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 Revisiting Methods For Modeling Longitudinal and Survival Data: The Framingham Heart Study

2021 ◽  
Author(s):  
Julius S Ngwa ◽  
Howard J Cabral ◽  
Debbie M Cheng ◽  
David R Gagnon ◽  
Michael P LaValley ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Longitudinal Data ◽  
Survival Data ◽  
Framingham Heart Study ◽  
Time Dependent ◽  
Time To Event ◽  
Longitudinal Measure ◽  
Heart Study ◽  
Longitudinal And Survival Data ◽  
Joint Method

Abstract Background: Statistical methods for modeling longitudinal and time-to-event data has received much attention in medical research and is becoming increasingly useful. In clinical studies, such as cancer and AIDS, longitudinal biomarkers are used to monitor disease progression and to predict survival. These longitudinal measures are often missing at failure times and may be prone to measurement errors. More importantly, time-dependent survival models that include the raw longitudinal measurements may lead to biased results. In previous studies these two types of data are frequently analyzed separately where a mixed effects model is used for the longitudinal data and a survival model is applied to the event outcome. Methods: In this paper we compare joint maximum likelihood methods, a two-step approach and a time dependent covariate method that link longitudinal data to survival data with emphasis on using longitudinal measures to predict survival. We apply a Bayesian semi-parametric joint method and maximum likelihood joint method that maximizes the joint likelihood of the time-to-event and longitudinal measures. We also implement the Two-Step approach, which estimates random effects separately, and a classic Time Dependent Covariate Model. We use simulation studies to assess bias, accuracy, and coverage probabilities for the estimates of the link parameter that connects the longitudinal measures to survival times. Results: Simulation results demonstrate that the Two-Step approach performed best at estimating the link parameter when variability in the longitudinal measure is low but is somewhat biased downwards when the variability is high. Bayesian semi-parametric and maximum likelihood joint methods yield higher link parameter estimates with low and high variability in the longitudinal measure. The Time Dependent Covariate method resulted in consistent underestimation of the link parameter. We illustrate these methods using data from the Framingham Heart Study in which lipid measurements and Myocardial Infarction data were collected over a period of 26 years.Conclusions: Traditional methods for modeling longitudinal and survival data, such as the time dependent covariate method, that use the observed longitudinal data, tend to provide downwardly biased estimates. The two-step approach and joint models provide better estimates, although a comparison of these methods may depend on the underlying residual variance.

scholarly journals A new joint model for longitudinal and survival data with a cure fraction

2004 ◽  
Vol 91 (1) ◽  
pp. 18-34 ◽  
Author(s):  
Ming-Hui Chen ◽  
Joseph G Ibrahim ◽  
Debajyoti Sinha
Keyword(s):  
Survival Data ◽  
Joint Model ◽  
Cure Fraction ◽  
Longitudinal And Survival Data

scholarly journals Revisiting Methods For Modeling Longitudinal and Survival Data: The Framingham Heart Study

2020 ◽  
Author(s):  
Julius S Ngwa ◽  
Howard J Cabral ◽  
Debbie M Cheng ◽  
David R Gagnon ◽  
Michael P LaValley ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Longitudinal Data ◽  
Survival Data ◽  
Framingham Heart Study ◽  
Time Dependent ◽  
Time To Event ◽  
Longitudinal Measure ◽  
Heart Study ◽  
Longitudinal And Survival Data ◽  
Joint Method

Abstract Background Statistical methods for modeling longitudinal and time-to-event data has received much attention in medical research and is becoming increasingly useful. In clinical studies, such as cancer and AIDS, longitudinal biomarkers are used to monitor disease progression and to predict survival. These longitudinal measures are often missing at failure times and may be prone to measurement errors. More importantly, time-dependent survival models that include the raw longitudinal measurements may lead to biased results. In previous studies these two types of data are frequently analyzed separately where a mixed effects model is used for the longitudinal data and a survival model is applied to the event outcome. Methods In this paper we compare joint maximum likelihood methods, a two-step approach and a time dependent covariate method that link longitudinal data to survival data with emphasis on using longitudinal measures to predict survival. We apply a Bayesian semi-parametric joint method and maximum likelihood joint method that maximizes the joint likelihood of the time-to-event and longitudinal measures. We also implement the Two-Step approach, which estimates random effects separately, and a classic Time Dependent Covariate Model. We use simulation studies to assess bias, accuracy and coverage probabilities for the estimates of the link parameter that connects the longitudinal measures to survival times. Results Simulation results demonstrate that Two-Step approach performed best at estimating the link parameter when variability in the longitudinal measure is low but is somewhat biased downwards when the variability is high. Bayesian semi-parametric and maximum likelihood joint methods yield higher link parameter estimates with low and high variability in the longitudinal measure. Time Dependent Covariate method resulted in consistent underestimation of the link parameter. We illustrate these methods using data from the Framingham Heart Study in which lipid measurements and Myocardial Infarction data were collected over a period of 26 years. Conclusions Traditional methods for modeling longitudinal and survival data, such as time dependent covariate method, that use the observed longitudinal data, tend to provide downward bias estimates. Two-step approach and joint models provide better estimates, although a comparison of these methods may depend on the underlying residual variance.

scholarly journals Complete Case versus Inverse Probability Weighting Methods of Fitting Incomplete Longitudinal and Survival Data Joint Models

2019 ◽  
pp. 1-10
Author(s):  
D. O. Nyaboga ◽  
A. Mwangi ◽  
D. Lusweti
Keyword(s):  
Missing Data ◽  
Survival Data ◽  
Joint Model ◽  
Information Criteria ◽  
Joint Models ◽  
Full Data ◽  
Complete Case ◽  
Inverse Probability ◽  
Longitudinal And Survival Data ◽  
The Impact

Missing data is a common problem in real word studies especially clinical studies. However, most people working with such data, often drop missing cases from individuals with incomplete observations that occur when patients do not complete the treatment or miss their scheduled visits. This may lead to misleading results and ultimately affect the decision of whether an intervention is good or bad for the patients under treatment. The comparison of Complete Case (CC) and Inverse Probability Weights (IPW) techniques of handling missing data in various models has been addressed, however little has been done to compare these methods when applied to joint models of longitudinal and time to event data. Therefore, this paper seeks to investigate the impact of assuming CC analysis on clinical data with missing cases, comparing it with IPW method when fitting joint models of longitudinal and survival data setting full data model as the baseline model. This paper made use of randomized aids clinical trial data. The model with Deviance Information Criteria (DIC) close to that of full data joint model is considered the best. From the results, joint models from full data, CC and IPW had DIC of 10603.94, 8410.33 and 10600.95 respectively. The joint model obtained from IPW data had a DIC too close to that of full data joint model as compared to model from CC data.

scholarly journals Aplicação da distribuição Burr XII discreta na análise de dados de produção animal

2018 ◽  
Vol 40 ◽  
pp. 25
Author(s):  
Josmar Mazucheli ◽  
Ricardo Puziol Oliveira ◽  
Danielle Peralta ◽  
Isabele P. Emanuelli
Keyword(s):  
Survival Data ◽  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Animal Production ◽  
Discrete Distributions ◽  
Likelihood Method ◽  
Discrete Version ◽  
Parameter Estimates ◽  
Goodness Of Fit Test ◽  
Burr Xii Distribution

In animal production, the models that mimicry the biological reality are of great importance for optimization and sustainability of the productive system. The continuous Burr XII distribution is widely used in survival data analysis, however, the same does not occur with its discrete version, recently proposed in the literature. The purpose of this work is to use the discrete Burr XII distribution, obtained by the discretization method proposed by Nakagawa and Osaki (1975), in the analysis of data related to animal production. The data analyzed describe the time, in days, from birth to first laying of yellow quail (Coturnix coturnix japonica) submitted to two diets. For this purpose the discretized versions of five distributions were used: the discrete Burr XII, the discrete Weibull, the discrete gamma, the discrete inverse-Gaussian and the discrete log-normal. For all distributions, the parameter estimates were obtained by the maximum likelihood method. Despite the similarity between the estimates it is natural to choose the discrete given the nature of the data and assuming the discrete distribution, it could be calculated exactly, for example, the probability of the time to the first posture, which is not possible if a continuous distribution is assumed. Thus, among the discrete distributions, the chi-square goodness-of-fit test showed that the Burr XII distribution was the only one indicated to describe the behavior of the data considered.

scholarly journals Joint Modeling of a Longitudinal Measurement and Parametric Survival Data with Application to Primary Biliary Cirrhosis Study

2020 ◽  
pp. 295-304
Author(s):  
Elif Dil ◽  
Duru Karasoy
Keyword(s):  
Longitudinal Data ◽  
Regression Model ◽  
Survival Data ◽  
Cox Regression ◽  
Joint Model ◽  
Linear Mixed Effect Model ◽  
Separate Analysis ◽  
Biliary Cirrhosis ◽  
Mixed Effect ◽  
Cox Regression Model

Although longitudinal and survival data are collected in the same study, they are usually analyzed separately. Measurement errors and missing data problems arise because of separate analysis of these two data. Therefore, joint model should be used instead of separate analysis. The standard joint model frequently used in the literature is obtained by combining the linear mixed effect model of longitudinal data and Cox regression model with survival data. Nevertheless, to use the Cox regression model for survival data, the assumption of proportional hazards must be provided. Parametric survival sub-models should be used instead of the Cox regression model for the survival sub-model of the JM where the assumption is not provided. In this article, parametric joint modeling of longitudinal data and survival data that do not provide the assumption of proportional hazards are investigated. For the survival data, the model with Exponential, Weibull, Log-normal, Log-logistic, and Gamma accelerated failure time models and the linear mixed effect model are combined with random effects and the models were applied in primary biliary cirrhosis data set obtained from Mayo Clinic. After determining the best parametric joint model according to Akaike and Bayesian information criterions, the best available model was compared with standard joint model and of separate analysis of survival data and longitudinal data. As a results, in the studies where longitudinal and survival data are obtained together, it is seen that the parametric joint model gives more better results than the standard joint model when the proportional hazard assumption is not provided.

scholarly journals Revisiting methods for modeling longitudinal and survival data: Framingham Heart Study

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Julius S. Ngwa ◽  
Howard J. Cabral ◽  
Debbie M. Cheng ◽  
David R. Gagnon ◽  
Michael P. LaValley ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Longitudinal Data ◽  
Survival Data ◽  
Framingham Heart Study ◽  
Time Dependent ◽  
Time To Event ◽  
Longitudinal Measure ◽  
Heart Study ◽  
Longitudinal And Survival Data ◽  
Joint Method

Abstract Background Statistical methods for modeling longitudinal and time-to-event data has received much attention in medical research and is becoming increasingly useful. In clinical studies, such as cancer and AIDS, longitudinal biomarkers are used to monitor disease progression and to predict survival. These longitudinal measures are often missing at failure times and may be prone to measurement errors. More importantly, time-dependent survival models that include the raw longitudinal measurements may lead to biased results. In previous studies these two types of data are frequently analyzed separately where a mixed effects model is used for the longitudinal data and a survival model is applied to the event outcome. Methods In this paper we compare joint maximum likelihood methods, a two-step approach and a time dependent covariate method that link longitudinal data to survival data with emphasis on using longitudinal measures to predict survival. We apply a Bayesian semi-parametric joint method and maximum likelihood joint method that maximizes the joint likelihood of the time-to-event and longitudinal measures. We also implement the Two-Step approach, which estimates random effects separately, and a classic Time Dependent Covariate Model. We use simulation studies to assess bias, accuracy, and coverage probabilities for the estimates of the link parameter that connects the longitudinal measures to survival times. Results Simulation results demonstrate that the Two-Step approach performed best at estimating the link parameter when variability in the longitudinal measure is low but is somewhat biased downwards when the variability is high. Bayesian semi-parametric and maximum likelihood joint methods yield higher link parameter estimates with low and high variability in the longitudinal measure. The Time Dependent Covariate method resulted in consistent underestimation of the link parameter. We illustrate these methods using data from the Framingham Heart Study in which lipid measurements and Myocardial Infarction data were collected over a period of 26 years. Conclusions Traditional methods for modeling longitudinal and survival data, such as the time dependent covariate method, that use the observed longitudinal data, tend to provide downwardly biased estimates. The two-step approach and joint models provide better estimates, although a comparison of these methods may depend on the underlying residual variance.

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