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Modeling the Cholesky factors of covariance matrices of multivariate longitudinal data.

ABSTRACT: Modeling the covariance matrix of multivariate longitudinal data is more challenging as compared to its univariate counterpart due to the presence of correlations among multiple responses. The modified Cholesky block decomposition reduces the task of covariance modeling into parsimonious modeling of its two matrix factors: the regression coefficient matrices and the innovation covariance matrices. These parameters are statistically interpretable, however ensuring positive-definiteness of several (innovation) covariance matrices presents itself as a new challenge. We address this problem using a subclass of Anderson's (1973) linear covariance models and model several covariance matrices using linear combinations of known positive-definite basis matrices with unknown non-negative scalar coefficients. A novelty of this approach is that positive-definiteness is guaranteed by construction; it removes a drawback of Anderson's model and hence makes linear covariance models more realistic and viable in practice. Maximum likelihood estimates are computed using a simple iterative majorization-minimization algorithm. The estimators are shown to be asymptotically normal and consistent. Simulation and a data example illustrate the applicability of the proposed method in providing good models for the covariance structure of a multivariate longitudinal data.

SUBMITTER: Kohli P

PROVIDER: S-EPMC11238179 | biostudies-literature | 2016 Mar

REPOSITORIES: biostudies-literature

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Modeling the Cholesky factors of covariance matrices of multivariate longitudinal data.

Kohli Priya P Garcia Tanya P TP Pourahmadi Mohsen M

Journal of multivariate analysis 20151214

Modeling the covariance matrix of multivariate longitudinal data is more challenging as compared to its univariate counterpart due to the presence of correlations among multiple responses. The modified Cholesky <i>block</i> decomposition reduces the task of covariance modeling into parsimonious modeling of its two matrix factors: the regression coefficient matrices and the innovation covariance matrices. These parameters are statistically interpretable, however ensuring positive-definiteness of ...[more]

PMID: 38993393

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Project description:BackgroundJoint modeling is appropriate when one wants to predict the time to an event with covariates that are measured longitudinally and are related to the event. An underlying random effects structure links the survival and longitudinal submodels and allows for individual-specific predictions. Multiple time-varying and time-invariant covariates can be included to potentially increase prediction accuracy. The goal of this study was to estimate a multivariate joint model on several longitudinal observational studies of Huntington's disease, examine external validity performance, and compute individual-specific predictions for characterizing disease progression. Emphasis was on the survival submodel for predicting the hazard of motor diagnosis.MethodsData from four observational studies was analyzed: Enroll-HD, PREDICT-HD, REGISTRY, and Track-HD. A Bayesian approach to estimation was adopted, and external validation was performed using a time-varying AUC measure. Individual-specific cumulative hazard predictions were computed based on a simulation approach. The cumulative hazard was used for computing predicted age of motor onset and also for a deviance residual indicating the discrepancy between observed diagnosis status and model-based status.ResultsThe joint model trained in a single study had very good performance in discriminating among diagnosed and pre-diagnosed participants in the remaining test studies, with the 5-year mean AUC = .83 (range .77-.90), and the 10-year mean AUC = .86 (range .82-.92). Graphical analysis of the predicted age of motor diagnosis showed an expected strong relationship with the trinucleotide expansion that causes Huntington's disease. Graphical analysis of the deviance-type residual revealed there were individuals who converted to a diagnosis despite having relatively low model-based risk, others who had not yet converted despite having relatively high risk, and the majority falling between the two extremes.ConclusionsJoint modeling is an improvement over traditional survival modeling because it considers all the longitudinal observations of covariates that are predictive of an event. Predictions from joint models can have greater accuracy because they are tailored to account for individual variability. These predictions can provide relatively accurate characterizations of individual disease progression, which might be important in the timing of interventions, determining the qualification for appropriate clinical trials, and general genotypic analysis.

Dataset Information

Modeling the Cholesky factors of covariance matrices of multivariate longitudinal data.

Publications

Modeling the Cholesky factors of covariance matrices of multivariate longitudinal data.

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