scholarly journals A joint model for longitudinal and survival data based on an AR(1) latent process

2016 ◽  
Vol 27 (5) ◽  
pp. 1285-1311 ◽  
Author(s):  
Silvia Bacci ◽  
Francesco Bartolucci ◽  
Silvia Pandolfi
Keyword(s):  
Survival Data ◽  
Random Effect ◽  
Information Matrix ◽  
Autoregressive Process ◽  
Joint Modeling ◽  
Joint Model ◽  
Parameter Estimates ◽  
Monte Carlo Simulation Study ◽  
Longitudinal Response ◽  
Latent Process

A critical problem in repeated measurement studies is the occurrence of nonignorable missing observations. A common approach to deal with this problem is joint modeling the longitudinal and survival processes for each individual on the basis of a random effect that is usually assumed to be time constant. We relax this hypothesis by introducing time-varying subject-specific random effects that follow a first-order autoregressive process, AR(1). We also adopt a generalized linear model formulation to accommodate for different types of longitudinal response (i.e. continuous, binary, count) and we consider some extended cases, such as counts with excess of zeros and multivariate outcomes at each time occasion. Estimation of the parameters of the resulting joint model is based on the maximization of the likelihood computed by a recursion developed in the hidden Markov literature. This maximization is performed on the basis of a quasi-Newton algorithm that also provides the information matrix and then standard errors for the parameter estimates. The proposed approach is illustrated through a Monte Carlo simulation study and the analysis of certain medical datasets.

scholarly journals Marginalized Two-Part Joint Modeling of Longitudinal Semi-Continuous Responses and Survival Data: With Application to Medical Costs

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2603
Author(s):  
Mohadeseh Shojaei Shahrokhabadi ◽  
(Din) Ding-Geng Chen ◽  
Sayed Jamal Mirkamali ◽  
Anoshirvan Kazemnejad ◽  
Farid Zayeri
Keyword(s):  
Survival Data ◽  
Joint Modeling ◽  
Medical Costs ◽  
Joint Model ◽  
Superior Performance ◽  
Parameter Estimates ◽  
Joint Models ◽  
Survival Status ◽  
Continuous Responses ◽  
Zero Values

Non-negative continuous outcomes with a substantial number of zero values and incomplete longitudinal follow-up are quite common in medical costs data. It is thus critical to incorporate the potential dependence of survival status and longitudinal medical costs in joint modeling, where censorship is death-related. Despite the wide use of conventional two-part joint models (CTJMs) to capture zero-inflation, they are limited to conditional interpretations of the regression coefficients in the model’s continuous part. In this paper, we propose a marginalized two-part joint model (MTJM) to jointly analyze semi-continuous longitudinal costs data and survival data. We compare it to the conventional two-part joint model (CTJM) for handling marginal inferences about covariate effects on average costs. We conducted a series of simulation studies to evaluate the superior performance of the proposed MTJM over the CTJM. To illustrate the applicability of the MTJM, we applied the model to a set of real electronic health record (EHR) data recently collected in Iran. We found that the MTJM yielded a smaller standard error, root-mean-square error of estimates, and AIC value, with unbiased parameter estimates. With this MTJM, we identified a significant positive correlation between costs and survival, which was consistent with the simulation results.

Joint modeling of longitudinal and survival data with a covariate subject to a limit of detection

2017 ◽  
Vol 28 (2) ◽  
pp. 486-502 ◽  
Author(s):  
Abdus Sattar ◽  
Sanjoy K Sinha
Keyword(s):  
Survival Data ◽  
Likelihood Function ◽  
Limit Of Detection ◽  
Joint Modeling ◽  
Parameter Estimates ◽  
Event Data ◽  
Time To Event ◽  
Time To Event Data ◽  
Longitudinal Response ◽  
Coverage Probabilities

We develop and study an innovative method for jointly modeling longitudinal response and time-to-event data with a covariate subject to a limit of detection. The joint model assumes a latent process based on random effects to describe the association between longitudinal and time-to-event data. We study the role of the association parameter on the regression parameters estimators. We model the longitudinal and survival outcomes using linear mixed-effects and Weibull frailty models, respectively. Because of the limit of detection, missing covariate (explanatory variable, x) values may lead to the non-ignorable missing, resulting in biased parameter estimates with poor coverage probabilities of the confidence interval. We define and estimate the probability of missing due to the limit of detection. Then we develop a novel joint density and hence the likelihood function that incorporates the effect of left-censored covariate. Monte Carlo simulations show that the estimators of the proposed method are approximately unbiased and provide expected coverage probabilities for both longitudinal and survival submodels parameters. We also present an application of the proposed method using a large clinical dataset of pneumonia patients obtained from the Genetic and Inflammatory Markers of Sepsis study.

scholarly journals A joint model for mixed and truncated longitudinal data and survival data, with application to HIV vaccine studies

Biostatistics ◽  
2017 ◽  
Vol 19 (3) ◽  
pp. 374-390 ◽  
Author(s):  
Tingting Yu ◽  
Lang Wu ◽  
Peter B Gilbert
Keyword(s):  
Longitudinal Data ◽  
Survival Data ◽  
Joint Model ◽  
Hiv Vaccine ◽  
Likelihood Inference ◽  
Likelihood Method ◽  
Parameter Estimates ◽  
Computationally Efficient ◽  
Approximate Likelihood ◽  
Longitudinal And Survival Data

SUMMARY In HIV vaccine studies, a major research objective is to identify immune response biomarkers measured longitudinally that may be associated with risk of HIV infection. This objective can be assessed via joint modeling of longitudinal and survival data. Joint models for HIV vaccine data are complicated by the following issues: (i) left truncations of some longitudinal data due to lower limits of quantification; (ii) mixed types of longitudinal variables; (iii) measurement errors and missing values in longitudinal measurements; (iv) computational challenges associated with likelihood inference. In this article, we propose a joint model of complex longitudinal and survival data and a computationally efficient method for approximate likelihood inference to address the foregoing issues simultaneously. In particular, our model does not make unverifiable distributional assumptions for truncated values, which is different from methods commonly used in the literature. The parameters are estimated based on the h-likelihood method, which is computationally efficient and offers approximate likelihood inference. Moreover, we propose a new approach to estimate the standard errors of the h-likelihood based parameter estimates by using an adaptive Gauss–Hermite method. Simulation studies show that our methods perform well and are computationally efficient. A comprehensive data analysis is also presented.

scholarly journals A Birnbaum-Saunders Model for Joint Survival and Longitudinal Analysis of Congestive Heart Failure Data

2020 ◽  
Vol 43 (1) ◽  
pp. 83-101
Author(s):  
Diana Carolina Franco Soto ◽  
Antonio Carlos Pedroso de Lima ◽  
Julio Da Motta Singer
Keyword(s):  
Heart Failure ◽  
Congestive Heart Failure ◽  
Linear Mixed Model ◽  
Traditional Approach ◽  
Joint Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Survival Times ◽  
Longitudinal Response ◽  
The Impact

We consider a parametric joint modelling of longitudinal measurements and survival times, motivated by a study conducted at the Heart Institute (Incor), São Paulo, Brazil, with the objective of evaluating the impact of B-type Natriuretic Peptide (BNP) collected at different instants on the survival of patients with Congestive Heart Failure (CHF). We employ a linear mixed model for the longitudinal response and a Birnbaum-Saunders model for the survival times, allowing the inclusion of subjects without longitudinal observations. We derive maximum likelihood estimators of the joint model parameters and conduct a simulation study to compare the true survival probabilities with dynamic predictions obtained from the fit of the proposed joint model and to evaluate the performance of the method for estimating the model parameters.The proposed joint model is applied to the cohort of 1609 patients with CHF, of which 1080 have no BNP measurements. The parameter estimates and their standard errors obtained via: i) the traditional approach, where only individuals with at least one measurement of the longitudinal response are included and ii) the proposed approach, which includes survival information from all individuals, are compared with those obtained via marginal (longitudinal and survival) models.

scholarly journals Dynamic predictions in Bayesian functional joint models for longitudinal and time-to-event data: An application to Alzheimer’s disease

2017 ◽  
Vol 28 (2) ◽  
pp. 327-342 ◽  
Author(s):  
Kan Li ◽  
Sheng Luo
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Survival Data ◽  
Functional Data ◽  
Joint Modeling ◽  
Joint Model ◽  
Repeated Measurements ◽  
Joint Models ◽  
Modeling Framework ◽  
Dynamic Prediction

In the study of Alzheimer’s disease, researchers often collect repeated measurements of clinical variables, event history, and functional data. If the health measurements deteriorate rapidly, patients may reach a level of cognitive impairment and are diagnosed as having dementia. An accurate prediction of the time to dementia based on the information collected is helpful for physicians to monitor patients’ disease progression and to make early informed medical decisions. In this article, we first propose a functional joint model to account for functional predictors in both longitudinal and survival submodels in the joint modeling framework. We then develop a Bayesian approach for parameter estimation and a dynamic prediction framework for predicting the subjects’ future outcome trajectories and risk of dementia, based on their scalar and functional measurements. The proposed Bayesian functional joint model provides a flexible framework to incorporate many features both in joint modeling of longitudinal and survival data and in functional data analysis. Our proposed model is evaluated by a simulation study and is applied to the motivating Alzheimer’s Disease Neuroimaging Initiative study.

scholarly journals Joint modeling of bivariate longitudinal and survival data in spouse pairs

2019 ◽  
Vol 53 (1) ◽  
pp. 1-25
Author(s):  
Jia-Yuh Chen ◽  
Richard Schulz ◽  
Stewart J. Anderson
Keyword(s):  
Random Effects ◽  
Survival Data ◽  
Cardiovascular Health ◽  
Proportional Hazards ◽  
Temporal Correlation ◽  
Joint Modeling ◽  
Health Study ◽  
Cardiovascular Health Study ◽  
Parameter Estimates ◽  
Survival Times

We investigated the association between longitudinally measured depression scores and survival times simultaneously for paired spouse data from the Cardiovascular Health Study (CHS). We propose a joint model incorporating within pair correlations, both in the longitudinal and survival processes. We use bivariate linear mixed-effects models for the longitudinal processes, where the random effects are used to model the temporal correlation within each subject and the correlation across outcomes between subjects. For the survival processes, we incorporate gamma frailties into Weibull proportional hazards models to account for the correlation between survival times within pairs. The two sub-models are then linked through shared random effects, where the longitudinal and survival processes are conditionally independent given the random effects. Parameter estimates are obtained via the EM algorithm by maximizing the joint likelihood for the bivariate longitudinal and bivariate survival data. We use our method to model data where the use of bivariate longitudinal and survival sub–models are apropos but where there are no competing risks, that is, the censoring of one spouse’s time–to–mortality is not necessarily guaranteed by the death of the other spouse.

scholarly journals Identifying Temporal Aggregation Effect on Crash-Frequency Modeling

2021 ◽  
Vol 13 (11) ◽  
pp. 6214
Author(s):  
Bumjoon Bae ◽  
Changju Lee ◽  
Tae-Young Pak ◽  
Sunghoon Lee
Keyword(s):  
Traffic Safety ◽  
Negative Binomial ◽  
Random Effect ◽  
Temporal Correlation ◽  
Negative Binomial Regression ◽  
Spatiotemporal Analysis ◽  
Parameter Estimates ◽  
Crash Frequency ◽  
Crash Frequency Modeling ◽  
Using Data

Aggregation of spatiotemporal data can encounter potential information loss or distort attributes via individual observation, which would influence modeling results and lead to an erroneous inference, named the ecological fallacy. Therefore, deciding spatial and temporal resolution is a fundamental consideration in a spatiotemporal analysis. The modifiable temporal unit problem (MTUP) occurs when using data that is temporally aggregated. While consideration of the spatial dimension has been increasingly studied, the counterpart, a temporal unit, is rarely considered, particularly in the traffic safety modeling field. The purpose of this research is to identify the MTUP effect in crash-frequency modeling using data with various temporal scales. A sensitivity analysis framework is adopted with four negative binomial regression models and four random effect negative binomial models having yearly, quarterly, monthly, and weekly temporal units. As the different temporal unit was applied, the result of the model estimation also changed in terms of the mean and significance of the parameter estimates. Increasing temporal correlation due to using the small temporal unit can be handled with the random effect models.

scholarly journals Joint modeling of multiple repeated measures and survival data using multidimensional latent trait linear mixed model

2018 ◽  
Vol 28 (10-11) ◽  
pp. 3392-3403 ◽  
Author(s):  
Jue Wang ◽  
Sheng Luo
Keyword(s):  
Survival Data ◽  
Repeated Measures ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Proportional Hazards Model ◽  
Latent Trait ◽  
Joint Modeling ◽  
Fine Motor ◽  
Terminal Event ◽  
Longitudinal Outcomes

Impairment caused by Amyotrophic lateral sclerosis (ALS) is multidimensional (e.g. bulbar, fine motor, gross motor) and progressive. Its multidimensional nature precludes a single outcome to measure disease progression. Clinical trials of ALS use multiple 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 develop a joint model consisting of a multidimensional latent trait linear mixed model (MLTLMM) for the multiple longitudinal outcomes, and a proportional hazards model with piecewise constant baseline hazard for the event time data. Shared random effects are used to link together two models. The model inference is conducted using a Bayesian framework via Markov chain Monte Carlo simulation implemented in Stan language. Our proposed model is evaluated by simulation studies and is applied to the Ceftriaxone study, a motivating clinical trial assessing the effect of ceftriaxone on ALS patients.

scholarly journals Deriving percentage study weights in multi-parameter meta-analysis models: with application to meta-regression, network meta-analysis and one-stage individual participant data models

2017 ◽  
Vol 27 (10) ◽  
pp. 2885-2905 ◽  
Author(s):  
Richard D Riley ◽  
Joie Ensor ◽  
Dan Jackson ◽  
Danielle L Burke
Keyword(s):  
Meta Analysis ◽  
Information Matrix ◽  
Indirect Evidence ◽  
Parameter Estimates ◽  
Individual Participant Data ◽  
One Stage ◽  
Individual Participant ◽  
Meta Regression ◽  
Multiple Treatments ◽  
Analysis Models

Many meta-analysis models contain multiple parameters, for example due to multiple outcomes, multiple treatments or multiple regression coefficients. In particular, meta-regression models may contain multiple study-level covariates, and one-stage individual participant data meta-analysis models may contain multiple patient-level covariates and interactions. Here, we propose how to derive percentage study weights for such situations, in order to reveal the (otherwise hidden) contribution of each study toward the parameter estimates of interest. We assume that studies are independent, and utilise a decomposition of Fisher’s information matrix to decompose the total variance matrix of parameter estimates into study-specific contributions, from which percentage weights are derived. This approach generalises how percentage weights are calculated in a traditional, single parameter meta-analysis model. Application is made to one- and two-stage individual participant data meta-analyses, meta-regression and network (multivariate) meta-analysis of multiple treatments. These reveal percentage study weights toward clinically important estimates, such as summary treatment effects and treatment-covariate interactions, and are especially useful when some studies are potential outliers or at high risk of bias. We also derive percentage study weights toward methodologically interesting measures, such as the magnitude of ecological bias (difference between within-study and across-study associations) and the amount of inconsistency (difference between direct and indirect evidence in a network meta-analysis).

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