Search

Dynamic event prediction, using joint modeling of survival time and longitudinal variables, is extremely useful in personalized medicine. However, the estimation of joint models including many longitudinal markers is still a computational challenge because of the high number of random effects and parameters to be estimated. In this paper, we propose a model averaging strategy to combine predictions from several joint models for the event, including one longitudinal marker only or pairwise longitudinal markers. The prediction is computed as the weighted mean of the predictions from the one-marker or two-marker models, with the time-dependent weights estimated by minimizing the time-dependent Brier score. This method enables us to combine a large number of predictions issued from joint models to achieve a reliable and accurate individual prediction. Advantages and limits of the proposed methods are highlighted in a simulation study by comparison with the predictions from well-specified and misspecified all-marker joint models as well as the one-marker and two-marker joint models. Using the PBC2 data set, the method is used to predict the risk of death in patients with primary biliary cirrhosis. The method is also used to analyze a French cohort study called the 3C data. In our study, seventeen longitudinal markers are considered to predict the risk of death.

Neurodegenerative diseases are characterized by numerous markers of progression and clinical endpoints. For instance, Multiple System Atrophy (MSA), a rare neurodegenerative synucleinopathy, is characterized by various combinations of progressive autonomic failure and motor dysfunction, and a very poor prognosis. Describing the progression of such complex and multi-dimensional diseases is particularly difficult. One has to simultaneously account for the assessment of multivariate markers over time, the occurrence of clinical endpoints, and a highly suspected heterogeneity between patients. Yet, such description is crucial for understanding the natural history of the disease, staging patients diagnosed with the disease, unravelling subphenotypes, and predicting the prognosis. Through the example of MSA progression, we show how a latent class approach modeling multiple repeated markers and clinical endpoints can help describe complex disease progression and identify subphenotypes for exploring new pathological hypotheses. The proposed joint latent class model includes class-specific multivariate mixed models to handle multivariate repeated biomarkers possibly summarized into latent dimensions and class-and-cause-specific proportional hazard models to handle time-to-event data. Maximum likelihood estimation procedure, validated through simulations is available in the lcmm R package. In the French MSA cohort comprising data of 598 patients during up to 13 years, five subphenotypes of MSA were identified that differ by the sequence and shape of biomarkers degradation, and the associated risk of death. In posterior analyses, the five subphenotypes were used to explore the association between clinical progression and external imaging and fluid biomarkers, while properly accounting for the uncertainty in the subphenotypes membership.

In health cohort studies, repeated measures of markers are often used to describe the natural history of a disease. Joint models allow to study their evolution by taking into account the possible informative dropout usually due to clinical events. However, joint modeling developments mostly focused on continuous Gaussian markers while, in an increasing number of studies, the actual quantity of interest is non-directly measurable; it constitutes a latent variable evaluated by a set of observed indicators from questionnaires or measurement scales. Classical examples include anxiety, fatigue, cognition. In this work,we explain how joint models can be extended to the framework of a latent quantity measured over time by indicators of different nature (e.g. continuous, binary, ordinal). The longitudinal submodel describes the evolution over time of the quantity of interest defined as a latent process in a structural mixed model, and links the latent process to each observation of the indicators through appropriate measurement models. Simultaneously, the risk of multi-cause event is modelled via a proportional cause-specific hazard model that includes a function of the mixed model elements as linear predictor to take into account the association between the latent process and the risk of event. Estimation, carried out in the maximum likelihood framework and implemented in the R-package JLPM, has been validated by simulations. The methodology is illustrated in the French cohort on Multiple-System Atrophy (MSA), a rare and fatal neurodegenerative disease, with the study of dysphagia progression over time stopped by the occurrence of death.

Item Response Theory (IRT) models have received growing interest in health science for analyzing latent constructs such as depression, anxiety, quality of life, or cognitive functioning from the information provided by each individual's items responses. However, in the presence of repeated item measures, IRT methods usually assume that the measurement occasions are made at the exact same time for all patients. In this paper, we show how the IRT methodology can be combined with the mixed model theory to provide a longitudinal IRT model which exploits the information of a measurement scale provided at the item level while simultaneously handling observation times that may vary across individuals and items. The latent construct is a latent process defined in continuous time that is linked to the observed item responses through a measurement model at each individual- and occasion-specific observation time; we focus here on a Graded Response Model for binary and ordinal items. The Maximum Likelihood Estimation procedure of the model is available in the R package lcmm. The proposed approach is contextualized in a clinical example in end-stage renal disease, the PREDIALA study. The objective is to study the trajectories of depressive symptomatology (as measured by 7 items of the Hospital Anxiety and Depression scale) according to the time from registration on the renal transplant waiting list and the renal replacement therapy. We also illustrate how the method can be used to assess Differential Item Functioning and lack of measurement invariance over time.

Implementations in R of classical general-purpose algorithms for local optimization generally have two major limitations which cause difficulties in applications to complex problems: too loose convergence criteria and too long calculation time. By relying on a Marquardt-Levenberg algorithm (MLA), a Newton-like method particularly robust for solving local optimization problems, we provide with marqLevAlg package an efficient and general-purpose local optimizer which (i) prevents convergence to saddle points by using a stringent convergence criterion based on the relative distance to minimum/maximum in addition to the stability of the parameters and of the objective function; and (ii) reduces the computation time in complex settings by allowing parallel calculations at each iteration. We demonstrate through a variety of cases from the literature that our implementation reliably and consistently reaches the optimum (even when other optimizers fail), and also largely reduces computational time in complex settings through the example of maximum likelihood estimation of different sophisticated statistical models., Comment: 20 pages, 4 figures

As other neurodegenerative diseases, Alzheimer's disease, the most frequent dementia in the elderly, is characterized by multiple progressive impairments in the brain structure and in clinical functions such as cognitive functioning and functional disability. Until recently, these components were mostly studied independently since no joint model for multivariate longitudinal data and time to event was available in the statistical community. Yet, these components are fundamentally inter-related in the degradation process towards dementia and should be analyzed together. We thus propose a joint model to simultaneously describe the dynamics of multiple correlated components. Each component, defined as a latent process, is measured by one or several continuous markers (not necessarily Gaussian). Rather than considering the associated time to diagnosis as in standard joint models, we assume diagnosis corresponds to the passing above a covariate-specific threshold (to be estimated) of a pathological process which is modelled as a combination of the component-specific latent processes. This definition captures the clinical complexity of diagnoses such as dementia diagnosis but also benefits from simplifications for the computation of Maximum Likelihood Estimates. We show that the model and estimation procedure can also handle competing clinical endpoints. The estimation procedure, implemented in a R package, is validated by simulations and the method is illustrated on a large French population-based cohort of cerebral aging in which we focused on the dynamics of three clinical manifestations and the associated risk of dementia and death before dementia.

The R package lcmm provides a series of functions to estimate statistical models based on linear mixed model theory. It includes the estimation of mixed models and latent class mixed models for Gaussian longitudinal outcomes (hlme), curvilinear and ordinal univariate longitudinal outcomes (lcmm) and curvilinear multivariate outcomes (multlcmm), as well as joint latent class mixed models (Jointlcmm) for a (Gaussian or curvilinear) longitudinal outcome and a time-to-event that can be possibly left-truncated right-censored and defined in a competing setting. Maximum likelihood esimators are obtained using a modified Marquardt algorithm with strict convergence criteria based on the parameters and likelihood stability, and on the negativity of the second derivatives. The package also provides various post-fit functions including goodness-of-fit analyses, classification, plots, predicted trajectories, individual dynamic prediction of the event and predictive accuracy assessment. This paper constitutes a companion paper to the package by introducing each family of models, the estimation technique, some implementation details and giving examples through a dataset on cognitive aging.