approaches for such joint analyses deal with continuous longitudinal outcomes. New statistical methods need to be developed for categorical longitudinal outcomes. We propose to simultaneously model the survival time with a stratified Cox proportional hazards model and the longitudinal categorical outcomes with a generalized linear mixed model. Random effects are introduced to account for the dependence between survival time and longitudinal outcomes due to unobserved factors. The Expectation-Maximization (EM) algorithm is used to derive the point estimates for the model parameters, and the observed information matrix is adopted to estimate their asymptotic variances. Asymptotic properties for our proposed maximum likelihood estimators are established using the theory of empirical processes. The method is demonstrated to perform well in finite samples via simulation studies. We illustrate our approach with data from the Carolina Head and Neck Cancer Study (CHANCE) and compare the results based on our simultaneous analysis and the separately conducted analyses using the generalized linear mixed model and the Cox proportional hazards model. Our proposed method identifies more predictors than by separate analyses.

Keywords: EM algorithm; Generalized linear mixed model; Maximum likelihood estimator; Random effect; Simultaneous modeling; Stratified Cox proportional hazards model

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