Estimation of extended mixed models using latent classes and latent processes: the R package lcmm

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

Methods

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.Modèles Dynamiques pour les Etudes Epidémiologiques Longitudinales sur les Maladies Chronique

PLoS One

Quantifying the association between lifetime exposures and the risk of developing a chronic disease is a recurrent challenge in epidemiology. Individual exposure trajectories are often heterogeneous and studying their associations with the risk of disease is not straightforward. We propose to use a latent class mixed model (LCMM) to identify profiles (latent classes) of exposure trajectories and estimate their association with the risk of disease. The methodology is applied to study the association between lifetime trajectories of smoking or occupational exposure to asbestos and the risk of lung cancer in males of the ICARE population-based case-control study. Asbestos exposure was assessed using a job exposure matrix. The classes of exposure trajectories were identified using two separate LCMM for smoking and asbestos, and the association between the identified classes and the risk of lung cancer was estimated in a second stage using weighted logistic regression and all subjects. A total of 2026/2610 cases/controls had complete information on both smoking and asbestos exposure, including 1938/1837 cases/controls ever smokers, and 1417/1520 cases/controls ever exposed to asbestos. The LCMM identified four latent classes of smoking trajectories which had different risks of lung cancer, all much stronger than never smokers. The most frequent class had moderate constant intensity over lifetime while the three others had either long-term, distant or recent high intensity. The latter had the strongest risk of lung cancer. We identified five classes of asbestos exposure trajectories which all had higher risk of lung cancer compared to men never occupationally exposed to asbestos, whatever the dose and the timing of exposure. The proposed approach opens new perspectives for the analyses of dose-time-response relationships between protracted exposures and the risk of developing a chronic disease, by providing a complete picture of exposure history in terms of intensity, duration, and timing of exposure

Stat Med

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 because no joint model for multivariate longitudinal data and time to event was available in the statistical community. Yet, these components are fundamentally interrelated in the degradation process toward 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 that is modeled 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 an 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

Quantile regression for incomplete longitudinal data with selection by death

International audienceQuantile regressions are increasingly used to provide population norms for quantitative variables. Indeed, they do not require any Gaussian assumption for the response and allow to characterize its entire distribution through different quantiles. Quantile regressions are especially useful to provide norms of cognitive scores in the elderly that may help general practitioners to identify subjects with unexpectedly low cognitive level in routine examinations. These norms may be estimated from cohorts of elderly using quantile regression for longitudinal data, but this requires to properly account for selection by death, dropout and intermittent missing data. In this work, we extend the weighted estimating equation approach to estimate conditional quantiles in the population currently alive from mortal cohorts with dropout and intermittent missing data. Suitable weight estimation procedures are provided for both monotone and intermittent missing data and under two missing-at-random assumptions, when the observation probability given that the subject is alive depends on the survival time (p-MAR assumption) or not (u-MAR assumption). Inference is performed through subject-level bootstrap. The method is validated in a simulation study and applied to the French cohort Paquid to estimate quantiles of a cognitive test in the elderly population currently alive. On one hand, the simulations show that the u-MAR analysis is quite robust when the true missingness mechanism is p-MAR. This is a useful result because computation of suitable weights for intermittent missing data under the p-MAR assumption is untractable. On the other hand, the simulations highlight, along with the real data analysis, the usefulness of suitable weights for intermittent missing data. This method is implemented in the R package weightQuant

Robust and Efficient Optimization Using a Marquardt-Levenberg Algorithm with R Package marqLevAlg

Optimization is an essential task in many computational problems. In statistical modelling for instance, in the absence of analytical solution, maximum likelihood estimators are often retrieved using iterative optimization algorithms. R software already includes a variety of optimizers from general-purpose optimization algorithms to more specific ones. Among Newton-like methods which have good convergence properties, the Marquardt-Levenberg algorithm (MLA) provides a particularly robust algorithm for solving optimization problems. Newton-like methods generally have two major limitations: (i) convergence criteria that are a little too loose, and do not ensure convergence towards a maximum, (ii) a calculation time that is often too long, which makes them unusable in complex problems. We propose in the marqLevAlg package an efficient and general implementation of a modified MLA combined with strict convergence criteria and parallel computations. Convergence to saddle points is avoided by using the relative distance to minimum/maximum criterion (RDM) in addition to the stability of the parameters and of the objective function. RDM exploits the first and second derivatives to compute the distance to a true local maximum. The independent multiple evaluations of the objective function at each iteration used for computing either first or second derivatives are called in parallel to allow a theoretical speed up to the square of the number of parameters. We show through the estimation of 7 relatively complex statistical models how parallel implementation can largely reduce computational time. We also show through the estimation of the same model using 3 different algorithms (BFGS of optim routine, an E-M, and MLA) the superior efficiency of MLA to correctly and consistently reach the maximum.Modèles Dynamiques pour les Etudes Epidémiologiques Longitudinales sur les Maladies ChroniquesBiodiversité des Ecosystèmes Marins et Dynamique du Carbone dans le secteur de Kerguelen : approche intégré

Eur J Epidemiol

The epidemiological and societal burden of dementia is expected to increase in the coming decades due to the world population aging. In this context, the evaluation of the potential impact of intervention scenarios aiming at reducing the prevalence of dementia risk factors is an active area of research. However, such studies must account for the associated changes in mortality and the dependence between the risk factors. Using micro-simulations, this study aims to estimate the changes in dementia burden in France in 2040 according to intervention scenarios targeting the prevention or treatment of hypertension, diabetes and physical inactivity. Accounting for their communality and their effects on mortality, the results show that the disappearance of hypertension, diabetes and physical inactivity in France in 2020 could decrease dementia prevalence by 33% among men and 26% among women in 2040 and increase the life expectancy without dementia at age 65 by 3.4 years (men) and 2.6 years (women). Among the three factors, the prevention of hypertension would be the most efficient. These projections rely on current estimates of the risk of dementia and death associated with risk factors. Thanks to the R package developed they could be refined for different countries or different interventions and updated with new estimates.Histoire naturelle du déclin cognitif et du besoin de soins chez le sujet âgéCOGINUT : Cognition, anti-oxydants, acides gras: approche interdisciplinaire du rôle de la nutrition dans le vieillissement du cervea

Br J Clin Pharmacol

AIMS: This article sought to study the association between patterns of benzodiazepine (BZD) use and the risk of hip and forearm fractures in people aged 50 and 75 years or more. METHODS: In a representative cohort of the French National Health Insurance Fund of individuals aged 50 years or older) (N=106 437), we followed up BZD dispensing (reflecting their patterns of use) and the most frequent fall-related fractures (hip and forearm) for 8 years. We used joint latent class models to simultaneously identify BZD dispensing trajectories and the risk of fractures in the entire cohort and in those 75 years or older). We used a survival model to estimate the adjusted hazard ratios (aHRs) between these trajectories and the risk of fractures. RESULTS: In the entire cohort, we identified 5 BZD trajectories: "non-users" (76.7% of the cohort); "occasional users" (15.2%); "decreasing users"(2.6%); "late increasing users" (3.0%); and "early increasing users" (2.4%). Compared with non-users, fracture risk was not increased in either occasional users (aHR = 0.99, 95% CI 0.99-1.00) or in decreasing users (aHR = 0.90, 95% CI 0.74-1.08). It was significantly higher in early increasing users (aHR = 1.86, 95% CI 1.62-2.14) and in late increasing users (aHR = 1.39, 95% CI 1.15-1.60). We observed similar trajectories and risk levels in the people older than 75 years. CONCLUSION: Occasional BZD use, which is compatible with current recommendations, was not associated with an excess risk of the most frequent fall-related fractures in people older than 50 or 75 years

Determinants of distinct trajectories of fatigue in patients undergoing chemotherapy for a metastatic colorectal cancer: 6-month follow-up using Growth Mixture Modeling

OBJECTIVE: This longitudinal prospective and observational study was designed to identify fatigue trajectories during a 6-month period of chemotherapy in patients with metastatic colorectal cancer, and examine the psychosocial factors predicting these trajectories. Associations between fatigue and survival were also investigated. METHODS: A total of 169 patients (M(age)=64.36 years, SD=10.5) reported their fatigue levels every 2 weeks for 6 months. Psychological variables (anxiety, depression, internal control, and coping) were assessed at baseline. A Growth Mixture Model was used to identify latent trajectories of fatigue, and a multinomial logistic regression tested covariate predictors of patients' trajectories. RESULTS: Four clinically distinct fatigue trajectories were identified: intense fatigue (6.51%), moderate fatigue (48.52%), no fatigue (33%), and increasing fatigue (11.83%). Fatigue severity was directly associated with overall survival. High depression levels were associated with fatigue severity over time for intense (OR=1.80 [1.32-2.47]) and for moderate (OR=1.58 [1.25-2.00]) fatigue, compared to patients reporting no fatigue. Patients who did not report fatigue were better adjusted, and had more resources, such as better internal control over the disease and less emotion-focused coping (guilt and avoidance), than those who reported intense (OR(control)=0.77 [0.65-0.92]) or moderate (OR(control)=0.89 [0.79-0.99] and OR(coping)=1.13 [1.02-1.24]) fatigue. CONCLUSIONS: Fatigue trajectories differed considerably across patients with metastatic colorectal cancer. This first longitudinal study on colorectal cancer patients involving transactional variables suggests that psychosocial interventions should target these specific outcomes, in order to help patients manage their fatigue