Joint analysis of time-to-event and multiple binary indicators of latent classes

Multiple categorical variables are commonly used in medical and epidemiological research to measure specific aspects of human health and functioning. To analyze such data, models have been developed considering these categorical variables as imperfect indicators of an individual's "true" status of health or functioning. In this article, the latent class regression model is used to model the relationship between covariates, a latent class variable (the unobserved status of health or functioning), and the observed indicators (e.g., variables from a questionnaire). The Cox model is extended to encompass a latent class variable as predictor of time-to-event, while using information about latent class membership available from multiple categorical indicators. The expectation-maximization (EM) algorithm is employed to obtain maximum likelihood estimates, and standard errors are calculated based on the profile likelihood, treating the nonparametric baseline hazard as a nuisance parameter. A sampling-based method for model checking is proposed. It allows for graphical investigation of the assumption of proportional hazards across latent classes. It may also be used for checking other model assumptions, such as no additional effect of the observed indicators given latent class. The usefulness of the model framework and the proposed techniques are illustrated in an analysis of data from the Women's Health and Aging Study concerning the effect of severe mobility disability on time-to-death for elderly women.     

Bayesian nonparametric hierarchical modeling

In biomedical research, hierarchical models are very widely used to accommodate dependence in multivariate and longitudinal data and for borrowing of information across data from different sources. A primary concern in hierarchical modeling is sensitivity to parametric assumptions, such as linearity and normality of the random effects. Parametric assumptions on latent variable distributions can be challenging to check and are typically unwarranted, given available prior knowledge. This article reviews some recent developments in Bayesian nonparametric methods motivated by complex, multivariate and functional data collected in biomedical studies. The author provides a brief review of flexible parametric approaches relying on finite mixtures and latent class modeling. Dirichlet process mixture models are motivated by the need to generalize these approaches to avoid assuming a fixed finite number of classes. Focusing on an epidemiology application, the author illustrates the practical utility and potential of nonparametric Bayes methods.     

Bayesian modeling of multiple episode occurrence and severity with a terminating event

An individual's health condition can affect the frequency and intensity of episodes that can occur repeatedly and that may be related to an event time of interest. For example, bleeding episodes during pregnancy may indicate problems predictive of preterm delivery. Motivated by this application, we propose a joint model for a multiple episode process and an event time. The frequency of occurrence and severity of the episodes are characterized by a latent variable model, which allows an individual's episode intensity to change dynamically over time. This latent episode intensity is then incorporated as a predictor in a discrete time model for the terminating event. Time-varying coefficients are used to distinguish among effects earlier versus later in gestation. Formulating the model within a Bayesian framework, prior distributions are chosen so that conditional posterior distributions are conjugate after data augmentation. Posterior computation proceeds via an efficient Gibbs sampling algorithm. The methods are illustrated using bleeding episode and gestational length data from a pregnancy study.     

Serum Interleukin (IL)-15 as a Biomarker of Alzheimer's Disease

Interleukin (IL-15), a pro-inflammatory cytokine has been studied as a possible marker of Alzheimer’s disease (AD); however its exact role in neuro-inflammation or the pathogenesis AD is not well understood yet. A Multiple Indicators Multiple Causes (MIMIC) approach was used to examine the relationship between serum IL-15 levels and AD in a well characterized AD cohort, the Texas Alzheimer''s Research and Care Consortium (TARCC). Instead of categorical diagnoses, we used two latent construct d (for dementia) and g’ (for cognitive impairments not contributing to functional impairments) in our analysis. The results showed that the serum IL-15 level has significant effects on cognition, exclusively mediated by latent construct d and g’. Contrasting directions of association lead us to speculate that IL-15’s effects in AD are mediated through functional networks as d scores have been previously found to be specifically related to default mode network (DMN). Our finding warrants the need for further research to determine the changes in structural and functional networks corresponding to serum based biomarkers levels.     

Latent variable models for longitudinal data with multiple continuous outcomes

Multiple outcomes are often used to properly characterize an effect of interest. This paper proposes a latent variable model for the situation where repeated measures over time are obtained on each outcome. These outcomes are assumed to measure an underlying quantity of main interest from different perspectives. We relate the observed outcomes using regression models to a latent variable, which is then modeled as a function of covariates by a separate regression model. Random effects are used to model the correlation due to repeated measures of the observed outcomes and the latent variable. An EM algorithm is developed to obtain maximum likelihood estimates of model parameters. Unit-specific predictions of the latent variables are also calculated. This method is illustrated using data from a national panel study on changes in methadone treatment practices.     

The Depression List for mood evaluation in psychogeriatrics: psychometric analysis and scalability

The Depression List is a Dutch self-report measure of depressive symptoms in persons with dementia. Fifteen items differ to the extent that they provide reliable measurements of latent constructs such as feeling depressed, tired or lonely. Item scalability and construct reliability were studied by administering the questionnaire to 599 consecutive visitors of a psychogeriatric day care department. Using confirmatory factor analysis three competing hypothetical models were tested for model fit. A four-factor model composed of latent constructs for feeling depressed, tired, lonesome and appetite or sleep disturbance provided an adequate fit to the clinical data, which did not apply to a two-factor model (distinguishing a construct of loneliness from a more general mood construct) and a one-factor model, that hypothesized a single general mood construct for all fifteen items. Nine items carried relatively small proportions of error variance. These reliable items were selected for the construction of three scales that satisfied the assumptions of Mokken's criteria for homogeneity. The resulting measures of feeling depressed, tired or lonely showed evidence of convergent validity for a latent affective construct. The affective measures were not associated with severity of cognitive impairment (discriminant validity). The three scales allow a reliable measurement of differences in affective function in cognitively impaired subjects.     

A longitudinal measurement error model with a semicontinuous covariate

Covariate measurement error in regression is typically assumed to act in an additive or multiplicative manner on the true covariate value. However, such an assumption does not hold for the measurement error of sleep-disordered breathing (SDB) in the Wisconsin Sleep Cohort Study (WSCS). The true covariate is the severity of SDB, and the observed surrogate is the number of breathing pauses per unit time of sleep, which has a nonnegative semicontinuous distribution with a point mass at zero. We propose a latent variable measurement error model for the error structure in this situation and implement it in a linear mixed model. The estimation procedure is similar to regression calibration but involves a distributional assumption for the latent variable. Modeling and model-fitting strategies are explored and illustrated through an example from the WSCS.     

A comparison of the multilevel MIMIC model to the multilevel regression and mixed ANOVA model for the estimation and testing of a cross-level interaction effect: A simulation study

When observing data on a patient-reported outcome measure in, for example, clinical trials, the variables observed are often correlated and intended to measure a latent variable. In addition, such data are also often characterized by a hierarchical structure, meaning that the outcome is repeatedly measured within patients. To analyze such data, it is important to use an appropriate statistical model, such as structural equation modeling (SEM). However, researchers may rely on simpler statistical models that are applied to an aggregated data structure. For example, correlated variables are combined into one sum score that approximates a latent variable. This may have implications when, for example, the sum score consists of indicators that relate differently to the latent variable being measured. This study compares three models that can be applied to analyze such data: the multilevel multiple indicators multiple causes (ML-MIMIC) model, a univariate multilevel model, and a mixed analysis of variance (ANOVA) model. The focus is on the estimation of a cross-level interaction effect that presents the difference over time on the patient-reported outcome between two treatment groups. The ML-MIMIC model is an SEM-type model that considers the relationship between the indicators and the latent variable in a multilevel setting, whereas the univariate multilevel and mixed ANOVA model rely on sum scores to approximate the latent variable. In addition, the mixed ANOVA model uses aggregated second-level means as outcome. This study showed that the ML-MIMIC model produced unbiased cross-level interaction effect estimates when the relationships between the indicators and the latent variable being measured varied across indicators. In contrast, under similar conditions, the univariate multilevel and mixed ANOVA model underestimated the cross-level interaction effect.     

Latent class model diagnosis

In many areas of medical research, such as psychiatry and gerontology, latent class variables are used to classify individuals into disease categories, often with the intention of hierarchical modeling. Problems arise when it is not clear how many disease classes are appropriate, creating a need for model selection and diagnostic techniques. Previous work has shown that the Pearson chi 2 statistic and the log-likelihood ratio G2 statistic are not valid test statistics for evaluating latent class models. Other methods, such as information criteria, provide decision rules without providing explicit information about where discrepancies occur between a model and the data. Identifiability issues further complicate these problems. This paper develops procedures for assessing Markov chain Monte Carlo convergence and model diagnosis and for selecting the number of categories for the latent variable based on evidence in the data using Markov chain Monte Carlo techniques. Simulations and a psychiatric example are presented to demonstrate the effective use of these methods.     

Semiparametric regression modeling with mixtures of Berkson and classical error, with application to fallout from the Nevada test site

We construct Bayesian methods for semiparametric modeling of a monotonic regression function when the predictors are measured with classical error. Berkson error, or a mixture of the two. Such methods require a distribution for the unobserved (latent) predictor, a distribution we also model semiparametrically. Such combinations of semiparametric methods for the dose response as well as the latent variable distribution have not been considered in the measurement error literature for any form of measurement error. In addition, our methods represent a new approach to those problems where the measurement error combines Berkson and classical components. While the methods are general, we develop them around a specific application, namely, the study of thyroid disease in relation to radiation fallout from the Nevada test site. We use this data to illustrate our methods, which suggest a point estimate (posterior mean) of relative risk at high doses nearly double that of previous analyses but that also suggest much greater uncertainty in the relative risk.     

Variable selection in joint frailty models of recurrent and terminal events

Recurrent event data are commonly encountered in biomedical studies. In many situations, they are subject to an informative terminal event, for example, death. Joint modeling of recurrent and terminal events has attracted substantial recent research interests. On the other hand, there may exist a large number of covariates in such data. How to conduct variable selection for joint frailty proportional hazards models has become a challenge in practical data analysis. We tackle this issue on the basis of the “minimum approximated information criterion” method. The proposed method can be conveniently implemented in SAS Proc NLMIXED for commonly used frailty distributions. Its finite-sample behavior is evaluated through simulation studies. We apply the proposed method to model recurrent opportunistic diseases in the presence of death in an AIDS study.     

Bayesian dynamic modeling of latent trait distributions

Studies of latent traits often collect data for multiple items measuring different aspects of the trait. For such data, it is common to consider models in which the different items are manifestations of a normal latent variable, which depends on covariates through a linear regression model. This article proposes a flexible Bayesian alternative in which the unknown latent variable density can change dynamically in location and shape across levels of a predictor. Scale mixtures of underlying normals are used in order to model flexibly the measurement errors and allow mixed categorical and continuous scales. A dynamic mixture of Dirichlet processes is used to characterize the latent response distributions. Posterior computation proceeds via a Markov chain Monte Carlo algorithm, with predictive densities used as a basis for inferences and evaluation of model fit. The methods are illustrated using data from a study of DNA damage in response to oxidative stress.     

国际前沿

高伟坚博士,英籍华人,1986年出生于英国。18岁以全优成绩考取曼彻斯特大学生命科学院。2008年以优等生荣誉毕业,获学士学位。2012年,获得该校博士学位。2004～2012年,先后获得“默沙东杰出学术成就奖”、英联邦帕金森氏病学会的“杰出研究和展示奖”、“曼彻斯特领袖项目”金奖、双重博士奖学金。他从小热爱生物医学,经过系统求学过程及严格的科研训练,在科研课题设计和科技论文撰写方面,表现出不菲的成绩。毕业后仅仅两年,便发表有影响的科技论文4篇。并参与Springer 组织的‘L-DOPA-induced dyskinesia in Parkinson ’ s disease ’一书的编撰工作。同时,还组织申请国际合作课题两项,参研课题四项。高博士现供职于法国波尔多第二大学,在华开展联合研发工作期间,多次表达了“自己作为华人,愿意为祖国生物医学发展贡献自己力量的想法”。也深知华人科学家因为语言障碍,而在科技论文发表和科研课题申请上遇到的重重困难。经我刊编委推荐及编辑部与部分专家讨论商议,特聘请高博士为两刊特约通讯员,开设专栏,希望高博士从信息获取、论文撰写、课题设计等方面开展工作,并定期向我刊介绍业内国际前沿动态,为我刊读者扩大视角。 本期推出神经科学研究中的动物选择和模型制作,欢迎读者就相关内容展开互动。     

Structured latent growth curves for twin data.

We describe methods to fit structured latent growth curves to data from MZ and DZ twins. The well-known Gompertz, logistic and exponential curves may be written as a function of three components - asymptote, initial value, and rate of change. These components are allowed to vary and covary within individuals in a structured latent growth model. Such models are highly economical, requiring a small number of parameters to describe covariation across many occasions of measurement. We extend these methods to analyse longitudinal data from MZ and DZ twins and focus on the estimation of genetic and environmental variation and covariation in each of the asymptote, initial and rate of growth factors. For illustration, the models are fitted to longitudinal Bayley Infant Mental Development Scale data published by McArdle (1986). In these data, all three components of growth appear strongly familial with the majority of variance associated with the shared environment; differences between the models were not great. Occasion-specific residual factors not associated with the curve components account for approximately 40% of variance of which a significant proportion is additive genetic. Though the growth curve model fit less well than some others, they make restrictive, falsifiable predictions about the mean, variance and twin covariance of other (not yet measured) occasions of measurement.     

A Semiparametric Joint Model for Longitudinal and Survival Data with Application to Hemodialysis Study

Summary .  In many longitudinal clinical studies, the level and progression rate of repeatedly measured biomarkers on each subject quantify the severity of the disease and that subject's susceptibility to progression of the disease. It is of scientific and clinical interest to relate such quantities to a later time-to-event clinical endpoint such as patient survival. This is usually done with a shared parameter model. In such models, the longitudinal biomarker data and the survival outcome of each subject are assumed to be conditionally independent given subject-level severity or susceptibility (also called frailty in statistical terms). In this article, we study the case where the conditional distribution of longitudinal data is modeled by a linear mixed-effect model, and the conditional distribution of the survival data is given by a Cox proportional hazard model. We allow unknown regression coefficients and time-dependent covariates in both models. The proposed estimators are maximizers of an exact correction to the joint log likelihood with the frailties eliminated as nuisance parameters, an idea that originated from correction of covariate measurement error in measurement error models. The corrected joint log likelihood is shown to be asymptotically concave and leads to consistent and asymptotically normal estimators. Unlike most published methods for joint modeling, the proposed estimation procedure does not rely on distributional assumptions of the frailties. The proposed method was studied in simulations and applied to a data set from the Hemodialysis Study.     

Efficient computation of the maximum a posteriori path and parameter estimation in integrate-and-fire and more general state-space models

A number of important data analysis problems in neuroscience can be solved using state-space models. In this article, we describe fast methods for computing the exact maximum a posteriori (MAP) path of the hidden state variable in these models, given spike train observations. If the state transition density is log-concave and the observation model satisfies certain standard assumptions, then the optimization problem is strictly concave and can be solved rapidly with Newton–Raphson methods, because the Hessian of the loglikelihood is block tridiagonal. We can further exploit this block-tridiagonal structure to develop efficient parameter estimation methods for these models. We describe applications of this approach to neural decoding problems, with a focus on the classic integrate-and-fire model as a key example.     

A Mixture Model for Bivariate Interval-Censored Failure Times with Dependent Susceptibility

Interval-censored failure times arise when the status with respect to an event of interest is only determined at intermittent examination times. In settings where there exists a sub-population of individuals who are not susceptible to the event of interest, latent variable models accommodating a mixture of susceptible and nonsusceptible individuals are useful. We consider such models for the analysis of bivariate interval-censored failure time data with a model for bivariate binary susceptibility indicators and a copula model for correlated failure times given joint susceptibility. We develop likelihood, composite likelihood, and estimating function methods for model fitting and inference, and assess asymptotic-relative efficiency and finite sample performance. Extensions dealing with higher-dimensional responses and current status data are also described.

     

Latent class regression on latent factors

In the research of public health, psychology, and social sciences, many research questions investigate the relationship between a categorical outcome variable and continuous predictor variables. The focus of this paper is to develop a model to build this relationship when both the categorical outcome and the predictor variables are latent (i.e. not observable directly). This model extends the latent class regression model so that it can include regression on latent predictors. Maximum likelihood estimation is used and two numerical methods for performing it are described: the Monte Carlo expectation and maximization algorithm and Gaussian quadrature followed by quasi-Newton algorithm. A simulation study is carried out to examine the behavior of the model under different scenarios. A data example involving adolescent health is used for demonstration where the latent classes of eating disorders risk are predicted by the latent factor body satisfaction.     

An experimental model for chronic lymphedema

Although a multitude of operations exist for the treatment of lymphedema, none is highly successful. An experimental model that reliably and easily produces chronic lymphedema in an extremity would be useful to study treatments in a controlled and comparative manner and would enhance our understanding of the physiology and treatment of lymphedema. Many models that simulate clinical lymphedema have been described, but they suffer from cumbersome protocols, high laboratory costs, and an inconsistent yield of permanent lymphedema. We describe an experimental model for chronic lymphedema in the lower extremity of the rat that creates a lymphatic block in the groin induced by radiation treatment and one operation--surgical division of the superficial and deep lymphatics. All animals develop stable chronic lymphedema of the lower extremity within days of operation, with swelling that persists for at least 9 months. A mortality rate of 8 percent was associated with this technique. Methods for quantification of limb swelling are described, as is analysis of the lymphatic block by lymphoscintigraphic imaging of lymph channels and nodes. This model has the advantages of simplicity of technique, cost-effective use of rodent subjects, reproducibility of lymphedema, and quantification of results.