Joint models reveal genetic architecture of pubertal stage transitions and their association with BMI in admixed Chilean population.

Early or late pubertal onset can lead to disease in adulthood, including cancer, obesity, type 2 diabetes, metabolic disorders, bone fractures, and psychopathologies. Thus, knowing the age at which puberty is attained is crucial as it can serve as a risk factor for future diseases. Pubertal development is divided into five stages of sexual maturation in boys and girls according to the standardized Tanner scale. We performed genome-wide association studies (GWAS) on the "Growth and Obesity Chilean Cohort Study" cohort composed of admixed children with mainly European and Native American ancestry. Using joint models that integrate time-to-event data with longitudinal trajectories of body mass index (BMI), we identified genetic variants associated with phenotypic transitions between pairs of Tanner stages. We identified $42$ novel significant associations, most of them in boys. The GWAS on Tanner $3\rightarrow 4$ transition in boys captured an association peak around the growth-related genes LARS2 and LIMD1 genes, the former of which causes ovarian dysfunction when mutated. The associated variants are expression and splicing Quantitative Trait Loci regulating gene expression and alternative splicing in multiple tissues. Further, higher individual Native American genetic ancestry proportions predicted a significantly earlier puberty onset in boys but not in girls. Finally, the joint models identified a longitudinal BMI parameter significantly associated with several Tanner stages' transitions, confirming the association of BMI with pubertal timing.

A joint Bayesian hierarchical model for estimating SARS-CoV-2 genomic and subgenomic RNA viral dynamics and seroconversion.

Understanding the viral dynamics of and natural immunity to the severe acute respiratory syndrome coronavirus 2 is crucial for devising better therapeutic and prevention strategies for coronavirus disease 2019 (COVID-19). Here, we present a Bayesian hierarchical model that jointly estimates the genomic RNA viral load, the subgenomic RNA (sgRNA) viral load (correlated to active viral replication), and the rate and timing of seroconversion (correlated to presence of antibodies). Our proposed method accounts for the dynamical relationship and correlation structure between the two types of viral load, allows for borrowing of information between viral load and antibody data, and identifies potential correlates of viral load characteristics and propensity for seroconversion. We demonstrate the features of the joint model through application to the COVID-19 post-exposure prophylaxis study and conduct a cross-validation exercise to illustrate the model's ability to impute the sgRNA viral trajectories for people who only had genomic RNA viral load data.

Bayesian joint models for multi-regional clinical trials.

In recent years, multi-regional clinical trials (MRCTs) have increased in popularity in the pharmaceutical industry due to their ability to accelerate the global drug development process. To address potential challenges with MRCTs, the International Council for Harmonisation released the E17 guidance document which suggests the use of statistical methods that utilize information borrowing across regions if regional sample sizes are small. We develop an approach that allows for information borrowing via Bayesian model averaging in the context of a joint analysis of survival and longitudinal data from MRCTs. In this novel application of joint models to MRCTs, we use Laplace's method to integrate over subject-specific random effects and to approximate posterior distributions for region-specific treatment effects on the time-to-event outcome. Through simulation studies, we demonstrate that the joint modeling approach can result in an increased rejection rate when testing the global treatment effect compared with methods that analyze survival data alone. We then apply the proposed approach to data from a cardiovascular outcomes MRCT.

A joint frailty model for recurrent and competing terminal events: Application to delirium in the ICU.

Joint models linking longitudinal biomarkers or recurrent event processes with a terminal event, for example, mortality, have been studied extensively. Motivated by studies of recurrent delirium events in patients receiving care in an intensive care unit (ICU), we devise a joint model for a recurrent event process and multiple terminal events. Being discharged alive from the ICU or experiencing mortality may be associated with a patient's hazard of delirium, violating the assumption of independent censoring. Moreover, the direction of the association between the hazards of delirium and mortality may be opposite of the direction of association between the hazards of delirium and ICU discharge. Hence treating either terminal event as independent censoring may bias inferences. We propose a competing joint model that uses a latent frailty to link a patient's recurrent and competing terminal event processes. We fit our model to data from a completed placebo-controlled clinical trial, which studied whether Haloperidol could prevent death and delirium among ICU patients. The clinical trial served as a foundation for a simulation study, in which we evaluate the properties, for example, bias and confidence interval coverage, of the competing joint model. As part of the simulation study, we demonstrate the shortcomings of using a joint model with a recurrent delirium process and a single terminal event to study delirium in the ICU. Lastly, we discuss limitations and possible extensions for the competing joint model. The competing joint model has been added to frailtypack, an R package for fitting an assortment of joint models.

Sample size estimation for recurrent event data using multifrailty and multilevel survival models.

In epidemiology and clinical research, recurrent events refer to individuals who are likely to experience transient clinical events repeatedly over an observation period. Examples include hospitalizations in patients with heart failure, fractures in osteoporosis studies and the occurrence of new lesions in oncology. We provided an in-depth analysis of the sample size required for the analysis of recurrent time-to-event data using multifrailty or multilevel survival models. We covered the topic from the simple shared frailty model to models with hierarchical or joint frailties. We relied on a Wald-type test statistic to estimate the sample size assuming either a single or multiple endpoints. Simulations revealed that the sample size increased as heterogeneity increased. We also observed that it was more attractive to include more patients and reduce the duration of follow-up than to include fewer patients and increase the duration of follow-up to obtain the number of events required. Each model investigated can address the question of the number of subjects for recurrent events. However, depending on the research question, one model will be more suitable than another. We illustrated our methodology with the AFFIRM-AHF trial investigating the effect of intravenous ferric carboxymaltose in patients hospitalised for acute heart failure.

Bayesian design of clinical trials using joint models for longitudinal and time-to-event data.

Joint models for longitudinal and time-to-event data are increasingly used for the analysis of clinical trial data. However, few methods have been proposed for designing clinical trials using these models. In this article, we develop a Bayesian clinical trial design methodology focused on evaluating the treatment's effect on the time-to-event endpoint using a flexible trajectory joint model. By incorporating the longitudinal outcome trajectory into the hazard model for the time-to-event endpoint, the joint modeling framework allows for non-proportional hazards (e.g., an increasing hazard ratio over time). Inference for the time-to-event endpoint is based on an average of a time-varying hazard ratio which can be decomposed according to the treatment's direct effect on the time-to-event endpoint and its indirect effect, mediated through the longitudinal outcome. We propose an approach for sample size determination for a trial such that the design has high power and a well-controlled type I error rate with both operating characteristics defined from a Bayesian perspective. We demonstrate the methodology by designing a breast cancer clinical trial with a primary time-to-event endpoint and where predictive longitudinal outcome measures are also collected periodically during follow-up.

Long-term peridialytic blood pressure changes are related to mortality.

BACKGROUND: In chronic haemodialysis (HD) patients, the relationship between long-term peridialytic blood pressure (BP) changes and mortality has not been investigated. METHODS: To evaluate whether long-term changes in peridialytic BP are related to mortality and whether treatment with HD or haemodiafiltration (HDF) differs in this respect, the combined individual participant data of three randomized controlled trials comparing HD with HDF were used. Time-varying Cox regression and joint models were applied. RESULTS: During a median follow-up of 2.94 years, 609 of 2011 patients died. As for pre-dialytic systolic BP (pre-SBP), a severe decline (≥21 mmHg) in the preceding 6 months was independently related to increased mortality [hazard ratio (HR) 1.61, P = .01] when compared with a moderate increase. Likewise, a severe decline in post-dialytic diastolic BP (DBP) was associated with increased mortality (adjusted HR 1.96, P < .0005). In contrast, joint models showed that every 5-mmHg increase in pre-SBP and post-DBP during total follow-up was related to reduced mortality (adjusted HR 0.97, P = .01 and 0.94, P = .03, respectively). No interaction was observed between BP changes and treatment modality. CONCLUSION: Severe declines in pre-SBP and post-DBP in the preceding 6 months were independently related to mortality. Therefore peridialytic BP values should be interpreted in the context of their changes and not solely as an absolute value.

Gaussian variational approximate inference for joint models of longitudinal biomarkers and a survival outcome.

The shared random effects joint model is one of the most widely used approaches to study the associations between longitudinal biomarkers and a survival outcome and make dynamic risk predictions using the longitudinally measured biomarkers. Various types of joint models have been developed under different settings in the past decades. One major limitation of joint models is that they could be computationally expensive for complex models where the number of the shared random effects is large. Moreover, the inferential accuracy of joint models could also be diminished for complex models due to approximation errors. However, complex models are frequently needed in practice, for example, when the longitudinal biomarkers have nonlinear trajectories over time or the number of longitudinal biomarkers of interest is large. In this article, we propose a novel Gaussian variational approximate inference approach for fitting joint models, which significantly improves computational efficiency while maintaining inferential accuracy. We conduct extensive simulation studies to evaluate the performance of our proposed method and compare it to existing methods. The performance of our proposed method is further demonstrated on a dataset of patients with primary biliary cirrhosis.

Supervised structural learning of semiparametric regression on high-dimensional correlated covariates with applications to eQTL studies.

Expression quantitative trait loci (eQTL) studies utilize regression models to explain the variance of gene expressions with genetic loci or single nucleotide polymorphisms (SNPs). However, regression models for eQTL are challenged by the presence of high dimensional non-sparse and correlated SNPs with small effects, and nonlinear relationships between responses and SNPs. Principal component analyses are commonly conducted for dimension reduction without considering responses. Because of that, this non-supervised learning method often does not work well when the focus is on discovery of the response-covariate relationship. We propose a new supervised structural dimensional reduction method for semiparametric regression models with high dimensional and correlated covariates; we extract low-dimensional latent features from a vast number of correlated SNPs while accounting for their relationships, possibly nonlinear, with gene expressions. Our model identifies important SNPs associated with gene expressions and estimates the association parameters via a likelihood-based algorithm. A GTEx data application on a cancer related gene is presented with 18 novel eQTLs detected by our method. In addition, extensive simulations show that our method outperforms the other competing methods in bias, efficiency, and computational cost.

Effect of Viral Replication and Liver Fibrosis on All-Cause Mortality in Human Immunodeficiency Virus-Hepatitis B Virus-Coinfected Individuals: A Retrospective Analysis of a 15-Year Longitudinal Cohort.

BACKGROUND: In individuals living with human immunodeficiency virus (HIV) and hepatitis B virus (HBV), widespread tenofovir (TDF)-containing antiretroviral therapy (ART) has led to substantial decreases in HBV-DNA and HIV-RNA detection. However, the links between viral replication, liver fibrosis, and mortality remain unclear. METHODS: A total of 300 individuals living with HIV-HBV and undergoing ART were prospectively followed. Virological and clinical data were obtained at baseline and every 6-12 months. We quantified the associations between HBV-DNA, HIV-RNA, and liver fibrosis with risk of all-cause mortality using a joint longitudinal survival model. Viral detection, viral loads, and time-averaged cumulative viral loads of HIV and HBV were modeled as 3 separate exposures. RESULTS: During a median of 10.5 years (interquartile range, 4.0-14.6), the proportion undergoing TDF-containing ART (baseline = 18.7%, end of follow-up = 79.1%) and with undetectable HBV-DNA (baseline = 36.7%, end of follow-up = 94.8%) substantially increased. 42 participants died (incidence rate = 1.30/100 person-years, 95% confidence interval [CI] = .96-1.76). The leading causes of death were non-AIDS/non-liver-related malignancies (28.6%), followed by liver-related (16.7%), AIDS-related (16.7%), and other (16.7%). All-cause mortality was associated with HBV-DNA viral load (adjusted hazards ratio [aHR] per log10 IU/mL = 1.41, 95% CI = 1.04-1.93, P = .03) or time-averaged cumulative HBV-DNA (aHR per log10 copy-years = 1.37, 95% CI = 1.03-1.83, P = .03), but not undetectable HBV-DNA. Advanced liver fibrosis at baseline was also associated with increased mortality rates (aHR = 2.35, 95% CI = 1.16-4.76, P = .02). No significant association between HIV-RNA replication and mortality was observed. CONCLUSIONS: Concurrent and historical HBV replication and liver fibrosis are important drivers of all-cause mortality in largely TDF-treated individuals living with HIV-HBV, despite one-fifth of deaths being liver-related. HBV-DNA and liver fibrosis remain important prognostic indicators for this patient population.

Longitudinal change in proteinuria and kidney outcomes in C3 glomerulopathy.

INTRODUCTION: The association between a change in proteinuria over time and its impact on kidney prognosis has not been analysed in complement component 3 (C3) glomerulopathy. This study aims to investigate the association between the longitudinal change in proteinuria and the risk of kidney failure. METHODS: This was a retrospective, multicentre observational cohort study in 35 nephrology departments belonging to the Spanish Group for the Study of Glomerular Diseases. Patients diagnosed with C3 glomerulopathy between 1995 and 2020 were enrolled. A joint modelling of linear mixed-effects models was applied to assess the underlying trajectory of a repeatedly measured proteinuria, and a Cox model to evaluate the association of this trajectory with the risk of kidney failure. RESULTS: The study group consisted of 85 patients, 70 C3 glomerulonephritis and 15 dense deposit disease, with a median age of 26 years (range 13-41). During a median follow-up of 42 months, 25 patients reached kidney failure. The longitudinal change in proteinuria showed a strong association with the risk of this outcome, with a doubling of proteinuria levels resulting in a 2.5-fold increase of the risk. A second model showed that a ≥50% proteinuria reduction over time was significantly associated with a lower risk of kidney failure (hazard ratio 0.79; 95% confidence interval 0.56-0.97; P < 0.001). This association was also found when the ≥50% proteinuria reduction was observed within the first 6 and 12 months of follow-up. CONCLUSIONS: The longitudinal change in proteinuria is strongly associated with the risk of kidney failure. The change in proteinuria over time can provide clinicians a dynamic prediction of kidney outcomes.

Consumption of differently processed milk products and the risk of asthma in children.

BACKGROUND: Consumption of unprocessed cow's milk has been associated with a lower risk of childhood asthma and/or atopy. Not much is known about differently processed milk products. We aimed to study the association between the consumption of differently processed milk products and asthma risk in a Finnish birth cohort. METHODS: We included 3053 children from the Finnish Type 1 Diabetes Prediction and Prevention (DIPP) Nutrition Study. Asthma and its subtypes were assessed at the age of 5 years, and food consumption by food records, at the age of 3 and 6 months and 1, 2, 3, 4, and 5 years. We used conventional and processing (heat treatment and homogenization)-based classifications for milk products. The data were analyzed using a joint model for longitudinal and time-to-event data. RESULTS: At the age of 5 years, 184 (6.0%) children had asthma, of whom 101 (54.9%) were atopic, 75 (40.8%) were nonatopic, and eight (4.3%) could not be categorized. Consumption of infant formulas [adjusted hazard ratio (95% confidence intervals) 1.15 (1.07, 1.23), p < .001] and strongly heat-treated milk products [1.06 (1.01, 1.10), p = .01] was associated with the risk of all asthma. Consumption of all cow's milk products [1.09 (1.03, 1.15), p = .003], nonfermented milk products [1.08 (1.02, 1.14), p = .008], infant formulas [1.23 (1.13, 1.34), p < .001], and strongly heat-treated milk products [1.08 (1.02, 1.15), p = .006] was associated with nonatopic asthma risk. All these associations remained statistically significant after multiple testing correction. CONCLUSIONS: High consumption of infant formula and other strongly heat-treated milk products may be associated with the development of asthma.

Bayesian semiparametric joint modeling of longitudinal explanatory variables of mixed types and a binary outcome.

Many prospective biomedical studies collect longitudinal clinical and lifestyle data that are both continuous and discrete. In some studies, there is interest in the association between a binary outcome and the values of these longitudinal measurements at a specific time point. A common problem in these studies is inconsistency in timing of measurements and missing follow-ups which can lead to few measurements at the time of interest. Some methods have been developed to address this problem, but are only applicable to continuous measurements. To address this limitation, we propose a new class of joint models for a binary outcome and longitudinal explanatory variables of mixed types. The longitudinal model uses a latent normal random variable construction with regression splines to model time-dependent trends in mean with a Dirichlet Process prior assigned to random effects to relax distribution assumptions. We also standardize timing of the explanatory variables by relating the binary outcome to imputed longitudinal values at a set time point. The proposed model is evaluated through simulation studies and applied to data from a cancer survivor study of participants in the Women's Health Initiative.

Landmarking 2.0: Bridging the gap between joint models and landmarking.

The problem of dynamic prediction with time-dependent covariates, given by biomarkers, repeatedly measured over time, has received much attention over the last decades. Two contrasting approaches have become in widespread use. The first is joint modeling, which attempts to jointly model the longitudinal markers and the event time. The second is landmarking, a more pragmatic approach that avoids modeling the marker process. Landmarking has been shown to be less efficient than correctly specified joint models in simulation studies, when data are generated from the joint model. When the mean model is misspecified, however, simulation has shown that joint models may be inferior to landmarking. The objective of this article is to develop methods that improve the predictive accuracy of landmarking, while retaining its relative simplicity and robustness. We start by fitting a working longitudinal model for the biomarker, including a temporal correlation structure. Based on that model, we derive a predictable time-dependent process representing the expected value of the biomarker after the landmark time, and we fit a time-dependent Cox model based on the predictable time-dependent covariate. Dynamic predictions based on this approach for new patients can be obtained by first deriving the expected values of the biomarker, given the measured values before the landmark time point, and then calculating the predicted probabilities based on the time-dependent Cox model. We illustrate the approach in predicting overall survival in liver cirrhosis patients based on prothrombin index.

Shared decision making of burdensome surveillance tests using personalized schedules and their burden and benefit.

Benchmark surveillance tests for detecting disease progression (eg, biopsies, endoscopies) in early-stage chronic noncommunicable diseases (eg, cancer, lung diseases) are usually burdensome. For detecting progression timely, patients undergo invasive tests planned in a fixed one-size-fits-all manner (eg, annually). We aim to present personalized test schedules based on the risk of disease progression, that optimize the burden (the number of tests) and the benefit (shorter time delay in detecting progression is better) better than fixed schedules, and enable shared decision making. Our motivation comes from the problem of scheduling biopsies in prostate cancer surveillance. Using joint models for time-to-event and longitudinal data, we consolidate patients' longitudinal data (eg, biomarkers) and results of previous tests, into individualized future cumulative-risk of progression. We then create personalized schedules by planning tests on future visits where the predicted cumulative-risk is above a threshold (eg, 5% risk). We update personalized schedules with data gathered over follow-up. To find the optimal risk threshold, we minimize a utility function of the expected number of tests (burden) and expected time delay in detecting progression (shorter is beneficial) for different thresholds. We estimate these two in a patient-specific manner for following any schedule, by utilizing a patient's predicted risk profile. Patients/doctors can employ these quantities to compare personalized and fixed schedules objectively and make a shared decision of a test schedule.

Protein intake, physical activity and grip strength in European and North American community-dwelling older adults: a pooled analysis of individual participant data from four longitudinal ageing cohorts.

INTRODUCTION: Higher dietary protein, alone or in combination with physical activity (PA), may slow the loss of age-related muscle strength in older adults. We investigated the longitudinal relationship between protein intake and grip strength, and the interaction between protein intake and PA, using four longitudinal ageing cohorts. METHODS: Individual participant data from 5584 older adults (52% women; median: 75, IQR: 71.6, 79.0 years) with up to 8.5 years (mean: 4.9, SD: 2.3 years) of follow-up from the Health ABC, NuAge, LASA and Newcastle 85+ cohorts were pooled. Baseline protein intake was assessed with food frequency questionnaires and 24h recalls and categorized into <0.8, 0.8-<1.0, 1.0-<1.2 and ≥1.2 g/kg adjusted body weight (aBW)/d. The prospective association between protein intake, its interaction with PA, and grip strength (sex- and cohort-specific) was determined using joint models (hierarchical linear mixed effects and a link function for Cox proportional hazards models). RESULTS: Grip strength declined on average by 0.018 SD (95%CI: -0.026, -0.006) every year. No associations were found between protein intake, measured at baseline, and grip strength, measured prospectively, or rate of decline of grip strength in models adjusted for sociodemographic, anthropometric, lifestyle and health variables (e.g., protein intake ≥1.2 vs <0.8 g/kg aBW/d: ß= -0.003, 95%CI: -0.014,0.005 SD per year). There also was no evidence of an interaction between protein intake and PA. CONCLUSIONS: We failed to find evidence in this study to support the hypothesis that higher protein intake, alone or in combination with higher PA, slowed the rate of grip strength decline in older adults.

Using joint models to study the association between CD4 count and the risk of death in TB/HIV data.

BACKGROUND: The association structure linking the longitudinal and survival sub-models is of fundamental importance in the joint modeling framework and the choice of this structure should be made based on the clinical background of the study. However, this information may not always be accessible and rationale for selecting this association structure has received relatively little attention in the literature. To this end, we aim to explore four alternative functional forms of the association structure between the CD4 count and the risk of death and provide rationale for selecting the optimal association structure for our data. We also aim to compare the results obtained from the joint model to those obtained from the time-varying Cox model. METHODS: We used data from the Centre for the AIDS Programme of Research in South Africa (CAPRISA) AIDS Treatment programme, the Starting Antiretroviral Therapy at Three Points in Tuberculosis (SAPiT) study, an open-label, three armed randomised, controlled trial between June 2005 and July 2010 (N=642). In our analysis, we combined the early and late integrated arms and compared results to the sequential arm. We utilized the Deviance Information Criterion (DIC) to select the final model with the best structure, with smaller values indicating better model adjustments to the data. RESULTS: Patient characteristics were similar across the study arms. Combined integrated therapy arms had a reduction of 55% in mortality (HR:0.45, 95% CI:0.28-0.72) compared to the sequential therapy arm. The joint model with a cumulative effects functional form was chosen as the best association structure. In particular, our joint model found that the area under the longitudinal profile of CD4 count was strongly associated with a 21% reduction in mortality (HR:0.79, 95% CI:0.72-0.86). Where as results from the time-varying Cox model showed a 19% reduction in mortality (HR:0.81, 95% CI:0.77-0.84). CONCLUSIONS: In this paper we have shown that the "current value" association structure is not always the best structure that expresses the correct relationship between the outcomes in all settings, which is why it is crucial to explore alternative clinically meaningful association structures that links the longitudinal and survival processes.

Associations of longitudinal D-Dimer and Factor II on early trauma survival risk.

BACKGROUND: Trauma-induced coagulopathy (TIC) is a disorder that occurs in one-third of severely injured trauma patients, manifesting as increased bleeding and a 4X risk of mortality. Understanding the mechanisms driving TIC, clinical risk factors are essential to mitigating this coagulopathic bleeding and is therefore essential for saving lives. In this retrospective, single hospital study of 891 trauma patients, we investigate and quantify how two prominently described phenotypes of TIC, consumptive coagulopathy and hyperfibrinolysis, affect survival odds in the first 25 h, when deaths from TIC are most prevalent. METHODS: We employ a joint survival model to estimate the longitudinal trajectories of the protein Factor II (% activity) and the log of the protein fragment D-Dimer ([Formula: see text]g/ml), representative biomarkers of consumptive coagulopathy and hyperfibrinolysis respectively, and tie them together with patient outcomes. Joint models have recently gained popularity in medical studies due to the necessity to simultaneously track continuously measured biomarkers as a disease evolves, as well as to associate them with patient outcomes. In this work, we estimate and analyze our joint model using Bayesian methods to obtain uncertainties and distributions over associations and trajectories. RESULTS: We find that a unit increase in log D-Dimer increases the risk of mortality by 2.22 [1.57, 3.28] fold while a unit increase in Factor II only marginally decreases the risk of mortality by 0.94 [0.91,0.96] fold. This suggests that, while managing consumptive coagulopathy and hyperfibrinolysis both seem to affect survival odds, the effect of hyperfibrinolysis is much greater and more sensitive. Furthermore, we find that the longitudinal trajectories, controlling for many fixed covariates, trend differently for different patients. Thus, a more personalized approach is necessary when considering treatment and risk prediction under these phenotypes. CONCLUSION: This study reinforces the finding that hyperfibrinolysis is linked with poor patient outcomes regardless of factor consumption levels. Furthermore, it quantifies the degree to which measured D-Dimer levels correlate with increased risk. The single hospital, retrospective nature can be understood to specify the results to this particular hospital's patients and protocol in treating trauma patients. Expanding to a multi-hospital setting would result in better estimates about the underlying nature of consumptive coagulopathy and hyperfibrinolysis with survival, regardless of protocol. Individual trajectories obtained with these estimates can be used to provide personalized dynamic risk prediction when making decisions regarding management of blood factors.

Development and testing of an artificial intelligence tool for predicting end-stage kidney disease in patients with immunoglobulin A nephropathy.

We have developed an artificial neural network prediction model for end-stage kidney disease (ESKD) in patients with primary immunoglobulin A nephropathy (IgAN) using a retrospective cohort of 948 patients with IgAN. Our tool is based on a two-step procedure of a classifier model that predicts ESKD, and a regression model that predicts development of ESKD over time. The classifier model showed a performance value of 0.82 (area under the receiver operating characteristic curve) in patients with a follow-up of five years, which improved to 0.89 at the ten-year follow-up. Both models had a higher recall rate, which indicated the practicality of the tool. The regression model showed a mean absolute error of 1.78 years and a root mean square error of 2.15 years. Testing in an independent cohort of 167patients with IgAN found successful results for 91% of the patients. Comparison of our system with other mathematical models showed the highest discriminant Harrell C index at five- and ten-years follow-up (81% and 86%, respectively), paralleling the lowest Akaike information criterion values (355.01 and 269.56, respectively). Moreover, our system was the best calibrated model indicating that the predicted and observed outcome probabilities did not significantly differ. Finally, the dynamic discrimination indexes of our artificial neural network, expressed as the weighted average of time-dependent areas under the curve calculated at one and two years, were 0.80 and 0.79, respectively. Similar results were observed over a 25-year follow-up period. Thus, our tool identified individuals who were at a high risk of developing ESKD due to IgAN and predicted the time-to-event endpoint. Accurate prediction is an important step toward introduction of a therapeutic strategy for improving clinical outcomes.

Bayesian joint modeling for partially linear mixed-effects quantile regression of longitudinal and time-to-event data with limit of detection, covariate measurement errors and skewness.

Joint modeling analysis of longitudinal and time-to-event data has been an active area of statistical methodological study and biomedical research, but the majority of them are based on mean-regression. Quantile regression (QR) can characterize the entire conditional distribution of the outcome variable, and may be more robust to outliers/heavy tails and misspecification of error distribution. Additionally, a parametric specification may be insufficient and inflexible to capture the complicated longitudinal pattern of biomarkers. Thus, this study proposes novel QR-based partially linear mixed-effects joint models with three components (QR-based longitudinal response, longitudinal covariate, and time-to-event processes), and applies to Multicenter AIDS Cohort Study (MACS). Many common data features, including left-censoring due to a limit of detection, covariate measurement error, and asymmetric distribution, are considered to obtain reliable parameter estimates. Many interesting findings are discovered by the complicated joint models under Bayesian inference framework. Simulation studies are also implemented to assess the performance of the proposed joint models under different scenarios.