In this paper, we consider a single-index mixed model with longitudinal data. A new set of estimating equations is proposed to estimate the single-index coefficient. The link function is estimated by using the local linear smoothing. Asymptotic normality is established for the proposed estimators. Also, the estimator of the link function achieves optimal convergence rates; and the estimators of variance components have root-$n$ consistency. These results facilitate the construction of confidence regions/intervals and hypothesis testing for the parameters of interest. Some simulations and an application to real data are included.
We present generalized additive latent and mixed models (GALAMMs) for analysis of clustered data with responses and latent variables depending smoothly on observed variables. A scalable maximum likelihood estimation algorithm is proposed, utilizing the Laplace approximation, sparse matrix computation, and automatic differentiation. Mixed response types, heteroscedasticity, and crossed random effects are naturally incorporated into the framework. The models developed were motivated by applications in cognitive neuroscience, and two case studies are presented. First, we show how GALAMMs can join…
Nonlinear mixed effects models have received a great deal of attention in the statistical literature in recent years because of their flexibility in handling longitudinal studies, including human immunodeficiency virus viral dynamics, pharmacokinetic analyses, and studies of growth and decay. A standard assumption in nonlinear mixed effects models for continuous responses is that the random effects and the within-subject errors are normally distributed, making the model sensitive to outliers. We present a novel class of asymmetric nonlinear mixed effects models that provides efficient paramete…
Rooted in genetics, human complex diseases are largely influenced by environmental factors. Existing literature has shown the power of integrative gene-environment interaction analysis by considering the joint effect of environmental mixtures on a disease risk. In this work, we propose a functional varying index coefficient model for longitudinal measurements of a phenotypic trait together with multiple environmental variables, and assess how the genetic effects on a longitudinal disease trait are nonlinearly modified by a mixture of environmental influences. We derive an estimation procedure …
In this article, we study a partially linear single-index model for longitudinal data under a general framework which includes both the sparse and dense longitudinal data cases. A semiparametric estimation method based on a combination of the local linear smoothing and generalized estimation equations (GEE) is introduced to estimate the two parameter vectors as well as the unknown link function. Under some mild conditions, we derive the asymptotic properties of the proposed parametric and nonparametric estimators in different scenarios, from which we find that the convergence rates and asympto…
Using latent representations to link disjoint longitudinal data for mixed-effects regression
Institute of Medical Biometry and Statistics (IMBI), Medical Faculty and Medical Center – University of Freiburg, Germany（医学生物统计学研究所（IMBI）、医学 faculty 和医疗中心——弗赖堡大学，德国）；Freiburg Center for Data Analysis, Modeling and AI – University of Freiburg, Germany（弗赖堡数据分析、建模和人工智能中心——弗赖堡大学，德国）；Department of Mathematical Stochastics, Mathematical Institute – University of Freiburg, Germany（数学随机过程系、数学研究所——弗赖堡大学，德国）；Department of Neuropediatrics and Muscle Disorders, Medical Faculty and Medical Center – University of Freiburg, Germany（神经发育学与肌肉疾病系、医学 faculty 和医疗中心——弗赖堡大学，德国）；Bonn Center for Mathematical Life Sciences – University of Bonn, Germany（波恩数学生命科学中心——波恩大学，德国）；Life and Medical Sciences (LIMES) Institute – University of Bonn, Germany（生命科学与医学科学（LIMES）研究所——波恩大学，德国）；CIBSS, Centre for Integrative Biological Signalling Studies – University of Freiburg, Germany（整合生物信号研究中心（CIBSS）——弗赖堡大学，德国）
The primary analysis of clinical trials in diabetes therapeutic area often involves a mixed-model repeated measure (MMRM) approach to estimate the average treatment effect for longitudinal continuous outcome, and a generalized linear mixed model (GLMM) approach for longitudinal binary outcome. In this paper, we considered another estimator of the average treatment effect, called targeted maximum likelihood estimator (TMLE). This estimator can be a one-step alternative to model either continuous or binary outcome. We compared those estimators by simulation studies and by analyzing real data fro…
Understanding how adult humans learn non-native speech categories such as tone information has shed novel insights into the mechanisms underlying experience-dependent brain plasticity. Scientists have traditionally examined these questions using longitudinal learning experiments under a multi-category decision making paradigm. Drift-diffusion processes are popular in such contexts for their ability to mimic underlying neural mechanisms. Motivated by these problems, we develop a novel Bayesian semiparametric inverse Gaussian drift-diffusion mixed model for multi-alternative decision making in l…
In this paper, we propose a general subgroup analysis framework based on semiparametric additive mixed effect models in longitudinal analysis, which can identify subgroups on each covariate and estimate the corresponding regression functions simultaneously. In addition, the proposed procedure is applicable for both balanced and unbalanced longitudinal data. A backfitting combined with k-means algorithm is developed to estimate each semiparametric additive component across subgroups and detect subgroup structure on each covariate respectively. The actual number of groups is estimated by minimiz…
A dynamic treatment regimen (DTR) is a pre-specified sequence of decision rules which maps baseline or time-varying measurements on an individual to a recommended intervention or set of interventions. Sequential multiple assignment randomized trials (SMARTs) represent an important data collection tool for informing the construction of effective DTRs. A common primary aim in a SMART is the marginal mean comparison between two or more of the DTRs embedded in the trial. This manuscript develops a mixed effects modeling and estimation approach for these primary aim comparisons based on a continuou…
A pressing challenge in medical research is to identify optimal treatments for individual patients. This is particularly challenging in mental health settings where mean responses are often similar across multiple treatments. For example, the mean longitudinal trajectories for patients treated with an active drug and placebo may be very similar but different treatments may exhibit distinctly different individual trajectory shapes. Most precision medicine approaches using longitudinal data often ignore information from the longitudinal data structure. This paper investigates a powerful precisio…
Electronic health records are being increasingly used in medical research to answer more relevant and detailed clinical questions; however, they pose new and significant methodological challenges. For instance, observation times are likely correlated with the underlying disease severity: patients with worse conditions utilise health care more and may have worse biomarker values recorded. Traditional methods for analysing longitudinal data assume independence between observation times and disease severity; yet, with healthcare data such assumptions unlikely holds. Through Monte Carlo simulation…
In epidemiological and clinical studies, identifying patients' phenotypes based on longitudinal profiles is critical to understanding the disease's developmental patterns. The current study was motivated by data from a Canadian birth cohort study, the CHILD Cohort Study. Our goal was to use multiple longitudinal respiratory traits to cluster the participants into subgroups with similar longitudinal respiratory profiles in order to identify clinically relevant disease phenotypes. To appropriately account for distinct structures and types of these longitudinal markers, we proposed a novel joint …
Bayesian Regression Analysis of Data with Random Effects Covariates from Nonlinear Longitudinal Measurements
多种响应变量和纵向测量的联合模型由混合效应模型组成，以拟合纵向轨迹，其随机效应作为协变量进入主要响应的广义线性模型。它们提供了一种有用的方法来评估这两种数据之间的关联，在临床研究中，这两种数据通常是在一系列个体上联合收集的，并且可以帮助理解，例如，某种疾病的恢复机制或给定疗法的疗效。该框架中最常见的联合模型是基于纵向数据的线性混合模型。然而，对于复杂的数据集，线性假设可能过于严格。一些工作已经考虑通过使用纵向轨迹的非线性混合效应模型来推广这种设置，但是De la Cruz等人（2011年）已经表明，基于似然近似的拟议估计程序表现出一些计算效率问题。在这篇文章中，我们提出了一个MCMC为基础的估计过程中的联合模型与非线性混合效应模型的纵向数据和广义线性模型的主要反应。此外，我们认为纵向模型中的误差可能是相关的。我们将我们的方法应用于分析在妊娠早期测量的激素水平，这些激素水平可用于预测正常与异常妊娠结局。我们还进行了模拟研究，以评估建模相关误差的重要性，并量化模型错误的后果。
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…
Characterization of long-term disease dynamics, from disease-free to end-stage, is integral to understanding the course of neurodegenerative diseases such as Parkinson's and Alzheimer's; and ultimately, how best to intervene. Natural history studies typically recruit multiple cohorts at different stages of disease and follow them longitudinally for a relatively short period of time. We propose a latent time joint mixed effects model to characterize long-term disease dynamics using this short-term data. Markov chain Monte Carlo methods are proposed for estimation, model selection, and inference…
Dynamic prediction of causal effects under different treatment regimes conditional on an individual's characteristics and longitudinal history is an essential problem in precision medicine. This is challenging in practice because outcomes and treatment assignment mechanisms are unknown in observational studies, an individual's treatment efficacy is a counterfactual, and the existence of selection bias is often unavoidable. We propose a Bayesian framework for identifying subgroup counterfactual benefits of dynamic treatment regimes by adapting Bayesian g-computation algorithm (J. Robins, 1986; …
We present a new modelling approach for longitudinal count data that is motivated by the increasing availability of longitudinal RNA-sequencing experiments. The distribution of RNA-seq counts typically exhibits overdispersion, zero-inflation and heavy tails; moreover, in longitudinal designs repeated measurements from the same subject are typically (positively) correlated. We propose a generalized linear mixed model based on the Poisson-Tweedie distribution that can flexibly handle each of the aforementioned features of longitudinal overdispersed counts. We develop a computational approach to …
We develop methods for analyzing discrete multivariate longitudinal data and apply them to functional disability data on the U.S. elderly population from the National Long Term Care Survey (NLTCS), 1982-2004. Our models build on a Mixed Membership framework, in which individuals are allowed multiple membership on a set of extreme profiles characterized by time-dependent trajectories of progression into disability. We also develop an extension that allows us to incorporate birth-cohort effects, in order to assess inter-generational changes. Applying these methods, we find that most individuals …
In mixed longitudinal studies, a group of subjects enter the study at different ages (cross-sectional) and are followed for successive years (longitudinal). In the context of such studies, we consider nonparametric covariance estimation with samples of noisy and partially observed functional trajectories. The proposed algorithm is based on a noniterative sequential-aggregation scheme with only basic matrix operations and closed-form solutions in each step. The good performance of the proposed method is supported by both theory and numerical experiments. We also apply the proposed procedure to …
This paper takes a quick look at Bayesian joint models (BJM) for longitudinal and survival data. A general formulation for BJM is examined in terms of the sampling distribution of the longitudinal and survival processes, the conditional distribution of the random effects and the prior distribution. Next a basic BJM defined in terms of a mixed linear model and a Cox survival regression models is discussed and some extensions and other Bayesian topics are briefly outlined.
The identification of factors associated with mental and behavioral disorders in early childhood is critical both for psychopathology research and the support of primary health care practices. Motivated by the Millennium Cohort Study, in this paper we study the effect of a comprehensive set of covariates on children's emotional and behavioural trajectories in England. To this end, we develop a Quantile Mixed Hidden Markov Model for joint estimation of multiple quantiles in a linear regression setting for multivariate longitudinal data. The novelty of the proposed approach is based on the Multi…
It is important to characterize the temporal trajectories of disease-related biomarkers in order to monitor progression and identify potential points of intervention. This is especially important for neurodegenerative diseases, as therapeutic intervention is most likely to be effective in the preclinical disease stages prior to significant neuronal damage. Longitudinal neuroimaging allows for the measurement of structural, functional, and metabolic integrity of the brain over time at the level of voxels. However, commonly used longitudinal analysis approaches, such as linear mixed effects mode…
We propose a Bayesian approach using improper priors for hierarchical linear mixed models with flexible random effects and residual error distributions. The error distribution is modelled using scale mixtures of normals, which can capture tails heavier than those of the normal distribution. This generalisation is useful to produce models that are robust to the presence of outliers. The case of asymmetric residual errors is also studied. We present general results for the propriety of the posterior that also cover cases with censored observations, allowing for the use of these models in the con…
We propose a comprehensive framework for additive regression models for non-Gaussian functional responses, allowing for multiple (partially) nested or crossed functional random effects with flexible correlation structures for, e.g., spatial, temporal, or longitudinal functional data as well as linear and nonlinear effects of functional and scalar covariates that may vary smoothly over the index of the functional response. Our implementation handles functional responses from any exponential family distribution as well as many others like Beta- or scaled non-central $t$-distributions. Developmen…
Bias in mixed models when analysing longitudinal data subject to irregular observation: when should we worry about it and how can recommended visit intervals help in specifying joint models when needed?
Approximation, Consistency, and Prediction in Generalized Neural Network Mixed Models for Longitudinal and Clustered Data
Pennsylvania State University-Altoona（宾夕法尼亚州立大学阿尔图纳分校）；Virginia Commonwealth University（弗吉尼亚联邦大学）；University of South Alabama（阿拉巴马大学南部分校）；Quinnipiac University（昆尼皮亚克大学）；Rhodes College（罗兹学院）
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 obtai…
Correcting for confounding in longitudinal experiments: positioning non-linear mixed effects modeling as implementation of standardization using latent conditional exchangeability
