Joint Modeling Framework Research Articles

Partial least squares for functional joint models with applications to the Alzheimer's disease neuroimaging initiative study.

Many biomedical studies have identified important imaging biomarkers that are associated with both repeated clinical measures and a survival outcome. The functional joint model (FJM) framework, proposed by Li and Luo in 2017, investigates the association between repeated clinical measures and survival data, while adjusting for both high-dimensional images and low-dimensional covariates based on the functional principal component analysis (FPCA). In this paper, we propose a novel algorithm for the estimation of FJM based on the functional partial least squares (FPLS). Our numerical studies demonstrate that, compared to FPCA, the proposed FPLS algorithm can yield more accurate and robust estimation and prediction performance in many important scenarios. We apply the proposed FPLS algorithm to a neuroimaging study. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI)database.

Modeling the duration and size of extended attack wildfires as dependent outcomes

AbstractUnderstanding the complex relationship between the duration and size of forest fires is important in order to better predict these key characteristics of fires for fire management purposes in a changing climate. Describing this relationship is also important for our fundamental understanding of fire science. Here, we develop and utilize novel techniques for characterizing the distribution of multiple outcomes related to a specific event, placed in the fire science context. In this framework, we jointly model time spent (duration), in days, and area burned (size), in hectares, from ground attack to final control of a fire as a bivariate survival outcome using two broad methodologies: a copula model that connects the two outcomes functionally and a joint modeling framework that connects the two outcomes with a shared random effect. We compare these two methodologies in terms of their utility and predictive power. We also consider how longitudinal environmental variables (e.g., precipitation, drought indices) are best incorporated in this context and the challenges related to the complexity of computation associated with the analysis of two outcomes considered jointly.

Semi-Parametric Joint Modeling of Survival and Longitudinal Data: The R Package JSM

This paper is devoted to the R package JSM which performs joint statistical modeling of survival and longitudinal data. In biomedical studies it has been increasingly common to collect both baseline and longitudinal covariates along with a possibly censored survival time. Instead of analyzing the survival and longitudinal outcomes separately, joint modeling approaches have attracted substantive attention in the recent literature and have been shown to correct biases from separate modeling approaches and enhance information. Most existing approaches adopt a linear mixed effects model for the longitudinal component and the Cox proportional hazards model for the survival component. We extend the Cox model to a more general class of transformation models for the survival process, where the baseline hazard function is completely unspecified leading to semiparametric survival models. We also offer a non-parametric multiplicative random effects model for the longitudinal process in JSM in addition to the linear mixed effects model. In this paper, we present the joint modeling framework that is implemented in JSM, as well as the standard error estimation methods, and illustrate the package with two real data examples: a liver cirrhosis data and a Mayo Clinic primary biliary cirrhosis data.

Logistic regression with missing covariates—Parameter estimation, model selection and prediction within a joint-modeling framework

Logistic regression is a common classification method in supervised learning. Surprisingly, there are very few solutions for performing logistic regression with missing values in the covariates. A complete approach based on a stochastic approximation version of the EM algorithm is proposed in order to perform statistical inference with missing values, including the estimation of the parameters and their variance, derivation of confidence intervals, and also a model selection procedure. The problem of prediction for new observations on a test set with missing covariate data is also tackled. Supported by a simulation study in which the method is compared to previous ones, it has proved to be computationally efficient, and has good coverage and variable selection properties. The approach is then illustrated on a dataset of severely traumatized patients from Paris hospitals by predicting the occurrence of hemorrhagic shock, a leading cause of early preventable death in severe trauma cases. The aim is to improve the current red flag procedure, a binary alert identifying patients with a high risk of severe hemorrhage. The method is implemented in the R package misaem.

A Bayesian approach to joint modeling of matrix-valued imaging data and treatment outcome with applications to depression studies.

In this paper, we propose a unified Bayesian joint modeling framework for studying association between a binary treatment outcome and a baseline matrix-valued predictor. Specifically, a joint modeling approach relating an outcome to a matrix-valued predictor through a probabilistic formulation of multilinear principal component analysis is developed. This framework establishes a theoretical relationship between the outcome and the matrix-valued predictor, although the predictor is not explicitly expressed in the model. Simulation studies are provided showing that the proposed method is superior or competitive to other methods, such as a two-stage approach and a classical principal component regression in terms of both prediction accuracy and estimation of association; its advantage is most notable when the sample size is small and the dimensionality in the imaging covariate is large. Finally, our proposed joint modeling approach is shown to be a very promising tool in an application exploring the association between baseline electroencephalography data and a favorable response to treatment in a depression treatment study by achieving a substantial improvement in prediction accuracy in comparison to competing methods.

Individualized dynamic prediction of survival with the presence of intermediate events.

Often, in follow‐up studies, patients experience intermediate events, such as reinterventions or adverse events, which directly affect the shapes of their longitudinal profiles. Our work is motivated by two studies in which such intermediate events have been recorded during follow‐up. In both studies, we are interested in the change of the longitudinal evolutions after the occurrence of the intermediate event and in utilizing this information to improve the accuracy of dynamic prediction of their risk. To achieve so, we propose a flexible joint modeling framework for longitudinal and time‐to‐event data, which includes features of the intermediate event as time‐varying covariates in both the longitudinal and survival submodels. We consider a set of joint models that postulate different effects of the intermediate event in the longitudinal profile and the risk of the clinical endpoint, with different formulations for the association structure while allowing its functional form to change after the occurrence of the intermediate event. Based on these models, we derive dynamic predictions of conditional survival probabilities which are adaptive to different scenarios with respect to the occurrence of the intermediate event. We evaluate the predictive accuracy of these predictions with a simulation study using the time‐dependent area under the receiver operating characteristic curve and the expected prediction error adjusted to our setting. The results suggest that accounting for the changes in the longitudinal profiles and the instantaneous risk for the clinical endpoint is important, and improves the accuracy of the dynamic predictions.

Mixed-effects models for health care longitudinal data with an informative visiting process: A Monte Carlo simulation study.

Electronic health records are being increasingly used in medical research to answer more relevant and detailed clinical questions; however, they pose new and significant methodological challenges. For instance, observation times are likely correlated with the underlying disease severity: Patients with worse conditions utilise health care more and may have worse biomarker values recorded. Traditional methods for analysing longitudinal data assume independence between observation times and disease severity; yet, with health care data, such assumptions unlikely hold. Through Monte Carlo simulation, we compare different analytical approaches proposed to account for an informative visiting process to assess whether they lead to unbiased results. Furthermore, we formalise a joint model for the observation process and the longitudinal outcome within an extended joint modelling framework. We illustrate our results using data from a pragmatic trial on enhanced care for individuals with chronic kidney disease, and we introduce user‐friendly software that can be used to fit the joint model for the observation process and a longitudinal outcome.

A Large-Scale Constrained Joint Modeling Approach for Predicting User Activity, Engagement, and Churn With Application to Freemium Mobile Games

We develop a constrained extremely zero inflated joint (CEZIJ) modeling framework for simultaneously analyzing player activity, engagement, and dropouts (churns) in app-based mobile freemium games. Our proposed framework addresses the complex interdependencies between a player’s decision to use a freemium product, the extent of her direct and indirect engagement with the product and her decision to permanently drop its usage. CEZIJ extends the existing class of joint models for longitudinal and survival data in several ways. It not only accommodates extremely zero-inflated responses in a joint model setting but also incorporates domain-specific, convex structural constraints on the model parameters. Longitudinal data from app-based mobile games usually exhibit a large set of potential predictors and choosing the relevant set of predictors is highly desirable for various purposes including improved predictability. To achieve this goal, CEZIJ conducts simultaneous, coordinated selection of fixed and random effects in high-dimensional penalized generalized linear mixed models. For analyzing such large-scale datasets, variable selection and estimation are conducted via a distributed computing based split-and-conquer approach that massively increases scalability and provides better predictive performance over competing predictive methods. Our results reveal codependencies between varied player characteristics that promote player activity and engagement. Furthermore, the predicted churn probabilities exhibit idiosyncratic clusters of player profiles over time based on which marketers and game managers can segment the playing population for improved monetization of app-based freemium games. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

A Model-Based Approach to Detection Limits in Studying Environmental Exposures and Human Fecundity.

Human exposure to persistent environmental pollutants often results in concentrations with a range of values below the laboratory detection limits. Growing evidence suggests that inadequate handling of concentrations below the limit of detection (LOD) may bias assessment of health effects in relation to environmental exposures. We seek to quantify such bias in models focusing on the day-specific probability of pregnancy during the fertile window and propose a model-based approach to reduce such bias. A multivariate skewed generalized t-distribution constrained by the LOD is assumed for the chemical concentrations, which realistically represents the underlying distribution. A latent variable-based framework is used to model fecundibility, which nonlinearly relates conception probability to chemical concentrations, daily intercourses, and other important covariates. The advantages of the proposed approach include the use of multiple chemical concentrations to aid the estimation of left censored chemical exposures, as well as the model-based feedback mechanism for fecundibility outcome to inform the estimations, and an adequate handling of model uncertainty through a joint modeling framework. A Markov chain Monte Carlo sampling algorithm is developed for implementing the Bayesian computations and the logarithm of pseudo-marginal likelihood measure is used for model choices. We conduct simulation studies to demonstrate the performance of the proposed approach and apply the framework to the Longitudinal Investigation of Fertility and the Environment study which evaluates the effects of exposures to environmental pollutants on the probability of pregnancy. We found that p,p'-DDT is negatively associated with the day-specific probability of pregnancy.

A joint modeling framework of responses and response times to assess learning outcomes

A general modeling framework of response accuracy and response times is proposed to track skill acquisition and provide additional diagnostic information on the change of latent speed in a learning environment. This framework consists of two types of models: a dynamic response model that captures the response accuracy and the change of discrete latent attribute profile upon factors such as practice, intervention effects, and other latent and observable covariates, and a dynamic response time model that describes the change of the continuous response latency due to change of latent attribute profile. These two types of models are connected through a parameter, describing the change rate of the latent speed through the learning process, and a covariate defined as a function of the latent attribute profile. A Bayesian estimation procedure is developed to calibrate the model parameters and measure the latent variables. The estimation algorithm is evaluated through several simulation studies under various conditions. The proposed models are applied to a real data set collected through a spatial rotation diagnostic assessment paired with learning tools.

A Copula-Based Joint Model to Capture the Interaction between Mode and Departure Time Choices in Urban Trips

Abstract Mode and departure time choices are two effective decisions on the urban travel demand. Previous studies have different assumptions for modeling these decisions. Some studies assume that mode and departure time choices are independent and other studies consider nested logit as a joint structure. Comparison of joint and independent models shows that these decisions are interrelated. This paper uses a copula-based joint modeling framework to depict this interrelation. To achieve better fitted model several copula functions including product, AMH and Frank are used. For mode choice and departure time choice models, multinomial logit and bivariate logit models are used, respectively and finally, a BL-MNL joint model is used to create linkage between mode and departure time choices. The data used in this study is drawn from the origin-destination data of Qazvin-Iran in 2010. Estimated copula dependence parameters with high statistical significance, approve the interrelation between error terms of two models.

Regression analysis of longitudinal data with outcome-dependent sampling and informative censoring.

We consider regression analysis of longitudinal data in the presence of outcome-dependent observation times and informative censoring. Existing approaches commonly require correct specification of the joint distribution of the longitudinal measurements, observation time process and informative censoring time under the joint modeling framework, and can be computationally cumbersome due to the complex form of the likelihood function. In view of these issues, we propose a semi-parametric joint regression model and construct a composite likelihood function based on a conditional order statistics argument. As a major feature of our proposed methods, the aforementioned joint distribution is not required to be specified and the random effect in the proposed joint model is treated as a nuisance parameter. Consequently, the derived composite likelihood bypasses the need to integrate over the random effect and offers the advantage of easy computation. We show that the resulting estimators are consistent and asymptotically normal. We use simulation studies to evaluate the finite-sample performance of the proposed method, and apply it to a study of weight loss data that motivated our investigation.

Joint modeling: an application in behavioural scoring

Survival analysis has become an appealing approach in credit scoring. It is able to readily incorporate time-dependent covariates and dynamically predict the survival probability. However, the difference between endogenous and exogenous covariates is ignored in the existing extended Cox models in behavioural scoring. In this paper, we apply joint modelling framework, which can be seen as an extension of survival analysis, to overcome such deficiency of survival models. We carefully design experiments on two datasets and verify the superiority of joint modelling over the extend Cox model through cross validation on dynamic discrimination and calibration performance measures. The experimental results indicate that the joint model performance is better, especially in the calibration measure. The key reason for the better performance is discussed and illustrated.

Prediction of hard failures with stochastic degradation signals using Wiener process and proportional hazards model

In this paper, we propose a method to predict the remaining useful life (RUL) of systems subject to hard failures, which are probabilistically linked to system degradation signals (health indictors). A joint modeling framework is adopted to incorporate both the degradation signals and time-to-event data. In the joint model, a Wiener process with drift is used to model stochastic degradation signals, and the proportional hazards (PH) model with nonparametric baseline hazard is used to model time-to-event data. With proposed joint model and Markovian property of the Wiener process, system RUL could be predicted. Extensive simulations and a case study are conducted to demonstrate the performance of the proposed method.

Bayesian functional joint models for multivariate longitudinal and time-to-event data

A multivariate functional joint model framework is proposed which enables the repeatedly measured functional outcomes, scalar outcomes, and survival process to be modeled simultaneously while accounting for association among the multiple (functional and scalar) longitudinal and survival processes. This data structure is increasingly common across medical studies of neurodegenerative diseases and is exemplified by the motivating Alzheimer’s Disease Neuroimaging Initiative (ADNI) study, in which serial brain imaging, clinical and neuropsychological assessments are collected to measure the progression of Alzheimer’s disease (AD). The proposed functional joint model consists of a longitudinal function-on-scalar submodel, a regular longitudinal submodel, and a survival submodel which allows time-dependent functional and scalar covariates. A Bayesian approach is adopted for parameter estimation and a dynamic prediction framework is introduced for predicting the subjects’ future health outcomes and risk of AD conversion. The proposed model is evaluated by a simulation study and is applied to the motivating ADNI study.

Macro-scale grid-based and subbasin-based hydrologic modeling: joint simulation and cross-calibration

Abstract Watershed hydrologic models often possess different structures and distinct methods and require dissimilar types of inputs. As spatially-distributed data are becoming widely available, macro-scale modeling plays an increasingly important role in water resources management. However, calibration of a macro-scale grid-based model can be a challenge. The objective of this study is to improve macro-scale hydrologic modeling by joint simulation and cross-calibration of different models. A joint modeling framework was developed, which linked a grid-based hydrologic model (GHM) and the subbasin-based Soil and Water Assessment Tool (SWAT) model. Particularly, a two-step cross-calibration procedure was proposed and implemented: (1) direct calibration of the subbasin-based SWAT model using observed streamflow data; and (2) indirect calibration of the grid-based GHM through the transfer of the well-calibrated SWAT simulations to the GHM. The joint GHM-SWAT modeling framework was applied to the Red River of the North Basin (RRB). The model performance was assessed using the Nash–Sutcliffe efficiency (NSE) and percent bias (PBIAS). The results highlighted the feasibility of the proposed cross-calibration strategy in taking advantage of both model structures to analyze the spatial/temporal trends of hydrologic variables. The modeling approaches developed in this study can be applied to other basins for macro-scale climatic-hydrologic modeling.

Towards integrated surveillance of zoonoses: spatiotemporal joint modeling of rodent population data and human tularemia cases in Finland

BackgroundThere are an increasing number of geo-coded information streams available which could improve public health surveillance accuracy and efficiency when properly integrated. Specifically, for zoonotic diseases, knowledge of spatial and temporal patterns of animal host distribution can be used to raise awareness of human risk and enhance early prediction accuracy of human incidence.MethodsTo this end, we develop a spatiotemporal joint modeling framework to integrate human case data and animal host data to offer a modeling alternative for combining multiple surveillance data streams in a novel way. A case study is provided of spatiotemporal modeling of human tularemia incidence and rodent population data from Finnish health care districts during years 1995–2012.ResultsSpatial and temporal information of rodent abundance was shown to be useful in predicting human cases and in improving tularemia risk estimates in 40 and 75% of health care districts, respectively. The human relative risk estimates’ standard deviation with rodent’s information incorporated are smaller than those from the model that has only human incidence.ConclusionsThese results support the integration of rodent population variables to reduce the uncertainty of tularemia risk estimates. However, more information on several covariates such as environmental, behavioral, and socio-economic factors can be investigated further to deeper understand the zoonotic relationship.

A copula model for joint modeling of longitudinal and time-invariant mixed outcomes.

Motivated by a preclinical study in a mouse model of breast cancer, we suggest a joint modeling framework for outcomes of mixed type and measurement structures (longitudinal versus single time/time-invariant). We present an approach based on the time-varying copula models, which is used to jointly model longitudinal outcomes of mixed types via a time-varying copula, and extend the scope of these models to handle outcomes with mixed measurement structures. Our framework allows the parameters corresponding to the longitudinal outcome to be time varying and thereby enabling researchers to investigate how the response-predictor relationships change with time. We investigate the finite sample performance of this new approach via a Monte Carlo simulation study and illustrate its usefulness by an empirical analysis of the motivating preclinical study, comparing the effect of various treatments on tumor volume (longitudinal continuous response) and the number of days until tumor volume triples (time-invariant count response). Through the real-life application and the simulation study, we demonstrate that, compared with marginal modeling, the joint modeling framework offers more precision in the estimation of model parameters.

Debt rollover-induced local volatility model

This paper introduces a structural scenario-based model with debt rollover risk and a higher-fidelity treatment of the bankruptcy procedure. The emerging stock price process is a generalized Brownian motion with state-dependent local volatility, and the resultant implied volatility smile is due exclusively to structural features (debt rollover and credit risks). Therefore, the model reinforces structural foundations of local volatility option pricing models. The paper advocates a joint modeling and calibration framework for multiple classes of derivatives on the firm’s asset value. In particular, an empirical application to Solar City equity and stock option valuation demonstrates the versatility and efficiency gains of the suggested model.

Representing heterogeneity in structural relationships among multiple choice variables using a latent segmentation approach

Travel model systems often adopt a single decision structure that links several activity-travel choices together. The single decision structure is then used to predict activity-travel choices, with those downstream in the decision-making chain influenced by those upstream in the sequence. The adoption of a singular sequential causal structure to depict relationships among activity-travel choices in travel demand model systems ignores the possibility that some choices are made jointly as a bundle as well as the possible presence of structural heterogeneity in the population with respect to decision-making processes. As different segments in the population may adopt and follow different causal decision-making mechanisms when making selected choices jointly, it would be of value to develop simultaneous equations model systems relating multiple endogenous choice variables that are able to identify population subgroups following alternative causal decision structures. Because the segments are not known a priori, they are considered latent and determined endogenously within a joint modeling framework proposed in this paper. The methodology is applied to a national mobility survey data set to identify population segments that follow different causal structures relating residential location choice, vehicle ownership, and car-share and mobility service usage. It is found that the model revealing three distinct latent segments best describes the data, confirming the efficacy of the modeling approach and the existence of structural heterogeneity in decision-making in the population. Future versions of activity-travel model systems should strive to incorporate such structural heterogeneity to better reflect varying decision processes across population subgroups.