Bayesian regularization for a nonstationary Gaussian linear mixed effects model.

In omics experiments, estimation and variable selection can involve thousands of proteins/genes observed from a relatively small number of subjects. Many regression regularization procedures have been developed for estimation and variable selection in such high-dimensional problems. However, approaches have predominantly focused on linear regression models that ignore correlation arising from long sequences of repeated measurements on the outcome. Our work is motivated by the need to identify proteomic biomarkers that improve the prediction of rapid lung-function decline for individuals with cystic fibrosis (CF) lung disease. We extend four Bayesian penalized regression approaches for a Gaussian linear mixed effects model with nonstationary covariance structure to account for the complicated structure of longitudinal lung function data while simultaneously estimating unknown parameters and selecting important protein isoforms to improve predictive performance. Different types of shrinkage priors are evaluated to induce variable selection in a fully Bayesian framework. The approaches are studied with simulations. We apply the proposed method to real proteomics and lung-function outcome data from our motivating CF study, identifying a set of relevant clinical/demographic predictors and a proteomic biomarker for rapid decline of lung function. We also illustrate the methods on CD4 yeast cell-cycle genomic data, confirming that the proposed method identifies transcription factors that have been highlighted in the literature for their importance as cell cycle transcription factors.

Longitudinal change in c-terminal fibroblast growth factor 23 and outcomes in patients with advanced chronic kidney disease.

BACKGROUND: Fibroblast growth factor23 (FGF23) is elevated in CKD and has been associated with outcomes such as death, cardiovascular (CV) events and progression to Renal Replacement therapy (RRT). The majority of studies have been unable to account for change in FGF23 over time and those which have demonstrate conflicting results. We performed a survival analysis looking at change in c-terminal FGF23 (cFGF23) over time to assess the relative contribution of cFGF23 to these outcomes. METHODS: We measured cFGF23 on plasma samples from 388 patients with CKD 3-5 who had serial measurements of cFGF23, with a mean of 4.2 samples per individual. We used linear regression analysis to assess the annual rate of change in cFGF23 and assessed the relationship between time-varying cFGF23 and the outcomes in a cox-regression analysis. RESULTS: Across our population, median baseline eGFR was 32.3mls/min/1.73m2, median baseline cFGF23 was 162 relative units/ml (RU/ml) (IQR 101-244 RU/mL). Over 70 months (IQR 53-97) median follow-up, 76 (19.6%) patients progressed to RRT, 86 (22.2%) died, and 52 (13.4%) suffered a major non-fatal CV event. On multivariate analysis, longitudinal change in cFGF23 was significantly associated with risk for death and progression to RRT but not non-fatal cardiovascular events. CONCLUSION: In our study, increasing cFGF23 was significantly associated with risk for death and RRT.

Robust joint modelling of longitudinal and survival data: Incorporating a time-varying degrees-of-freedom parameter.

Monitoring of individual biomarkers has the potential of explaining the hazard of survival outcomes. In practice, these measurements are intermittently observed and are known to be subject to substantial measurement error. Joint modelling of longitudinal and survival data enables us to associate intermittently measured error-prone biomarkers with risks of survival outcomes and thus plays an important role in the analysis of medical data. Most of the joint models available in the literature have been built on the Gaussian assumption. This makes them sensitive to outliers. In this work, we study a range of robust models to address this issue. Of particular interest is the common occurrence in medical data that outliers can occur with different frequencies over time, for example, in the period when patients adjust to treatment changes. Motivated by the analysis of data gathered from patients with primary biliary cirrhosis, a new model with a time-varying robustness is introduced. Through both the motivating example and a simulation study, this research not only stresses the need to account for longitudinal outliers in the analysis of medical data and in joint modelling research but also highlights the bias and inefficiency from not properly estimating the degrees-of-freedom parameter. This work presents a number of methods in addition to the time-varying robustness, and each method can be fitted using the R package robjm.

Web-based integrated bipolar parenting intervention for parents with bipolar disorder: a randomised controlled pilot trial.

BACKGROUND: People with bipolar disorder (BD) experience additional parenting challenges associated with mood driven fluctuations in communication, impulse control and motivation. This paper describes a novel web-based self-management approach (Integrated Bipolar Parenting Intervention; IBPI) to support parents with BD. METHOD: Parents with BD with children aged 3-10 years randomised to IBPI plus treatment as usual (TAU) or waitlist control (WL). IBPI offered 16 weeks access to interactive self-management information concerning BD and parenting issues. Feasibility was through recruitment, retention and web usage. Clinical outcomes were assessed at baseline, 16, 24, 36 and 48 weeks. TRIAL REGISTRATION NUMBER: ISRCTN75279027. RESULTS: Ninety seven participants were recruited with 98% retention to end of intervention and 90% to final follow-up (56%-94% data analysed of retained participants; higher rates for observer measures). 77% of IBPI participants accessed the website (53% accessed parenting modules). Child behaviour, parenting sense of competence and parenting stress improved significantly in IBPI compared to WL to end of intervention, sustained to 48 weeks. Impacts of IBPI on family functioning, parent mood and time to mood relapse were not significant. CONCLUSIONS: Online self-management support for parents with BD is feasible, with promising improvements in parenting and child behaviour outcomes. A definitive clinical and cost-effectiveness trial is required to confirm and extend these findings.

Assessing Feasibility and Acceptability of Web-Based Enhanced Relapse Prevention for Bipolar Disorder (ERPonline): A Randomized Controlled Trial.

BACKGROUND: Interventions that teach people with bipolar disorder (BD) to recognize and respond to early warning signs (EWS) of relapse are recommended but implementation in clinical practice is poor. OBJECTIVES: The objective of this study was to test the feasibility and acceptability of a randomized controlled trial (RCT) to evaluate a Web-based enhanced relapse prevention intervention (ERPonline) and to report preliminary evidence of effectiveness. METHODS: A single-blind, parallel, primarily online RCT (n=96) over 48 weeks comparing ERPonline plus usual treatment with "waitlist (WL) control" plus usual treatment for people with BD recruited through National Health Services (NHSs), voluntary organizations, and media. Randomization was independent, minimized on number of previous episodes (<8, 8-20, 21+). Primary outcomes were recruitment and retention rates, levels of intervention use, adverse events, and participant feedback. Process and clinical outcomes were assessed by telephone and Web and compared using linear models with intention-to-treat analysis. RESULTS: A total of 280 people registered interest online, from which 96 met inclusion criteria, consented, and were randomized (49 to WL, 47 to ERPonline) over 17 months, with 80% retention in telephone and online follow-up at all time points, except at week 48 (76%). Acceptability was high for both ERPonline and trial methods. ERPonline cost approximately £19,340 to create, and £2176 per year to host and maintain the site. Qualitative data highlighted the importance of the relationship that the users have with Web-based interventions. Differences between the group means suggested that access to ERPonline was associated with: a more positive model of BD at 24 weeks (10.70, 95% CI 0.90 to 20.5) and 48 weeks (13.1, 95% CI 2.44 to 23.93); increased monitoring of EWS of depression at 48 weeks (-1.39, 95% CI -2.61 to -0.163) and of hypomania at 24 weeks (-1.72, 95% CI -2.98 to -0.47) and 48 weeks (-1.61, 95% CI -2.92 to -0.30), compared with WL. There was no evidence of impact of ERPonline on clinical outcomes or medication adherence, but relapse rates across both arms were low (15%) and the sample remained high functioning throughout. One person died by suicide before randomization and 5 people in ERPonline and 6 in WL reported ideas of suicide or self-harm. None were deemed study related by an independent Trial Steering Committee (TSC). CONCLUSIONS: ERPonline offers a cheap accessible option for people seeking ongoing support following successful treatment. However, given high functioning and low relapse rates in this study, testing clinical effectiveness for this population would require very large sample sizes. Building in human support to use ERPonline should be considered. TRIAL REGISTRATION: International Standard Randomized Controlled Trial Number (ISRCTN): 56908625; http://www.isrctn.com/ISRCTN56908625 (Archived by WebCite at http://www.webcitation.org/6of1ON2S0).

Real-time monitoring of progression towards renal failure in primary care patients.

Chronic renal failure is a progressive condition that, typically, is asymptomatic for many years. Early detection of incipient kidney failure enables ameliorative treatment that can slow the rate of progression to end-stage renal failure, at which point expensive and invasive renal replacement therapy (dialysis or transplantation) is required. We use routinely collected clinical data from a large sample of primary care patients to develop a system for real-time monitoring of the progression of undiagnosed incipient renal failure. Progression is characterized as the rate of change in a person's kidney function as measured by the estimated glomerular filtration rate, an adjusted version of serum creatinine level in a blood sample. Clinical guidelines in the UK suggest that a person who is losing kidney function at a relative rate of at least 5% per year should be referred to specialist secondary care. We model the time-course of a person's underlying kidney function through a combination of explanatory variables, a random intercept and a continuous-time, non-stationary stochastic process. We then use the model to calculate for each person the predictive probability that they meet the clinical guideline for referral to secondary care. We suggest that probabilistic predictive inference linked to clinical criteria can be a useful component of a real-time surveillance system to guide, but not dictate, clinical decision-making.

Short-term and long-term effects of acute kidney injury in chronic kidney disease patients: A longitudinal analysis.

We use data from an ongoing cohort study of chronic kidney patients at Salford Royal NHS Foundation Trust, Greater Manchester, United Kingdom, to investigate the influence of acute kidney injury (AKI) on the subsequent rate of change of kidney function amongst patients already diagnosed with chronic kidney disease (CKD). We use a linear mixed effects modelling framework to enable estimation of both acute and chronic effects of AKI events on kidney function. We model the fixed effects by a piece-wise linear function with three change-points to capture the acute changes in kidney function that characterise an AKI event, and the random effects by the sum of three components: a random intercept, a stationary stochastic process with Matérn correlation structure, and measurement error. We consider both multivariate Normal and multivariate t versions of the random effects. For either specification, we estimate model parameters by maximum likelihood and evaluate the plug-in predictive distributions of the random effects given the data. We find that following an AKI event the average long-term rate of decline in kidney function is almost doubled, regardless of the severity of the event. We also identify and present examples of individual patients whose kidney function trajectories diverge substantially from the population-average.

Dynamic predictions of kidney graft survival in the presence of longitudinal outliers.

In kidney transplantation, dynamic predictions of graft survival may be obtained from joint modelling of longitudinal and survival data for which a common assumption is that random-effects and error terms in the longitudinal sub-model are Gaussian. However, this assumption may be too restrictive, e.g. in the presence of outliers, and more flexible distributions would be required. In this study, we relax the Gaussian assumption by defining a robust joint modelling framework with t-distributed random-effects and error terms to obtain dynamic predictions of graft survival for kidney transplant patients. We take a Bayesian paradigm for inference and dynamic predictions and sample from the joint posterior densities. While previous research reported improved performances of robust joint models compared to the Gaussian version in terms of parameter estimation, dynamic prediction accuracy obtained from such approach has not been yet evaluated. Our results based on a training sample from the French DIVAT kidney transplantation cohort illustrate that estimates for the slope parameters in the longitudinal and survival sub-models are sensitive to the distributional assumptions. From both an internal validation sample from the DIVAT cohort and an external validation sample from the Lille (France) and Leuven (Belgium) transplantation centers, calibration and discrimination performances appeared to be better under the robust joint models compared to the Gaussian version, illustrating the need to accommodate outliers in the dynamic prediction context. Simulation results support the findings of the validation studies.

External Validation of the DynPG for Kidney Transplant Recipients.

BACKGROUND: In kidney transplantation, dynamic prediction of patient and kidney graft survival (DynPG) may help to promote therapeutic alliance by delivering personalized evidence-based information about long-term graft survival for kidney transplant recipients. The objective of the current study is to externally validate the DynPG. METHODS: Based on 6 baseline variables, the DynPG can be updated with any new serum creatinine measure available during the follow-up. From an external validation sample of 1637 kidney recipients with a functioning graft at 1-year posttransplantation from 2 European transplantation centers, we assessed the prognostic performance of the DynPG. RESULTS: As one can expect from an external validation sample, differences in several recipient, donor, and transplantation characteristics compared with the learning sample were observed. Patients were mainly transplanted from deceased donors (91.6% versus 84.8%; P < 0.01), were less immunized against HLA class I (18.4% versus 32.7%; P < 0.01) and presented less comorbidities (62.2% for hypertension versus 82.7%, P < 0.01; 25.1% for cardiovascular disease versus 33.9%, P < 0.01). Despite these noteworthy differences, the area under the ROC curve varied from 0.70 (95% confidence interval [CI], 0.64-0.76) to 0.76 (95% CI, 0.64-0.88) for prediction times at 1 and 6 years posttransplantation respectively, and calibration plots revealed reasonably accurate predictions. CONCLUSIONS: We validated the prognostic capacities of the DynPG in terms of both discrimination and calibration. Our study showed the robustness of the DynPG for informing both the patient and the physician, and its transportability for a cohort presenting different features than the one used for the DynPG development.

The influence of multiple episodes of acute kidney injury on survival and progression to end stage kidney disease in patients with chronic kidney disease.

BACKGROUND: Acute kidney injury (AKI) and chronic kidney disease (CKD) are common syndromes associated with significant morbidity, mortality and cost. The extent to which repeated AKI episodes may cumulatively affect the rate of progression of all-cause CKD has not previously been investigated. In this study, we explored the hypothesis that repeated episodes of AKI increase the rate of renal functional deterioration loss in patients recruited to a large, all-cause CKD cohort. METHODS: Patients from the Salford Kidney Study (SKS) were considered. Application of KDIGO criteria to all available laboratory measurements of renal function identified episodes of AKI. A competing risks model was specified for four survival events: Stage 1 AKI; stage 2 or 3 AKI; dialysis initiation or transplant before AKI event; death before AKI event. The model was adjusted for patient age, gender, smoking status, alcohol intake, diabetic status, cardiovascular co-morbidities, and primary renal disease. Analyses were performed for patients' first, second, and third or more AKI episodes. RESULTS: A total of 48,338 creatinine measurements were available for 2287 patients (median 13 measures per patient [IQR 6-26]). There was a median age of 66.8years, median eGFR of 28.4 and 31.6% had type 1 or 2 diabetes. Six hundred and forty three (28.1%) patients suffered one or more AKI events; 1000 AKI events (58% AKI 1) in total were observed over a median follow-up of 2.6 years [IQR 1.1-3.2]. In patients who suffered an AKI, a second AKI was more likely to be a stage 2 or 3 AKI than stage 1 [HR 2.04, p 0.01]. AKI events were associated with progression to RRT, with multiple episodes of AKI progressively increasing likelihood of progression to RRT [HR 14.4 after 1 episode of AKI, HR 28.4 after 2 episodes of AKI]. However, suffering one or more AKI events was not associated with an increased risk of mortality. CONCLUSIONS: AKI events are associated with more rapid CKD deterioration as hypothesised, and also with a greater severity of subsequent AKI. However, our study did not find an association of AKI with increased mortality risk in this CKD cohort.

Joint modelling of repeated measurement and time-to-event data: an introductory tutorial.

BACKGOUND: The term 'joint modelling' is used in the statistical literature to refer to methods for simultaneously analysing longitudinal measurement outcomes, also called repeated measurement data, and time-to-event outcomes, also called survival data. A typical example from nephrology is a study in which the data from each participant consist of repeated estimated glomerular filtration rate (eGFR) measurements and time to initiation of renal replacement therapy (RRT). Joint models typically combine linear mixed effects models for repeated measurements and Cox models for censored survival outcomes. Our aim in this paper is to present an introductory tutorial on joint modelling methods, with a case study in nephrology. METHODS: We describe the development of the joint modelling framework and compare the results with those obtained by the more widely used approaches of conducting separate analyses of the repeated measurements and survival times based on a linear mixed effects model and a Cox model, respectively. Our case study concerns a data set from the Chronic Renal Insufficiency Standards Implementation Study (CRISIS). We also provide details of our open-source software implementation to allow others to replicate and/or modify our analysis. RESULTS: The results for the conventional linear mixed effects model and the longitudinal component of the joint models were found to be similar. However, there were considerable differences between the results for the Cox model with time-varying covariate and the time-to-event component of the joint model. For example, the relationship between kidney function as measured by eGFR and the hazard for initiation of RRT was significantly underestimated by the Cox model that treats eGFR as a time-varying covariate, because the Cox model does not take measurement error in eGFR into account. CONCLUSIONS: Joint models should be preferred for simultaneous analyses of repeated measurement and survival data, especially when the former is measured with error and the association between the underlying error-free measurement process and the hazard for survival is of scientific interest.

Flexible multivariate marginal models for analyzing multivariate longitudinal data, with applications in R.

Most of the available multivariate statistical models dictate on fitting different parameters for the covariate effects on each multiple responses. This might be unnecessary and inefficient for some cases. In this article, we propose a modelling framework for multivariate marginal models to analyze multivariate longitudinal data which provides flexible model building strategies. We show that the model handles several response families such as binomial, count and continuous. We illustrate the model on the Kenya Morbidity data set. A simulation study is conducted to examine the parameter estimates. An R package mmm2 is proposed to fit the model.

mmm: an R package for analyzing multivariate longitudinal data with multivariate marginal models.

Modeling multivariate longitudinal data has many challenges in terms of both statistical and computational aspects. Statistical challenges occur due to complex dependence structures. Computational challenges are due to the complex algorithms, the use of numerical methods, and potential convergence problems. Therefore, there is a lack of software for such data. This paper introduces an R package mmm prepared for marginal modeling of multivariate longitudinal data. Parameter estimations are achieved by generalized estimating equations approach. A real life data set is applied to illustrate the core features of the package, and sample R code snippets are provided. It is shown that the multivariate marginal models considered in this paper and mmm are valid for binary, continuous and count multivariate longitudinal responses.