Joint Modeling Method Research Articles

Bayesian Joint Modeling of Longitudinal Measurements and Time-to-Event Data Using Robust Distributions

Distributional assumptions of most of the existing methods for joint modeling of longitudinal measurements and time-to-event data cannot allow incorporation of outlier robustness. In this article, we develop and implement a joint modeling of longitudinal and time-to-event data using some powerful distributions for robust analyzing that are known as normal/independent distributions. These distributions include univariate and multivariate versions of the Student’s t, the slash, and the contaminated normal distributions. The proposed model implements a linear mixed effects model under a normal/independent distribution assumption for both random effects and residuals of the longitudinal process. For the time-to-event process a parametric proportional hazard model with a Weibull baseline hazard is used. Also, a Bayesian approach using the Markov-chain Monte Carlo method is adopted for parameter estimation. Some simulation studies are performed to investigate the performance of the proposed method under presence and absence of outliers. Also, the proposed methods are applied for analyzing a real AIDS clinical trial, with the aim of comparing the efficiency and safety of two antiretroviral drugs, where CD4 count measurements are gathered as longitudinal outcomes. In these data, time to death or dropout is considered as the interesting time-to-event outcome variable. Different model structures are developed for analyzing these data sets, where model selection is performed by the deviance information criterion (DIC), expected Akaike information criterion (EAIC), and expected Bayesian information criterion (EBIC).

Laser-vision-based quality inspection system for small-bead laser welding

A laser-vision-based weld quality inspection system was developed and implemented for non-destructive weld measurement and defect detection. Our laser vision sensor module is designed based on the principle of laser triangulation. This paper summarizes our work on weld joint profile extraction, feature point extraction, weld bead size measurement, and defect detection. The configuration of the laser vision sensor is described and analyzed in detail, as well as the proposed image processing algorithms. A fast and reliable approach for detecting feature points on the laser stripe profile is proposed by using a sliding vector method. Weld joint modeling and dimension measurement methods are discussed in detail. The system allows the three-dimensional (3D) profile of the weld surface to be reconstructed in real time to allow weld monitoring and control, as well as post-weld quality inspection. Some experiments were implemented for size measurement and defect detection, using the laser-vision-based weld quality inspection system for small-sized beads. Experimental results show that the proposed system achieves highly accurate and satisfactory performance for real-time inspection requirements.

Sample size formula for joint modelling of longitudinal and time-to-event data in clinical trials

In many clinical trials, longitudinal or repeated measures data is collected in order to monitor the patient's progress over time towards a clinical end-point. One method of accounting for the two outcomes is by using joint modelling methods. However, little work has been done on sample size calculations for studies which use joint modelling of longitudinal and time-to-event data to establish treatment effects. We propose a sample size formula based on the random effects formulation of the joint model. The method calculates the sample size and power based on the number of longitudinal time points by extending the Schoenfeld [1] approach to sample size for the proportional hazards model. We derive the required number of events using the score statistic [2] based on the random effects joint model [3].

Semiparametric Bayesian joint modeling of a binary and continuous outcome with applications in toxicological risk assessment

Many dose-response studies collect data on correlated outcomes. For example, in developmental toxicity studies, uterine weight and presence of malformed pups are measured on the same dam. Joint modeling can result in more efficient inferences than independent models for each outcome. Most methods for joint modeling assume standard parametric response distributions. However, in toxicity studies, it is possible that response distributions vary in location and shape with dose, which may not be easily captured by standard models. To address this issue, we propose a semiparametric Bayesian joint model for a binary and continuous response. In our model, a kernel stick-breaking process prior is assigned to the distribution of a random effect shared across outcomes, which allows flexible changes in distribution shape with dose shared across outcomes. The model also includes outcome-specific fixed effects to allow different location effects. In simulation studies, we found that the proposed model provides accurate estimates of toxicological risk when the data do not satisfy assumptions of standard parametric models. We apply our method to data from a developmental toxicity study of ethylene glycol diethyl ether.

Kinematics Simulation for the Baler's Locking Device Based on ADAMS

By using Solid Edge, the virtual prototype of the steel stripe locking device of the baler can be set up. The kinematics analysis can be accomplished through ADAMS. According to this joint modeling method, the simulation of the parts of the power input and output are analyzed. According to this kinematics simulation analysis, the foundation for the mechanical optimized design of steel stripe locking device will be laid. By this joint virtual prototype simulation, complex virtual prototype mechanism design has a certain practical reference value.

Sparse integrative clustering of multiple omics data sets

High resolution microarrays and second-generation sequencing platforms are powerful tools to investigate genome-wide alterations in DNA copy number, methylation, and gene expression associated with a disease. An integrated genomic profiling approach measuring multiple omics data types simultaneously in the same set of biological samples would render an integrated data resolution that would not be available with any single data type. In this study, we use penalized latent variable regression methods for joint modeling of multiple omics data types to identify common latent variables that can be used to cluster patient samples into biologically and clinically relevant disease subtypes. We consider lasso (Tibshirani, 1996), elastic net (Zou and Hastie, 2005), and fused lasso (Tibshirani et al., 2005) methods to induce sparsity in the coefficient vectors, revealing important genomic features that have significant contributions to the latent variables. An iterative ridge regression is used to compute the sparse coefficient vectors. In model selection, a uniform design (Fang and Wang, 1994) is used to seek "experimental" points that scattered uniformly across the search domain for efficient sampling of tuning parameter combinations. We compared our method to sparse singular value decomposition (SVD) and penalized Gaussian mixture model (GMM) using both real and simulated data sets. The proposed method is applied to integrate genomic, epigenomic, and transcriptomic data for subtype analysis in breast and lung cancer data sets.

Statistical Considerations Are Necessary in Assessing Associations between Micronutrient Intake and Times to Clinical Events

Dear Editor, Recently, de Oliveira Otto et al. (1) studied the associations of incidence of three clinical conditions with intake of certain micronutrients. The authors used Cox regression analysis to model times to metabolic syndrome (MetS), Type 2 diabetes, and cardiovascular disease (CVD) given baseline characteristics, including nutrient intake based on responses to an FFQ. To test for linear trends between nutrient intake and the outcomes, they treated intakes as continuous variables using the medians for each quintile. However, the baseline nutrient intake and follow-up biological measurements may be subject to substantial error. Mismeasured covariates in Cox models may lead to biased estimates, and hence, misleading inference (2,3). Statistical literature considers traditional methods that fail to account for covariate error as “naive” and recommends several methods for modeling of time-to-event data and covariates measured with error (4). Two-stage joint-modeling methods such as those used by Dafni and Tsiatis (3) model the covariate process using a mixed effects model and the time-to-event outcome by a Cox model based on the predicted covariate values. Many are approximate, requiring regression calibration (RC). Tsiatis and Davidian (5) propose a conditional score estimator that relaxes the assumption of normal random effects. Others capture extraneous variability via latent variables or latent classes, which may be useful for heterogeneous populations with potentially different baseline hazards. In the Nutrition Prevention of Cancer trials, Lin et al. (6) use latent class joint-modeling to investigate the association between selenium and prostate cancer. Simulation extrapolation (SIMEX) has also been used recently. RC is preferable to SIMEX when there is substantial measurement error, but it is not robust to misspecification of the measurement error distribution (7,8). When measurement error is understated, RC underestimates risk; when measurement error is overstated, RC overestimates risk (7). Two-stage joint models may be implemented in software such as SAS using standard procedures for mixed models and Cox models (4). Lin et al. (6) are willing to provide code in S Plus. Joint models are generally less biased and more powerful than naive approaches (3,5). Therefore, some conclusions by de Oliveira Otto et al. (1) may be suspect. Random measurement error, which biases estimates toward the null, is especially acute in nutritional epidemiological studies. Joint modeling may illuminate significant associations that were biased toward the null in the study by de Oliveira Otto et al. (1). Examples include the associations in model 2 of MetS with vitamin E and zinc as well as of CVD with zinc from red meat, adjusted for total heme iron. There may also be bias away from the null. A covariate that should be highly predictive of the event may carry residual error that artificially inflates the effect of another covariate. Consequently, the reported significant associations in the study by de Oliveira Otto et al. (1) may in fact be spurious and nonsignificant in a joint model. Dafni and Tsiatis (3) simulated an HIV treatment independent of AIDS progression after adjusting for CD4 counts, a highly variable biomarker predictive of the event time. Estimates ignoring error in CD4 counts were biased away from the null, incorrectly highlighting a treatment effect. Analyzing the data in the study by de Oliveira Otto et al. (1) with methodology that accounts for covariate measurement error constitutes better statistical practice and would strengthen the validity of the study.

Approximate nonparametric corrected-score method for joint modeling of survival and longitudinal data measured with error

We consider the problem of jointly modeling survival time and longitudinal data subject to measurement error. The survival times are modeled through the proportional hazards model and a random effects model is assumed for the longitudinal covariate process. Under this framework, we propose an approximate nonparametric corrected-score estimator for the parameter, which describes the association between the time-to-event and the longitudinal covariate. The term nonparametric refers to the fact that assumptions regarding the distribution of the random effects and that of the measurement error are unnecessary. The finite sample size performance of the approximate nonparametric corrected-score estimator is examined through simulation studies and its asymptotic properties are also developed. Furthermore, the proposed estimator and some existing estimators are applied to real data from an AIDS clinical trial.

Treatment of Death in the Analysis of Longitudinal Studies of Gerontological Outcomes

Longitudinal studies in gerontology are characterized by termination of measurement from death. Death is related to many important gerontological outcomes, such as functional disability, and may, over time, change the composition of an older study population. For these reasons, treating death as noninformative censoring of a longitudinal outcome may result in biased estimates of regression coefficients related to that outcome. In a longitudinal study of community-living older persons, we analytically and graphically illustrate the dependence between death and functional disability. Relative to survivors, decedents display a rapid decline of functional ability in the months preceding death. Death's strong relationship with functional disability demonstrates that death is not independent of this outcome and, hence, leads to informative censoring. We also demonstrate the "healthy survivor effect" that results from death's selection effect, with respect to functional disability, on the longitudinal makeup of an older study population. We briefly survey commonly used approaches for longitudinal modeling of gerontological outcomes, with special emphasis on their treatment of death. Most common methods treat death as noninformative censoring. However, joint modeling methods are described that take into account any dependency between death and a longitudinal outcome. In longitudinal studies of older persons, death is often related to gerontological outcomes and, therefore, cannot be safely assumed to represent noninformative censoring. Such analyzes must account for the dependence between outcomes and death as well as the changing nature of the cohort.

A Case Study of the Korean Traditional Wood House-Mindori

The purpose of this study is to show logical member models considering the Korean traditional construction method and present a simple but rational modeling method of the whole structure to evaluate the structural stability of the KTWS. For this purpose, one of the KTWS, the Mindori House is selected and a structure analysis is performed considering its construction stage and load transfer mechanism. The variation of the behaviors according to joint modeling methods is studied using SAP2000 program and its results are compared with those of manual calculation.

A Bayesian approach to joint modeling of protein–DNA binding, gene expression and sequence data

The genome-wide DNA-protein-binding data, DNA sequence data and gene expression data represent complementary means to deciphering global and local transcriptional regulatory circuits. Combining these different types of data can not only improve the statistical power, but also provide a more comprehensive picture of gene regulation. In this paper, we propose a novel statistical model to augment protein-DNA-binding data with gene expression and DNA sequence data when available. We specify a hierarchical Bayes model and use Markov chain Monte Carlo simulations to draw inferences. Both simulation studies and an analysis of an experimental data set show that the proposed joint modeling method can significantly improve the specificity and sensitivity of identifying target genes as compared with conventional approaches relying on a single data source.

Functional variance estimation using penalized splines with principal component analysis

In many fields of empirical research one is faced with observations arising from a functional process. If so, classical multivariate methods are often not feasible or appropriate to explore the data at hand and functional data analysis is prevailing. In this paper we present a method for joint modeling of mean and variance in longitudinal data using penalized splines. Unlike previous approaches we model both components simultaneously via rich spline bases. Estimation as well as smoothing parameter selection is carried out using a mixed model framework. The resulting smooth covariance structures are then used to perform principal component analysis. We illustrate our approach by several simulations and an application to financial interest data.

Using Experimental Designs, Assisted History-Matching Tools, and Bayesian Framework To Get Probabilistic Gas-Storage Pressure Forecasts

Summary One of the main concerns in the oil and gas business is generating reliable reservoir hydrodynamics forecasts. Such profiles are the cornerstones of optimal technico-economical management decisions. A workflow combining different methods to integrate and reduce most of the subsurface uncertainties using multiple history matched models (explaining the past) to infer reasonably reliable forecasts is proposed. A sensitivity study is first performed using experimental design to scan the whole range of static and dynamic uncertainty parameters using a proxy model of the fluid-flow simulator. Only the most sensitive ones with respect to an objective function (OF) (quantifying the mismatch between the simulation results and the observations) are retained for subsequent steps. Assisted history-matching tools are then used to obtain multiple history-matched models. To obtain probabilistic pressure profiles, multiple history-matched models are combined with the uncertain parameters not retained in the sensitivity study, using the joint modeling method. Another way to constrain uncertain parameters with observation data is to use Bayesian framework where a posteriori distributions of the input parameters are derived from the a priori distributions and the likelihood function. The latter is computed through a nonlinear proxy model using experimental design, kriging, and dynamic training techniques. These two workflows have been applied to a real gas storage case submitted to significant seasonal pressure variations. The obtained probabilistic operational pressure profiles for a given period are then compared to the actual gas storage dynamic behavior so that we can compare the two approaches and assess the added value of both proposed workflows.

A semiparametric joint model for longitudinal and survival data with application to hemodialysis study.

In many longitudinal clinical studies, the level and progression rate of repeatedly measured biomarkers on each subject quantify the severity of the disease and that subject's susceptibility to progression of the disease. It is of scientific and clinical interest to relate such quantities to a later time-to-event clinical endpoint such as patient survival. This is usually done with a shared parameter model. In such models, the longitudinal biomarker data and the survival outcome of each subject are assumed to be conditionally independent given subject-level severity or susceptibility (also called frailty in statistical terms). In this article, we study the case where the conditional distribution of longitudinal data is modeled by a linear mixed-effect model, and the conditional distribution of the survival data is given by a Cox proportional hazard model. We allow unknown regression coefficients and time-dependent covariates in both models. The proposed estimators are maximizers of an exact correction to the joint log likelihood with the frailties eliminated as nuisance parameters, an idea that originated from correction of covariate measurement error in measurement error models. The corrected joint log likelihood is shown to be asymptotically concave and leads to consistent and asymptotically normal estimators. Unlike most published methods for joint modeling, the proposed estimation procedure does not rely on distributional assumptions of the frailties. The proposed method was studied in simulations and applied to a data set from the Hemodialysis Study.

Unsupervised joint prosody labeling and modeling for Mandarin speech

An unsupervised joint prosody labeling and modeling method for Mandarin speech is proposed, a new scheme intended to construct statistical prosodic models and to label prosodic tags consistently for Mandarin speech. Two types of prosodic tags are determined by four prosodic models designed to illustrate the hierarchy of Mandarin prosody: the break of a syllable juncture to demarcate prosodic constituents and the prosodic state to represent any prosodic domain's pitch-level variation resulting from its upper-layered prosodic constituents' influences. The performance of the proposed method was evaluated using an unlabeled read-speech corpus articulated by an experienced female announcer. Experimental results showed that the estimated parameters of the four prosodic models were able to explore and describe the structures and patterns of Mandarin prosody. Besides, certain corresponding relationships between the break indices labeled and the associated words were found, and manifested the connections between prosodic and linguistic parameters, a finding further verifying the capability of the method presented. Finally, a quantitative comparison in labeling results between the proposed method and human labelers indicated that the former was more consistent and discriminative than the latter in prosodic feature distributions, a merit of the method developed here on the applications of prosody modeling.

Robust Joint Modeling of Longitudinal Measurements and Competing Risks Failure Time Data

Existing methods for joint modeling of longitudinal measurements and survival data can be highly influenced by outliers in the longitudinal outcome. We propose a joint model for analysis of longitudinal measurements and competing risks failure time data which is robust in the presence of outlying longitudinal observations during follow-up. Our model consists of a linear mixed effects sub-model for the longitudinal outcome and a proportional cause-specific hazards frailty sub-model for the competing risks data, linked together by latent random effects. Instead of the usual normality assumption for measurement errors in the linear mixed effects sub-model, we adopt a t -distribution which has a longer tail and thus is more robust to outliers. We derive an EM algorithm for the maximum likelihood estimates of the parameters and estimate their standard errors using a profile likelihood method. The proposed method is evaluated by simulation studies and is applied to a scleroderma lung study.

Hip joint modeling for the control of the joint center and the range of motions

This paper presents a medical visualization tool implementing a hip joint modeling method that offers the control of the hip joint center and the assessment of the hip range of motions. As the shape of the femoral head is not a perfect sphere, it is in fact close to a 3D conchoid shape, the resulting articulation center cannot be modeled as the center of the sphere that best approximates the femoral head. In order to correctly assess the range of motion of a patient's hip, the medical doctor cannot proceed with such an approximation method. An automatic computation methodology of the hip joint center location is being designed and implemented based on the shape of the acetabular rim. And more, the extreme ranges of motions are calculated on the bony hip model.

Simultaneous analysis of quality of life and survival data.

In many phase III clinical trials, particularly in the field of cancer, the comparison of treatments is based on both length of survival and quality of life. Subjects are followed over time until death and during this period, quality of life is assessed on a number of occasions. Simultaneous analysis of these two outcomes supplements the comparison of treatments in terms of each outcome independently with an assessment of the net effect. In addition, it provides a means of accounting for the informative dropout due to death of patients within the time frame of the quality of life study. The methods also have the potential to be extended to allow for informative dropout from the quality of life study prior to death. There are a number of broad approaches for the simultaneous analysis of quality of life and survival data. The most widely used approach in clinical research is quality-adjusted survival analysis, where treatments are compared in terms of a composite measure of quality and quantity of life. The paper reviews the different techniques for quality-adjusted survival analysis, illustrating the methodology by application to data from a phase III clinical trial in pancreatic cancer. In addition, alternative approaches using multistate survival analysis and joint modelling methods are also discussed.