Analysis Of Multivariate Longitudinal Data Research Articles

Joint analysis of multivariate longitudinal, imaging, and time-to-event data

Abstract Alzheimer’s (AD) is a progressive neurodegenerative disease frequently associated with memory deficits and cognitive decline. Despite its irreversible once onset, some discoveries revealed the existence of a certain percentage of people who are non-susceptible to AD. This study proposes a joint analysis of multivariate longitudinal data, survival data with a non-susceptible fraction, and ultrahigh-dimensional imaging data. The proposed model comprises three major components. The first component is a mixture proportional hazards cure model with images to examine the potential predictors of the non-susceptible probability and hazards of interest. The second component is a dynamic factor analysis model with images to characterize group-specific latent factors through multiple observed variables. The last component is a semiparametric trajectory model to reveal the change patterns of the dynamic latent factors in the ‘non-susceptible’ and ‘susceptible’ groups. A two-stage approach is developed for statistical inference. The first stage manages the imaging data through high-dimensional functional principal component analysis. The second stage develops a Bayesian approach coupled with penalized splines, data augmentation, and Markov chain Monte Carlo techniques to perform estimation. The application to the Alzheimer’s Disease Neuroimaging Initiative dataset sheds new insight into the pathology of AD.

Multivariate linear mixed models with censored and nonignorable missing outcomes, with application to AIDS studies.

The analysis of multivariate longitudinal data could encounter some complications due to censorship induced by detection limits of the assay and nonresponse occurring when participants missed scheduled visits intermittently or discontinued participation. This paper establishes a generalization of the multivariate linear mixed model that can accommodate censored responses and nonignorable missing outcomes simultaneously. To account for the nonignorable missingness, the selection approach which decomposes the joint distribution as a marginal distribution for the primary outcome variables and a model describing the missing process conditional on the hypothetical complete data is used. A computationally feasible Monte Carlo expectation conditional maximization algorithm is developed for parameter estimation with the maximum likelihood (ML) method. Furthermore, a general information-based approach is presented to assess the variability of ML estimators. The techniques for the prediction of censored responses and imputation of missing outcomes are also discussed. The methodology is motivated and exemplified by a real dataset concerning HIV-AIDS clinical trials. A simulation study is conducted to examine the performance of the proposed method compared with other traditionalapproaches.

Robust modeling of multivariate longitudinal data using modified Cholesky and hypersphere decompositions

Due to the convenience of the statistical interpretation and parameter estimation, a normal distribution is typically assumed for multivariate longitudinal data analysis. However, this assumption may be questionable in practice, because it is possible that outliers exist or that the underlying data will show heavy tails. In addition, since the covariance matrix should explain complex correlation structures, it must be positive-definite, and as it is also high-dimensional, the modeling of the covariance matrix is not easy. To solve these problems, we propose the robust modeling of multivariate longitudinal data by considering multivariate t distribution, and we exploit modified Cholesky and hypersphere decompositions to model the covariance matrix. The estimation of the models is shown to be robust when the data include outliers and exhibit heavy tails. The performance of our proposed model and algorithm is illustrated using a nonalcoholic fatty liver disease data set and several simulation studies.

Analysis of Multivariate Longitudinal Data with Ordered and Continuous Variables

Analysis of Multivariate Longitudinal Data with Ordered and Continuous Variables

Graphical models for mean and covariance of multivariate longitudinal data.

Joint mean-covariance modeling of multivariate longitudinal data helps to understand the relative changes among multiple longitudinally measured and correlated outcomes. A key challenge in the analysis of multivariate longitudinal data is the complex covariance structure. This is due to the contemporaneous and cross-temporal associations between multiple longitudinal outcomes. Graphical and data-driven tools that can aid in visualizing the dependence patterns among multiple longitudinal outcomes are not readily available. In this work, we show the role of graphical techniques: profile plots, and multivariate regressograms, in developing mean and covariance models for multivariate longitudinal data. We introduce an R package MLGM (Multivariate Longitudinal Graphical Models) to facilitate visualization and modeling mean and covariance patterns. Through two real studies, microarray data from the T-cell activation study and Mayo Clinic's primary biliary cirrhosis of the liver study, we show the key features of MLGM. We evaluate the finite sample performance of the proposed mean-covariance estimation approach through simulations.

Analysis of multivariate longitudinal data using dynamic lasso-regularized copula models with application to large pediatric cardiovascular studies

The National Heart, Lung and Blood Institute Growth and Health Study (NGHS) is a large longitudinal study of childhood health. A main objective of the study is to estimate the joint distributions of cardiovascular risk outcomes at any two time points conditioning on a large number of covariates. Existing multivariate longitudinal methods are not suitable for outcomes at multiple time points. We present a dynamic copula approach for estimating an outcome's joint distributions at two time points given a large number of time-varying covariates. Our models depend on the outcome's time-varying distributions at one time point, the bivariate copula densities and the functional copula parameters. We develop a three-step procedure for variable selection and estimation, which selects the influential covariates using a machine learning procedure based on spline Lasso-regularized least squares, computes the outcome's single-time distribution using splines, and estimates the functional copula parameter of the dynamic copula models. Pointwise confidence intervals are constructed through the resampling-subject bootstrap. We apply our procedure to the NGHS cardiovascular risk data and illustrate the clinical interpretations of the conditional distributions of a set of risk outcomes. We demonstrate the statistical properties of the dynamic models and estimation procedure through a simulation study.

Determination of correlations in multivariate longitudinal data with modified Cholesky and hypersphere decomposition using Bayesian variable selection approach.

In this article, we present a Bayesian framework for multivariate longitudinal data analysis with a focus on selection of important elements in the generalized autoregressive matrix. An efficient Gibbs sampling algorithm was developed for the proposed model and its implementation in a comprehensive R package called MLModelSelection is available on the comprehensive R archive network. The performance of the proposed approach was studied via a comprehensive simulation study. The effectiveness of the methodology was illustrated using a nonalcoholic fatty liver disease dataset to study correlations in multiple responses over time to explain the joint variability of lung functions and body mass index. Supplementary materials for this article, including a standardized description of the materials needed to reproduce the work, are available as an online supplement.

A Comparison of Three Models in Multivariate Binary Longitudinal Data Analysis: Application to FDCS Study

Multivariate longitudinal data analysis plays an important role in many biomedical and social problems. In this article, we present three methods for analyzing multiple and correlated binary outcomes; each one can be beneficial for determined aims. We review methods one and two, and we proposed method three. The three methods estimate the marginal means using the GEE approach for multivariate binary longitudinal data. The first method addresses the question of estimating one group of covariate parameters for many binary outcomes while accounting for their multivariate structure. The second method addresses the question of estimating the covariate parameters for each binary outcome separately. The third method is an estimation of the covariate parameters for each combination of outcomes. Our goal is to investigate the differences among the parameter estimations of the three methods. In the application element, we present a follow-up study (Florida Dental Care Study) that measured three binary outcomes and five covariates at four intervals. The FDCS study is useful explanation of the variation between outcomes since the outcomes were highly correlated.

The Role of Time in the Quest for Understanding Psychological Mechanisms

The lead-lag structure of multivariate time-ordered observations and the possibility to disentangle between-person (BP) from within-person (WP) sources of variance are major assets of longitudinal (panel) data. Hence, psychologists are making increasing use of such data, often with the intent to delineate the dynamic properties of psychological mechanisms, understood as a sequence of causal effects that govern psychological functioning. However, even with longitudinal data, psychological mechanisms are not easily identified. In this article, we show how an adequate representation of time may enhance the tenability of causal interpretations in the context of multivariate longitudinal data analysis. We anchor our considerations with an example that illustrates some of the main problems and questions faced by applied researchers and practitioners. We distinguish between static versus dynamic and discrete versus continuous time modeling approaches and discuss their advantages and disadvantages. We place particular emphasis on different ways of addressing BP differences and stress their dual role as potential confounds versus valuable sources of information for improving estimation and aiding causal inference. We conclude by outlining an approach that offers the potential of better integration of information on BP differences and WP changes in the search for causal mechanisms along with a discussion of current problems and limitations.

Multivariate longitudinal data analysis with censored and intermittent missing responses.

The multivariate linear mixed model (MLMM) has emerged as an important analytical tool for longitudinal data with multiple outcomes. However, the analysis of multivariate longitudinal data could be complicated by the presence of censored measurements because of a detection limit of the assay in combination with unavoidable missing values arising when subjects miss some of their scheduled visits intermittently. This paper presents a generalization of the MLMM approach, called the MLMM-CM, for a joint analysis of the multivariate longitudinal data with censored and intermittent missing responses. A computationally feasible expectation maximization-based procedure is developed to carry out maximum likelihood estimation within the MLMM-CM framework. Moreover, the asymptotic standard errors of fixed effects are explicitly obtained via the information-based method. We illustrate our methodology by using simulated data and a case study from an AIDS clinical trial. Experimental results reveal that the proposed method is able to provide more satisfactory performance as compared with the traditional MLMM approach.

Consensus Clustering of temporal profiles for the identification of metabolic markers of pre-diabetes in childhood (EarlyBird 73)

In longitudinal clinical studies, methodologies available for the analysis of multivariate data with multivariate methods are relatively limited. Here, we present Consensus Clustering (CClust) a new computational method based on clustering of time profiles and posterior identification of correlation between clusters and predictors. Subjects are first clustered in groups according to a response variable temporal profile, using a robust consensus-based strategy. To discover which of the remaining variables are associated with the resulting groups, a non-parametric hypothesis test is performed between groups at every time point, and then the results are aggregated according to the Fisher method. Our approach is tested through its application to the EarlyBird cohort database, which contains temporal variations of clinical, metabolic, and anthropometric profiles in a population of 150 children followed-up annually from age 5 to age 16. Our results show that our consensus-based method is able to overcome the problem of the approach-dependent results produced by current clustering algorithms, producing groups defined according to Insulin Resistance (IR) and biological age (Tanner Score). Moreover, it provides meaningful biological results confirmed by hypothesis testing with most of the main clinical variables. These results position CClust as a valid alternative for the analysis of multivariate longitudinal data.

Smoking, Gender, and Overweight Are Important Influencing Factors on Monocytic HLA-DR before and after Major Cancer Surgery.

Background Monocytic human leukocyte antigen D related (mHLA-DR) is essential for antigen-presentation. Downregulation of mHLA-DR emerged as a general biomarker of impaired immunity seen in patients with sepsis and pneumonia and after major surgery. Influencing factors of mHLA-DR such as age, overweight, diabetes, smoking, and gender remain unclear. Methods We analyzed 20 patients after esophageal or pancreatic resection of a prospective, randomized, placebo-controlled, double-blind trial (placebo group). mHLA-DR was determined from day of surgery (od) until postoperative day (pod) 5. Statistical analyses were performed using multivariate generalized estimating equation analyses (GEE), nonparametric multivariate analysis of longitudinal data, and univariate post hoc nonparametric Mann–Whitney tests. Results In GEE, smoking and gender were confirmed as significant influencing factors over time. Univariate analyses of mHLA-DR between smokers and nonsmokers showed lower preoperative levels (p = 0.010) and a trend towards lower levels on pod5 (p = 0.056) in smokers. Lower mHLA-DR was seen in men on pod3 (p = 0.038) and on pod5 (p = 0.026). Overweight patients (BMI > 25 kg/m2) had lower levels of mHLA-DR on pod3 (p = 0.039) and pod4 (p = 0.047). Conclusion Smoking is an important influencing factor on pre- and postoperative immune function while postoperative immune function was influenced by gender and overweight. Clinical trial registered with ISRCTN27114642.

Multivariate Longitudinal Analysis with Bivariate Correlation Test.

In the context of multivariate multilevel data analysis, this paper focuses on the multivariate linear mixed-effects model, including all the correlations between the random effects when the dimensional residual terms are assumed uncorrelated. Using the EM algorithm, we suggest more general expressions of the model’s parameters estimators. These estimators can be used in the framework of the multivariate longitudinal data analysis as well as in the more general context of the analysis of multivariate multilevel data. By using a likelihood ratio test, we test the significance of the correlations between the random effects of two dependent variables of the model, in order to investigate whether or not it is useful to model these dependent variables jointly. Simulation studies are done to assess both the parameter recovery performance of the EM estimators and the power of the test. Using two empirical data sets which are of longitudinal multivariate type and multivariate multilevel type, respectively, the usefulness of the test is illustrated.

Some comments on "The analysis of multivariate longitudinal data: A review".

We provide a commentary on "The analysis of multivariate longitudinal data: a review" by Verbeke etal. The authors provide a comprehensive review of the issues in the analysis of multivariate longitudinal data and use examples to demonstrate the pros and cons of several approaches. In this commentary, we indicate some important omissions in their review paper.

A new nested Cholesky decomposition and estimation for the covariance matrix of bivariate longitudinal data

In this paper, we propose a nested modified Cholesky decomposition for modeling the covariance structure in multivariate longitudinal data analysis. The entries of this decomposition have simple structures and can be interpreted as the generalized moving average coefficient matrices and innovation covariance matrices. We model the elements of these matrices by a class of unconstrained linear models, and develop a Fisher scoring algorithm to compute the maximum likelihood estimator of the regression parameters. The consistency and asymptotic normality of the estimators are established. Furthermore, we employ the smoothly clipped absolute deviation (SCAD) penalty to select the relevant variables in the models. The resulting SCAD estimators are shown to be asymptotically normal and have the oracle property. Some simulations are conducted to examine the finite sample performance of the proposed method. A real dataset is analyzed for illustration.

The analysis of multivariate longitudinal data using multivariate marginal models

Longitudinal studies often involve multiple outcomes measured repeatedly from the same subject. The analysis of multivariate longitudinal data can be challenging due to its complex correlated nature. In this paper, we develop multivariate marginal models in longitudinal studies with multiple response variables, and improve parameter estimation by incorporating informative correlation structures. In theory, we show that the proposed method yields a consistent and efficient estimator which follows an asymptotic normal distribution. Monte Carlo studies indicate that the proposed method performs well in the sense of reducing bias and improving estimation efficiency. In addition, the proposed approach is applied to a real longitudinal data example of transportation safety with different response families.

Multivariate longitudinal data analysis with mixed effects hidden Markov models.

Multiple longitudinal responses are often collected as a means to capture relevant features of the true outcome of interest, which is often hidden and not directly measurable. We outline an approach which models these multivariate longitudinal responses as generated from a hidden disease process. We propose a class of models which uses a hidden Markov model with separate but correlated random effects between multiple longitudinal responses. This approach was motivated by a smoking cessation clinical trial, where a bivariate longitudinal response involving both a continuous and a binomial response was collected for each participant to monitor smoking behavior. A Bayesian method using Markov chain Monte Carlo is used. Comparison of separate univariate response models to the bivariate response models was undertaken. Our methods are demonstrated on the smoking cessation clinical trial dataset, and properties of our approach are examined through extensive simulation studies.

Surveillance of cardiovascular diseases using a multivariate dynamic screening system.

In the SHARe Framingham Heart Study of the National Heart, Lung and Blood Institute, one major task is to monitor several health variables (e.g., blood pressure and cholesterol level) so that their irregular longitudinal pattern can be detected as soon as possible and some medical treatments applied in a timely manner to avoid some deadly cardiovascular diseases (e.g., stroke). To handle this kind of applications effectively, we propose a new statistical methodology called multivariate dynamic screening system (MDySS) in this paper. The MDySS method combines the major strengths of the multivariate longitudinal data analysis and the multivariate statistical process control, and it makes decisions about the longitudinal pattern of a subject by comparing it with other subjects cross sectionally and by sequentially monitoring it as well. Numerical studies show that MDySS works well in practice.

A Joint Modeling Approach for Right Censored High Dimensional Multivariate Longitudinal Data.

Analysis of multivariate longitudinal data becomes complicated when the outcomes are of high dimension and informative right censoring is prevailing. Here, we propose a likelihood based approach for high dimensional outcomes wherein we jointly model the censoring process along with the slopes of the multivariate outcomes in the same likelihood function. We utilized pseudo likelihood function to generate parameter estimates for the population slopes and Empirical Bayes estimates for the individual slopes. The proposed approach was applied to jointly model longitudinal measures of blood urea nitrogen, plasma creatinine, and estimated glomerular filtration rate which are key markers of kidney function in a cohort of renal transplant patients followed from kidney transplant to kidney failure. Feasibility of the proposed joint model for high dimensional multivariate outcomes was successfully demonstrated and its performance was compared to that of a pairwise bivariate model. Our simulation study results suggested that there was a significant reduction in bias and mean squared errors associated with the joint model compared to the pairwise bivariate model.

A Bayesian approach to joint analysis of multivariate longitudinal data and parametric accelerated failure time.

Impairment caused by Parkinson's disease (PD) is multidimensional (e.g., sensoria, functions, and cognition) and progressive. Its multidimensional nature precludes a single outcome to measure disease progression. Clinical trials of PD use multiple categorical and continuous longitudinal outcomes to assess the treatment effects on overall improvement. A terminal event such as death or dropout can stop the follow-up process. Moreover, the time to the terminal event may be dependent on the multivariate longitudinal measurements. In this article, we consider a joint random-effects model for the correlated outcomes. A multilevel item response theory model is used for the multivariate longitudinal outcomes and a parametric accelerated failure time model is used for the failure time because of the violation of proportional hazard assumption. These two models are linked via random effects. The Bayesian inference via MCMC is implemented in 'BUGS' language. Our proposed method is evaluated by a simulation study and is applied to DATATOP study, a motivating clinical trial to determine if deprenyl slows the progression of PD.