Joint Modelling of Longitudinal and Survival Data with Applications in Heart Valve Data

__Abstract__ The heart is one of the most important organs in the entire human body. Specifically, it is a pump composed of muscle which pumps blood throughout the blood vessels to various parts of the body by repeated rhythmic contractions. The four heart valves determine the pathway of blood flow through the heart and they normally allow blood flow in only one direction through the heart. Moreover, they open or close incumbent upon differential blood pressure on each side. Specifically, the four valves are: the tricuspid valve, the pulmonary valve, the mitral valve and the aortic valve. Figure 1.1, represents graphically the heart anatomy. The blood flows from the right atrium to the right ventricle through the tricuspid valve. Thereafter, the blood flows through the pulmonary valve to the lungs, where oxygenation takes place. Next, the blood re-enters the heart into the left atrium, through the mitral valve into the left ventricle. Finally, it enters the aorta through the aortic valve. Another important part of the heart is the aortic root which connects the heart to the systemic circulation. Heart valve disease occurs when one or more valves are not functioning properly due to stenosis and/or regurgitation. Valve stenosis is the disease in which the opening of the valve is narrowed, while valve regurgitation or insufficiency is the leaking of the valve that causes blood to flow in the reverse direction during ventricular diastole. Echoca

Improved Dynamic Predictions from Joint Models of Longitudinal and Survival Data with Time-Varying Effects using P-splines

In the field of cardio-thoracic surgery, valve function is monitored over time after surgery. The motivation for our research comes from a study which includes patients who received a human tissue valve in the aortic position. These patients are followed prospectively over time by standardized echocardiographic assessment of valve function. Loss of follow-up could be caused by valve intervention or the death of the patient. One of the main characteristics of the human valve is that its durability is limited. Therefore, it is of interest to obtain a prognostic model in order for the physicians to scan trends in valve function over time and plan their next intervention, accounting for the characteristics of the data. Several authors have focused on deriving predictions under the standard joint modeling of longitudinal and survival data framework that assumes a constant effect for the coefficient that links the longitudinal and survival outcomes. However, in our case this may be a restrictive assumption. Since the valve degenerates, the association between the biomarker with survival may change over time. To improve dynamic predictions we propose a Bayesian joint model that allows a time-varying coefficient to link the longitudinal and the survival processes, using P-splines. We evaluate the performance of the model in terms of discrimination and calibration, while accounting for censoring

Integrating Latent Classes in the Bayesian Shared Parameter Joint Model of Longitudinal and Survival Outcomes

Cystic fibrosis is a chronic lung disease which requires frequent patient monitoring to maintain lung function over time and minimize onset of acute respiratory events known as pulmonary exacerbations. From the clinical point of view it is important to characterize the association between key biomarkers such as $FEV_1$ and time-to first exacerbation. Progression of the disease is heterogeneous, yielding different sub-groups in the population exhibiting distinct longitudinal profiles. It is desirable to categorize these unobserved sub-groups (latent classes) according to their distinctive trajectories. Accounting for these latent classes, in other words heterogeneity, will lead to improved estimates of association arising from the joint longitudinal-survival model. The joint model of longitudinal and survival data constitutes a popular framework to analyze such data arising from heterogeneous cohorts. In particular, two paradigms within this framework are the shared parameter joint models and the joint latent class models. The former paradigm allows one to quantify the strength of the association between the longitudinal and survival outcomes but does not allow for latent sub-populations. The latter paradigm explicitly postulates the existence of sub-populations but does not directly quantify the strength of the association. We propose to integrate latent classes in the shared parameter joint model in a fully Bayesian approach, which allows us to investigate the association between $FEV_1$ and time-to first exacerbation within each latent class. We, furthermore, focus on the selection of the optimal number of latent classes

Dynamic Predictions with Time-Dependent Covariates in Survival Analysis using Joint Modeling and Landmarking

A key question in clinical practice is accurate prediction of patient prognosis. To this end, nowadays, physicians have at their disposal a variety of tests and biomarkers to aid them in optimizing medical care. These tests are often performed on a regular basis in order to closely follow the progression of the disease. In this setting it is of medical interest to optimally utilize the recorded information and provide medically-relevant summary measures, such as survival probabilities, that will aid in decision making. In this work we present and compare two statistical techniques that provide dynamically-updated estimates of survival probabilities, namely landmark analysis and joint models for longitudinal and time-to-event data. Special attention is given to the functional form linking the longitudinal and event time processes, and to measures of discrimination and calibration in the context of dynamic prediction.Comment: 34 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1303.279

A Bayesian joint model for zero‐inflated integers and left‐truncated event times with a time‐varying association: Applications to senior health care

Population aging in most industrialized societies has led to a dramatic increase in emergency medical demand among the elderly. In the context of private health care, an optimal allocation of the medical resources for seniors is commonly done by forecasting their life spans. Accounting for each subject's particularities is therefore indispensable, so the available data must be processed at an individual level. We use a large and unique dataset of insured parties aged 65 and older to appropriately relate the emergency care usage with mortality risk. Longitudinal and time‐to‐event processes are jointly modeled, and their underlying relationship can therefore be assessed. Such an application, however, requires some special features to also be considered. First, longitudinal demand for emergency services exhibits a nonnegative integer response with an excess of zeros due to the very nature of the data. These subject‐specific responses are handled by a zero‐inflated version of the hierarchical negative binomial model. Second, event times must account for the left truncation derived from the fact that policyholders must reach the age of 65 before they may begin to be observed. Consequently, a delayed entry bias arises for those individuals entering the study after this age threshold. Third, and as the main challenge of our analysis, the association parameter between both processes is expected to be age‐dependent, with an unspecified association structure. This is well‐approximated through a flexible functional specification provided by penalized B‐splines. The parameter estimation of the joint model is derived under a Bayesian scheme

Multivariate joint modeling to identify markers of growth and lung function decline that predict cystic fibrosis pulmonary exacerbation onset

BACKGROUND: Attenuated decreases in lung function can signal the onset of acute respiratory events known as pulmonary exacerbations (PEs) in children and adolescents with cystic fibrosis (CF). Univariate joint modeling facilitates dynamic risk prediction of PE onset and accounts for measurement error of the lung function marker. However, CF is a multi-system disease and the extent to which simultaneously modeling growth and nutrition markers improves PE predictive accuracy is unknown. Furthermore, it is unclear which routinely collected clinical indicators of growth and nutrition in early life predict PE onset in CF. METHODS: Using a longitudinal cohort of 17,100 patients aged 6-20 years (US Cystic Fibrosis Foundation Patient Registry; 2003-2015), we fit a univariate joint model of lung-function decline and PE onset and contrasted its predictive performance with a class of multivariate joint models that included combinations of growth markers as additional submodels. Outcomes were longitudinal lung function (forced expiratory volume in 1 s of % predicted), percentiles of body mass index, weight-for-age and height-for-age and PE onset. Relevant demographic/clinical covariates were included in submodels. We implemented a univariate joint model of lung function and time-to-PE and four multivariate joint models including growth outcomes. RESULTS: All five joint models showed that declining lung function corresponded to slightly increased risk of PE onset (hazard ratio from univariate joint model: 0.97, P  0.70). None of the growth markers alongside lung function as outcomes in multivariate joint modeling appeared to have an association with hazard of PE. Jointly modeling only lung function and PE onset yielded the most accurate (area under the receiver-operator characteristic curve = 0.75) and precise (narrowest interquartile range) predictions. Dynamic predictions were accurate across forecast horizons (0.5, 1 and 2 years) and precision improved with age. CONCLUSIONS: Including growth markers via multivariate joint models did not yield gains in prediction performance, compared to a univariate joint model with lung function. Individualized dynamic predictions from joint modeling could enhance physician monitoring of CF disease progression by providing PE risk assessment over a patient's clinical course

Integrating latent classes in the Bayesian shared parameter joint model of longitudinal and survival outcomes

Cystic fibrosis is a chronic lung disease requiring frequent lung-function monitoring to track acute respiratory events (pulmonary exacerbations). The association between lung-function trajectory and time-to-first exacerbation can be characterized using joint longitudinal-survival modeling. Joint models specified through the shared parameter framework quantify the strength of association between such outcomes but do not incorporate latent sub-populations reflective of heterogeneous disease progression. Conversely, latent class joint models explicitly postulate the existence of sub-populations but do not directly quantify the strength of association. Furthermore, choosing the optimal number of classes using established metrics like deviance information criterion is computationally intensive in complex models. To overcome these limitations, we integrate latent classes in the shared parameter joint model through a fully Bayesian approach. To choose the optimal number of classes, we construct a mixture model assuming more latent classes than present in the data, thereby asymptotically “emptying” superfluous latent classes, provided the Dirichlet prior on class proportions is sufficiently uninformative. Model properties are evaluated in simulation studies. Application to data from the US Cystic Fibrosis Registry supports the existence of three sub-populations corresponding to lung-function trajectories with high initial forced expiratory volume in 1 s (FEV1), rapid FEV1 decline, and low but steady FEV1 progression. The association between FEV1 and hazard of exacerbation was negative in each class, but magnitude varied

Diffusion weighted imaging in cystic fibrosis disease: beyond morphological imaging

To explore the feasibility of diffusion-weighted imaging (DWI) to assess inflammatory lung changes in patients with Cystic Fibrosis (CF) METHODS: CF patients referred for their annual check-up had spirometry, chest-CT and MRI on the same day. MRI was performed in a 1.5 T scanner with BLADE and EPI-DWI sequences (b = 0-600 s/mm(2)). End-inspiratory and end-expiratory scans were acquired in multi-row scanners. DWI was scored with an established semi-quantitative scoring system. DWI score was correlated to CT sub-scores for bronchiectasis (CF-CTBE), mucus (CF-CTmucus), total score (CF-CTtotal-score), FEV1, and BMI. T-test was used to assess differences between patients with and without DWI-hotspots

Dynamic prediction of outcome for patients with severe aortic stenosis: Application of joint models for longitudinal and time-to-event data

Background: Physicians utilize different types of information to predict patient prognosis. For example: confronted with a new patient suffering from severe aortic stenosis (AS), the cardiologist considers not only the severity of the AS but also patient characteristics, medical history, and markers such as BNP. Intuitively, doctors adjust their prediction of prognosis over time, with the change in clinical status, aortic valve area and BNP at each outpatient clinic visit. With the help of novel statistical approaches to model outcomes, it is now possible t

Airway disease on chest computed tomography of preschool children with cystic fibrosis is associated with school-age bronchiectasis

Airway wall thickening and mucus plugging are important characteristics of cystic fibrosis (CF) lung disease in the first 5 years of life.The aim of this study is to investigate the association of lung disease in preschool children (age, 2-6) with bronchiectasis and other clinical outcome measures in the school age (age >7). Deidentified computed tomography-scans were annotated using Perth-Rotterdam annotated grid morphometric analysis for CF. Preschool %disease (a composite score of %airway wall thickening, %mucus plugging, and %bronchiectasis) and %MUPAT (a composite score of %airway wall thickening and %mucus plugging) were used as predictors for %bronchiectasis and several other school-age clinical outcomes. For statistical analysis, we used regression analysis, linear mixed-effects models and two-way mixed models. Sixty-one patients were included. %Disease increased significantly with age (P .05). Cross-sectional, %disease in school-age was associated with a low FEV1% predicted and low quality of life (P =.01 and P =.007, respectively). %Disease can be considered an early marker of diffuse airways disease and is a risk factor for school-age bronchiectasis