Inference in Semi‐Parametric Dynamic Models for Repeated Count Data

This paper deals with a longitudinal semi‐parametric regression model in a generalised linear model setup for repeated count data collected from a large number of independent individuals. To accommodate the longitudinal correlations, we consider a dynamic model for repeated counts which has decaying auto‐correlations as the time lag increases between the repeated responses. The semi‐parametric regression function involved in the model contains a specified regression function in some suitable time‐dependent covariates and a non‐parametric function in some other time‐dependent covariates. As far as the inference is concerned, because the non‐parametric function is of secondary interest, we estimate this function consistently using the independence assumption‐based well‐known quasi‐likelihood approach. Next, the proposed longitudinal correlation structure and the estimate of the non‐parametric function are used to develop a semi‐parametric generalised quasi‐likelihood approach for consistent and efficient estimation of the regression effects in the parametric regression function. The finite sample performance of the proposed estimation approach is examined through an intensive simulation study based on both large and small samples. Both balanced and unbalanced cluster sizes are incorporated in the simulation study. The asymptotic performances of the estimators are given. The estimation methodology is illustrated by reanalysing the well‐known health care utilisation data consisting of counts of yearly visits to a physician by 180 individuals for four years and several important primary and secondary covariates.     

Testing for constancy in varying coefficient models

We consider varying coefficient models, which are an extension of the classical linear regression models in the sense that the regression coefficients are replaced by functions in certain variables (for example, time), the covariates are also allowed to depend on other variables. Varying coefficient models are popular in longitudinal data and panel data studies, and have been applied in fields such as finance and health sciences. We consider longitudinal data and estimate the coefficient functions by the flexible B-spline technique. An important question in a varying coefficient model is whether an estimated coefficient function is statistically different from a constant (or zero). We develop testing procedures based on the estimated B-spline coefficients by making use of nice properties of a B-spline basis. Our method allows longitudinal data where repeated measurements for an individual can be correlated. We obtain the asymptotic null distribution of the test statistic. The power of the proposed testing procedures are illustrated on simulated data where we highlight the importance of including the correlation structure of the response variable and on real data.     

Quantile regression for longitudinal data based on latent Markov subject-specific parameters

We propose a latent Markov quantile regression model for longitudinal data with non-informative drop-out. The observations, conditionally on covariates, are modeled through an asymmetric Laplace distribution. Random effects are assumed to be time-varying and to follow a first order latent Markov chain. This latter assumption is easily interpretable and allows exact inference through an ad hoc EM-type algorithm based on appropriate recursions. Finally, we illustrate the model on a benchmark data set.     

A Bayesian method for estimating the accuracy of recalled depression

Summary.  We develop a Bayesian method that allows us to compare weekly depression states recalled for a 3-month period to cross-sectionally assessed measurements of current depression assessed during randomly timed phone interviews. Using these data, we examine the accuracy of recalled depression by linking a spline model for recalled depression and a logistic model for current depression. The logistic model includes the model-based probability of depression based on recall as a covariate and covariates potentially related to the accuracy of recall. The model that we propose allows variability in both measures and can be modified to examine general relationships between longitudinal and cross-sectional measurements.     

Semiparametric models of longitudinal and time-to-event data with applications to HIV viral dynamics and CD4 counts

We propose a semiparametric approach based on proportional hazards and copula method to jointly model longitudinal outcomes and the time-to-event. The dependence between the longitudinal outcomes on the covariates is modeled by a copula-based times series, which allows non-Gaussian random effects and overcomes the limitation of the parametric assumptions in existing linear and nonlinear random effects models. A modified partial likelihood method using estimated covariates at failure times is employed to draw statistical inference. The proposed model and method are applied to analyze a set of progression to AIDS data in a study of the association between the human immunodeficiency virus viral dynamics and the time trend in the CD4/CD8 ratio with measurement errors. Simulations are also reported to evaluate the proposed model and method.     

Multivariate generalized linear mixed models with random intercepts to analyze cardiovascular risk markers in type-1 diabetic patients

Statistical approaches tailored to analyzing longitudinal data that have multiple outcomes with different distributions are scarce. This paucity is due to the non-availability of multivariate distributions that jointly model outcomes with different distributions other than the multivariate normal. A plethora of research has been done on the specific combination of binary-Gaussian bivariate outcomes but a more general approach that allows other mixtures of distributions for multiple longitudinal outcomes has not been thoroughly demonstrated and examined. Here, we study a multivariate generalized linear mixed models approach that jointly models multiple longitudinal outcomes with different combinations of distributions and incorporates the correlations between the various outcomes through separate yet correlated random intercepts. Every outcome is linked to the set of covariates through a proper link function that allows the incorporation and joint modeling of different distributions. A novel application was demonstrated on a cohort study of Type-1 diabetic patients to jointly model a mix of longitudinal cardiovascular outcomes and to explore for the first time the effect of glycemic control treatment, plasma prekallikrein biomarker, gender and age on cardiovascular risk factors collectively.     

A Dynamic Latent Model for Poverty Measurement

The main purpose of this paper is the longitudinal analysis of the poverty phenomenon. By interpreting poverty as a latent variable, we are able to resort to the statistical methodology developed for latent structure analysis. In particular, we propose to use the mixture latent Markov model which allows us to achieve two goals: (i) a time-invariant classification of households into homogenous groups, representing different levels of poverty; (ii) the dynamic analysis of the poverty phenomenon which highlights the distinction between transitory and permanent poverty situations. Furthermore, we exploit the flexibility provided by the model in order to achieve the measurement of poverty in a multidisciplinary framework, using several socio-economic indicators as covariates and identifying the main relevant factors which influence permanent and transitory poverty. The analysis of the longitudinal data of the Survey on Households Income and Wealth of the Bank of Italy provides the identification of two groups of households which are characterized by different dynamic features. Moreover, the inclusion of socio-economic covariates such as level of education, employment status, geographical area and residence size of the household head shows a direct association with permanent poverty.     

Cluster‐Specific Variable Selection for Product Partition Models

We propose a random partition model that implements prediction with many candidate covariates and interactions. The model is based on a modified product partition model that includes a regression on covariates by favouring homogeneous clusters in terms of these covariates. Additionally, the model allows for a cluster‐specific choice of the covariates that are included in this evaluation of homogeneity. The variable selection is implemented by introducing a set of cluster‐specific latent indicators that include or exclude covariates. The proposed model is motivated by an application to predicting mortality in an intensive care unit in Lisboa, Portugal.     

A beta-inflated mean regression model with mixed effects for fractional response variables

Abstract

In this article we propose a new mixed-effects regression model for fractional bounded response variables. Our model allows us to incorporate covariates directly to the expected value, so we can quantify exactly the influence of these covariates in the mean of the variable of interest rather than to the conditional mean. Estimation is carried out from a Bayesian perspective. Due to the complexity of the augmented posterior distribution, we use a Hamiltonian Monte Carlo algorithm, the No-U-Turn sampler, implemented using the Stan software. A simulation study was performed showing that our model has a better performance than other traditional longitudinal models for bounded variables. Finally, we applied our beta-inflated mean mixed-effects regression model to real data which consists of utilization of credit lines in the peruvian financial system.     

Mixed Correlated Bivariate Ordinal and Negative Binomial Longitudinal Responses with Nonignorable Missing Values

Regression models with random effects are proposed for joint analysis of negative binomial and ordinal longitudinal data with nonignorable missing values under fully parametric framework. The presented model simultaneously considers a multivariate probit regression model for the missing mechanisms, which provides the ability of examining the missing data assumptions and a multivariate mixed model for the responses. Random effects are used to take into account the correlation between longitudinal responses of the same individual. A full likelihood-based approach that allows yielding maximum likelihood estimates of the model parameters is used. The model is applied to a medical data, obtained from an observational study on women, where the correlated responses are the ordinal response of osteoporosis of the spine and negative binomial response is the number of joint damage. A sensitivity of the results to the assumptions is also investigated. The effect of some covariates on all responses are investigated simultaneously.     

A general joint model for longitudinal measurements and competing risks survival data with heterogeneous random effects

This article studies a general joint model for longitudinal measurements and competing risks survival data. The model consists of a linear mixed effects sub-model for the longitudinal outcome, a proportional cause-specific hazards frailty sub-model for the competing risks survival data, and a regression sub-model for the variance–covariance matrix of the multivariate latent random effects based on a modified Cholesky decomposition. The model provides a useful approach to adjust for non-ignorable missing data due to dropout for the longitudinal outcome, enables analysis of the survival outcome with informative censoring and intermittently measured time-dependent covariates, as well as joint analysis of the longitudinal and survival outcomes. Unlike previously studied joint models, our model allows for heterogeneous random covariance matrices. It also offers a framework to assess the homogeneous covariance assumption of existing joint models. A Bayesian MCMC procedure is developed for parameter estimation and inference. Its performances and frequentist properties are investigated using simulations. A real data example is used to illustrate the usefulness of the approach.     

Bayesian inference for generalized additive mixed models based on Markov random field priors

Most regression problems in practice require flexible semiparametric forms of the predictor for modelling the dependence of responses on covariates. Moreover, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal or spatial data. We present a unified approach for Bayesian inference via Markov chain Monte Carlo simulation in generalized additive and semiparametric mixed models. Different types of covariates, such as the usual covariates with fixed effects, metrical covariates with non-linear effects, unstructured random effects, trend and seasonal components in longitudinal data and spatial covariates, are all treated within the same general framework by assigning appropriate Markov random field priors with different forms and degrees of smoothness. We applied the approach in several case-studies and consulting cases, showing that the methods are also computationally feasible in problems with many covariates and large data sets. In this paper, we choose two typical applications.     

Inferences in dynamic logit models in semi-parametric setup for repeated binary data

Binary dynamic fixed and mixed logit models are extensively studied in the literature. These models are developed to examine the effects of certain fixed covariates through a parametric regression function as a part of the models. However, there are situations where one may like to consider more covariates in the model but their direct effect is not of interest. In this paper we propose a generalization of the existing binary dynamic logit (BDL) models to the semi-parametric longitudinal setup to address this issue of additional covariates. The regression function involved in such a semi-parametric BDL model contains (i) a parametric linear regression function in some primary covariates, and (ii) a non-parametric function in certain secondary covariates. We use a simple semi-parametric conditional quasi-likelihood approach for consistent estimation of the non-parametric function, and a semi-parametric likelihood approach for the joint estimation of the main regression and dynamic dependence parameters of the model. The finite sample performance of the estimation approaches is examined through a simulation study. The asymptotic properties of the estimators are also discussed. The proposed model and the estimation approaches are illustrated by reanalysing a longitudinal infectious disease data.     

Jointly modeling skew longitudinal survival data with missingness and mismeasured covariates

Jointly modeling longitudinal and survival data has been an active research area. Most researches focus on improving the estimating efficiency but ignore many data features frequently encountered in practice. In the current study, we develop the joint models that concurrently accounting for longitudinal and survival data with multiple features. Specifically, the proposed model handles skewness, missingness and measurement errors in covariates which are typically observed in the collection of longitudinal survival data from many studies. We employ a Bayesian inferential method to make inference on the proposed model. We applied the proposed model to an real data study. A few alternative models under different conditions are compared. We conduct extensive simulations in order to evaluate how the method works.     

Modelling Survival Events with Longitudinal Covariates Measured with Error

In survival analysis, time-dependent covariates are usually present as longitudinal data collected periodically and measured with error. The longitudinal data can be assumed to follow a linear mixed effect model and Cox regression models may be used for modelling of survival events. The hazard rate of survival times depends on the underlying time-dependent covariate measured with error, which may be described by random effects. Most existing methods proposed for such models assume a parametric distribution assumption on the random effects and specify a normally distributed error term for the linear mixed effect model. These assumptions may not be always valid in practice. In this article, we propose a new likelihood method for Cox regression models with error-contaminated time-dependent covariates. The proposed method does not require any parametric distribution assumption on random effects and random errors. Asymptotic properties for parameter estimators are provided. Simulation results show that under certain situations the proposed methods are more efficient than the existing methods.     

Latent class models for longitudinal studies of the elderly with data missing at random

The elderly population in the USA is expected to double in size by the year 2025, making longitudinal health studies of this population of increasing importance. The degree of loss to follow-up in studies of the elderly, which is often because elderly people cannot remain in the study, enter a nursing home or die, make longitudinal studies of this population problematic. We propose a latent class model for analysing multiple longitudinal binary health outcomes with multiple-cause non-response when the data are missing at random and a non-likelihood-based analysis is performed. We extend the estimating equations approach of Robins and co-workers to latent class models by reweighting the multiple binary longitudinal outcomes by the inverse probability of being observed. This results in consistent parameter estimates when the probability of non-response depends on observed outcomes and covariates (missing at random) assuming that the model for non-response is correctly specified. We extend the non-response model so that institutionalization, death and missingness due to failure to locate, refusal or incomplete data each have their own set of non-response probabilities. Robust variance estimates are derived which account for the use of a possibly misspecified covariance matrix, estimation of missing data weights and estimation of latent class measurement parameters. This approach is then applied to a study of lower body function among a subsample of the elderly participating in the 6-year Longitudinal Study of Aging.     

基于贝叶斯推断的HIV非线性混合效应联合模型研究

 在纵向数据研究中,混合效应模型的随机误差通常采用正态性假设。而诸如病毒载量和CD4细胞数目等病毒性数据通常呈现偏斜性,因此正态性假设可能影响模型结果甚至导致错误的结论。在HIV动力学研究中,病毒响应值往往与协变量相关,且协变量的测量值通常存在误差,为此论文中联立协变量过程建立具有偏正态分布的非线性混合效应联合模型,并用贝叶斯推断方法估计模型的参数。由于协变量能够解释个体内的部分变化,因此协变量过程的模型选择对病毒载量的拟合效果有重要的影响。该文提出了一次移动平均模型作为协变量过程的改进模型,比较后发现当协变量采用移动平均模型时,病毒载量模型的拟合效果更好。该结果对协变量模型的研究具有重要的指导意义。     

A generalized linear mixed model for longitudinal binary data with a marginal logit link function

Longitudinal studies of a binary outcome are common in the health, social, and behavioral sciences. In general, a feature of random effects logistic regression models for longitudinal binary data is that the marginal functional form, when integrated over the distribution of the random effects, is no longer of logistic form. Recently, Wang and Louis (2003) proposed a random intercept model in the clustered binary data setting where the marginal model has a logistic form. An acknowledged limitation of their model is that it allows only a single random effect that varies from cluster to cluster. In this paper, we propose a modification of their model to handle longitudinal data, allowing separate, but correlated, random intercepts at each measurement occasion. The proposed model allows for a flexible correlation structure among the random intercepts, where the correlations can be interpreted in terms of Kendall's τ. For example, the marginal correlations among the repeated binary outcomes can decline with increasing time separation, while the model retains the property of having matching conditional and marginal logit link functions. Finally, the proposed method is used to analyze data from a longitudinal study designed to monitor cardiac abnormalities in children born to HIV-infected women.     

A multi-index model for quantile regression with ordinal data

In this paper, we propose a quantile approach to the multi-index semiparametric model for an ordinal response variable. Permitting non-parametric transformation of the response, the proposed method achieves a root-n rate of convergence and has attractive robustness properties. Further, the proposed model allows additional indices to model the remaining correlations between covariates and the residuals from the single-index, considerably reducing the error variance and thus leading to more efficient prediction intervals (PIs). The utility of the model is demonstrated by estimating PIs for functional status of the elderly based on data from the second longitudinal study of aging. It is shown that the proposed multi-index model provides significantly narrower PIs than competing models. Our approach can be applied to other areas in which the distribution of future observations must be predicted from ordinal response data.     

Analysis of longitudinal data with irregular, outcome-dependent follow-up

Summary.  A frequent problem in longitudinal studies is that subjects may miss scheduled visits or be assessed at self-selected points in time. As a result, observed outcome data may be highly unbalanced and the availability of the data may be directly related to the outcome measure and/or some auxiliary factors that are associated with the outcome. If the follow-up visit and outcome processes are correlated, then marginal regression analyses will produce biased estimates. Building on the work of Robins, Rotnitzky and Zhao, we propose a class of inverse intensity-of-visit process-weighted estimators in marginal regression models for longitudinal responses that may be observed in continuous time. This allows us to handle arbitrary patterns of missing data as embedded in a subject's visit process. We derive the large sample distribution for our inverse visit-intensity-weighted estimators and investigate their finite sample behaviour by simulation. Our approach is illustrated with a data set from a health services research study in which homeless people with mental illness were randomized to three different treatments and measures of homelessness (as percentage days homeless in the past 3 months) and other auxiliary factors were recorded at follow-up times that are not fixed by design.