In this paper, we propose a semiparametric, tree based joint latent class modeling approach (JLCT) to model the joint behavior of longitudinal and time-to-event data. Existing joint latent class modeling approaches are parametric and can suffer from high computational cost. The most common parametric approach, the joint latent class model (JLCM), further restricts analysis to using time-invariant covariates in modeling survival risks and latent class memberships. Instead, the proposed JLCT is fast to fit, and can use time-varying covariates in all of its modeling components. We demonstrate the prognostic value of using time-varying covariates, and therefore the advantage of JLCT over JLCM on simulated data. We further apply JLCT to the PAQUID data set and confirm its superior prediction performance and orders-of-magnitude speedup over JLCM.
We are interested in survival analysis of hemodialysis patients for whom several biomarkers are recorded over time. Motivated by this challenging problem, we propose a general framework for multivariate joint longitudinal-survival modeling that can be used to examine the association between several longitudinally recorded covariates and a time-to-event endpoint. Our method allows for simultaneous modeling of longitudinal covariates by taking their correlation into account. This leads to a more efficient method for modeling their trajectories over time, and hence, it can better capture their re…
Joint models for longitudinal biomarkers and time-to-event data are widely used in longitudinal studies. Many joint modeling approaches have been proposed to deal with different types of longitudinal biomarkers and survival outcomes. However, most existing joint modeling methods cannot deal with a large number of longitudinal biomarkers simultaneously, such as the longitudinally collected gene expression profiles. In this article, we propose a new joint modeling method under the Bayesian framework, which is able to deal with longitudinal biomarkers of high dimension. Specifically, we assume th…
In survival studies it is important to record the values of key longitudinal covariates until the occurrence of event of a subject. For this reason, it is essential to study the association between longitudinal and time-to-event outcomes using the joint model. In this paper, profile likelihood approach has been used to estimate the cumulative hazard and regression parameters from the joint model of survival and longitudinal data. Moreover, we show the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the …
Joint modelling of longitudinal and time-to-event data is usually described by a joint model which uses shared or correlated latent effects to capture associations between the two processes. Under this framework, the joint distribution of the two processes can be derived straightforwardly by assuming conditional independence given the random effects. Alternative approaches to induce interdependency into sub-models have also been considered in the literature and one such approach is using copulas to introduce non-linear correlation between the marginal distributions of the longitudinal and time…
In various data situations joint models are an efficient tool to analyze relationships between time dependent covariates and event times or to correct for event-dependent dropout occurring in regression analysis. Joint modeling connects a longitudinal and a survival submodel within a single joint likelihood which then can be maximized by standard optimization methods. Main burdens of these conventional methods are that the computational effort increases rapidly in higher dimensions and they do not offer special tools for proper variable selection. Gradient boosting techniques are well known am…
Joint models for longitudinal and survival data have gained a lot of attention in recent years, with the development of myriad extensions to the basic model, including those which allow for multivariate longitudinal data, competing risks and recurrent events. Several software packages are now also available for their implementation. Although mathematically straightforward, the inclusion of multiple longitudinal outcomes in the joint model remains computationally difficult due to the large number of random effects required, which hampers the practical application of this extension. We present a…
Longitudinal and survival sub-models are two building blocks for joint modelling of longitudinal and time to event data. Extensive research indicates separate analysis of these two processes could result in biased outputs due to their associations. Conditional independence between measurements of biomarkers and event time process given latent classes or random effects is a common approach for characterising the association between the two sub-models while taking the heterogeneity among the population into account. However, this assumption is tricky to validate because of the unobservable laten…
Joint modelling of longitudinal and time-to-event data has received much attention recently. Increasingly, extensions to standard joint modelling approaches are being proposed to handle complex data structures commonly encountered in applied research. In this paper we propose a joint model for hierarchical longitudinal and time-to-event data. Our motivating application explores the association between tumor burden and progression-free survival in non-small cell lung cancer patients. We define tumor burden as a function of the sizes of target lesions clustered within a patient. Since a patient …
Often in Phase 3 clinical trials measuring a long-term time-to-event endpoint, such as overall survival or progression-free survival, investigators also collect repeated measures on biomarkers which may be predictive of the primary endpoint. Although these data may not be leveraged directly to support early stopping decisions, can we make greater use of these data to increase efficiency and improve interim decision making? We present a joint model for longitudinal and time-to-event data and a method which establishes the distribution of successive estimates of parameters in the joint model acr…
On a penalised likelihood approach for joint modelling of longitudinal covariates and partly interval-censored data -- an application to the Anti-PD1 brain collaboration trial
Joint models initially dedicated to a single longitudinal marker and a single time-to-event need to be extended to account for the rich longitudinal data of cohort studies. Multiple causes of clinical progression are indeed usually observed, and multiple longitudinal markers are collected when the true latent trait of interest is hard to capture (e.g. quality of life, functional dependency, cognitive level). These multivariate and longitudinal data also usually have nonstandard distributions (discrete, asymmetric, bounded,...). We propose a joint model based on a latent process and latent clas…
In medical and biological research, longitudinal data and survival data types are commonly seen. Traditional statistical models mostly consider to deal with either of the data types, such as linear mixed models for longitudinal data, and the Cox models for survival data, while they do not adjust the association between these two different data types. It is desirable to have a joint modeling approach which accomadates both data types and the dependency between them. In this paper, we extend traditional single-index models to a new joint modeling approach, by replacing the single-index component…
Functional forms in joint models for longitudinal and time-to-event data: A practical guide with application and interpretation
Erasmus University Medical Center（伊拉斯姆斯大学医学中心）；European Organisation for Research and Treatment of Cancer（欧洲癌症研究与治疗组织）；University Medical Center Utrecht（乌得勒支大学医学中心）
Joint multivariate longitudinal and time-to-event data are gaining increasing attention in the biomedical sciences where subjects are followed over time to monitor the progress of a disease or medical condition. In the insurance context, claims outcomes may be related to a policyholder's dropout or decision to lapse a policy. This paper introduces a generalized method of moments technique to estimate dependence parameters where associations are represented using copulas. A simulation study demonstrates the viability of the approach. The paper describes how the joint model provides new informat…
Semiparametric joint models of longitudinal and competing risks data are computationally costly and their current implementations do not scale well to massive biobank data. This paper identifies and addresses some key computational barriers in a semiparametric joint model for longitudinal and competing risks survival data. By developing and implementing customized linear scan algorithms, we reduce the computational complexities from $O(n^2)$ or $O(n^3)$ to $O(n)$ in various components including numerical integration, risk set calculation, and standard error estimation, where $n$ is the number …
Joint Models for longitudinal and time-to-event data have gained a lot of attention in the last few years as they are a helpful technique to approach common a data structure in clinical studies where longitudinal outcomes are recorded alongside event times. Those two processes are often linked and the two outcomes should thus be modeled jointly in order to prevent the potential bias introduced by independent modelling. Commonly, joint models are estimated in likelihood based expectation maximization or Bayesian approaches using frameworks where variable selection is problematic and which do no…
Joint modeling of geometric features of longitudinal process and discrete survival time measured on nested timescales: an application to fecundity studies
When Method Choice Changes Statistical Inference: A Comparison of a Baseline Two-Stage Approach and Bayesian Joint Modeling for Longitudinal and Survival Data in an HIV Clinical Trial
The analysis of data arising from environmental health studies which collect a large number of measures of exposure can benefit from using latent variable models to summarize exposure information. However, difficulties with estimation of model parameters may arise since existing fitting procedures for linear latent variable models require correctly specified residual variance structures for unbiased estimation of regression parameters quantifying the association between (latent) exposure and health outcomes. We propose an estimating equations approach for latent exposure models with longitudin…
We propose a flexible joint longitudinal-survival framework to examine the association between longitudinally collected biomarkers and a time-to-event endpoint. More specifically, we use our method for analyzing the survival outcome of end-stage renal disease patients with time-varying serum albumin measurements. Our proposed method is robust to common parametric assumptions in that it avoids explicit distributional assumptions on longitudinal measures and allows for subject-specific baseline hazard in the survival component. Fully joint estimation is performed to account for the uncertainty i…
The joint modeling of longitudinal and time-to-event data is an active area of statistics research that has received a lot of attention in the recent years. More recently, a new and attractive application of this type of models has been to obtain individualized predictions of survival probabilities and/or of future longitudinal responses. The advantageous feature of these predictions is that they are dynamically updated as extra longitudinal responses are collected for the subjects of interest, providing real time risk assessment using all recorded information. The aim of this paper is two-fol…
In many medical studies, patients are followed longitudinally and interest is on assessing the relationship between longitudinal measurements and time to an event. Recently, various authors have proposed joint modeling approaches for longitudinal and time-to-event data for a single longitudinal variable. These joint modeling approaches become intractable with even a few longitudinal variables. In this paper we propose a regression calibration approach for jointly modeling multiple longitudinal measurements and discrete time-to-event data. Ideally, a two-stage modeling approach could be applied…
Adressing Separation: A Firth-corrected Joint Model for Longitudinal and Time-to-event Data with an Application on Dropout from Vocational Training
Georg-August University Göttingen（哥廷根乔治-奥古斯特大学）；Chair of Spatial Data Science and Statistical Learning（空间数据科学与统计学习教席）；Campus Institute Data Science (CIDAS)（校园数据科学研究所（CIDAS））
In biostatistics and medical research, longitudinal data are often composed of repeated assessments of a variable (e.g., blood pressure or other biomarkers) and dichotomous indicators to mark an event of interest (e.g., recovery from disease, or death). Consequently, joint modeling of longitudinal and time-to-event data has generated much interest in these disciplines over the previous decade. In psychology, too, often we are interested in relating individual trajectories (e.g., cognitive performance or well-being across many years) and discrete events (e.g., death, diagnosis of dementia, or o…
Rheumatoid arthritis clinical trials are strategically designed to collect the disease activity score of each patient over multiple clinical visits, meanwhile a patient may drop out before their intended completion due to various reasons. The dropout terminates the longitudinal data collection on the patients activity score. In the presence of informative dropout, that is, the dropout depends on latent variables from the longitudinal process, simply applying a model to analyze the longitudinal outcomes may lead to biased results because the assumption of random dropout is violated. In this pap…
The paper considers mediation analysis with longitudinal data under latent growth curve models within a counterfactual framework. Estimators and their standard errors are derived for natural direct and indirect effects when the mediator, the outcome, and possibly also the exposure can be modeled by an underlying latent variable giving rise to a growth curve. Settings are also considered in which the exposure is instead fixed at a single point in time.
Health economic evaluations based on patient-level data collected alongside clinical trials~(e.g. health related quality of life and resource use measures) are an important component of the process which informs resource allocation decisions. Almost inevitably, the analysis is complicated by the fact that some individuals drop out from the study, which causes their data to be unobserved at some time point. Current practice performs the evaluation by handling the missing data at the level of aggregated variables (e.g. QALYs), which are obtained by combining the economic data over the duration o…
Intensive longitudinal studies are becoming progressively more prevalent across many social science areas, especially in psychology. New technologies like smart-phones, fitness trackers, and the Internet of Things make it much easier than in the past for data collection in intensive longitudinal studies, providing an opportunity to look deep into the underlying characteristics of individuals under a high temporal resolution. In this paper, we introduce a new modeling framework for latent curve analysis that is more suitable for the analysis of intensive longitudinal data than existing latent c…
Bayesian Joint Modelling of Longitudinal Creatinine Trajectories in Children with Auto-Immune Disorders to Predict Paediatric Kidney Disease Risk in a Single Centre Study
We seek to elucidate the impact of social activity, physical activity and functional health status (factors) on depressive symptoms (outcome) in the China Health and Retirement Longitudinal Study (CHARLS), a multi-year study of aging involving 20,000 participants 45 years of age and older. Although a variety of statistical methods are available for analyzing longitudinal data, modeling the dynamics within a complex system remains a difficult methodological challenge. We develop an Autoregressive Structural Model (ASM) to examine these factors on depressive symptoms while accounting for tempora…
Massachusetts Institute of Technology（麻省理工学院）；Dana-Farber Cancer Institute（达纳-法伯癌症研究所）
Effective learning from electronic health records (EHR) data for prediction of clinical outcomes is often challenging because of features recorded at irregular timesteps and loss to follow-up as well as competing events such as death or disease progression. To that end, we propose a generative time-to-event model, SurvLatent ODE, which adopts an Ordinary Differential Equation-based Recurrent Neural Networks (ODE-RNN) as an encoder to effectively parameterize dynamics of latent states under irregularly sampled input data. Our model then utilizes the resulting latent embedding to flexibly estima…
We propose a Bayesian inference approach for a class of latent Markov models. These models are widely used for the analysis of longitudinal categorical data, when the interest is in studying the evolution of an individual unobservable characteristic. We consider, in particular, the basic latent Markov, which does not account for individual covariates, and its version that includes such covariates in the measurement model. The proposed inferential approach is based on a system of priors formulated on a transformation of the initial and transition probabilities of the latent Markov chain. This s…
Examination of Nonlinear Longitudinal Processes with Latent Variables, Latent Processes, Latent Changes, and Latent Classes in the Structural Equation Modeling Framework: The R package nlpsem
