A joint model for multivariate longitudinal and survival data to discover the conversion to Alzheimer's disease

Fast and flexible inference for joint models of multivariate longitudinal and survival data using integrated nested Laplace approximations

Modeling longitudinal and survival data jointly offers many advantages such as addressing measurement error and missing data in the longitudinal processes, understanding and quantifying the association between the longitudinal markers and the survival events, and predicting the risk of events based on the longitudinal markers. A joint model involves multiple submodels (one for each longitudinal/survival outcome) usually linked together through correlated or shared random effects. Their estimation is computationally expensive (particularly due to a multidimensional integration of the likelihood over the random effects distribution) so that inference methods become rapidly intractable, and restricts applications of joint models to a small number of longitudinal markers and/or random effects. We introduce a Bayesian approximation based on the integrated nested Laplace approximation algorithm implemented in the R package R-INLA to alleviate the computational burden and allow the estimation of multivariate joint models with fewer restrictions. Our simulation studies show that R-INLA substantially reduces the computation time and the variability of the parameter estimates compared with alternative estimation strategies. We further apply the methodology to analyze five longitudinal markers (3 continuous, 1 count, 1 binary, and 16 random effects) and competing risks of death and transplantation in a clinical trial on primary biliary cholangitis. R-INLA provides a fast and reliable inference technique for applying joint models to the complex multivariate data encountered in health research.

Multiparametric Quantitative Imaging Biomarker as a Multivariate Descriptor of Health: A Roadmap

Multiparametric quantitative imaging biomarkers (QIBs) offer distinct advantages over single, univariate descriptors because they provide a more complete measure of complex, multidimensional biological systems. In disease, where structural and functional disturbances occur across a multitude of subsystems, multivariate QIBs are needed to measure the extent of system malfunction. This paper, the first Use Case in a series of articles on multiparameter imaging biomarkers, considers multiple QIBs as a multidimensional vector to represent all relevant disease constructs more completely. The approach proposed offers several advantages over QIBs as multiple endpoints and avoids combining them into a single composite that obscures the medical meaning of the individual measurements. We focus on establishing statistically rigorous methods to create a single, simultaneous measure from multiple QIBs that preserves the sensitivity of each univariate QIB while incorporating the correlation among QIBs. Details are provided for metrological methods to quantify the technical performance. Methods to reduce the set of QIBs, test the superiority of the mp-QIB model to any univariate QIB model, and design study strategies for generating precision and validity claims are also provided. QIBs of Alzheimer's Disease from the ADNI merge data set are used as a case study to illustrate the methods described.

Multivariate analysis in data science for the geospatial distribution of the breast cancer mortality rate in Colombia

This research is framed in the area of biomathematics and contributes to the epidemiological surveillance entities in Colombia to clarify how breast cancer mortality rate (BCM) is spatially distributed in relation to the forest area index (FA) and circulating vehicle index (CV). In this regard, the World Health Organization has highlighted the scarce generation of knowledge that relates mortality from tumor diseases to environmental factors. Quantitative methods based on geospatial data science are used with cross-sectional information from the 2018 census; it's found that the BCM in Colombia is not spatially randomly distributed, but follows cluster aggregation patterns. Under multivariate modeling methods, the research provides sufficient statistical evidence in terms of not rejecting the hypothesis that if a spatial unit has high FA and low CV, then it has significant advantages in terms of lower BCM.

Joint analysis of multivariate failure time data with latent variables

We propose a joint modeling approach to investigate the observed and latent risk factors of the multivariate failure times of interest. The proposed model comprises two parts. The first part is a distribution-free confirmatory factor analysis model that characterizes the latent factors by correlated multiple observed variables. The second part is a multivariate additive hazards model that assesses the observed and latent risk factors of the failure times. A hybrid procedure that combines the borrow-strength estimation approach and the asymptotically distribution-free generalized least square method is developed to estimate the model parameters. The asymptotic properties of the proposed estimators are derived. Simulation studies demonstrate that the proposed method performs well for practical settings. An application to a study concerning the risk factors of multiple diabetic complications is provided.