Fast Covariance Estimation for Multivariate Sparse Functional Data

Dynamic prediction of survival using multivariate functional principal component analysis: A strict landmarking approach

Dynamically predicting patient survival probabilities using longitudinal measurements has become of great importance with routine data collection becoming more common. Many existing models utilize a multi-step landmarking approach for this problem, mostly due to its ease of use and versatility but unfortunately most fail to do so appropriately. In this article we make use of multivariate functional principal component analysis to summarize the available longitudinal information, and employ a Cox proportional hazards model for prediction. Additionally, we consider a centred functional principal component analysis procedure in an attempt to remove the natural variation incurred by the difference in age of the considered subjects. We formalize the difference between a 'relaxed' landmarking approach where only validation data is landmarked and a 'strict' landmarking approach where both the training and validation data are landmarked. We show that a relaxed landmarking approach fails to effectively use the information contained in the longitudinal outcomes, thereby producing substantially worse prediction accuracy than a strict landmarking approach.

Latent factor model for multivariate functional data

For multivariate functional data, a functional latent factor model is proposed, extending the traditional latent factor model for multivariate data. The proposed model uses unobserved stochastic processes to induce the dependence among the different functions, and thus, for a large number of functions, may provide a more parsimonious and interpretable characterization of the otherwise complex dependencies between the functions. Sufficient conditions are provided to establish the identifiability of the proposed model. The performance of the proposed model is assessed through simulation studies and an application to electroencephalography data.

Accurate prediction of HCC risk after SVR in patients with hepatitis C cirrhosis based on longitudinal data

BACKGROUND

Most existing predictive models of hepatocellular carcinoma (HCC) risk after sustained virologic response (SVR) are built on data collected at baseline and therefore have limited accuracy. The current study aimed to construct an accurate predictive model incorporating longitudinal data using a novel modeling strategy. The predictive performance of the longitudinal model was also compared with a baseline model.

METHODS

A total of 400 patients with HCV-related cirrhosis who achieved SVR with direct-acting antivirals (DAA) were enrolled in the study. Patients were randomly divided into a training set (70%) and a validation set (30%). Informative features were extracted from the longitudinal variables and then put into the random survival forest (RSF) to develop the longitudinal model. A baseline model including the same variables was built for comparison.

RESULTS

During a median follow-up time of approximately 5 years, 25 patients (8.9%) in the training set and 11 patients (9.2%) in the validation set developed HCC. The areas under the receiver-operating characteristics curves (AUROC) for the longitudinal model were 0.9507 (0.8838-0.9997), 0.8767 (0.6972,0.9918), and 0.8307 (0.6941,0.9993) for 1-, 2- and 3-year risk prediction, respectively. The brier scores of the longitudinal model were also relatively low for the 1-, 2- and 3-year risk prediction (0.0283, 0.0561, and 0.0501, respectively). In contrast, the baseline model only achieved mediocre AUROCs of around 0.6 (0.6113, 0.6213, and 0.6480, respectively).

CONCLUSIONS

Our longitudinal model yielded accurate predictions of HCC risk in patients with HCV-relate cirrhosis, outperforming the baseline model. Our model can provide patients with valuable prognosis information and guide the intensity of surveillance in clinical practice.

Modeling longitudinal data using matrix completion

In clinical practice and biomedical research, measurements are often collected sparsely and irregularly in time, while the data acquisition is expensive and inconvenient. Examples include measurements of spine bone mineral density, cancer growth through mammography or biopsy, a progression of defective vision, or assessment of gait in patients with neurological disorders. Practitioners often need to infer the progression of diseases from such sparse observations. A classical tool for analyzing such data is a mixed-effect model where time is treated as both a fixed effect (population progression curve) and a random effect (individual variability). Alternatively, researchers use Gaussian processes or functional data analysis, assuming that observations are drawn from a certain distribution of processes. While these models are flexible, they rely on probabilistic assumptions, require very careful implementation, and tend to be slow in practice. In this study, we propose an alternative elementary framework for analyzing longitudinal data motivated by matrix completion. Our method yields estimates of progression curves by iterative application of the Singular Value Decomposition. Our framework covers multivariate longitudinal data, and regression and can be easily extended to other settings. As it relies on existing tools for matrix algebra, it is efficient and easy to implement. We apply our methods to understand trends of progression of motor impairment in children with Cerebral Palsy. Our model approximates individual progression curves and explains 30% of the variability. Low-rank representation of progression trends enables identification of different progression trends in subtypes of Cerebral Palsy.

BAYESIAN INFERENCE AND DYNAMIC PREDICTION FOR MULTIVARIATE LONGITUDINAL AND SURVIVAL DATA

Alzheimer's disease (AD) is a complex neurological disorder impairing multiple domains such as cognition and daily functions. To better understand the disease and its progression, many AD research studies collect multiple longitudinal outcomes that are strongly predictive of the onset of AD dementia. We propose a joint model based on a multivariate functional mixed model framework (referred to as MFMM-JM) that simultaneously models the multiple longitudinal outcomes and the time to dementia onset. We develop six functional forms to fully investigate the complex association between longitudinal outcomes and dementia onset. Moreover, we use the Bayesian methods for statistical inference and develop a dynamic prediction framework that provides accurate personalized predictions of disease progressions based on new subject-specific data. We apply the proposed MFMM-JM to two large ongoing AD studies: the Alzheimer's Disease Neuroimaging Initiative (ADNI) and National Alzheimer's Coordinating Center (NACC), and identify the functional forms with the best predictive performance. our method is also validated by extensive simulation studies with five settings.

Multivariate functional mixed model with MRI data: An application to Alzheimer's disease

Alzheimer's Disease (AD) is the leading cause of dementia and impairment in various domains. Recent AD studies, (ie, Alzheimer's Disease Neuroimaging Initiative (ADNI) study), collect multimodal data, including longitudinal neurological assessments and magnetic resonance imaging (MRI) data, to better study the disease progression. Adopting early interventions is essential to slow AD progression for subjects with mild cognitive impairment (MCI). It is of particular interest to develop an AD predictive model that leverages multimodal data and provides accurate personalized predictions. In this article, we propose a multivariate functional mixed model with MRI data (MFMM-MRI) that simultaneously models longitudinal neurological assessments, baseline MRI data, and the survival outcome (ie, dementia onset) for subjects with MCI at baseline. Two functional forms (the random-effects model and instantaneous model) linking the longitudinal and survival process are investigated. We use Markov Chain Monte Carlo (MCMC) method based on No-U-Turn Sampling (NUTS) algorithm to obtain posterior samples. We develop a dynamic prediction framework that provides accurate personalized predictions of longitudinal trajectories and survival probability. We apply MFMM-MRI to the ADNI study and identify significant associations among longitudinal outcomes, MRI data, and the risk of dementia onset. The instantaneous model with voxels from the whole brain has the best prediction performance among all candidate models. The simulation study supports the validity of the estimation and dynamic prediction method.

A patient-centric modeling framework captures recovery from SARS-CoV-2 infection

The biology driving individual patient responses to severe acute respiratory syndrome coronavirus 2 infection remains ill understood. Here, we developed a patient-centric framework leveraging detailed longitudinal phenotyping data and covering a year after disease onset, from 215 infected individuals with differing disease severities. Our analyses revealed distinct 'systemic recovery' profiles, with specific progression and resolution of the inflammatory, immune cell, metabolic and clinical responses. In particular, we found a strong inter-patient and intra-patient temporal covariation of innate immune cell numbers, kynurenine metabolites and lipid metabolites, which highlighted candidate immunologic and metabolic pathways influencing the restoration of homeostasis, the risk of death and that of long COVID. Based on these data, we identified a composite signature predictive of systemic recovery, using a joint model on cellular and molecular parameters measured soon after disease onset. New predictions can be generated using the online tool http://shiny.mrc-bsu.cam.ac.uk/apps/covid-19-systemic-recovery-prediction-app , designed to test our findings prospectively.

Joint model for survival and multivariate sparse functional data with application to a study of Alzheimer's Disease

Studies of Alzheimer's disease (AD) often collect multiple longitudinal clinical outcomes, which are correlated and predictive of AD progression. It is of great scientific interest to investigate the association between the outcomes and time to AD onset. We model the multiple longitudinal outcomes as multivariate sparse functional data and propose a functional joint model linking multivariate functional data to event time data. In particular, we propose a multivariate functional mixed model to identify the shared progression pattern and outcome-specific progression patterns of the outcomes, which enables more interpretable modeling of associations between outcomes and AD onset. The proposed method is applied to the Alzheimer's Disease Neuroimaging Initiative study (ADNI) and the functional joint model sheds new light on inference of five longitudinal outcomes and their associations with AD onset. Simulation studies also confirm the validity of the proposed model. Data used in preparation of this article were obtained from the ADNI database.

Multivariate functional additive mixed models

Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary such as precipitation, temperature and wind speeds over time at a given weather station. We propose a multivariate functional additive mixed model (multiFAMM) and show its application to both data situations using examples from sports science (movement trajectories of snooker players) and phonetic science (acoustic signals and articulation of consonants). The approach includes linear and nonlinear covariate effects and models the dependency structure between the dimensions of the responses using multivariate functional principal component analysis. Multivariate functional random intercepts capture both the auto-correlation within a given function and cross-correlations between the multivariate functional dimensions. They also allow us to model between-function correlations as induced by, for example, repeated measurements or crossed study designs. Modelling the dependency structure between the dimensions can generate additional insight into the properties of the multivariate functional process, improves the estimation of random effects, and yields corrected confidence bands for covariate effects. Extensive simulation studies indicate that a multivariate modelling approach is more parsimonious than fitting independent univariate models to the data while maintaining or improving model fit.

Dynamic prediction using joint models of longitudinal and recurrent event data: A Bayesian perspective

In cardiovascular disease (CVD) studies, the events of interest may be recurrent (multiple occurrences from the same individual). During the study follow-up, longitudinal measurements are often available and these measurements are highly predictive of event recurrences. It is of great clinical interest to make personalized prediction of the next occurrence of recurrent events using the available clinical information, because it enables clinicians to make more informed and personalized decisions and recommendations. To this end, we propose a joint model of longitudinal and recurrent event data. We develop a Bayesian approach for model inference and a dynamic prediction framework for predicting target subjects' future outcome trajectories and risk of next recurrent event, based on their data up to the prediction time point. To improve computation efficiency, embarrassingly parallel MCMC (EP-MCMC) method is utilized. It partitions the data into multiple subsets, runs MCMC sampler on each subset, and applies random partition trees to combine the posterior draws from all subsets. Our method development is motivated by and applied to the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT), one of the largest CVD studies to compare the effectiveness of medications to treat hypertension.