Joint Modeling of Survival and Longitudinal Data: Likelihood Approach Revisited

Hsieh, Fushing; Tseng, Yi Kuan; Wang, Jane Ling

doi:10.1111/j.1541-0420.2006.00570.x

Cited by 176 publications

(189 citation statements)

References 22 publications

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“…Another issue is about the robustness to the normality assumption of the random effects. It has been noted by Song et al [19] and Hsieh et al [36] that the estimation procedure is robust to the normality assumption in some joint models of longitudinal and survival data with a single failure type. We have not investigated this issue in this paper although we expect similar conclusions.…”

Section: Discussionmentioning

confidence: 99%

An approach to joint analysis of longitudinal measurements and competing risks failure time data

Elashoff

2006

Statistics in Medicine

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SUMMARYJoint analysis of longitudinal measurements and survival data has received much attention in recent years. However, previous work has primarily focused on a single failure type for the event time. In this paper we consider joint modelling of repeated measurements and competing risks failure time data to allow for more than one distinct failure type in the survival endpoint which occurs frequently in clinical trials. Our model uses latent random variables and common covariates to link together the sub-models for the longitudinal measurements and competing risks failure time data, respectively. An EM-based algorithm is derived to obtain the parameter estimates, and a profile likelihood method is proposed to estimate their standard errors. Our method enables one to make joint inference on multiple outcomes which is often necessary in analyses of clinical trials. Furthermore, joint analysis has several advantages compared with separate analysis of either the longitudinal data or competing risks survival data. By modelling the event time, the analysis of longitudinal measurements is adjusted to allow for non-ignorable missing data due to informative dropout, which cannot be appropriately handled by the standard linear mixed effects models alone. In addition, the joint model utilizes information from both outcomes, and could be substantially more efficient than the separate analysis of the competing risk survival data as shown in our simulation study. The performance of our method is evaluated and compared with separate analyses using both simulated data and a clinical trial for the scleroderma lung disease.

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Section: Discussionmentioning

confidence: 99%

An approach to joint analysis of longitudinal measurements and competing risks failure time data

Elashoff

2006

Statistics in Medicine

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“…For comparison with the analysis by Tseng et al (2005), we use the same longitudinal model they did (also used in Hsieh et al 2006), and we also consider more flexible alternatives. They noted that scatterplots of temporal profiles of egg production suggested the nonlinear form that corresponds to a gamma kernel, namely t b 1 e b 2 (t−1) , with different b 1 and b 2 for each medfly.…”

Section: Longevity Of Medfliesmentioning

confidence: 99%

Predictive comparison of joint longitudinal-survival modeling: a case study illustrating competing approaches

2010

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The joint modeling of longitudinal and survival data has received extraordinary attention in the statistics literature recently, with models and methods becoming increasingly more complex. Most of these approaches pair a proportional hazards survival with longitudinal trajectory modeling through parametric or nonparametric specifications. In this paper we closely examine one data set previously analyzed using a two parameter parametric model for Mediterranean fruit fly (medfly) egg-laying trajectories paired with accelerated failure time and proportional hazards survival models. We consider parametric and nonparametric versions of these two models, as well as a proportional odds rate model paired with a wide variety of longitudinal trajectory assumptions reflecting the types of analyses seen in the literature. In addition to developing novel nonparametric Bayesian methods for joint models, we emphasize the importance of model selection from among joint and non joint models. The default in the literature is to omit at the outset non joint models from consideration. For the medfly data, a predictive diagnostic criterion suggests that both the choice of survival model and longitudinal assumptions can grossly affect model adequacy and prediction. Specifically for these data, the simple joint model used in by Tseng et al. (Biometrika 92:587-603, 2005) and models with much more flexibility in their longitudinal components are predictively outperformed by simpler analyses. This case study underscores the need for data analysts to compare on the basis of predictive performance different joint models and to include non joint models in the pool of candidates under consideration.

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“…However, this is a huge matrix in the joint modeling setting, due to the high dimensionality of the baseline hazard function. There is no shortcut to invert it in any joint modeling approach as explained in Hsieh et al (2006). We thus revert to the bootstrap procedure to estimate the variance (or covariance) of θ.…”

Section: Variance Estimationmentioning

confidence: 99%

Modeling Longitudinal Data with Nonparametric Multiplicative Random Effects Jointly with Survival Data

Ding

Wang

2008

Biometrics

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SummaryIn clinical studies, longitudinal biomarkers are often used to monitor disease progression and failure time. Joint modeling of longitudinal and survival data has certain advantages and has emerged as an effective way to mutually enhance information. Typically, a parametric longitudinal model is assumed to facilitate the likelihood approach. However, the choice of a proper parametric model turns out to be more elusive than models for standard longitudinal studies in which no survival endpoint occurs. In this article, we propose a nonparametric multiplicative random effects model for the longitudinal process, which has many applications and leads to a flexible yet parsimonious nonparametric random effects model. A proportional hazards model is then used to link the biomarkers and event time. We use B-splines to represent the nonparametric longitudinal process, and select the number of knots and degrees based on a version of the Akaike information criterion (AIC). Unknown model parameters are estimated through maximizing the observed joint likelihood, which is iteratively maximized by the Monte Carlo Expectation Maximization (MCEM) algorithm. Due to the simplicity of the model structure, the proposed approach has good numerical stability and compares well with the competing parametric longitudinal approaches. The new approach is illustrated with primary biliary cirrhosis (PBC) data, aiming to capture nonlinear patterns of serum bilirubin time courses and their relationship with survival time of PBC patients.

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Joint Modeling of Survival and Longitudinal Data: Likelihood Approach Revisited

Cited by 176 publications

References 22 publications

An approach to joint analysis of longitudinal measurements and competing risks failure time data

An approach to joint analysis of longitudinal measurements and competing risks failure time data

Predictive comparison of joint longitudinal-survival modeling: a case study illustrating competing approaches

Modeling Longitudinal Data with Nonparametric Multiplicative Random Effects Jointly with Survival Data

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