Mixed models for longitudinal left-censored repeated measures

Longitudinal studies could be complicated by left-censored repeated measures. For example, in Human Immunodeficiency Virus infection, there is a detection limit of the assay used to quantify the plasma viral load. Simple imputation of the limit of the detection or of half of this limit for left-censored measures biases estimations and their standard errors. In this paper, we review two likelihood-based methods proposed to handle left-censoring of the outcome in linear mixed model. We show how to fit these models using SAS Proc NLMIXED and we compare this tool with other programs. Indications and limitations of the programs are discussed and an example in the field of HIV infection is shown

A location-scale joint model for studying the link between the time-dependent subject-specific variability of blood pressure and competing events

Given the high incidence of cardio and cerebrovascular diseases (CVD), and its association with morbidity and mortality, its prevention is a major public health issue. A high level of blood pressure is a well-known risk factor for these events and an increasing number of studies suggest that blood pressure variability may also be an independent risk factor. However, these studies suffer from significant methodological weaknesses. In this work we propose a new location-scale joint model for the repeated measures of a marker and competing events. This joint model combines a mixed model including a subject-specific and time-dependent residual variance modeled through random effects, and cause-specific proportional intensity models for the competing events. The risk of events may depend simultaneously on the current value of the variance, as well as, the current value and the current slope of the marker trajectory. The model is estimated by maximizing the likelihood function using the Marquardt-Levenberg algorithm. The estimation procedure is implemented in a R-package and is validated through a simulation study. This model is applied to study the association between blood pressure variability and the risk of CVD and death from other causes. Using data from a large clinical trial on the secondary prevention of stroke, we find that the current individual variability of blood pressure is associated with the risk of CVD and death. Moreover, the comparison with a model without heterogeneous variance shows the importance of taking into account this variability in the goodness-of-fit and for dynamic predictions

Score Test for Conditional Independence Between Longitudinal Outcome and Time to Event Given the Classes in the Joint Latent Class Model

Latent class models have been recently developed for the joint analysis of a longitudinal quantitative outcome and a time to event. These models assume that the population is divided in  G  latent classes characterized by different risk functions for the event, and different profiles of evolution for the markers that are described by a mixed model for each class. However, the key assumption of conditional independence between the marker and the event given the latent classes is difficult to evaluate because the latent classes are not observed. Using a joint model with latent classes and shared random effects, we propose a score test for the null hypothesis of independence between the marker and the outcome given the latent classes versus the alternative hypothesis that the risk of event depends on one or several random effects from the mixed model in addition to the latent classes. A simulation study was performed to compare the behavior of the score test to other previously proposed tests, including situations where the alternative hypothesis or the baseline risk function are misspecified. In all the investigated situations, the score test was the most powerful. The methodology was applied to develop a prognostic model for recurrence of prostate cancer given the evolution of prostate-specific antigen in a cohort of patients treated by radiation therapy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79185/1/j.1541-0420.2009.01234.x.pd

Estimation of dynamical model parameters taking into account undetectable marker values

BACKGROUND: Mathematical models are widely used for studying the dynamic of infectious agents such as hepatitis C virus (HCV). Most often, model parameters are estimated using standard least-square procedures for each individual. Hierarchical models have been proposed in such applications. However, another issue is the left-censoring (undetectable values) of plasma viral load due to the lack of sensitivity of assays used for quantification. A method is proposed to take into account left-censored values for estimating parameters of non linear mixed models and its impact is demonstrated through a simulation study and an actual clinical trial of anti-HCV drugs. METHODS: The method consists in a full likelihood approach distinguishing the contribution of observed and left-censored measurements assuming a lognormal distribution of the outcome. Parameters of analytical solution of system of differential equations taking into account left-censoring are estimated using standard software. RESULTS: A simulation study with only 14% of measurements being left-censored showed that model parameters were largely biased (from -55% to +133% according to the parameter) with the exception of the estimate of initial outcome value when left-censored viral load values are replaced by the value of the threshold. When left-censoring was taken into account, the relative bias on fixed effects was equal or less than 2%. Then, parameters were estimated using the 100 measurements of HCV RNA available (with 12% of left-censored values) during the first 4 weeks following treatment initiation in the 17 patients included in the trial. Differences between estimates according to the method used were clinically significant, particularly on the death rate of infected cells. With the crude approach the estimate was 0.13 day(-1 )(95% confidence interval [CI]: 0.11; 0.17) compared to 0.19 day(-1 )(CI: 0.14; 0.26) when taking into account left-censoring. The relative differences between estimates of individual treatment efficacy according to the method used varied from 0.001% to 37%. CONCLUSION: We proposed a method that gives unbiased estimates if the assumed distribution is correct (e.g. lognormal) and that is easy to use with standard software

Modèles conjoints pour données longitudinales et données de survie incomplètes appliqués à l'étude du vieillissement cognitif

Dans l'étude du vieillissement cérébral, le suivi des personnes âgées est soumis à une forte sélection avec un risque de décès associé à de faibles performances cognitives. La modélisation de l'histoire naturelle du vieillissement cognitif est complexe du fait de données longitudinales et données de survie incomplètes. Par ailleurs, un déclin accru des performances cognitives est souvent observé avant le diagnostic de démence sénile, mais le début de cette accélération n'est pas facile à identifier. Les profils d'évolution peuvent être variés et associés à des risques différents de survenue d'un événement; cette hétérogénéité des déclins cognitifs de la population des personnes âgées doit être prise en compte. Ce travail a pour objectif d'étudier des modèles conjoints pour données longitudinales et données de survie incomplètes afin de décrire l'évolution cognitive chez les personnes âgées. L'utilisation d'approches à variables latentes a permis de tenir compte de ces phénomènes sous-jacents au vieillissement cognitif que sont l'hétérogénéité et l'accélération du déclin. Au cours d'un premier travail, nous comparons deux approches pour tenir compte des données manquantes dans l'étude d'un processus longitudinal. Dans un second travail, nous proposons un modèle conjoint à état latent pour modéliser simultanément l'évolution cognitive et son accélération pré-démentielle, le risque de démence et le risque de décès.In cognitive ageing study, older people are highly selected by a risk of death associated with poor cognitive performances. Modeling the natural history of cognitive decline is difficult in presence of incomplete longitudinal and survival data. Moreover, the non observed cognitive decline acceleration beginning before the dementia diagnosis is difficult to evaluate. Cognitive decline is highly heterogeneous, e.g. there are various patterns associated with different risks of survival event. The objective is to study joint models for incomplete longitudinal and survival data to describe the cognitive evolution in older people. Latent variable approaches were used to take into account the non-observed mechanisms, e.g. heterogeneity and decline acceleration. First, we compared two approaches to consider missing data in longitudinal data analysis. Second, we propose a joint model with a latent state to model cognitive evolution and its pre-dementia acceleration, dementia risk and death risk.BORDEAUX2-Bib. électronique (335229905) / SudocSudocFranceF

Modèles de sélection pour données longitudinales gaussiennes : application à l'étude du vieillissement cognitif

National audienceCet article concerne les methodes d'analyse de donnees longitudinales gaussiennes lorsque la variable reponse est observee de facon incomplete. Si la probabilite d'observation de la variable reponse ne depend que des valeurs des reponses observees aux temps precedents et eventuellement de covariables, les donnees manquantes sont ignorables et la methode du maximum de vraisemblance fournit des estimateurs asymptotiquement non biaises. Nous montrons cependant sur un exemple que l'estimateur empirique de la moyenne est biaise. Si la probabilite d'observation depend des valeurs non observees de la variable reponse, une approche frequente consiste a modeliser conjointement la reponse et la probabilite d'observation en utilisant un modele de selection. L'objectif de cet article est de presenter les deux categories de modele de selection en insistant sur les hypotheses sous-jacentes. L'utilisation et les limites d'un modele variable-reponse dependant et d'un modele eets-aleatoires dependant sont illustrees sur une etude de la deterioration cognitive du sujet ^age. Le premier modele appara^t beaucoup plus sensible au choix des variables d'ajustement que le second. Malgre leurs faiblesses, ces modeles sont utiles pour evaluer la sensibilite des estimations a dierentes hypotheses concernant le processus d'observation

Modélisation longitudinale de marqueurs du VIH

L'étude de l'évolution et de la valeur pronostique des marqueurs est très fréquente en épidémiologie. Le taux de lymphocytes T CD4+ et la charge virale plasmatique sont des marqueurs très importants de l'infection par le virus de l'immunodéficience humaine (VIH). La modélisation de l'évolution de ces marqueurs présente plusieurs difficultés méthodologiques. D'une part, il s'agit de données répétées incomplètes c'est à dire pouvant être manquantes du fait de la sortie d'étude de certains sujets et de la censure de la charge virale liée à une limite de détection inférieure des techniques de mesure. D'autre part, ces deux marqueurs étant corrélés, il est important de prendre en compte cette information dans le modèle. Nous avons proposé des méthodes basées sur le maximum de vraisemblance pour estimer les paramètres de modèles linéaires mixtes prenant en compte l'ensemble de ces difficultés. Nous avons montré l'impact significatif de ces méthodes biostatistiques sur les estimations et donc nous avons souligné l'importance de leur utilisation dans le cadre des marqueurs du VIH. Pour promouvoir leur diffusion, nous avons présenté des possibilités d'implémentation de certaines des méthodes proposées dans des logiciels statistiques communs.BORDEAUX2-BU Santé (330632101) / SudocSudocFranceF