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A Bayesian Framework for Functional Mapping through Joint Modeling of Longitudinal and Time-to-Event Data  [PDF]
Kiranmoy Das,Runze Li,Zhongwen Huang,Junyi Gai,Rongling Wu
International Journal of Plant Genomics , 2012, DOI: 10.1155/2012/680634
Abstract: The most powerful and comprehensive approach of study in modern biology is to understand the whole process of development and all events of importance to development which occur in the process. As a consequence, joint modeling of developmental processes and events has become one of the most demanding tasks in statistical research. Here, we propose a joint modeling framework for functional mapping of specific quantitative trait loci (QTLs) which controls developmental processes and the timing of development and their causal correlation over time. The joint model contains two submodels, one for a developmental process, known as a longitudinal trait, and the other for a developmental event, known as the time to event, which are connected through a QTL mapping framework. A nonparametric approach is used to model the mean and covariance function of the longitudinal trait while the traditional Cox proportional hazard (PH) model is used to model the event time. The joint model is applied to map QTLs that control whole-plant vegetative biomass growth and time to first flower in soybeans. Results show that this model should be broadly useful for detecting genes controlling physiological and pathological processes and other events of interest in biomedicine. 1. Introduction To study biology, a classic approach is dimension reduction in which a biological phenomenon or process is dissected into several discrete features over time and space. Most efforts in the past decades have been made to understand biological details of individual features and then use knowledge from each feature to draw an inference about biology as a whole. There has been increasing recognition of the limitation of this approach because it fails to detect a rule that governs the transition from one feature to next, thus leading to a significant loss of information behind the development of a biological trait. More recently, tremendous developments in statistics and computer science have enabled scientists to model and compute the dynamic behavior of a biological phenomenon and construct a comprehensive view of how a cell, tissue, or organ grows and develops across the time-space scale. A statistical dynamic model, called functional mapping, is one of the products of such developments [1, 2]. The merit of functional mapping lies in its biological relevance to study the tempo-spatial pattern of change for the trait and further predict the physiological or pathological status of trait phenotype. Functional mapping has proven to be powerful for elucidating the dynamic genetic architecture of
JM: An R Package for the Joint Modelling of Longitudinal and Time-to-Event Data  [PDF]
Dimitris Rizopoulos
Journal of Statistical Software , 2010,
Abstract: In longitudinal studies measurements are often collected on different types of outcomes for each subject. These may include several longitudinally measured responses (such as blood values relevant to the medical condition under study) and the time at which an event of particular interest occurs (e.g., death, development of a disease or dropout from the study). These outcomes are often separately analyzed; however, in many instances, a joint modeling approach is either required or may produce a better insight into the mechanisms that underlie the phenomenon under study. In this paper we present the R package JM that fits joint models for longitudinal and time-to-event data.
The R Package JMbayes for Fitting Joint Models for Longitudinal and Time-to-Event Data using MCMC  [PDF]
Dimitris Rizopoulos
Statistics , 2014,
Abstract: Joint models for longitudinal and time-to-event data constitute an attractive modeling framework that has received a lot of interest in the recent years. This paper presents the capabilities of the R package JMbayes for fitting these models under a Bayesian approach using Markon chain Monte Carlo algorithms. JMbayes can fit a wide range of joint models, including among others joint models for continuous and categorical longitudinal responses, and provides several options for modeling the association structure between the two outcomes. In addition, this package can be used to derive dynamic predictions for both outcomes, and offers several tools to validate these predictions in terms of discrimination and calibration. All these features are illustrated using a real data example on patients with primary biliary cirrhosis.
Combining Dynamic Predictions from Joint Models for Longitudinal and Time-to-Event Data using Bayesian Model Averaging  [PDF]
Dimitris Rizopoulos,Laura A. Hatfield,Bradley P. Carlin,Johanna J. M. Takkenberg
Statistics , 2013,
Abstract: The joint modeling of longitudinal and time-to-event data is an active area of statistics research that has received a lot of attention in the recent years. More recently, a new and attractive application of this type of models has been to obtain individualized predictions of survival probabilities and/or of future longitudinal responses. The advantageous feature of these predictions is that they are dynamically updated as extra longitudinal responses are collected for the subjects of interest, providing real time risk assessment using all recorded information. The aim of this paper is two-fold. First, to highlight the importance of modeling the association structure between the longitudinal and event time responses that can greatly influence the derived predictions, and second, to illustrate how we can improve the accuracy of the derived predictions by suitably combining joint models with different association structures. The second goal is achieved using Bayesian model averaging, which, in this setting, has the very intriguing feature that the model weights are not fixed but they are rather subject- and time-dependent, implying that at different follow-up times predictions for the same subject may be based on different models.
HIV dynamics and natural history studies: Joint modeling with doubly interval-censored event time and infrequent longitudinal data  [PDF]
Li Su,Joseph W. Hogan
Statistics , 2011, DOI: 10.1214/10-AOAS391
Abstract: Hepatitis C virus (HCV) coinfection has become one of the most challenging clinical situations to manage in HIV-infected patients. Recently the effect of HCV coinfection on HIV dynamics following initiation of highly active antiretroviral therapy (HAART) has drawn considerable attention. Post-HAART HIV dynamics are commonly studied in short-term clinical trials with frequent data collection design. For example, the elimination process of plasma virus during treatment is closely monitored with daily assessments in viral dynamics studies of AIDS clinical trials. In this article instead we use infrequent cohort data from long-term natural history studies and develop a model for characterizing post-HAART HIV dynamics and their associations with HCV coinfection. Specifically, we propose a joint model for doubly interval-censored data for the time between HAART initiation and viral suppression, and the longitudinal CD4 count measurements relative to the viral suppression. Inference is accomplished using a fully Bayesian approach. Doubly interval-censored data are modeled semiparametrically by Dirichlet process priors and Bayesian penalized splines are used for modeling population-level and individual-level mean CD4 count profiles. We use the proposed methods and data from the HIV Epidemiology Research Study (HERS) to investigate the effect of HCV coinfection on the response to HAART.
A Two-Stage Joint Model for Nonlinear Longitudinal Response and a Time-to-Event with Application in Transplantation Studies  [PDF]
Magdalena Murawska,Dimitris Rizopoulos,Emmanuel Lesaffre
Journal of Probability and Statistics , 2012, DOI: 10.1155/2012/194194
Abstract: In transplantation studies, often longitudinal measurements are collected for important markers prior to the actual transplantation. Using only the last available measurement as a baseline covariate in a survival model for the time to graft failure discards the whole longitudinal evolution. We propose a two-stage approach to handle this type of data sets using all available information. At the first stage, we summarize the longitudinal information with nonlinear mixed-effects model, and at the second stage, we include the Empirical Bayes estimates of the subject-specific parameters as predictors in the Cox model for the time to allograft failure. To take into account that the estimated subject-specific parameters are included in the model, we use a Monte Carlo approach and sample from the posterior distribution of the random effects given the observed data. Our proposal is exemplified on a study of the impact of renal resistance evolution on the graft survival. 1. Introduction Many medical studies involve analyzing responses together with event history data collected for each patient. A well-known and broadly studied example can be found in AIDS research, where CD4 cell counts taken at different time points are related to the time to death. These data need to be analyzed using a joint modeling approach in order to properly take into account the association between the longitudinal data and the event times. The requirement for a joint modeling approach is twofold. Namely, when focus is on the longitudinal outcome, events cause nonrandom dropout that needs to be accounted for in order to obtain valid inferences. When focus is on the event times, the longitudinal responses cannot be simply included in a relative risk model because they represent the output of an internal time-dependent covariate [1]. In this paper, we focus on a setting that shares some similarities with the standard joint modeling framework described above, but also has important differences. In particular, we are interested in the association between longitudinal responses taken before the actual followup for the time-to-event has been initiated. This setting is frequently encountered in transplantation studies, where patients in the waiting list provide a series of longitudinal outcomes that may be related to events occurring after transplantation. A standard analysis in transplantation studies is to ignore the longitudinal information and use only the last available measurement as a baseline covariate in a model for the allograft survival. It is, however, evident that such an approach
Longitudinal Survey, Nonmonotone, Nonresponse, Imputation, Nonparametric Regression  [PDF]
Sarah Pyeye, Charles K. Syengo, Leo Odongo, George O. Orwa, Romanus O. Odhiambo
Open Journal of Statistics (OJS) , 2016, DOI: 10.4236/ojs.2016.66092
Abstract: The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-dependent finite populations means. The asymptotic properties (unbiasedness and consistency) of the proposed estimator are investigated. Comparisons between different parametric and nonparametric estimators are performed based on the bootstrap standard deviation, mean square error and percentage relative bias. A simulation study is carried out to determine the best performing estimator of the time-dependent finite population means. The simulation results show that local linear regression estimator yields good properties.
Nonparametric Bayesian multiple testing for longitudinal performance stratification  [PDF]
James G. Scott
Statistics , 2010, DOI: 10.1214/09-AOAS252
Abstract: This paper describes a framework for flexible multiple hypothesis testing of autoregressive time series. The modeling approach is Bayesian, though a blend of frequentist and Bayesian reasoning is used to evaluate procedures. Nonparametric characterizations of both the null and alternative hypotheses will be shown to be the key robustification step necessary to ensure reasonable Type-I error performance. The methodology is applied to part of a large database containing up to 50 years of corporate performance statistics on 24,157 publicly traded American companies, where the primary goal of the analysis is to flag companies whose historical performance is significantly different from that expected due to chance.
nparLD: An R Software Package for the Nonparametric Analysis of Longitudinal Data in Factorial Experiments  [PDF]
Kimihiro Noguchi,Yulia R. Gel,Edgar Brunner,Frank Konietschke
Journal of Statistical Software , 2012,
Abstract: Longitudinal data from factorial experiments frequently arise in various fields of study, ranging from medicine and biology to public policy and sociology. In most practical situations, the distribution of observed data is unknown and there may exist a number of atypical measurements and outliers. Hence, use of parametric and semi-parametric procedures that impose restrictive distributional assumptions on observed longitudinal samples becomes questionable. This, in turn, has led to a substantial demand for statistical procedures that enable us to accurately and reliably analyze longitudinal measurements in factorial experiments with minimal conditions on available data, and robust nonparametric methodology offering such a possibility becomes of particular practical importance. In this article, we introduce a new R package nparLD which provides statisticians and researchers from other disciplines an easy and user-friendly access to the most up-to-date robust rank-based methods for the analysis of longitudinal data in factorial settings. We illustrate the implemented procedures by case studies from dentistry, biology, and medicine.
Joint modelling of longitudinal and multi-state processes: application to clinical progressions in prostate cancer  [PDF]
Lo?c Ferrer,Virginie Rondeau,James J. Dignam,Tom Pickles,Hélène Jacqmin-Gadda,Cécile Proust-Lima
Statistics , 2015,
Abstract: Joint modelling of longitudinal and survival data is increasingly used in clinical trials on cancer. In prostate cancer for example, these models permit to account for the link between longitudinal measures of prostate-specific antigen (PSA) and the time of clinical recurrence when studying the risk of relapse. In practice, multiple types of relapse may occur successively. Distinguishing these transitions between health states would allow to evaluate, for example, how PSA trajectory and classical covariates impact the risk of dying after a distant recurrence post-radiotherapy, or to predict the risk of one specific type of clinical recurrence post-radiotherapy, from the PSA history. In this context, we present a joint model for a longitudinal process and a multi-state process which is divided into two sub-models: a linear mixed sub-model for longitudinal data, and a multi-state sub-model with proportional hazards for transition times, both linked by shared random effects. Parameters of this joint multi-state model are estimated within the maximum likelihood framework using an EM algorithm coupled to a quasi-Newton algorithm in case of slow convergence. It is implemented under R, by combining and extending the mstate and JM packages. The estimation program is validated by simulations and applied on pooled data from two cohorts of men with localized prostate cancer and treated by radiotherapy. Thanks to the classical covariates available at baseline and the PSA measurements collected repeatedly during the follow-up, we are able to assess the biomarker's trajectory, define the risks of transitions between health states, and quantify the impact of the PSA dynamics on each transition intensity.
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