Joint Modeling Approach Research Articles

Joint modeling of longitudinal changes of blood pressure and time to remission of hypertensive patients receiving treatment: Bayesian approach.

Hypertension is a widespread condition when the blood's force on the artery walls is extremely high to develop adverse health effects. This paper aimed to jointly model the longitudinal change of blood pressures (systolic and diastolic) and time to the first remission of hypertensive outpatients receiving treatment. A retrospective study design was used to collect appropriate data on longitudinal changes in blood pressure and time-to-event from the medical charts of 301 hypertensive outpatients under follow-up at Felege Hiwot referral hospital, Ethiopia. The data exploration was done using summary statistics measures, individual profile plots, Kaplan-Meier plots, and log-rank tests. To get wide-ranging information about the progression, joint multivariate models were employed. A total of 301 hypertensive patients who take treatment was taken from Felege Hiwot referral hospital recorded between Sep. 2018 to Feb. 2021. Of this 153 (50.8%) were male, and 124 (49.2%) were residents from rural areas. About 83(27.6%), 58 (19.3%), 82 (27.2%), and 25 (8.3%) have a history of diabetes mellitus, cardiovascular disease, stroke, and HIV respectively. The median time of hypertensive patients to have first remission time was 11 months. The hazard of the patient's first remission time for males was 0.63 times less likely than the hazard for females. The time to attain the first remission for patients who had a history of diabetes mellitus was 46% lower than for those who had no history of diabetes mellitus. Blood pressure dynamics significantly affect the time to the first remission of hypertensive outpatients receiving treatment. The patients who had a good follow-up, lower BUN, lower serum calcium, lower serum sodium, lower hemoglobin, and take the treatment enalapril showed an opportunity in decreasing their blood pressure. This compels patients to experience the first remission early. Besides, age, patient's history of diabetes, patient's history of cardiovascular disease, and treatment type were the joint determinant factors for the longitudinal change of BP and the first remission time. The Bayesian joint model approach provides specific dynamic predictions, wide-ranging information about the disease transitions, and better knowledge of disease etiology.

Causal Mediation Analysis for Multivariate Longitudinal Data and Survival Outcomes

This study proposes a joint modeling approach to conduct causal mediation analysis that accommodates multivariate longitudinal data, dynamic latent mediator, and survival outcome. First, we introduce a confirmatory factor analysis model to characterize a time-varying latent mediator through multivariate longitudinal observable variables. Then, we establish a growth curve model to describe the linear trajectory of the dynamic latent mediator and simultaneously explore the relationship between the exposure and the mediating process. Finally, we link the mediating process to the survival outcome through a proportional hazards model. In addition, we use the mediation formula approach to assess the natural direct and indirect effects and prove the identifiability of the causal effects under sequential ignorability assumptions. A Bayesian approach incorporating the Markov chain Monte Carlo algorithm is developed to estimate the causal effects efficiently. Simulation studies are conducted to evaluate the empirical performance of the proposed method. An application to the Alzheimer’s Disease Neuroimaging Initiative study further confirms the utility of the proposed method.

Incorporating delayed entry into the joint frailty model for recurrent events and a terminal event.

In studies of recurrent events, joint modeling approaches are often needed to allow for potential dependent censoring by a terminal event such as death. Joint frailty models for recurrent events and death with an additional dependence parameter have been studied for cases in which individuals are observed from the start of the event processes. However, samples are often selected at a later time, which results in delayed entry so that only individuals who have not yet experienced the terminal event will be included. In joint frailty models such left truncation has effects on the frailty distribution that need to be accounted for in both the recurrence process and the terminal event process, if the two are associated. We demonstrate, in a comprehensive simulation study, the effects that not adjusting for late entry can have and derive the correctly adjusted marginal likelihood, which can be expressed as a ratio of two integrals over the frailty distribution. We extend the estimation method of Liu and Huang (Stat Med 27:2665-2683, 2008. https://doi.org/10.1002/sim.3077 ) to include potential left truncation. Numerical integration is performed by Gaussian quadrature, the baseline intensities are specified as piecewise constant functions, potential covariates are assumed to have multiplicative effects on the intensities. We apply the method to estimate age-specific intensities of recurrent urinary tract infections and mortality in an older population.

Joint modeling of the longitudinal student mark and the competing events of degree completion and academic dropout

Within educational data mining, it is common to model students’ academic performance using a linear regression model or the time to degree completion or dropout using the cause-specific hazard model. Yet to our knowledge, no studies have simultaneously modeled the longitudinal performance and the hazard models. We propose a joint modeling approach in which we estimate the effect of a student’s semester longitudinal weighted mark obtained after attempting t credit points, on the hazard of degree completion and academic dropout. Evidence suggests that the joint modeling approach is substantially more efficient compared to the separate modeling of the longitudinal and the time-to-event outcomes. We observe similarities in the parameter estimates of the longitudinal submodels, but smaller standard errors of the estimates in the joint model. However, the parameter estimates of the competing risk models from both analysis methods are different. A unit increase in the average log weighted mark results in a 18.5 fold increase in the hazard associated with degree completion, but reduces the risk of dropout by 49 per cent. Being in a university-type residence, not having financial aid, and having a higher number of high school matriculation points all increase the hazard rate of degree completion.

A parametric model to jointly characterize rate, duration, and severity of exacerbations in episodic diseases

BackgroundThe natural history of many chronic diseases is characterized by periods of increased disease activity, commonly referred to as flare-ups or exacerbations. Accurate characterization of the burden of these exacerbations is an important research objective.MethodsThe purpose of this work was to develop a statistical framework for nuanced characterization of the three main features of exacerbations: their rate, duration, and severity, with interrelationships among these features being a particular focus. We jointly specified a zero-inflated accelerated failure time regression model for the rate, an accelerated failure time regression model for the duration, and a logistic regression model for the severity of exacerbations. Random effects were incorporated into each component to capture heterogeneity beyond the variability attributable to observed characteristics, and to describe the interrelationships among these components.ResultsWe used pooled data from two clinical trials in asthma as an exemplary application to illustrate the utility of the joint modeling approach. The model fit clearly indicated the presence of heterogeneity in all three components. A novel finding was that the new therapy reduced not just the rate but also the duration of exacerbations, but did not have a significant impact on their severity. After controlling for covariates, exacerbations among more frequent exacerbators tended to be shorter and less likely to be severe.ConclusionsWe conclude that a joint modeling framework, programmable in available software, can provide novel insights about how the rate, duration, and severity of episodic events interrelate, and enables consistent inference on the effect of treatments on different disease outcomes.Trial registration Ethics approval was obtained from the University of British Columbia Human Ethics Board (H17-00938).

Regression analysis of logistic model with latent variables.

We propose a joint modeling approach to investigating the effects of social-psychological factors on the onset of depression. The proposed model comprises two components. The first one is a confirmatory factor analysis model that summarizes latent factors through multiple correlated observed variables. The second one is a logistic regression model that investigates the effects of observed and latent influence factors on the occurrence of depression. We develop a hybrid procedure based on the borrow-strength estimation procedure and the weighted score function to estimate the model parameters. The asymptotic properties of the proposed estimators are established. Simulation studies demonstrate that the method we proposed performs well. An application to a study concerning the social-psychological factors of depression is provided.

Dynamic predictions from longitudinal CD4 count measures and time to death of HIV/AIDS patients using a Bayesian joint model

A Bayesian joint modeling approach to dynamic prediction of HIV progression and mortality allows individualized predictions to be made for HIV patients, based on monitoring of their CD4 counts. This study aims to provide predictions of patient-specific trajectories of HIV disease progression and survival. Longitudinal data on 254 HIV/AIDS patients who received ART between 2009 and 2014, and who had at least one CD4 count observed, were employed in a Bayesian joint model of disease progression. Different forms of association structure that relate the longitudinal CD4 biomarker and time to death were assessed; and predictions were averaged over the different models using Bayesian model averaging. The individual follow-up times ranged from 1 to 120 months, with a median of 22 months and IQR 7–39 months. The estimates of the association structure parameters from two of the three models considered indicated that the HIV mortality hazard at any time point is associated with the rate of change in the underlying value of the CD4 count. Model averaging the dynamic predictions resulted in only one of the hypothesized association structures having non-zero weight in almost all time points for each individual, with the exception of twelve patients, for whom other association structures were preferred at a few time points. The predictions were found to be different when we averaged them over models than when we derived them from the highest posterior weight model alone. The model with highest posterior weight for almost all time points for each individual gave an estimate of the association parameter of −0.02 implying that for a unit increase in the CD4 count, the hazard of HIV mortality decreases by a factor (hazard ratio) of 0.98. Functional status and alcohol intake are important contributing factors that affect the mean square root of CD4 measurements.

A Semiparametric Bayesian Joint Modelling of Skewed Longitudinal and Competing Risks Failure Time Data: With Application to Chronic Kidney Disease

In clinical and epidemiological studies, when the time-to-event(s) and the longitudinal outcomes are associated, modelling them separately may give biased estimates. A joint modelling approach is required to obtain unbiased results and to evaluate their association. In the joint model, a subject may be exposed to more than one type of failure event (competing risks). Considering the competing event as an independent censoring of the time-to-event process may underestimate the true survival probability and give biased results. Within the joint model, longitudinal outcomes may have nonlinear (irregular) trajectories over time and exhibit skewness with heavy tails. Accordingly, fully parametric mixed-effect models may not be flexible enough to model this type of complex longitudinal data. In addition, assuming a Gaussian distribution for model errors may be too restrictive to adequately represent within-individual variations and may lack robustness against deviation from distributional assumptions. To simultaneously overcome these issues, in this paper, we presented semiparametric joint models for competing risks failure time and skewed-longitudinal data by using a smoothing spline approach and a multivariate skew-t distribution. We also considered different parameterization approaches in the formulation of joint models and used a Bayesian approach to make the statistical inference. We illustrated the proposed methods by analyzing real data on a chronic kidney disease. To evaluate the performance of the methods, we also carried out simulation studies. The results of both the application and simulation studies revealed that the joint modelling approach proposed in this study performed well when the semiparametric, random-effects parameterization, and skew-t distribution specifications were taken into account.

Association Between Body Mass Index Variation and Early Mortality Among 834 Ethiopian Adults Living with HIV on ART: A Joint Modelling Approach.

Body mass index (BMI) is a simple and cost-effective tool for monitoring the clinical responses of patients living with human immunodeficiency virus (HIV) after antiretroviral therapy (ART) initiation, especially in resource-limited settings where access to laboratory tests are limited. Current evidence on the association between longitudinal BMI variation and clinical outcomes among adults living with HIV receiving ART is essential to inform clinical guidelines. Therefore, this study examines the association between BMI variation and premature mortality in adults living with HIV on ART. An institution-based retrospective cohort study was conducted among 834 adults living with HIV receiving ART from June 2014 to June 2020 at Debre Markos Comprehensive Specialized Hospital in Northwest Ethiopia. We first identified predictors of mortality and BMI variation using proportional hazards regression and linear mixed models, respectively. Then, the two models were combined to form an advanced joint model to examine the effect of longitudinal BMI variation on mortality. Of the 834 participants, 49 (5.9%) died, with a mortality rate of 4.1 (95% CI 3.1, 5.4) per 100 person-years. A unit increase in BMI after ART initiation corresponded to an 18% reduction in mortality risk. Patients taking tuberculosis preventive therapy (TPT), mild clinical disease stage, and changing ART regimens were at lower risk of death. However, patients with ambulatory/bedridden functional status were at higher risk of death. Regarding BMI variation over time, patients presenting with opportunistic infections (OIs), underweight patients, patients who started a Dolutegravir (DGT)-based ART regimen, and those with severe immunodeficiency had a higher BMI increase over time. However, patients from rural areas and overweight/obese patients experienced a lower BMI increase over time. BMI improvement after ART initiation was strongly associated with a lower mortality risk, regardless of BMI category. This finding implies that BMI may be used as a better predictor tool for death risk in adults living with HIV in Ethiopia. Additionally, patients who took a DGT-based ART regimen had a higher BMI increase rate over time, which aligns with possible positive effects, such as weight gain, of the DGT-based ART regimen in developing countries.

Shared Frailty Model for Joint Survival Data - A Simulation Study

Performing a survival analysis, allows investigating factors that contribute to outcome over time. Though a considerable amount of literature has addressed this area, analysis of multiple survival responses has not received sufficient attention in past literature. The joint modeling fits well when there are multiple survival responses for the same study unit and it can provide improved results than fitting univariate models separately since the correlation between the responses can be captured through a joint model. Therefore, the aim of this study was to propose a joint modeling approach, in which the linkage between two survival responses(for simplicity, in this research bivariate lifetime data have been considered) was derived by sharing a common random effect under different random effect distributions through parametric forms of the baseline hazard function. In this study, Gamma and Normal random effect distributions and Exponential and Weibull parametric survival distributions were considered. The performance of the Shared Frailty model was compared with two Ordinary Proportional Hazard models through a simulation study, by fitting models for simulated data in three different sample sizes with 20% and 40% censoring proportions in different correlation structures. Bias, Coverage Probability (CP) and Mean Squared Error (MSE) were the performance measures used. Parameter estimates showing relatively low bias, high CP, and minimal MSE under the joint random effect model confirmed the suitability of the proposed model to capture joint survival data, surpassing the fit of two univariate models. Also, the results interpreted, Gamma distributed random effects to be more suitable with Exponential survival times while Normal random effects with Weibull survival times.

Trajectory-driven planning of electric taxi charging stations based on cumulative prospect theory

• Trajectory data provides a new perspective for studying charging station planning. • The peak charging time for ETs is in the afternoon. • ET drivers’ attitude toward the risk of battery depletion influences the charging decision. • Results confirm correlation between charging station planning and users’ charging behavior decisions. • Simulation results show the impact of EV charging demand by the user's per-unit time cost. The charging station planning is crucial to facilitate convenient and efficient charging of electric taxis (ETs). As typical transportation and mobile power load, the accurate modeling of driving and charging behaviors of ETs is the basis for charging station planning. Therefore, this paper proposes a joint modeling approach for user charging behavior decision-making and charging station planning. First, the open-source taxi trajectory dataset is used to characterize the driving behavior of ETs. The temporal and spatial distribution characteristics of passenger trips can be obtained through data mining and modeling. Then, an ET charging demand simulation model based on cumulative prospect theory (CPT) is developed. The CPT captures individuals’ attitudes and preferences against the battery-depleting risk in decision-making. By analyzing the operating characteristics of ETs, a more practical charging simulation algorithm is developed. Finally, the joint modeling of user charging behavior decisions and charging station planning is realized to elucidate their interplay. Case studies are conducted in a practical area in Xi'an, China. The results show that the layout of charging stations and the driver's per-unit time cost influence the charging decisions of ET drivers. The proposed approach models the interaction mechanism between traffic and electrical attributes of ETs, user behavior decision-making, and charging station planning, which is significantly lacking in existing studies. The proposed approach is applicable to the problem of planning charging stations in urban areas.

Analyzing recurrent and nonrecurrent terminal events data in discrete time.

Joint analysis of recurrent and nonrecurrent terminal events has attracted substantial attention in literature. However, there lacks formal methodology for such analysis when the event time data are on discrete scales, even though some modeling and inference strategies have been developed for discrete-time survival analysis. We propose a discrete-time joint modeling approach for the analysis of recurrent and terminal events where the two types of events may be correlated with each other. The proposed joint modeling assumes a shared frailty to account for the dependence among recurrent events and between the recurrent and the terminal terminal events. Also, the joint modeling allows for time-dependent covariates and rich families of transformation models for the recurrent and terminal events. A major advantage of our approach is that it does not assume a distribution for the frailty, nor does it assume a Poisson process for the analysis of the recurrent event. The utility of the proposed analysis is illustrated by simulation studies and two real applications, where the application to the biochemists' rank promotion data jointly analyzes the biochemists' citation numbers and times to rank promotion, and the application to the scleroderma lung study data jointly analyzes the adverse events and off-drug time among patients with the symptomatic scleroderma-related interstitial lungdisease.

Association of dynamic change in patient-reported pain with survival in metastatic castrate sensitive prostate cancer-exploratory analysis of LATITUDE study.

Pain is an important dimension of quality-of-life in patients with metastatic castrate-sensitive prostate cancer (mCSPC). However, it is unclear if dynamic change in pain over time can predict for overall survival (OS) or progression-free survival (PFS) in these patients. This is an exploratory analysis of LATITUDE, a phase III randomized study, in which men with de novo mCSPC were randomized to receive either ADT plus abiraterone versus ADT alone. Information was collected on patient-reported worst pain score (WPS) and pain-interference score (PIS) from the Brief Pain Inventory-Short Form. A Bayesian joint modelling approach was used determine the association of dynamic change in WPS and PIS with OS and PFS. Overall, 1125 patients with at least 3 measurements on pain scores were eligible. On Cox multivariable regression, increase in baseline WPS was associated with inferior OS (hazard ratio [HR] 1.049 [95% confidence intervals [CI] 1.015-1.085]; time dependent area under curve [tAUC] 0.64) and PFS (HR 1.045 [1.011-1.080]; tAUC: 0.64). Increase in baseline PIS was associated with inferior OS (HR 1.062 [1.020-1.105]; tAUC: 0.63) but not with PFS (HR 1.038 [0.996-1.08]). On independent joint models, an increase in the current value of WPS by 1-unit was associated with inferior OS (HR 1.316 [1.258-1.376]; tAUC 0.74) and PFS (HR 1.319 [1.260-1.382]; tAUC 0.70). Similar association was seen for increase in the current value of PIS with OS (HR 1.319 [1.261-1.381]; tAUC 0.73) and PFS (HR 1.282 [1.224-1.344]; tAUC 0.73). The above findings highlight the potential dynamic interplay between patient-reported pain with OS and PFS in mCSPC. Compared to baseline pain, such dynamic assessment of pain was found to have superior predictive ability and thus has the potential to tailor subsequent treatment based on response to initial therapy beyond its role as a very important dimension of quality-of-life.

Substantive model compatible multilevel multiple imputation: A joint modeling approach.

Substantive model compatible multiple imputation (SMC-MI) is a relatively novel imputation method that is particularly useful when the analyst's model includes interactions, non-linearities, and/or partially observed random slope variables. Here we thoroughly investigate a SMC-MI strategy based on joint modeling of the covariates of the analysis model. We provide code to apply the proposed strategy and we perform an extensive simulation work to test it in various circumstances. We explore the impact on the results of various factors, including whether the missing data are at the individual or cluster level, whether there are non-linearities and whether the imputation model is correctly specified. Finally, we apply the imputation methods to the motivating example data. SMC-JM appears to be superior to standard JM imputation, particularly in presence of large variation in random slopes, non-linearities, and interactions. Results seem to be robust to slight mis-specification of the imputation model for the covariates. When imputing level 2 data, enough clusters have to be observed in order to obtain unbiased estimates of the level 2 parameters. SMC-JM is preferable to standard JM imputation in presence of complexities in the analysis model of interest, such as non-linearities or random slopes.

Depressive symptoms before and after Parkinson's diagnosis-A longitudinal analysis.

BackgroundDepression is common in Parkinson’s disease (PD). It is however unclear when and how depressive symptoms develop and progress in the course of PD development.ObjectiveTo assess how depressive symptoms evolve in PD, using repeated measures.MethodsIn 2994 older adults, ages 70–79 years, depressive symptoms were assessed 8 times over 11 years using the 10-item Center for Epidemiologic Studies Depression Scale (CESD-10). For each PD patient at each time point, we calculated the difference between CESD-10 score and its expected value estimated based on data from individuals without PD, and then realigned the time scale in reference to the year of PD diagnosis. We examined longitudinal changes in CESD-10 scores before and after PD diagnosis using a joint modeling approach to account for competing risks of non-participation and death.ResultsA total of 79 PD patients were identified at enrollment or during the follow-up, with repeatedly assessed depressive symptom data up to 9 years before and after PD diagnosis. We found a monotonic trend of increasing CESD-10 score in PD patients throughout the observational period (p = 0.002). The observed scores became higher than expected approximately 7 years before PD diagnosis and significantly different 1 year before PD diagnosis.ConclusionsIncreasing depressive symptomatology appears to precede PD diagnosis by a few years.

Multiple imputation approaches for handling incomplete three-level data with time-varying cluster-memberships.

Three‐level data arising from repeated measures on individuals clustered within higher‐level units are common in medical research. A complexity arises when individuals change clusters over time, resulting in a cross‐classified data structure. Missing values in these studies are commonly handled via multiple imputation (MI). If the three‐level, cross‐classified structure is modeled in the analysis, it also needs to be accommodated in the imputation model to ensure valid results. While incomplete three‐level data can be handled using various approaches within MI, the performance of these in the cross‐classified data setting remains unclear. We conducted simulations under a range of scenarios to compare these approaches in the context of an acute‐effects cross‐classified random effects substantive model, which models the time‐varying cluster membership via simple additive random effects. The simulation study was based on a case study in a longitudinal cohort of students clustered within schools. We evaluated methods that ignore the time‐varying cluster memberships by taking the first or most common cluster for each individual; pragmatic extensions of single‐ and two‐level MI approaches within the joint modeling (JM) and the fully conditional specification (FCS) frameworks, using dummy indicators (DI) and/or imputing repeated measures in wide format to account for the cross‐classified structure; and a three‐level FCS MI approach developed specifically for cross‐classified data. Results indicated that the FCS implementations performed well in terms of bias and precision while JM approaches performed poorly. Under both frameworks approaches using the DI extension should be used with caution in the presence of sparse data.

The Effect of Low Glycemic Index Mediterranean Diet and Combined Exercise Program on Metabolic-Associated Fatty Liver Disease: A Joint Modeling Approach.

Background: Excessive caloric intake and reduced energy expenditure are associated with the onset of metabolic-associated fatty liver disease (MAFLD). The aim of this study was to probe the benefits of a low glycemic index Mediterranean diet (LGIMD) and a combined exercise program (CEP) on MAFLD by monitoring the clinical process through anthropometric measurement, body mass index (BMI), and specific biomarkers, such as the Homeostatic Model Assessment for Insulin Resistance (HOMA-IR). Methods: The study was conducted at the National Institute of Gastroenterology, ‘S. de Bellis’, Italy. Subjects were invited to join the study for 12 months. Results: 54 participants were enrolled. Joint modeling of longitudinal and time-to-event data was applied. Overall, a statistically significant direct effect of LGIMD/CEP adherence on ln (BMI), a statistically significant direct effect of LGIMD/CEP adherence on time-to-event and a strong statistically significant direct effect of log (BMI) on time-to-event were observed. In addition, a statistically significant direct effect of LGIMD/CEP adherence on ln(HOMA-IR), a statistically significant direct effect of LGIMD/CEP adherence on time-to-event and a statistically significant direct effect of ln(HOMA-IR) on time-to-event were observed. Conclusions: LGIMD/CEP significantly improved MAFLD status; in addition, longitudinal BMI and HOMA-IR were good predictors of the disappearance of diagnostic criteria for MAFLD.

EditVAE: Unsupervised Parts-Aware Controllable 3D Point Cloud Shape Generation

This paper tackles the problem of parts-aware point cloud generation. Unlike existing works which require the point cloud to be segmented into parts a priori, our parts-aware editing and generation are performed in an unsupervised manner. We achieve this with a simple modification of the Variational Auto-Encoder which yields a joint model of the point cloud itself along with a schematic representation of it as a combination of shape primitives. In particular, we introduce a latent representation of the point cloud which can be decomposed into a disentangled representation for each part of the shape. These parts are in turn disentangled into both a shape primitive and a point cloud representation, along with a standardising transformation to a canonical coordinate system. The dependencies between our standardising transformations preserve the spatial dependencies between the parts in a manner that allows meaningful parts-aware point cloud generation and shape editing. In addition to the flexibility afforded by our disentangled representation, the inductive bias introduced by our joint modeling approach yields state-of-the-art experimental results on the ShapeNet dataset.

Comparison in tensile behaviour of conventional and high-strength steel welded-plate preloaded T-stubs

High-strength steels have been attracting more and more attention for engineering application due to their advantage in strength, but they are inferior in material ductility than conventional structural steels. In this paper the tensile behaviour of Q690 high-strength steel T-stubs connected by preloaded high-strength bolts was investigated by comparative experimental and numerical studies with those made of conventional structural steels. The test results revealed that the high-strength steel T-stubs provided about 12% higher ultimate resistance than conventional steel T-stubs of the same flange thickness and preloaded bolt type, but 18–41% lower ultimate deformation capacity on the basis of similar ultimate resistance. The β or βu factor based on the plastic or ultimate resistance of the T-stub components, respectively, might not capture accurately the actual failure modes. The limit in Eurocode 3 on the maximum flange thickness could be relaxed to be 20% higher for the high-strength steel T-stubs to obtain a better overall deformation capacity by exploiting the bolt-flange deformation balance, but the deformation capacity was also affected by bolt stripping, which needs further clarification. Finite-element analysis results evidenced that the design formulae in Eurocode 3 could be still applied to high-strength steel T-stubs in terms of the initial stiffness and plastic resistance, as well as the joint modelling approach. Jaspart and Maquoi’s formulae are recommended over the design formulae in Eurocode 3 to calculate the plastic resistance of preloaded T-stubs, regardless of the steel grades.

The joint modeling approach with a simulation study for evaluating the association between the trajectory of serum albumin levels and mortality in peritoneal dialysis patients

We aimed to study the association between mortality and trajectory of serum albumin levels (g/dL) in peritoneal dialysis patients via a joint modeling approach. Joint modeling is a statistical method used to evaluate the relationship between longitudinal and time-to-event processes by fitting both sub-models simultaneously. A comprehensive simulation study was conducted to evaluate model performances and generalize the findings to more general scenarios. Model performances and prediction accuracies were evaluated using the time-dependent ROC area under the curve (AUC) and Brier score (BS). According to the real-life dataset results, the trajectory of serum albumin levels was inversely associated with mortality increasing the risk of death 2.21 times (p=0.003). The simulation results showed that the model performances increased with sample size. However, the model complexity had increased as more repeated measurements were taken from patients and resulted in lower prediction accuracy unless the sample size was increased. In conclusion, using the trajectory of risk predictors rather than baseline (or averaged) values provided better predictive accuracy and prevented biased results. Finally, the study design (e.g., number of samples and repeated measurements) should be carefully defined since it played an important role in model performances.