Joint Analysis of Longitudinal Data Comprising Repeated Measures and Times to Events

Xu, Jing; Zeger, Scott L.

doi:10.1111/1467-9876.00241

Cited by 177 publications

(154 citation statements)

References 28 publications

(23 reference statements)

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“…The random intercept U i ~ N(0, 0.5) was independent of the measurement error ε i j , which was distributed as N(0, 0.25). We simulated two competing risks for event times, say risk 1 and risk 2, with the marginal probability for risk 1 specified as (18) and the following conditional hazards for the two risks:…”

Section: Simulation Studymentioning

confidence: 99%

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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: Simulation Studymentioning

confidence: 99%

“…Joint modelling of the two different types of endpoints simultaneously has received considerable attention in recent years [9][10][11][12][13][14][15][16][17][18][19][20]. Tsiatis and Davidian provided a nice overview of joint models [21].…”

Section: Introductionmentioning

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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“…The frequently used approach for a univariate case assumes that the longitudinal data follow a linear mixed-effects model [13] and that the hazard depends both on the random effects and other time-independent covariates through a Cox proportional hazard relationship [14][15][16]. Xu and Zeger [17] extended the model using the generalized linear model for the longitudinal process to allow for continuous or discrete covariates. Wang and Taylor [18] included a stochastic (an integrated Ornstein-Uhlenbeck) process into the model of longitudinal data to allow for random fluctuations of individual measurements around the population average.…”

Section: Introductionmentioning

confidence: 99%

Stochastic model for analysis of longitudinal data on aging and mortality

Yashin

Arbeev

Akushevich

et al. 2007

Mathematical Biosciences

133

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Aging-related changes in a human organism follow dynamic regularities, which contribute to the observed age patterns of incidence and mortality curves. An organism's "optimal" (normal) physiological state changes with age, affecting the values of risks of disease and death. The resistance to stresses, as well as adaptive capacity, declines with age. An exposure to improper environment results in persisting deviation of individuals' physiological (and biological) indices from their normal state (due to allostatic adaptation), which, in turn, increases chances of disease and death. Despite numerous studies investigating these effects, there is no conceptual framework, which would allow for putting all these findings together, and analyze longitudinal data taking all these dynamic connections into account. In this paper we suggest such a framework, using a new version of stochastic process model of aging and mortality. Using this model, we elaborated a statistical method for analyses of longitudinal data on aging, health and longevity and tested it using different simulated data sets. The results show that the model may characterize complicated interplay among different components of aging-related changes in humans and that the model parameters are identifiable from the data.

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“…We further establish a joint model for TMA corelevel data and survival outcome via a shared random effect. There is a large literature on joint modeling of longitudinal data and survival [9][10][11][12][13][14][15][16]. These methods have been developed predominantly for modeling survival and CD4 counts in AIDS patients; here their application to Tissue Microarray data in cancer biomarker studies is novel.…”

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confidence: 99%

Modeling intra‐tumor protein expression heterogeneity in tissue microarray experiments

Shen¹,

Ghosh²,

Taylor³

2008

Statistics in Medicine

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SUMMARYTissue Microarrays (TMAs) measure tumor-specific protein expression via high-density immunohistochemical staining assays. They provide a proteomic platform for validating cancer biomarkers emerging from large-scale DNA microarray studies. Repeated observations within each tumor result in substantial biological and experimental variability. This variability is usually ignored when associating the TMA expression data with patient survival outcome. It generates biased estimates of hazard ratio in proportional hazards models. We propose a Latent Expression Index (LEI) as a surrogate protein expression estimate in a two-stage analysis. Several estimators of LEI are compared: an Empirical Bayes (EB), a Full Bayes (FB), and a Varying Replicate Number (VRN) estimator. In addition, we jointly model survival and TMA expression data via a shared random effects model. Bayesian estimation is carried out using a Markov Chain Monte Carlo (MCMC) method. Simulation studies were conducted to compare the two-stage methods and the joint analysis in estimating the Cox regression coefficient. We show the two-stage methods reduce bias relative to the naive approach, but still lead to under-estimated hazard ratios. The joint model consistently outperforms the two-stage methods in terms of both bias and coverage property in various simulation scenarios. In case studies using prostate cancer TMA data sets, the two stage methods yields a good approximation in one data set while an insufficient one in the other. A general advice is to use the joint model inference whenever results differ between the two-stage methods and the joint analysis.

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Joint Analysis of Longitudinal Data Comprising Repeated Measures and Times to Events

Cited by 177 publications

References 28 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

Stochastic model for analysis of longitudinal data on aging and mortality

Modeling intra‐tumor protein expression heterogeneity in tissue microarray experiments

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