Scalable Joint Models for Reliable Uncertainty-Aware Event Prediction.

A fast EM algorithm for fitting joint models of a binary response and multiple longitudinal covariates subject to detection limits

<p>Joint models for longitudinal and survival data have been widely discussed in the literature. This thesis proposes a joint model using a stereotype model for the longitudinal ordinal responses and a Cox proportional hazards model for survival time. Our current joint model has a new feature since no literature has examined the joint model under the stereotype model. The stereotype model can improve the fit by adding extra score parameters, but it still has the advantage of requiring only a single parameter to describe the effect of a predictor on the item response levels. We give an example to model longitudinal ordinal data and survival data for patients being followed up after treatments. The main focus is on modeling both the quality of life data and the survival data simultaneously with a goal of understanding the association between the two processes over time. These two models are linked through a latent variable that characterizes the quality of life of an individual and is assumed to underlie the hazard rate. In other words, the latent variable serves as a shared variable in the joint model. We present the joint model in two different aspects: one based on a Bayesian approach and the other one a semiparametric approach using the EM algorithm. For the Bayesian approach, the latent variable is treated as a continuous variable and is assumed to have a multivariate normal distribution. The partial survival likelihood function is used in the survival component of the Bayesian joint model, while the full likelihood function is considered in the semiparametric joint model. In the latter approach the baseline hazard is assumed to be a step function and has no parametric form. The latent variable in the semiparametric joint model is then treated as a discrete variable. We illustrate our methodologies by analyzing data from the Staccato study, a randomized trial to compare two treatment methods, for Human Immunodeficiency Virus (HIV) infection of Thai patients on Highly Active Antiretroviral Therapy (HAART), in which the quality of life was assessed with a HIV Medical Outcome Study (MOS-HIV) questionnaire. Furthermore, we extend the study further to the case of multiple failure types in the survival component. Thus, the extension of the joint model consists of the stereotype model and the competing risks model. The Bayesian method is employed to estimate all unknown parameters in this extended joint model. The results we obtained are consistent for both the Bayesian joint model and the semiparametric joint model. Both models show that patients who had a better quality of life were associated with a lower hazard of HIV progression. Patients on continuous treatment also had a lower hazard of HIV progression compared with patients on CD4-guided interruption treatment.</p>

Many statistical models have been proposed in the literature for the analysis of longitudinal data. One may propose to model two or more correlated longitudinal processes simultaneously, with a goal of understanding their association over time. Joint modeling is then required to carefully study the association structure among the outcomes as well as drawing joint inferences about the different outcomes. In this study, we sought to model the associations among six nutrition outcomes while circumventing the computational challenge posed by their clustered and high-dimensional nature. We analyzed data from a 2 2 randomized crossover trial conducted in Kenya, to compare the effect of high-dose and low-dose iodine in household salt on systolic blood pressure (SBP) and diastolic blood pressure (DBP) in women of reproductive age and their household matching pair of school-aged children. Two additional outcomes, namely, urinary iodine concentration (UIC) in women and children were measured repeatedly to monitor the amount of iodine excreted through urine. We extended the model proposed by Mwangi etal. (2021, Communications in Statistics: Case Studies, Data Analysis and Applications, 7(3), 413-431) allowing flexible piecewise joint models for six outcomes to depend on separate random effects, which are themselves correlated. This entailed fitting 15 bivariate general linear mixed models and deriving inference for the joint model using pseudo-likelihood theory. We analyzed the outcomes separately and jointly using piecewise linear mixed-effects (PLME) model and further validated the results using current state-of-the-art Jones and Kenward methodology (JKME model) used for analyzing randomized crossover trials. The results indicate that high-dose iodine in salt significantly reduced blood pressure (BP) compared to low-dose iodine in salt. Estimates for the random effects and residual error components showed that SBP and DBP had strong positive correlation, with effect of the random slope indicating that significantly related outcomes are strongly associated in their evolution. There was a moderately strong inverse relationship between evolutions of UIC and BP both in women and children. These findings confirmed the original hypothesis that high-dose iodine salt has significant lowering effect on BP. We further sought to evaluate the performance of our proposed PLME model against the widely used JKME model, within the multivariate joint modeling framework through a simulation study mimicking a crossover design. From our findings, the multivariate joint PLME model performed exceptionally well both in estimation of random-effects matrix (G) and Hessian matrix (H), allowing satisfactory model convergence during estimation. It allowed a more complex fit to the data with both random intercepts and slopes effects compared to the multivariate joint JKME model that allowed for random intercepts only. When a hierarchical viewpoint is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive definite. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters. The key highlight in this evaluation shows that multivariate joint JKME model is a powerful tool especially while fitting mixed models with random intercepts only, in crossover design settings. Addition of random slopes may lead to model complexities in most cases, resulting in unsatisfactory model convergence during estimation. To circumvent convergence pitfalls, extention of JKME model to PLME model allows a more flexible fit to the data (generated from crossover design settings), especially in the multivariate joint modelingframework.

A predictive joint shared parameter model is proposed for discrete time-to-event and longitudinal data. A discrete survival model with frailty and a generalized linear mixed model for the longitudinal data are joined to predict the probability of events. This joint model focuses on predicting discrete time-to-event outcome, taking advantage of repeated measurements. We show that the probability of an event in a time window can be more precisely predicted by incorporating the longitudinal measurements. The model was investigated by comparison with a two-step model and a discrete-time survival model. Results from both a study on the occurrence of tuberculosis and simulated data show that the joint model is superior to the other models in discrimination ability, especially as the latent variables related to both survival times and the longitudinal measurements depart from 0.

Modular design is a dynamic process and obtains rational architecture of product family continuously. It needs modeling technology to prepare skeleton for evolution of product system, and adapt to the dynamic characteristic. In this paper, a joint modeling technique is proposed to prepare for evolution of product system, which considers design process as one part of the product system. According to close-loop process of modular design, modeling techniques are analysed and a joint modeling approach is advanced. By comparing interface propagation with network, correlative information is organized in the form of network, and it is collected into a tri-view model. Then collaborative model is given by modular layouts and model of product family is established. In this way, a two-way channel for application and optimization of modular scheme is taken shape. Finally, a case is presented to illustrate the application of this approach, which proved the effectiveness of this approach.

Paired pectoral fins that are capable of rowing motions are an important actuation mechanism for robotic fish. Existing work in this area typically adopts a rigid connection between the actuator and the pectoral fins, which requires a faster actuation speed in the power stroke than in the recovery stroke to produce a net thrust or moment. In addition to increasing the control complexity, the latter requirement leads to slow robot speeds due to prolonged deceleration during the recovery stroke. In this paper, we propose the design of a novel flexible passive joint that connects the servomotor arm to the pectoral fin, to overcome the aforementioned problem. A dynamic model is developed for the joint and for a robotic fish equipped with such joints. The design and the model are evaluated with extensive experimental results. With symmetric actuation patterns during the power and recovery strokes, the robotic fish with the proposed joints shows clear speed advantage over the case involving rigid joints and asymmetric actuation. Motivated by the need for design optimization, the model is further utilized to investigate the influence of the joint length and stiffness on the robot locomotion performance and efficiency. It is found that, for low fin-beat frequencies, longer or more flexible joints lead to higher speeds, and the trend is reversed at high fin-beat frequencies. On the other hand, while the mechanical efficiency shows a decreasing trend when the frequency increases, it is higher with shorter joints. These findings suggest the utility of the proposed model for multiobjective design of the joint and its operating frequency.

A flexible joint model and the corresponding mechanism synthesis approach are proposed in this article for simultaneously optimizing the topology and dimension configuration of planar mechanisms. The proposed approach leverages topology optimization, enabling the generation of diverse configurations without any predetermined baseline mechanism. The flexible joint model proposed in this article consists of a revolute joint and two orthogonal prismatic joints, which represent the relative motions of the adjacent rigid bodies in three degrees of freedom (DOF). The zero-length springs are employed to restrict the relative motion DOF, thereby emulating the functionality of different joint types. The flexible joint model allows for the configuration of the mechanism to be expressed using only a few parameters. The synthesis problem of the path-generating mechanism is converted into a numerical parameter optimization problem based on the strain energy of the flexible joint model and solved by the sequential quadratic programming (SQP) algorithm. To address inaccuracies in the calculation of degrees of freedom in the Grübler–Kutzbach (G–K) formulation, a supplementary constraint function based on the strain energy of the flexible joint is proposed. To demonstrate the validity of the proposed approach, several mechanism synthesis problems are solved by this approach.

In some clinical trials and epidemiologic studies, investigators are interested in knowing whether the variability of a biomarker is independently predictive of clinical outcomes. This question is often addressed via a naïve approach where a sample-based estimate (e.g., standard deviation) is calculated as a surrogate for the "true" variability and then used in regression models as a covariate assumed to be free of measurement error. However, it is well known that the measurement error in covariates causes underestimation of the true association. The issue of underestimation can be substantial when the precision is low because of limited number of measures per subject. The joint analysis of survival data and longitudinal data enables one to account for the measurement error in longitudinal data and has received substantial attention in recent years. In this paper we propose a joint model to assess the predictive effect of biomarker variability. The joint model consists of two linked sub-models, a linear mixed model with patient-specific variance for longitudinal data and a full parametric Weibull distribution for survival data, and the association between two models is induced by a latent Gaussian process. Parameters in the joint model are estimated under Bayesian framework and implemented using Markov chain Monte Carlo (MCMC) methods with WinBUGS software. The method is illustrated in the Ocular Hypertension Treatment Study to assess whether the variability of intraocular pressure is an independent risk of primary open-angle glaucoma. The performance of the method is also assessed by simulation studies.

ABSTRACTIt often happens in longitudinal studies that repeated measurements of markers are observed with various data features of a heterogeneous population comprising of several subclasses, left-censoring due to a limit of detection (LOD) and covariates measured with error. Moreover, repeatedly measured markers in time may be associated with a time-to-event of interest. Inferential procedures may become very complicated when one analyzes data with these features together. This article explores a finite mixture of hierarchical joint models of event times and longitudinal measures with an attempt to alleviate departures from homogeneous characteristics, tailor observations below LOD as missing values, mediate accuracy from measurement error in covariate and overcome shortages of confidence in specifying a parametric time-to-event model with a nonparametric distribution. The Bayesian joint modeling is employed to not only estimate all parameters in mixture of joint models, but also evaluate probabilities of class membership. A real data example is analyzed to demonstrate the methodology by jointly modeling the viral dynamics and the time to decrease in CD4/CD8 ratio in the presence of CD4 cell counts with measurement error and the analytic results are reported by comparing potential models for various scenarios. Supplementary materials for this article are available online.

BackgroundEvaluating engagement with an intervention is a key component of understanding its efficacy. With an increasing interest in developing behavioral interventions in the mobile health (mHealth) space, appropriate methods for evaluating engagement in this context are necessary. Data collected to evaluate mHealth interventions are often collected much more frequently than those for clinic-based interventions. Additionally, missing data on engagement is closely linked to level of engagement resulting in the potential for informative missingness. Thus, models that can accommodate intensively collected data and can account for informative missingness are required for unbiased inference when analyzing engagement with an mHealth intervention.ObjectiveThe objectives of this paper are to discuss the utility of the joint modeling approach in the analysis of longitudinal engagement data in mHealth research and to illustrate the application of this approach using data from an mHealth intervention designed to support illness management among people with schizophrenia.MethodsEngagement data from an evaluation of an mHealth intervention designed to support illness management among people with schizophrenia is analyzed. A joint model is applied to the longitudinal engagement outcome and time-to-dropout to allow unbiased inference on the engagement outcome. Results are compared to a naïve model that does not account for the relationship between dropout and engagement.ResultsThe joint model shows a strong relationship between engagement and reduced risk of dropout. Using the mHealth app 1 day more per week was associated with a 23% decreased risk of dropout (P<.001). The decline in engagement over time was steeper when the joint model was used in comparison with the naïve model.ConclusionsNaïve longitudinal models that do not account for informative missingness in mHealth data may produce biased results. Joint models provide a way to model intensively collected engagement outcomes while simultaneously accounting for the relationship between engagement and missing data in mHealth intervention research.

Aiming at the problem of fast and accurate prediction of torsional stiffness of vehicle body, an optimization method based on the simplified model of flexible joint is proposed. Primarily, a simplified model of flexible joint is established by using mathematical model and simulation analysis method. On this basis, an accurate and reliable whole vehicle wire frame model is established by combining with flexible joint and beam element. In the task of new vehicle development, two joints which need to be optimized are positioned quickly by using the model and sensitivity analysis. And then, orthogonal test is designed to calculate the optimization degree of joint stiffness under the optimal cost and weight conditions. The results show that the optimization method based on the simplified model of flexible joints improves the torsional stiffness of the vehicle body by 17%, reduces the cost of components by 12%, and reduces the weight by 0.5 kg compared with the traditional method, which achieves the effect of improving the quality and reducing the cost.

Estimating Healthcare Demand for an Aging Population: A Flexible and Robust Bayesian Joint Model

Multiple imputation methods can generally be divided into two broad frameworks: joint model (JM) imputation and fully conditional specification (FCS) imputation. JM draws missing values simultaneously for all incomplete variables using a multivariate distribution, whereas FCS imputes variables one at a time from a series of univariate conditional distributions. In single-level multivariate normal data, these two approaches have been shown to be equivalent, but less is known about their similarities and differences with multilevel data. This study examined four multilevel multiple imputation approaches: JM approaches proposed by Schafer and Yucel and Asparouhov and Muthén and FCS methods described by van Buuren and Carpenter and Kenward. Analytic work and computer simulations showed that Asparouhov and Muthén and Carpenter and Kenward methods are most flexible, as they produce imputations that preserve distinct within- and between-cluster covariance structures. As such, these approaches are applicable to random intercept models that posit level-specific relations among variables (e.g., contextual effects analyses, multilevel structural equation models). In contrast, methods from Schafer and Yucel and van Buuren are more restrictive and impose implicit equality constraints on functions of the within- and between-cluster covariance matrices. The analytic work and simulations underscore the conclusion that researchers should not expect to obtain the same results from alternative imputation routines. Rather, it is important to choose an imputation method that partitions variation in a manner that is consistent with the analysis model of interest. A real data analysis example illustrates the various approaches.

In clinical studies, longitudinal and survival data are often obtained simultaneously from the same individual. Linear mixed effects models are widely used for analyzing longitudinal continuous outcome data, while survival models are used for analyzing time-to-event data. It is a common practice to analyze these longitudinal and time-to-event data separately. However, when multivariate outcomes are obtained from a given individual, they can be correlated by nature, and one can attain considerable gain in efficiency by jointly analyzing the outcomes. An objective of this study is to analyze such multivariate data by jointly modeling longitudinally measured continuous outcomes and time-to-event data. In this joint modeling, we formulate a joint likelihood function for both outcomes and use the maximum likelihood method to estimate the parameters in the two sub-models (longitudinal and survival models). We demonstrate the merits of joint modeling by considering a joint analysis of longitudinally measured serum albumin (biomarker) and time-to-all-cause mortality data obtained from a hemodialysis (HEMO) study. This HEMO study was a large NIH (National Institute of Health) sponsored multicenter clinical trial contrasting the effects of dialysis dose and dialysis membrane permeability in end-stage renal disease patients receiving hemodialysis. We find that the parameter estimates obtained under joint modeling of HEMO data are more efficient than those obtained under separate modeling of the outcome variables.

Joint models for longitudinal and time-to-event data have gained a lot of attention in the last few years as they are a helpful technique clinical studies where longitudinal outcomes are recorded alongside event times. Those two processes are often linked and the two outcomes should thus be modeled jointly in order to prevent the potential bias introduced by independent modeling. Commonly, joint models are estimated in likelihood-based expectation maximization or Bayesian approaches using frameworks where variable selection is problematic and that do not immediately work for high-dimensional data. In this paper, we propose a boosting algorithm tackling these challenges by being able to simultaneously estimate predictors for joint models and automatically select the most influential variables even in high-dimensional data situations. We analyze the performance of the new algorithm in a simulation study and apply it to the Danish cystic fibrosis registry that collects longitudinal lung function data on patients with cystic fibrosis together with data regarding the onset of pulmonary infections. This is the first approach to combine state-of-the art algorithms from the field of machine-learning with the model class of joint models, providing a fully data-driven mechanism to select variables and predictor effects in a unified framework of boosting joint models.