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Accurate prediction of remaining useful life (RUL) for in‐service systems plays an important role in ensuring efficient operation of industrial equipment and in preventing unexpected equipment failures. In this paper, we present a prognostic framework for real‐time RUL prediction based on joint modeling of both degradation signals and time‐to‐event data. The proposed model employs a change point‐based general path model to capture signal non‐linearity and Neural network (NN) based Cox model to link the time‐to‐event data with the estimated degradation trend. An empirical two‐step scheme for hyperparameter estimation is proposed to enhance prognostic accuracy. Furthermore, an efficient Bayesian model updating procedure, integrated with recursive particle filtering, is used to facilitate online prediction, achieving accurate RUL prediction in real‐time and accounting for uncertainties in RUL prediction. Simulation and real‐life case studies demonstrate the advantages of the proposed method over existing approaches. [ABSTRACT FROM AUTHOR]

Background: There is still a lack of clinically validated biomarkers to screen lung cancer patients suitable for programmed dead cell-1 (PD-1)/programmed dead cell receptor-1 (PD-L1) immunotherapy. Detection of PD-L1 expression is invasively operated, and some PD-L1-negative patients can also benefit from immunotherapy; thus, the joint modeling of both deep learning images and clinical features was used to improve the prediction performance of PD-L1 expression in non-small cell lung cancer (NSCLC). Methods: Retrospective collection of 101 patients diagnosedwith pathology in our hospital who underwent 18F FDG PET/CT scans, with lung cancer tissue Tumor Propulsion Score (TPS) =1% as a positive expression. Lesions were extracted after preprocessing PET/CT images, and using deep learning 3D DenseNet121 to learn lesions in PET, CT, and PET/CT images, 1,024 fully connected features were extracted; clinical features (age, gender, smoking/no smoking history, lesion diameter, lesion volume, maximum standard uptake value of lesions [SUVmax], mean standard uptake value of lesions [SUVmean], total lesion glycolysis [TLG]) were combined for joint modeling based on the structured data Category Embedding Model. Results: Area under a receiver operating characteristic (ROC) curve (AUC) and accuracy of predicting PD-L1 positive for PET, CT, and PET/CT test groups were 0.814 ± 0.0152, 0.7212 ± 0.0861, and 0.90 ± 0.0605, 0.806 ± 0.023, 0.70 ± 0.074, and 0.950 ± 0.0250, respectively. After joint clinical feature modeling, the AUC and accuracy of predicting PD-L1 positive for PET/CT were 0.96 ± 0.00905 and 0.950 ± 0.0250, respectively. Conclusion: This study combines the features of 18F-FDG PET/CT images with clinical features using deep learning to predict the expression of PD-L1 in NSCLC, suggesting that 18F-FDG PET/CT images can be conducted as biomarkers for PD-L1 expression. [ABSTRACT FROM AUTHOR]

This tutorial shows how various Bayesian survival models can be fitted using the integrated nested Laplace approximation in a clear, legible, and comprehensible manner using the INLA and INLAjoint R‐packages. Such models include accelerated failure time, proportional hazards, mixture cure, competing risks, multi‐state, frailty, and joint models of longitudinal and survival data, originally presented in the article "Bayesian survival analysis with BUGS." In addition, we illustrate the implementation of a new joint model for a longitudinal semicontinuous marker, recurrent events, and a terminal event. Our proposal aims to provide the reader with syntax examples for implementing survival models using a fast and accurate approximate Bayesian inferential approach. [ABSTRACT FROM AUTHOR]

Incomplete longitudinal data are common in life-course epidemiology and may induce bias leading to incorrect inference. Multiple imputation (MI) is increasingly preferred for handling missing data, but few studies explore MI-method performance and feasibility in real-data settings. We compared 3 MI methods using real data under 9 missing-data scenarios, representing combinations of 10%, 20%, and 30% missingness and missing completely at random, at random, and not at random. Using data from Health and Retirement Study (HRS) participants, we introduced record-level missingness to a sample of participants with complete data on depressive symptoms (1998-2008), mortality (2008-2018), and relevant covariates. We then imputed missing data using 3 MI methods (normal linear regression, predictive mean matching, variable-tailored specification), and fitted Cox proportional hazards models to estimate effects of 4 operationalizations of longitudinal depressive symptoms on mortality. We compared bias in hazard ratios, root mean square error, and computation time for each method. Bias was similar across MI methods, and results were consistent across operationalizations of the longitudinal exposure variable. However, our results suggest that predictive mean matching may be an appealing strategy for imputing life-course exposure data, given consistently low root mean square error, competitive computation times, and few implementation challenges.

Joint models for longitudinal and time‐to‐event data are receiving increasing attention owing to its capability of capturing the possible association between these two types of data. Typically, a joint model consists of a longitudinal submodel for longitudinal processes and a survival submodel for the time‐to‐event response, and links two submodels by common covariates that may carry both fixed and random effects. However, research gaps still remain on how to simultaneously select fixed and random effects from the two submodels under the joint modeling framework efficiently and effectively. In this article, we propose a novel block‐coordinate gradient descent (BCGD) algorithm to simultaneously select multiple longitudinal covariates that may carry fixed and random effects in the joint model. Specifically, for the multiple longitudinal processes, a linear mixed effect model is adopted where random intercepts and slopes serve as essential covariates of the trajectories, and for the survival submodel, the popular proportional hazard model is employed. A penalized likelihood estimation is used to control the dimensionality of covariates in the joint model and estimate the unknown parameters, especially when estimating the covariance matrix of random effects. The proposed BCGD method can successfully capture the useful covariates of both fixed and random effects with excellent selection power, and efficiently provide a relatively accurate estimate of fixed and random effects empirically. The simulation results show excellent performance of the proposed method and support its effectiveness. The proposed BCGD method is further applied on two real data sets, and we examine the risk factors for the effects of different heart valves, differing on type of tissue, implanted in the aortic position and the risk factors for the diagnosis of primary biliary cholangitis. [ABSTRACT FROM AUTHOR]

Process data refers to data recorded in computer-based assessments that reflect the problem-solving processes of participants and provide greater insight into how they solve problems. Action time, namely the amount of time required to complete a state transition, is also included in such data along with actions. In this study, an action-level joint model of action sequences and action time is proposed, in which the sequential response model (SRM) is used as the measurement model for action sequences, and a new log-normal action time model is proposed as the measurement model for action time. The proposed model can be regarded as an extension of the SRM by incorporating action time within the joint-hierarchical modeling framework and as an extension of the conventional item-level joint models in process data analysis. Results of the empirical and simulation studies demonstrated that the model setup was justified, model parameters could be interpreted, parameter estimates were accurate, and taking into account participants' action time further was beneficial for obtaining a deep understanding of participants' behavioral patterns. Overall, the proposed action-level joint model provides an innovative modeling framework for analyzing process data in computer-based assessments from the latent variable modeling perspective. [ABSTRACT FROM AUTHOR]

Background: Diabetes mellitus (DM) is a global public health problem characterized by an elevated blood glucose level. Monitoring blood sugar levels is vital for effective diabetes management and preventing complications. However, the association between longitudinal biomarkers and the incidence of diabetic complications is often overlooked. Therefore, this study aimed to assess the incidence of diabetic retinopathy, predictors, and association with longitudinal fasting blood sugar level changes among diabetes mellitus patients in Ethiopia. Methods: A multicenter retrospective follow-up study was carried out in referral hospitals in Amhara region, Ethiopia. A random sample of 462 newly diagnosed DM patients was selected. The proportional hazard assumption was checked for the survival sub-model, and for the longitudinal sub-model, the normality assumption was checked. Then the joint modeling with time-dependent lagged parameterizations was fitted. Model assumptions and comparisons were checked. Finally, the hazard ratio with a 95% confidence interval (CI) with a corresponding P-value<0.05 was used to identify predictors. Results: In this study, Overall, 54 patients developed DR, and the incidence rate was 2.33 per 1000 person-months over the follow-up period, with a 95% CI of [1.78, 3.05]. Rural residence (AHR = 2.21, 95% CI: [1.21, 4.05]), hypertension comorbidity (AHR = 3.01, 95% CI: [1.85, 6.53]), and longer duration of DM (>5 years) (AHR = 2.28, 95% CI: [1.91, 5.15]) were important predictors for the incidence of DR. In addition, the incidence of DR was substantially correlated with the timedependent lagged value of FBS change (AHR = 4.20, 95% CI [1.62, 10.85]). Conclusions: In this study, the incidence of diabetic retinopathy was somewhat high when compared to prior similar studies in Ethiopia. A joint model of longitudinal fasting blood sugar level changes was significantly associated with an increased risk of DR. Besides, being rural residence, hypertension comorbidity, and a longer duration of DM were significant predictors for the incidence of DR. Therefore, public awareness, an integrated care approach, and prioritizing glycemic control are highly recommended. [ABSTRACT FROM AUTHOR]

The complexity of cancer development involves intricate interactions among multiple biomarkers, such as gene-environment interactions. Utilizing microarray gene expression profile data for cancer classification is anticipated to be effective, thus drawing considerable interest in the fields of bioinformatics and computational biology. Due to the characteristics of genomic data, problems of high-dimensional interactions and noise interference do exist during the analysis process. When building cancer diagnosis models, we often face the dilemma of model adaptation errors due to an imbalance of data types. To mitigate the issues, we apply the SMOTE-Tomek procedure to rectify the imbalance problem. Following this, we utilize the overlapping group screening method alongside a binary logistic regression model to integrate gene pathway information, facilitating the identification of significant biomarkers associated with clinically imbalanced cancer or normal outcomes. Simulation studies across different imbalanced rates and gene structures validate our proposed method's effectiveness, surpassing common machine learning techniques in terms of classification prediction accuracy. We also demonstrate that prediction performance improves with SMOTE-Tomek treatment compared to no imbalance treatment and SMOTE treatment across various imbalance rates. In the real-world application, we integrate clinical and gene expression data with prior pathway information. We employ SMOTE-Tomek and our proposed methods to identify critical biomarkers and gene-environment interactions linked to the imbalanced binary outcomes (cancer or normal) in patients from the Cancer Genome Atlas datasets of lung adenocarcinoma and breast invasive carcinoma. Our proposed method consistently achieves satisfactory classification accuracy. Additionally, we have identified biomarkers indicative of gene-environment interactions relevant to cancer and have provided corresponding estimates of odds ratios. Moreover, in high-dimensional imbalanced data, for achieving good prediction results, we recommend considering the order of balancing processing and feature screening. [ABSTRACT FROM AUTHOR]

This article proposes a Bayesian approach for jointly estimating marginal conditional quantiles of multi-response longitudinal data with multivariate mixed effects model. The multivariate asymmetric Laplace distribution is employed to construct the working likelihood of the considered model. Penalization priors on regression parameters are incorporated into the working likelihood to conduct Bayesian high-dimensional inference. Markov chain Monte Carlo algorithm is used to obtain the fully conditional posterior distributions of all parameters and latent variables. Monte Carlo simulations are conducted to evaluate the sample performance of the proposed joint quantile regression approach. Finally, we analyze a longitudinal medical dataset of the primary biliary cirrhosis sequential cohort study to illustrate the real application of the proposed modeling method. [ABSTRACT FROM AUTHOR]

Joint modeling of longitudinal data such as quality of life data and survival data is important for palliative care researchers to draw efficient inferences because it can account for the associations between those two types of data. Modeling quality of life on a retrospective from death time scale is useful for investigators to interpret the analysis results of palliative care studies which have relatively short life expectancies. However, informative censoring remains a complex challenge for modeling quality of life on the retrospective time scale although it has been addressed for joint models on the prospective time scale. To fill this gap, we develop a novel joint modeling approach that can address the challenge by allowing informative censoring events to be dependent on patients' quality of life and survival through a random effect. There are two sub-models in our approach: a linear mixed effect model for the longitudinal quality of life and a competing-risk model for the death time and dropout time that share the same random effect as the longitudinal model. Our approach can provide unbiased estimates for parameters of interest by appropriately modeling the informative censoring time. Model performance is assessed with a simulation study and compared with existing approaches. A real-world study is presented to illustrate the application of the new approach. [ABSTRACT FROM AUTHOR]

Background: A one-time gait speed measurement predicts mortality risk. A framework for updating a clinician’s mortality risk perception with new information from each clinic visit is needed. We used joint modeling of longitudinal and survival data for dynamic prediction of mortality risk. Methods: We fit sex-stratified joint models to 20-meter (bi)annual longitudinal gait speed measured every 6 months and 14-year survival data from the Health, Aging and Body Composition Study allowing for non-linear fluctuations of gait speed and controlling for important covariates such as age, recent hospitalization, blood pressure, obesity, and comorbidities. Results: Participants (N = 3048) were 74 years old with gait speed 1.18 m/s. They were 42% Black, and 52% died over 14 years. Higher gait speed of 0.1 m/s was associated with 23% (95% confidence interval or CI = 20–25%) and 25% (CI = 21–28%) reductions in mortality risk in men and women; and a 0.05 m/s annualized slowing (slope) with 31% (CI = 13–51%) increase in men (all p < 0.05), with findings persisting after covariate adjustment. Distant gait speed history over a year prior contributed little for mortality risk prediction with mean change of only 1–2% in 5-year risk. Conclusion: The two most recent gait speeds appear sufficient to consider for mortality risk in the present initial analysis. More frequent gait speeds need to be considered in mortality risk prediction before definitive conclusions supporting real-world application.

BackgroundThere is still a lack of clinically validated biomarkers to screen lung cancer patients suitable for programmed dead cell-1 (PD-1)/programmed dead cell receptor-1 (PD-L1) immunotherapy. Detection of PD-L1 expression is invasively operated, and some PD-L1-negative patients can also benefit from immunotherapy; thus, the joint modeling of both deep learning images and clinical features was used to improve the prediction performance of PD-L1 expression in non-small cell lung cancer (NSCLC).MethodsRetrospective collection of 101 patients diagnosed with pathology in our hospital who underwent 18F FDG PET/CT scans, with lung cancer tissue Tumor Propulsion Score (TPS) ≥1% as a positive expression. Lesions were extracted after preprocessing PET/CT images, and using deep learning 3D DenseNet121 to learn lesions in PET, CT, and PET/CT images, 1,024 fully connected features were extracted; clinical features (age, gender, smoking/no smoking history, lesion diameter, lesion volume, maximum standard uptake value of lesions [SUVmax], mean standard uptake value of lesions [SUVmean], total lesion glycolysis [TLG]) were combined for joint modeling based on the structured data Category Embedding Model.ResultsArea under a receiver operating characteristic (ROC) curve (AUC) and accuracy of predicting PD-L1 positive for PET, CT, and PET/CT test groups were 0.814 ± 0.0152, 0.7212 ± 0.0861, and 0.90 ± 0.0605, 0.806 ± 0.023, 0.70 ± 0.074, and 0.950 ± 0.0250, respectively. After joint clinical feature modeling, the AUC and accuracy of predicting PD-L1 positive for PET/CT were 0.96 ± 0.00905 and 0.950 ± 0.0250, respectively.ConclusionThis study combines the features of 18F-FDG PET/CT images with clinical features using deep learning to predict the expression of PD-L1 in NSCLC, suggesting that 18F-FDG PET/CT images can be conducted as biomarkers for PD-L1 expression.

INTRODUCTION: The course of depressive symptoms and dementia risk is unclear, as are potential structural neuropathological common causes. METHODS: Utilizing joint latent class mixture models, we identified longitudinal trajectories of annually assessed depressive symptoms and dementia risk over 21 years in 957 older women (baseline age 72.7 years old) from the Women's Health Initiative Memory Study. In a subsample of 569 women who underwent structural magnetic resonance imaging, we examined whether estimates of cerebrovascular disease and Alzheimer's disease (AD)‐related neurodegeneration were associated with identified trajectories. RESULTS: Five trajectories of depressive symptoms and dementia risk were identified. Compared to women with minimal symptoms, women who reported mild and stable and emerging depressive symptoms were at the highest risk of developing dementia and had more cerebrovascular disease and AD‐related neurodegeneration. DISCUSSION: There are heterogeneous profiles of depressive symptoms and dementia risk. Common neuropathological factors may contribute to both depression and dementia. Highlights: The progression of depressive symptoms and concurrent dementia risk is heterogeneous.Emerging depressive symptoms may be a prodromal symptom of dementia.Cerebrovascular disease and AD are potentially shared neuropathological factors. [ABSTRACT FROM AUTHOR]

Point process data have become increasingly popular these days. For example, many of the data captured in electronic health records (EHR) are in the format of point process data. It is of great interest to study the association between a point process predictor and a scalar response using generalized functional linear regression models. Various generalized functional linear regression models have been developed under different settings in the past decades. However, existing methods can only deal with functional or longitudinal predictors, not point process predictors. In this article, we propose a novel generalized functional linear regression model for a point process predictor. Our proposed model is based on the joint modeling framework, where we adopt a log‐Gaussian Cox process model for the point process predictor and a generalized linear regression model for the outcome. We also develop a new algorithm for fast model estimation based on the Gaussian variational approximation method. We conduct extensive simulation studies to evaluate the performance of our proposed method and compare it to competing methods. The performance of our proposed method is further demonstrated on an EHR dataset of patients admitted into the intensive care units of the Beth Israel Deaconess Medical Center between 2001 and 2008. [ABSTRACT FROM AUTHOR]

A great deal of literature has been established for regression analysis of longitudinal data and in particular, many methods have been proposed for the situation where there exist some change points. However, most of these methods only apply to continuous response and focus on the situations where the change point only occurs on the response or the trend of the individual trajectory. In this article, we propose a new joint modeling approach that allows not only the change point to vary for different subjects or be subject-specific but also the effect heterogeneity of the covariates before and after the change point. The method combines a generalized linear mixed effect model with a random change point for the longitudinal response and a log-linear regression model for the random change point. For inference, a maximum likelihood estimation procedure is developed and the asymptotic properties of the resulting estimators, which differ from the standard asymptotic results, are established. A simulation study is conducted and suggests that the proposed method works well for practical situations. An application to a set of real data on COVID-19 is provided. [ABSTRACT FROM AUTHOR]

Modeling longitudinal and survival data jointly offers many advantages such as addressing measurement error and missing data in the longitudinal processes, understanding and quantifying the association between the longitudinal markers and the survival events, and predicting the risk of events based on the longitudinal markers. A joint model involves multiple submodels (one for each longitudinal/survival outcome) usually linked together through correlated or shared random effects. Their estimation is computationally expensive (particularly due to a multidimensional integration of the likelihood over the random effects distribution) so that inference methods become rapidly intractable, and restricts applications of joint models to a small number of longitudinal markers and/or random effects. We introduce a Bayesian approximation based on the integrated nested Laplace approximation algorithm implemented in the R package R-INLA to alleviate the computational burden and allow the estimation of multivariate joint models with fewer restrictions. Our simulation studies show that R-INLA substantially reduces the computation time and the variability of the parameter estimates compared with alternative estimation strategies. We further apply the methodology to analyze five longitudinal markers (3 continuous, 1 count, 1 binary, and 16 random effects) and competing risks of death and transplantation in a clinical trial on primary biliary cholangitis. R-INLA provides a fast and reliable inference technique for applying joint models to the complex multivariate data encountered in health research. [ABSTRACT FROM AUTHOR]

The role of visit-to-visit variability of a biomarker in predicting related disease has been recognized in medical science. Existing measures of biological variability are criticized for being entangled with random variability resulted from measurement error or being unreliable due to limited measurements per individual. In this article, we propose a new measure to quantify the biological variability of a biomarker by evaluating the fluctuation of each individual-specific trajectory behind longitudinal measurements. Given a mixed-effects model for longitudinal data with the mean function over time specified by cubic splines, our proposed variability measure can be mathematically expressed as a quadratic form of random effects. A Cox model is assumed for time-to-event data by incorporating the defined variability as well as the current level of the underlying longitudinal trajectory as covariates, which, together with the longitudinal model, constitutes the joint modeling framework in this article. Asymptotic properties of maximum likelihood estimators are established for the present joint model. Estimation is implemented via an Expectation-Maximization (EM) algorithm with fully exponential Laplace approximation used in E-step to reduce the computation burden due to the increase of the random effects dimension. Simulation studies are conducted to reveal the advantage of the proposed method over the two-stage method, as well as a simpler joint modeling approach which does not take into account biomarker variability. Finally, we apply our model to investigate the effect of systolic blood pressure variability on cardiovascular events in the Medical Research Council elderly trial, which is also the motivating example for this article. [ABSTRACT FROM AUTHOR]

In biomedical studies, longitudinal processes are collected till time-to-event, sometimes on nested timescales (example, days within months). Most of the literature in joint modeling of longitudinal and time-to-event data has focused on modeling the mean or dispersion of the longitudinal process with the hazard for time-to-event. However, based on the motivating studies, it may be of interest to investigate how the cycle-level geometric features (such as the curvature, location and height of a peak), of a cyclical longitudinal process is associated with the time-to-event being studied. We propose a shared parameter joint model for a cyclical longitudinal process and a discrete survival time, measured on nested timescales, where the cycle-varying geometric feature is modeled through a linear mixed effects model and a proportional hazards model for the discrete survival time. The proposed approach allows for prediction of survival probabilities for future subjects based on their available longitudinal measurements. Our proposed model and approach is illustrated through simulation and analysis of Stress and Time-to-Pregnancy, a component of Oxford Conception Study. A joint modeling approach was used to assess whether the cycle-specific geometric features of the lutenizing hormone measurements, such as its peak or its curvature, are associated with time-to-pregnancy (TTP). [ABSTRACT FROM AUTHOR]

Combination therapy, a treatment modality that involves multiple treatment agents, has become imperative for improving treatment effectiveness and addressing resistance in the field of oncology. However, determining the most effective dose for these combinations, particularly when dealing with intricate drug interactions and diverse toxicity patterns, presents a substantial challenge. This paper introduces a novel Bayesian dose-finding design for combination therapies with information borrowing, named the DOD-Combo design. Leveraging historical single-agent trials and the meta-analytic-predictive (MAP) power prior, our approach utilizes a copula-type model to connect individual drug priors with joint toxicity probabilities in combination treatments. The MAP power prior allows the integration of information from multiple historical trials, constructing informative priors for each agent. Extensive simulations confirm our method’s superior performance compared to combination designs with no information borrowing. By adaptively incorporating historical data, our approach reduces sample sizes and enhances efficiency in selecting the maximum tolerated dose (MTD), effectively addressing the intricate challenges presented by combination trials. [ABSTRACT FROM AUTHOR]

Objectives: To investigate the accuracy of longitudinal trajectories of blood biomarkers for predicting future onset of AD among MCI participants as well as to demonstrate dynamic prediction of the individual conversion risk applying joint modeling. Methods: A total of 446 participants with MCI at baseline from the Alzheimer's Disease Neuroimaging Initiative database were included. We introduced joint modeling to analyze the effects of the longitudinal blood biomarkers on the conversion risk to AD, and further to build individual‐specific prediction risk model. Results: During the follow‐up, 345 participants remained with MCI and 101 progressed to AD, and were categorized as non‐progression and progression group, respectively. Longitudinally, the positive association of the concentration dynamics of plasma p‐tau181 and NfL with the conversion risk to AD from MCI was also demonstrated, with Hazard Ratio (HR) = 5.83 and HR = 4.18, respectively. When incorporating plasma p‐tau181 and NfL together to predict AD progression, we observed improved performance (AUC = 0.701, Brier Score = 0.119). Two participants were chosen to exemplify the individual‐specific risk prediction at different follow‐up time for comparative analysis. Conclusions: Plasma p‐tau181 and NfL could serve as biomarkers for the prediction of AD onset, and the individualized prediction opens up the possibility to provide clinical information at a personal level. Key points: Dynamic risk prediction of AD from MCI applying joint modeling using blood biomarkers and easily accessible participant characteristics.Plasma p‐tau181 and NfL could serve as biomarkers for the prediction of AD onset in the primary care settings and yield significant public health benefit. [ABSTRACT FROM AUTHOR]

It is of interest to health policy research to estimate the population-averaged longitudinal medical cost trajectory from initial cancer diagnosis to death, and understand how the trajectory curve is affected by patient characteristics. This research question leads to a number of statistical challenges because the longitudinal cost data are often non-normally distributed with skewness, zero-inflation, and heteroscedasticity. The trajectory is nonlinear, and its length and shape depend on survival, which are subject to censoring. Modeling the association between multiple patient characteristics and nonlinear cost trajectory curves of varying lengths should take into consideration parsimony, flexibility, and interpretation. We propose a novel longitudinal varying coefficient single-index model. Multiple patient characteristics are summarized in a single-index, representing a patient's overall propensity for healthcare use. The effects of this index on various segments of the cost trajectory depend on both time and survival, which is flexibly modeled by a bivariate varying coefficient function. The model is estimated by generalized estimating equations with an extended marginal mean structure to accommodate censored survival time as a covariate. We established the pointwise confidence interval of the varying coefficient and a test for the covariate effect. The numerical performance was extensively studied in simulations. We applied the proposed methodology to medical cost data of prostate cancer patients from the Surveillance, Epidemiology, and End Results-Medicare-Linked Database. [ABSTRACT FROM AUTHOR]

We consider Bayesian nonparametric inference for event time distributions based on current status data. We show that under dependent censoring conventional mixture priors, including the popular Dirichlet process mixture prior, lead to biologically uninterpretable results as they unnaturally skew the probability mass for the event times toward the extremes of the observed data. Simple assumptions on dependent censoring can fix the problem. We then extend the discussion to bivariate current status data with partial ordering of the two outcomes. In addition to dependent censoring, we also exploit some minimal known structure relating the two event times. We design a Markov chain Monte Carlo algorithm for posterior simulation. Applied to a recurrent infection study, the method provides novel insights into how symptoms-related hospital visits are affected by covariates. [ABSTRACT FROM AUTHOR]

BackgroundDiabetes mellitus (DM) is a global public health problem characterized by an elevated blood glucose level. Monitoring blood sugar levels is vital for effective diabetes management and preventing complications. However, the association between longitudinal biomarkers and the incidence of diabetic complications is often overlooked. Therefore, this study aimed to assess the incidence of diabetic retinopathy, predictors, and association with longitudinal fasting blood sugar level changes among diabetes mellitus patients in Ethiopia.MethodsA multicenter retrospective follow-up study was carried out in referral hospitals in Amhara region, Ethiopia. A random sample of 462 newly diagnosed DM patients was selected. The proportional hazard assumption was checked for the survival sub-model, and for the longitudinal sub-model, the normality assumption was checked. Then the joint modeling with time-dependent lagged parameterizations was fitted. Model assumptions and comparisons were checked. Finally, the hazard ratio with a 95% confidence interval (CI) with a corresponding P-value5 years) (AHR = 2.28, 95% CI: [1.91, 5.15]) were important predictors for the incidence of DR. In addition, the incidence of DR was substantially correlated with the time-dependent lagged value of FBS change (AHR = 4.20, 95% CI [1.62, 10.85]).ConclusionsIn this study, the incidence of diabetic retinopathy was somewhat high when compared to prior similar studies in Ethiopia. A joint model of longitudinal fasting blood sugar level changes was significantly associated with an increased risk of DR. Besides, being rural residence, hypertension co-morbidity, and a longer duration of DM were significant predictors for the incidence of DR. Therefore, public awareness, an integrated care approach, and prioritizing glycemic control are highly recommended.

By conducting in-depth exploration on the key factors affecting repeat complaints of telecom operators, this study aimed to improve service quality and construct a risk prediction model.Based on the operator’s customer service data, the study employed Logistic regression, BP neural network, and their combined modeling methods.The Logistic regression model identified five major influencing factors, predicting the probability of repeat complaints with an accuracy of 80.0%.The BP neural network selected 81 influencing factors, achieving a prediction accuracy of 90.6%.On this basis, a combined model was constructed with an accuracy rate of up to 92.8%.After practical application in a provincial telecom operator, the repeat complaint rate decreased by 3.2%, demonstrating a significant impact.Strong support is provided for improving the service quality of telecom operators and reducing repeat complaints, which is of great significance for the development of the telecom industry in China.

In this paper, we propose a jointly-optimized stacked-two-stage speech enhancement. In the first stage, a convolutional recurrent network (CRN)-based masking is integrated with the signal analysis (fast Fourier transform (FFT)) and resynthesis (inverse FFT (IFFT)) parts as extra joint layers (FFT-CRN-IFFT). This joint FFT-CRN-IFFT model is used to separate time domain (TD) speech and noise signals. Additionally, we propose new constrained phase-sensitive magnitude ratio masks (cPSIRMs) for speech and noise sources, which are estimated at this stage by the CRN in relation to the ultimate time-domain signals. In the second stage, a deep neural network integrated with the decoder layers of a deep autoencoder (DNN-DEC) is used to further enhance the separated signals and reduce distortions. We also introduce a supervised multi-objective step-wise learning approach to gradually map the input to the main output of the unified two-stage model (CRN+DNN-DEC), through multiple training steps (e.g., a 4-step mapping as our final suggestion). In this approach, the learned layers of each step serve as pre-training for the next step, with the final step fine-tuning the entire integrated end-to-end model. This unified model not only estimates low-level structural features as direct intermediate targets but also high-level signals as main targets. Experimental results show that the proposed approaches achieve up to a 0.6 improvement in the average perceptual evaluation of speech quality (PESQ) compared to the prior methods.

Measures of substance concentration in urine, serum or other biological matrices often have an assay limit of detection. When concentration levels fall below the limit, exact measures cannot be obtained, and thus are left censored. The problem becomes more challenging when the censored data come from heterogeneous populations consisting of exposed and non‐exposed subjects. If the censored data come from non‐exposed subjects, their measures are always zero and hence censored, forming a latent class governed by a distinct censoring mechanism compared with the exposed subjects. The exposed group's censored measurements are always greater than zero, but less than the detection limit. It is very often that the exposed and non‐exposed subjects may have different disease traits or different relationships with outcomes of interest, so we need to disentangle the two different populations for valid inference. In this article, we aim to fill the methodological gaps in the literature by developing a novel joint modeling approach to not only address the censoring issue in predictors, but also untangle different relationships of exposed and non‐exposed subjects with the outcome. Simulation studies are performed to assess the numerical performance of our proposed approach when the sample size is small to moderate. The joint modeling approach is also applied to examine associations between plasma metabolites and blood pressure in Bogalusa Heart Study, and identify new metabolites that are highly associated with blood pressure. [ABSTRACT FROM AUTHOR]

High-dimensional complex survey data of general structures (e.g. containing continuous, binary, categorical, and ordinal variables), such as the US Department of Defense's Health-Related Behaviors Survey (HRBS), often confound procedures designed to impute any missing survey data. Imputation by fully conditional specification (FCS) is often considered the state of the art for such datasets due to its generality and flexibility. However, FCS procedures contain a theoretical flaw that is exposed by HRBS data—HRBS imputations created with FCS are shown to diverge across iterations of Markov Chain Monte Carlo. Imputation by joint modeling lacks this flaw; however, current joint modeling procedures are neither general nor flexible enough to handle HRBS data. As such, we introduce an algorithm that efficiently and flexibly applies multiple imputation by joint modeling in data of general structures. This procedure draws imputations from a latent joint multivariate normal model that underpins the generally structured data and models the latent data via a sequence of conditional linear models, the predictors of which can be specified by the user. We perform rigorous evaluations of HRBS imputations created with the new algorithm and show that they are convergent and of high quality. Lastly, simulations verify that the proposed method performs well compared to existing algorithms including FCS. [ABSTRACT FROM AUTHOR]

Most of the literature on joint modeling of longitudinal and competing-risk data is based on cause-specific hazards, although modeling of the cumulative incidence function (CIF) is an easier and more direct approach to evaluate the prognosis of an event. We propose a flexible class of shared parameter models to jointly model a normally distributed marker over time and multiple causes of failure using CIFs for the survival submodels, with CIFs depending on the "true" marker value over time (i.e., removing the measurement error). The generalized odds rate transformation is applied, thus a proportional subdistribution hazards model is a special case. The requirement that the all-cause CIF should be bounded by 1 is formally considered. The proposed models are extended to account for potential failure cause misclassification, where the true failure causes are available in a small random sample of individuals. We also provide a multistate representation of the whole population by defining mutually exclusive states based on the marker values and the competing risks. Based solely on the assumed joint model, we derive fully Bayesian posterior samples for state occupation and transition probabilities. The proposed approach is evaluated in a simulation study and, as an illustration, it is fitted to real data from people with HIV. [ABSTRACT FROM AUTHOR]

With the ongoing development of treatments and the resulting increase in survival in oncology, clinical trials based on endpoints such as overall survival may require long follow-up periods to observe sufficient events and ensure adequate statistical power. This increase in follow-up time may compromise the feasibility of the study. The use of surrogate endpoints instead of final endpoints may be attractive for these studies. However, before a surrogate can be used in a clinical trial, it must be statistically validated. In this article, we propose an approach to validate surrogates when both the surrogate and final endpoints are censored event times. This approach is developed for meta-analytic data and uses a mediation analysis to decompose the total effect of the treatment on the final endpoint as a direct effect and an indirect effect through the surrogate. The meta-analytic nature of the data is accounted for in a joint model with random effects at the trial level. The proportion of the indirect effect over the total effect of the treatment on the final endpoint can be computed from the parameters of the model and used as a measure of surrogacy. We applied this method to investigate time-to-relapse as a surrogate endpoint for overall survival in resectable gastric cancer. [ABSTRACT FROM AUTHOR]

Missing data are a prevalent problem in psychological research that can reduce statistical power and bias parameter estimates. These problems can be mostly resolved with multiple imputation, a modern missing data treatment that is increasingly used. Imputation, however, requires the number of variables to be smaller than the number of observations (i.e., non-missing values), and this number is often exceeded due to, e.g., large assessments, high missing data rates, the inclusion of variables predictive of missing values, and the inclusion of non-linear transformations. Even when the ratio of variables to observations meets the minimum requirement, convergence failure can occur in large, complex models. Specialized techniques have been developed to overcome the challenges related to having too many variables in an imputation model, but they are still relatively unknown by researchers in psychology. Accordingly, this paper presents an overview of four imputation techniques that can be used to reduce the number of predictors in an imputation model: item aggregation with scales and parcels, passive imputation, principal component analysis (PcAux) and two-fold fully conditional specification. The purpose, advantages, limitations, and applications of each method are discussed, along with recommendations and illustrative examples, with the aims of (1) understanding different imputation methods and (2) identifying methods that could be useful for one's imputation problem. [ABSTRACT FROM AUTHOR]

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Physical activity (PA) guidelines recommend that PA be accumulated in bouts of 10 minutes or more in duration. Recently, researchers have sought to better understand how participants in PA interventions increase their activity. Participants can increase their daily PA by increasing the number of PA bouts per day while keeping the duration of the bouts constant; they can keep the number of bouts constant but increase the duration of each bout; or participants can increase both the number of bouts and their duration. We propose a novel joint modeling framework for modeling PA bouts and their duration over time. Our joint model is comprised of two sub‐models: a mixed‐effects Poisson hurdle sub‐model for the number of bouts per day and a mixed‐effects location scale gamma regression sub‐model to characterize the duration of the bouts and their variance. The model allows us to estimate how daily PA bouts and their duration vary together over the course of an intervention and by treatment condition and is specifically designed to capture the unique distributional features of bouted PA as measured by accelerometer: frequent measurements, zero‐inflated bouts, and skewed bout durations. We apply our methods to the Make Better Choices study, a longitudinal lifestyle intervention trial to increase PA. We perform a simulation study to evaluate how well our model is able to estimate relationships between outcomes. [ABSTRACT FROM AUTHOR]

The joint models for longitudinal and survival data have recently received significant attention in medical and epidemiological studies. Joint models typically combine linear mixed effects models for repeated measurement data and Cox models for survival time. When we are jointly modeling the longitudinal and survival data, variable selection and efficient estimation of parameters are especially important for performing reliable statistical analyzes, both of which are currently lacking in the literature. In this paper we discuss the pretest and shrinkage estimation methods for jointly modeling longitudinal data and survival time data when some of the covariates in both longitudinal and survival components may not be relevant for predicting survival times. In this situation, we fit two models: the full model that contains all the covariates and the subset model that contains a reduced number of covariates. We combine the full model estimators and the estimators that are restricted by a linear hypothesis to define pretest and shrinkage estimators. We provide their numerical mean squared errors (MSE) and relative MSE. We show that if the shrinkage dimension exceeds two, the risk of the shrinkage estimators is strictly less than that of the full model estimators. Our proposed methods are illustrated by extensive simulation studies and a real-data example. [ABSTRACT FROM AUTHOR]

Markov random field is a common tool to characterize interactions among a fixed collection of variables. In recent biomedical research, there arise new concerns about the discovery of regulatory and co-expression relationships among different types of features across multiple biological classes. Consequently, we propose a data integration framework to jointly learn multiple mixed graphical models simultaneously. To address the common asymmetry problem in neighborhood selection, we construct a new estimator using regularized pseudo-likelihood, which produces symmetric and consistent estimates of network topologies. We demonstrate the practical merits of our method through learning synthetic networks as well as constructing gene regulatory networks from TCGA data. [ABSTRACT FROM AUTHOR]

The complexity of cancer development involves intricate interactions among multiple biomarkers, such as gene-environment interactions. Utilizing microarray gene expression profile data for cancer classification is anticipated to be effective, thus drawing considerable interest in the fields of bioinformatics and computational biology. Due to the characteristics of genomic data, problems of high-dimensional interactions and noise interference do exist during the analysis process. When building cancer diagnosis models, we often face the dilemma of model adaptation errors due to an imbalance of data types. To mitigate the issues, we apply the SMOTE-Tomek procedure to rectify the imbalance problem. Following this, we utilize the overlapping group screening method alongside a binary logistic regression model to integrate gene pathway information, facilitating the identification of significant biomarkers associated with clinically imbalanced cancer or normal outcomes. Simulation studies across different imbalanced rates and gene structures validate our proposed method’s effectiveness, surpassing common machine learning techniques in terms of classification prediction accuracy. We also demonstrate that prediction performance improves with SMOTE-Tomek treatment compared to no imbalance treatment and SMOTE treatment across various imbalance rates. In the real-world application, we integrate clinical and gene expression data with prior pathway information. We employ SMOTE-Tomek and our proposed methods to identify critical biomarkers and gene-environment interactions linked to the imbalanced binary outcomes (cancer or normal) in patients from the Cancer Genome Atlas datasets of lung adenocarcinoma and breast invasive carcinoma. Our proposed method consistently achieves satisfactory classification accuracy. Additionally, we have identified biomarkers indicative of gene-environment interactions relevant to cancer and have provided corresponding estimates of odds ratios. Moreover, in high-dimensional imbalanced data, for achieving good prediction results, we recommend considering the order of balancing processing and feature screening.

Summary: In immuno‐oncology clinical trials, multiple immunological biomarkers are usually examined over time to comprehensively and appropriately evaluate the efficacy of treatments. Because predicting patients' future survival statuses on the basis of such recorded longitudinal information might be of great interest, joint modeling of longitudinal and time‐to‐event data has been intensively discussed as a toolkit to implement such a prediction. To achieve a desirable predictive performance, averaging over multiple candidate predictive models to account for the model uncertainty might be a more suitable statistical approach than selecting the single best model. Although Bayesian model averaging can be one of the approaches, several problems related to model weights with marginal likelihoods have been discussed. To address these problems, we here propose a Bayesian predictive model averaging (BPMA) method that uses Bayesian leave‐one‐out cross‐validation predictive densities to account for the subject‐specific and time‐dependent nature of the prediction. We examine the operating characteristics of the proposed BPMA method in terms of the predictive accuracy (ie, the calibration and discrimination abilities) in extensive simulation studies. In addition, we discuss the strengths and limitations of the proposed method by applying it to an immuno‐oncology clinical trial in patients with advanced ovarian cancer. [ABSTRACT FROM AUTHOR]

Background: Chronic hypertension, a major global health concern, contributes significantly to cardiovascular diseases, stroke, and chronic kidney disease. In India, it stands as the seventh leading cause of death. Understanding the dynamics of blood pressure (BP) is crucial for effective management, especially in resource-constrained settings. This study explores the interplay between systolic (SBP) and diastolic (DBP) blood pressure in hypertensive patients, investigating the variables influencing their longitudinal variations. Methods: A prospective follow-up research was conducted at the hypertension clinic in SLN Medical College and Hospital, Odisha. Structured questionnaires captured socio-demographic and clinical variables from 1100 hypertensive patients aged 18 or older, resulting in 4400 observations. Bivariate longitudinal mixed effect models were employed for joint analysis of SBP and DBP evolution over time. Results: The mean SBP and DBP decreased over the 6-month follow-up period. Significant factors influencing SBP and DBP included sex, age, diabetes, coffee consumption, alcohol use, khat chewing, and physical exercise. A joint model indicated a positive correlation between SBP and DBP developments. Discussion: The study revealed a declining trend in both SBP and DBP over time, emphasizing the impact of modifiable risk factors. Sex, age, lifestyle choices, and medical history played significant roles in influencing blood pressure parameters. Regular exercise emerged as a protective factor. Conclusion: The joint mixed effect model provided valuable insights into the correlated dynamics of SBP and DBP. Targeted prevention and management strategies should focus on modifiable risk factors identified in the study. Healthcare professionals can use these findings to tailor interventions for hypertensive patients and impede the progression of hypertension. [ABSTRACT FROM AUTHOR]

Preknowledge cheating jeopardizes the validity of inferences based on test results. Many methods have been developed to detect preknowledge cheating by jointly analyzing item responses and response times. Gaze fixations, an essential eye-tracker measure, can be utilized to help detect aberrant testing behavior with improved accuracy beyond using product and process data types in isolation. As such, this study proposes a mixture hierarchical model that integrates item responses, response times, and visual fixation counts collected from an eye-tracker (a) to detect aberrant test takers who have different levels of preknowledge and (b) to account for nuances in behavioral patterns between normally-behaved and aberrant examinees. A Bayesian approach to estimating model parameters is carried out via an MCMC algorithm. Finally, the proposed model is applied to experimental data to illustrate how the model can be used to identify test takers having preknowledge on the test items. [ABSTRACT FROM AUTHOR]

Recurrent events are commonly encountered in biomedical studies. In many situations, there exist terminal events, such as death, which are potentially related to the recurrent events. Joint models of recurrent and terminal events have been proposed to address the correlation between recurrent events and terminal events. However, there is a dearth of suitable methods to rigorously investigate the causal mechanisms between specific exposures, recurrent events, and terminal events. For example, it is of interest to know how much of the total effect of the primary exposure of interest on the terminal event is through the recurrent events, and whether preventing recurrent event occurrences could lead to better overall survival. In this work, we propose a formal causal mediation analysis method to compute the natural direct and indirect effects. A novel joint modeling approach is used to take the recurrent event process as the mediator and the survival endpoint as the outcome. This new joint modeling approach allows us to relax the commonly used "sequential ignorability" assumption. Simulation studies show that our new model has good finite sample performance in estimating both model parameters and mediation effects. We apply our method to an AIDS study to evaluate how much of the comparative effectiveness of the two treatments and the effect of CD4 counts on the overall survival are mediated by recurrent opportunistic infections. [ABSTRACT FROM AUTHOR]

Summary: Neurodegenerative diseases are characterized by numerous markers of progression and clinical endpoints. For instance, multiple system atrophy (MSA), a rare neurodegenerative synucleinopathy, is characterized by various combinations of progressive autonomic failure and motor dysfunction, and a very poor prognosis. Describing the progression of such complex and multi‐dimensional diseases is particularly difficult. One has to simultaneously account for the assessment of multivariate markers over time, the occurrence of clinical endpoints, and a highly suspected heterogeneity between patients. Yet, such description is crucial for understanding the natural history of the disease, staging patients diagnosed with the disease, unravelling subphenotypes, and predicting the prognosis. Through the example of MSA progression, we show how a latent class approach modeling multiple repeated markers and clinical endpoints can help describe complex disease progression and identify subphenotypes for exploring new pathological hypotheses. The proposed joint latent class model includes class‐specific multivariate mixed models to handle multivariate repeated biomarkers possibly summarized into latent dimensions and class‐and‐cause‐specific proportional hazard models to handle time‐to‐event data. Maximum likelihood estimation procedure, validated through simulations is available in the lcmm R package. In the French MSA cohort comprising data of 598 patients during up to 13 years, five subphenotypes of MSA were identified that differ by the sequence and shape of biomarkers degradation, and the associated risk of death. In posterior analyses, the five subphenotypes were used to explore the association between clinical progression and external imaging and fluid biomarkers, while properly accounting for the uncertainty in the subphenotypes membership. [ABSTRACT FROM AUTHOR]

In observational studies, the time origin of interest for time-to-event analysis is often unknown, such as the time of disease onset. Existing approaches to estimating the time origins are commonly built on extrapolating a parametric longitudinal model, which rely on rigid assumptions that can lead to biased inferences. In this paper, we introduce a flexible semiparametric curve registration model. It assumes the longitudinal trajectories follow a flexible common shape function with person-specific disease progression pattern characterized by a random curve registration function, which is further used to model the unknown time origin as a random start time. This random time is used as a link to jointly model the longitudinal and survival data where the unknown time origins are integrated out in the joint likelihood function, which facilitates unbiased and consistent estimation. Since the disease progression pattern naturally predicts time-to-event, we further propose a new functional survival model using the registration function as a predictor of the time-to-event. The asymptotic consistency and semiparametric efficiency of the proposed models are proved. Simulation studies and two real data applications demonstrate the effectiveness of this new approach. for this article are available online. [ABSTRACT FROM AUTHOR]

Aim: Understanding the distribution of marine organisms is essential for effective management of highly mobile marine predators that face a variety of anthropogenic threats. Recent work has largely focused on modelling the distribution and abundance of marine mammals in relation to a suite of environmental variables. However, biotic interactions can largely drive distributions of these predators. We aim to identify how biotic and abiotic variables influence the distribution and abundance of a particular marine predator, the bottlenose dolphin (Tursiops truncatus), using multiple modelling approaches and conducting an extensive literature review. Location: Western North Atlantic continental shelf. Methods: We combined widespread marine mammal and fish and invertebrate surveys in an ensemble modelling approach to assess the relative importance and capacity of the environment and other marine species to predict the distribution of both coastal and offshore bottlenose dolphin ecotypes. We corroborate the modelled results with a systematic literature review on the prey of dolphins throughout the region to help explain patterns driven by prey availability, as well as reveal new ones that may not necessarily be a predator–prey relationship. Results: We find that coastal bottlenose dolphin distributions are associated with one family of fishes, the Sciaenidae, or drum family, and predictions slightly improve when using only fish versus only environmental variables. The literature review suggests that this tight coupling is likely a predator–prey relationship. Comparatively, offshore dolphin distributions are more strongly related to environmental variables, and predictions are better for environmental‐only models. As revealed by the literature review, this may be due to a mismatch between the animals caught in the fish and invertebrate surveys and the predominant prey of offshore dolphins, notably squid. Main Conclusions: Incorporating prey species into distribution models, especially for coastal bottlenose dolphins, can help inform ecological relationships and predict marine predator distributions. [ABSTRACT FROM AUTHOR]

High Tibial Osteotomy is frequently performed to correct varus knees misalignment and thus to prevent end-stage osteoarthritis. Traditional systems lack pre-surgical planning and custom-fit fixation plates. A new 3D printed system has been developed for a personalized surgical procedure. This starts with careful correction planning based on a standard preoperative long leg radiograph and a 3D scan of the knee by Cone-Beam CT, both in weight-bearing. From the latter, a 3D model of the proximal tibia is reconstructed, on which the surgery is planned. This allows the design of the surgical guide and fixation plate to match the tibial surface topology and 3D printed in medical grade titanium alloy using selective-laser-sintering. During surgery, the guided osteotomy and controlled opening mechanism ensure an accurate correction; this is stabilized with the custom-fit plate secured to the proximal tibia using locking screws of appropriate length. After a brief learning curve, the mean discrepancy between the plan and the achieved alignment was 1. 2 ∘ ± 1. 4 ∘ . The surgical time was reduced by an average of approximately 30%. From medical imaging of the patient to product delivery to the hospital, the overall timeframe was about 15 days. [ABSTRACT FROM AUTHOR]

Standard endpoints such as objective response rate are usually poorly correlated with overall survival (OS) for treatment with immune checkpoint inhibitors. Longitudinal tumor size may serve as a more useful predictor of OS, and establishing a quantitative relationship between tumor kinetics (TK) and OS is a crucial step for successfully predicting OS based on limited tumor size measurements. This study aims to develop a population TK model in combination with a parametric survival model by sequential and joint modeling approaches to characterize durvalumab phase I/II data from patients with metastatic urothelial cancer, and to evaluate and compare the performance of the two modeling approaches in terms of parameter estimates, TK and survival predictions, and covariate identification. The tumor growth rate constant was estimated to be greater for patients with OS ≤ 16 weeks as compared to that for patients with OS > 16 weeks with the joint modeling approach (kg= 0.130 vs. 0.0551 week−1, p-value < 0.0001), but similar for both groups (kg = 0.0624 vs.0.0563 week−1, p-value = 0.37) with the sequential modeling approach. The predicted TK profiles by joint modeling appeared better aligned with clinical observations. Joint modeling also predicted OS more accurately than the sequential approach according to concordance index and Brier score. The sequential and joint modeling approaches were also compared using additional simulated datasets, and survival was predicted better by joint modeling in the case of a strong association between TK and OS. In conclusion, joint modeling enabled the establishment of a robust association between TK and OS and may represent a better choice for parametric survival analyses over the sequential approach. [ABSTRACT FROM AUTHOR]