Analysis of Longitudinal and Survival Data: Joint Modeling, Inference Methods, and Issues

In the past two decades, joint models of longitudinal and survival data have received much attention in the literature. These models are often desirable in the following situations: (i) survival models with measurement errors or missing data in time-dependent covariates, (ii) longitudinal models with informative dropouts, and (iii) a survival process and a longitudinal process are associated via latent variables. In these cases, separate inferences based on the longitudinal model and the survival model may lead to biased or inefficient results. In this paper, we provide a brief overview of joint models for longitudinal and survival data and commonly used methods, including the likelihood method and two-stage methods.

Download Full-text

Serum Lipids and Cardiovascular Disease Mortality in Iranian Population: Joint Modeling of Longitudinal and Survival Data in Tehran Lipid and Glucose Study (TLGS) Cohort

10.31661/gmj.v8i0.1516 ◽

2019 ◽

Vol 8 ◽

pp. 1516

Author(s):

Bagher Pahlavanzade ◽

Farid Zayeri ◽

Taban Baghfalaki ◽

Farzad Hadaeg ◽

Davood Khalili ◽

...

Keyword(s):

Risk Factors ◽

Cardiovascular Disease ◽

Survival Data ◽

Hdl Cholesterol ◽

Joint Modeling ◽

Lipid Markers ◽

Time Dependent Covariates ◽

Longitudinal And Survival Data ◽

Lipid Abnormalities ◽

Cvd Mortality

Background: Lipid abnormalities are major risk factors of death from cardiovascular disease (CVD). As well as, lipid markers are time-dependent covariates that change with aging. Previous cohort studies have only investigated baseline measurements of lipid markers on CVD mortality. Materials and Methods: The study sample consisted of 4,148 individuals aged over 40 years. Total cholesterol (TC), LDL-cholesterol (LDL-C), and HDL-cholesterol (HDL-C) were measured in five phases. A joint model analysis was used to investigate the association between each longitudinal lipid markers and CVD mortality in men, women and pooled sample. All analysis was performed using the survival and joint modeling packages in R 3.3.3. Results: Totally, 233 CVD deaths occurred during a median follow-up of 12.4 years. For men, CVD mortality increased by 28% (confidence interval [CI]: 14%,44%) for a 10% increased in TC. For women, CVD mortality increased by 43% (CI: 22%, 68%) and 21% (CI:7%, 37%) for 10 % increase in TC and LDL-C and decreased by ‌18% (CI:7%, 27%) for a 10% increase in HDL-C. Conclusion: Association of lipid ‎markers with CVD mortality is different in men and women, such that high levels of TC ‎and ‎LDL-C and low levels of HDL-C are risk factors of CVD mortality in women, but only TC is a risk ‎factor of CVD mortality in men. [GMJ.2019;8:e1516]

Download Full-text

Basic Concepts and Methods for Joint Models of Longitudinal and Survival Data

Journal of Clinical Oncology ◽

10.1200/jco.2009.25.0654 ◽

2010 ◽

Vol 28 (16) ◽

pp. 2796-2801 ◽

Cited By ~ 164

Author(s):

Joseph G. Ibrahim ◽

Haitao Chu ◽

Liddy M. Chen

Keyword(s):

Clinical Trials ◽

Survival Data ◽

Eastern Cooperative Oncology Group ◽

Joint Modeling ◽

Operating Characteristics ◽

Joint Models ◽

Free Survival ◽

Introductory Overview ◽

Longitudinal And Survival Data

Joint models for longitudinal and survival data are particularly relevant to many cancer clinical trials and observational studies in which longitudinal biomarkers (eg, circulating tumor cells, immune response to a vaccine, and quality-of-life measurements) may be highly associated with time to event, such as relapse-free survival or overall survival. In this article, we give an introductory overview on joint modeling and present a general discussion of a broad range of issues that arise in the design and analysis of clinical trials using joint models. To demonstrate our points throughout, we present an analysis from the Eastern Cooperative Oncology Group trial E1193, as well as examine some operating characteristics of joint models through simulation studies.

Download Full-text

Bayesian Joint Modeling of Skew-Positive Longitudinal-Survival Data Using Birnbaum-Saunders Distribution

Journal of Biostatistics and Epidemiology ◽

10.18502/jbe.v6i1.4757 ◽

2020 ◽

Author(s):

Tohid Jafari-Koshki ◽

Sayed Mohsen Hosseini ◽

Shahram Arsang-Jang

Keyword(s):

Survival Data ◽

Real Data ◽

Information Criterion ◽

Joint Modeling ◽

Multivariate Modeling ◽

Joint Models ◽

Wide Range ◽

Longitudinal Part ◽

Research Questions ◽

Longitudinal And Survival Data

Background: There has been a great interest in joint modeling of longitudinal and survival data in recent two decades. Joint models have less restrictive assumptions in multivariate modeling and could address various research questions. This has led to their wide applications in practice. However, earlier models had normality assumption on the distribution in longitudinal part that is usually violated in real data. Hence, recent research have focused on circumventing this issue. Using various skewed distributions has been proposed and applied in the literature. Nevertheless, the flexibility of the proposed methods is limited especially when the data are skew positive. Methods: In this paper, we introduce the use of Birnbaum-Saunders (BS) distribution in joint modeling context. BS distribution is more flexible and could cover a wide range of skew, kurtotic or bimodal data. Results: We analyzed publicly available ddI/ddC data both with normal and BS distributions in Bayesian setting and compared their fit by Widely Applicable Information Criterion (WAIC). The joint BS model showed a better fit to the data. Conclusion: We introduced and applied BS distribution in joint modeling of longitudinal-survival data. Using multi-parameter distributions such as BS in Bayesian setting could improve the fit of models without limitations that arise in transformation of data from original scale.

Download Full-text

Consistent estimation of a joint model for multivariate longitudinal and survival data with latent variables

Journal of Multivariate Analysis ◽

10.1016/j.jmva.2021.104827 ◽

2021 ◽

pp. 104827

Author(s):

Kang Kai ◽

Song Xinyuan

Keyword(s):

Survival Data ◽

Latent Variables ◽

Joint Model ◽

Consistent Estimation ◽

Longitudinal And Survival Data

Download Full-text

Sample size and power determination in joint modeling of longitudinal and survival data

Statistics in Medicine ◽

10.1002/sim.4263 ◽

2011 ◽

Vol 30 (18) ◽

pp. 2295-2309 ◽

Cited By ~ 31

Author(s):

Liddy M. Chen ◽

Joseph G. Ibrahim ◽

Haitao Chu

Keyword(s):

Sample Size ◽

Survival Data ◽

Joint Modeling ◽

Longitudinal And Survival Data

Download Full-text

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

Biostatistics ◽

10.1093/biostatistics/kxx047 ◽

2017 ◽

Vol 19 (3) ◽

pp. 374-390 ◽

Cited By ~ 2

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.

Download Full-text