Semiparametric Mixed-effects Models Research Articles

Hearing function in patients living with HIV/AIDS.

During the earlier years of the HIV/AIDS epidemic, initial reports described sensorineural hearing loss in up to 49% of individuals with HIV/AIDS. During those years, patients commonly progressed to advanced stages of HIV disease and frequently had neurological complications. However, the abnormalities on pure-tone audiometry and brainstem-evoked responses outlined in small studies were not always consistently correlated with advanced stages of HIV/AIDS. Moreover, these studies could not exclude the confounding effect of concurrent opportunistic infections and syphilis. Additional reports also have indicated that some antiretroviral medications may be ototoxic; thus, it has been difficult to make conclusions regarding the cause of changes in hearing function in HIV-infected patients. More recently, accelerated aging has been suggested as a potential explanation for the disproportionate increase in complications of aging described in many HIV-infected patients; hence, accelerated aging-associated hearing loss may also be playing a role in these patients. We conducted a large cross-sectional analysis of hearing function in over 300 patients with HIV-1 infection and in 137 HIV-uninfected controls. HIV-infected participants and HIV-uninfected controls underwent a 2-hr battery of hearing tests including the Hearing Handicap Inventory, standard audiometric pure-tone air and bone conduction testing, tympanometric testing, and speech reception and discrimination testing. Three-way analysis of variance (ANOVA) and logistic regression analysis of 278 eligible HIV-infected subjects stratified by disease stage in early HIV disease (n = 127) and late HIV disease (n = 148) and 120 eligible HIV-uninfected controls revealed no statistically significant differences among the three study groups in either overall 4-frequency pure-tone average (4-PTA) or hearing loss prevalence in either ear. Three-way ANOVA showed significant differences in word recognition scores in the right ear among groups, a significant group effect on tympanogram static admittance in both ears and a significant group effect on tympanic gradient in the right ear. There was significantly larger admittance and gradient in controls as compared to the HIV-infected group at late stage of disease. Hearing loss in the HIV-infected groups was associated with increased age and was similar to that described in the literature for the general population. Three-way ANOVA analysis also indicated significantly greater pure-tone thresholds (worse hearing) at low frequencies in HIV patients in the late stage of disease compared with HIV-uninfected controls. This difference was also found by semi-parametric mixed effects models. Despite reports of "premature" or "accelerated" aging in HIV-infected subjects, we found no evidence of hearing loss occurring at an earlier age in HIV-infected patients compared to HIV-uninfected controls. Similar to what is described in the general population, the probability of hearing loss increased with age in the HIV-infected subjects and was more common in patients over 60 years of age. Interestingly, HIV-infected subjects had worse hearing at lower frequencies and have significant differences in tympanometry compared to HIV-uninfected controls; these findings deserve further study.

Semi-parametric mixed effects models for longitudinal data with applications in business and economics

Longitudinal data is becoming increasingly common in business, social sciences, and biological sciences due to the advantages it offers over cross-section data in modeling and incorporating heterogeneity among subjects and in being able to make causal inferences from observational data. Parametric models and methods are widely used for analyzing longitudinal data for continuous, discrete, and count data occurring in these disciplines. Some popular models are Gaussian, Logit, and Poisson fixed and random effects models. These models are unreliable in situations in which the link function is nonlinear and the form of nonlinearity is not known with certainty. This paper employs a semi-parametric extension of fixed and random effects models called generalized additive mixed models (GAMMs) to analyze several longitudinal data sets. These semi-parametric models are flexible and robust extensions of generalized linear models. Following Wood [19], the GAMMs are represented using penalized regression splines and estimated by penalized regression methods treating the penalized component of each smooth as a random effect term and the unpenalized component as a fixed effect term. The degree of smoothness for the unknown functions in the linear predictor part of the GAMM is estimated as the variance parameter of the term. Applications of GAMMs studied include analysis of anti-social behavior, decision to use a professional tax preparer, and analysis of patent data on manufacturing firms. For each application, several GAMMs are compared with their parametric counterparts. Keywords: Generalized Additive Mixed Models (GAMMS), Generalized Linear Mixed Models (GLMMS), Logit Models, Poisson Regression Models, Penalized Regression Splines.

Estimation, prediction and interpretation of NGG random effects models: an application to Kevlar fibre failure times

We propose a class of Bayesian semiparametric mixed-effects models; its distinctive feature is the randomness of the grouping of observations, which can be inferred from the data. The model can be viewed under a more natural perspective, as a Bayesian semiparametric regression model on the log-scale; hence, in the original scale, the error is a mixture of Weibull densities mixed on both parameters by a normalized generalized gamma random measure, encompassing the Dirichlet process. As an estimate of the posterior distribution of the clustering of the random-effects parameters, we consider the partition minimizing the posterior expectation of a suitable class of loss functions. As a merely illustrative application of our model we consider a Kevlar fibre lifetime dataset (with censoring). We implement an MCMC scheme, obtaining posterior credibility intervals for the predictive distributions and for the quantiles of the failure times under different stress levels. Compared to a previous parametric Bayesian analysis, we obtain narrower credibility intervals and a better fit to the data. We found that there are three main clusters among the random-effects parameters, in accordance with previous frequentist analysis.

Optimal Blood Pressure for Cognitive Function: Findings from an Elderly African‐American Cohort Study

To report the results from a prospective cohort study on the association between blood pressure (BP) and cognitive function in elderly African Americans. Prospective cohort study conducted from 1997 to 2009. Community-based study in Indianapolis. African Americans aged 65 years or older (N = 3,145). At each assessment, participant cognitive function was measured using the Community Screening Interview for Dementia. Other measurements included BP, height, weight, education level, antihypertensive medication use, alcohol use, smoking, and history of chronic medical conditions. Longitudinal assessments (n = 5,995) contributed by 2,721 participants with complete independent variables were analyzed using a semiparametric mixed-effects model. Systolic BP (SBP) of approximately 135 mmHg and diastolic BP (DBP) of approximately 80 mmHg were associated with optimal cognitive function after adjusting for other variables (P = .02). Weight loss with body mass index < 30.0 kg/m(2) was significantly related to poorer cognitive performance (P < .001). Older age at first assessment, lower education level; smoking; and history of depression, stroke, and diabetes mellitus were related to worse cognitive function; taking antihypertensive medication and drinking alcohol were associated with better cognitive function. High and low BP were associated with poorer cognitive performance. A joint optimal region of SBP and DBP for cognitive function has been identified, which may provide useful clinical information on optimal BP control in cognitive health and lead to better quality of life for elderly adults.

Model Tumor Pattern and Compare Treatment Effects Using Semiparametric Linear Mixed-Effects Models

To analyze responses of solid tumor to treatments and to compare treatment effects with antitumor therapies, we applied semiparametric mixed-effects models to fit tumor volumes measured over a period. The population and individual nonparametric functions were approximated by smoothing spline. We also proposed an intuitive method for a comparison of the antitumor effects of two different treatments. Biological interpretation was also discussed.

Semiparametric mixed-effects models for clustered doubly censored data

The Cox proportional frailty model with a random effect has been proposed for the analysis of right-censored data which consist of a large number of small clusters of correlated failure time observations. For right-censored data, Cai et al. [3] proposed a class of semiparametric mixed-effects models which provides useful alternatives to the Cox model. We demonstrate that the approach of Cai et al. [3] can be used to analyze clustered doubly censored data when both left- and right-censoring variables are always observed. The asymptotic properties of the proposed estimator are derived. A simulation study is conducted to investigate the performance of the proposed estimator.

Kernel smoothers and bootstrapping for semiparametric mixed effects models

While today linear mixed effects models are frequently used tools in different fields of statistics, in particular for studying data with clusters, longitudinal or multi-level structure, the nonparametric formulation of mixed effects models is still quite recent. In this paper we discuss and compare different nonparametric estimation methods. In this context we introduce a computationally inexpensive bootstrap method, which is used to estimate local mean squared errors, to construct confidence intervals and to find locally optimal smoothing parameters. The theoretical considerations are accompanied by the provision of algorithms and simulation studies of the finite sample behavior of the methods. We show that our confidence intervals have good coverage probabilities, and that our bandwidth selection method succeeds to minimize the mean squared error for the nonparametric function locally.

Penalized likelihood estimation for semiparametric mixed models, with application to alcohol treatment research

In this article, we implement a practical computational method for various semiparametric mixed effects models, estimating nonlinear functions by penalized splines. We approximate the integration of the penalized likelihood with respect to random effects with the use of adaptive Gaussian quadrature, which we can conveniently implement in SAS procedure NLMIXED. We carry out the selection of smoothing parameters through approximated generalized cross-validation scores. Our method has two advantages: (1) the estimation is more accurate than the current available quasi-likelihood method for sparse data, for example, binary data; and (2) it can be used in fitting more sophisticated models. We show the performance of our approach in simulation studies with longitudinal outcomes from three settings: binary, normal data after Box-Cox transformation, and count data with log-Gamma random effects. We also develop an estimation method for a longitudinal two-part nonparametric random effects model and apply it to analyze repeated measures of semicontinuous daily drinking records in a randomized controlled trial of topiramate.

How individual characteristics affect university students drop-out: a semiparametric mixed-effects model for an Italian case study

University drop-out is a topic of increasing concern in Italy as well as in other countries. In empirical analysis, university drop-out is generally measured by means of a binary variable indicating the drop-out versus retention. In this paper, we argue that the withdrawal decision is one of the possible outcomes of a set of four alternatives: retention in the same faculty, drop out, change of faculty within the same university, and change of institution. We examine individual-level data collected by the administrative offices of “Sapienza” University of Rome, which cover 117 072 students enrolling full-time for a 3-year degree in the academic years from 2001/2002 to 2006/2007. Relying on a non-parametric maximum likelihood approach in a finite mixture context, we introduce a multinomial latent effects model with endogeneity that accounts for both heterogeneity and omitted covariates. Our estimation results show that the decisions to change faculty or university have their own peculiarities, thus we suggest that caution should be used in interpreting results obtained without modeling all the relevant alternatives that students face.

Semiparametric modeling of autonomous nonlinear dynamical systems with application to plant growth

We propose a semiparametric model for autonomous nonlinear dynamical systems and devise an estimation procedure for model fitting. This model incorporates subject-specific effects and can be viewed as a nonlinear semiparametric mixed effects model. We also propose a computationally efficient model selection procedure. We show by simulation studies that the proposed estimation as well as model selection procedures can efficiently handle sparse and noisy measurements. Finally, we apply the proposed method to a plant growth data used to study growth displacement rates within meristems of maize roots under two different experimental conditions.

Flexible estimation of covariance function by penalized spline with application to longitudinal family data.

Longitudinal data are routinely collected in biomedical research studies. A natural model describing longitudinal data decomposes an individual's outcome as the sum of a population mean function and random subject-specific deviations. When parametric assumptions are too restrictive, methods modeling the population mean function and the random subject-specific functions nonparametrically are in demand. In some applications, it is desirable to estimate a covariance function of random subject-specific deviations. In this work, flexible yet computationally efficient methods are developed for a general class of semiparametric mixed effects models, where the functional forms of the population mean and the subject-specific curves are unspecified. We estimate nonparametric components of the model by penalized spline (P-spline, Biometrics 2001; 57:253-259), and reparameterize the random curve covariance function by a modified Cholesky decomposition (Biometrics 2002; 58:121-128) which allows for unconstrained estimation of a positive-semidefinite matrix. To provide smooth estimates, we penalize roughness of fitted curves and derive closed-form solutions in the maximization step of an EM algorithm. In addition, we present models and methods for longitudinal family data where subjects in a family are correlated and we decompose the covariance function into a subject-level source and observation-level source. We apply these methods to the multi-level Framingham Heart Study data to estimate age-specific heritability of systolic blood pressure nonparametrically.

Simultaneous Bayesian Inference for Linear, Nonlinear and Semiparametric Mixed-Effects Models with Skew-Normality and Measurement Errors in Covariates

In recent years, various mixed-effects models have been suggested for estimating viral decay rates in HIV dynamic models for complex longitudinal data. Among those models are linear mixed-effects (LME), nonlinear mixed-effects (NLME), and semiparametric nonlinear mixed-effects (SNLME) models. However, a critical question is whether these models produce coherent estimates of viral decay rates, and if not, which model is appropriate and should be used in practice. In addition, one often assumes that a model random error is normally distributed, but the normality assumption may be unrealistic, particularly if the data exhibit skewness. Moreover, some covariates such as CD4 cell count may be often measured with substantial errors. This paper addresses these issues simultaneously by jointly modeling the response variable with skewness and a covariate process with measurement errors using a Bayesian approach to investigate how estimated parameters are changed or different under these three models. A real data set from an AIDS clinical trial study was used to illustrate the proposed models and methods. It was found that there was a significant incongruity in the estimated decay rates in viral loads based on the three mixed-effects models, suggesting that the decay rates estimated by using Bayesian LME or NLME joint models should be interpreted differently from those estimated by using Bayesian SNLME joint models. The findings also suggest that the Bayesian SNLME joint model is preferred to other models because an arbitrary data truncation is not necessary; and it is also shown that the models with a skew-normal distribution and/or measurement errors in covariate may achieve reliable results when the data exhibit skewness.

A score test for variance components in a semiparametric mixed-effects model under non-normality

In this paper, we propose a score test for variance components in a semiparametric mixed-effects model when the random-effects and measurement errors are not normally distributed. The asymptotic null distribution of the test statistic is shown to be a simple chi-squared distribution with the degrees of freedom being the number of linearlyindependent variance components. The simulation results show that the proposed score test is robust against the nonnormality of the random-effects and the measurement errors and performs well in terms of both size and power. The score test is illustrated via an application to a real longitudinal data set collected in a clinical trial study. AMS 2000 subject classifications: Primary 62G10, 62G20; secondary 62G08.

Local polynomial inference for small area statistics: estimation, validation and prediction

Small area statistics has received considerable attention in the last two decades from both public and private sectors. More recently, semiparametric mixed-effects models have been proposed for a more flexible modelling. Surprisingly, although model specification testing is of particular importance in small area statistics, this has been less explored. Its importance is based on the fact that small area statistics applies model-based estimation and prediction. Local polynomials can nest typically used parametric models without bias – independent of the smoothing parameter – and are therefore particularly useful in practice. First, estimation and testing with local polynomials is introduced for mixed-effects models. Several extensions for further structural modelling with dimension-reducing effects are discussed. Second, different computationally attractive specification tests are proposed and compared. The methods are compared along simulation studies. Its usefulness is underpinned by the small-area regression problems of forest stand and farm production.

Longitudinal Data Analysis with Event Time as a Covariate

We consider the estimation of a nonparametric smooth function of some event time in a semiparametric mixed effects model from repeatedly measured data when the event time is subject to right censoring. The within-subject correlation is captured by both cross-sectional and time-dependent random effects, where the latter is modeled by a nonhomogeneous Ornstein–Uhlenbeck stochastic process. When the censoring probability depends on other variables in the model, which often happens in practice, the event time data are not missing completely at random. Hence, the complete case analysis by eliminating all the censored observations may yield biased estimates of the regression parameters including the smooth function of the event time, and is less efficient. To remedy, we derive the likelihood function for the observed data by modeling the event time distribution given other covariates. We propose a two-stage pseudo-likelihood approach for the estimation of model parameters by first plugging an estimator of the conditional event time distribution into the likelihood and then maximizing the resulting pseudo-likelihood function. Empirical evaluation shows that the proposed method yields negligible biases while significantly reduces the estimation variability. This research is motivated by the project of hormone profile estimation around age at the final menstrual period for the cohort of women in the Michigan Bone Health and Metabolism Study.

Predicting Enhanced Vegetation Index (EVI) curves for ecosystem modeling applications

Vegetation indices derived from remote sensing data provide information about the variability in stature, growth and vigor of the vegetation across a region, and have been used to model plant processes. For example, the Enhanced Vegetation Index (EVI) provides a measure of greenness of the vegetation that can be used to predict net primary production. However, ecosystem models relying on remote sensing data for EVI or other vegetation indices are limited by the time series of the satellite data record. Our objective was to develop a statistical model to predict EVI in order to extend the time series for modeling applications. To explain the functional behavior of the seasonal EVI curves, a two-stage multiple regression fitting procedure within a semi-parametric mixed effect (SPME) model framework was used. First, a linear mixed effect (LME) model was fitted to the EVI with climate indexes, crop and irrigation information as predictor variables. Second, Penalized B-splines were used to explain the behavior of the smooth residuals, which result from a smooth model fit to the smooth EVI data curve, in order to describe the uncertainty of the EVI curve. Individual models were fit within individual Major Land Resources Areas (MLRAs). Predicted seasonal EVI, derived from our regression equations, showed a strong agreement with the observed EVI and was able to capture the site by site and year by year variation in the EVI curve. Out-of-sample prediction produced excellent results for a majority of the sites, except for sites without clear seasonal patterns, which may have resulted from cloud contamination and/or snow cover. Therefore, given the appropriate climate, crop, and irrigation information, the proposed approach can be used to predict seasonal EVI curves for extending the time series into the past and future.

Bayesian Analysis of Semiparametric Mixed-Effects Models for Zero-Inflated Count Data

In recent years, zero-inflated count data models, such as zero-inflated Poisson (ZIP) models, are widely used as the count data with extra zeros are very common in many practical problems. In order to model the correlated count data which are either clustered or repeated and to assess the effects of continuous covariates or of time scales in a flexible way, a class of semiparametric mixed-effects models for zero-inflated count data is considered. In this article, we propose a fully Bayesian inference for such models based on a data augmentation scheme that reflects both random effects of covariates and mixture of zero-inflated distribution. A computational efficient MCMC method which combines the Gibbs sampler and M-H algorithm is implemented to obtain the estimate of the model parameters. Finally, a simulation study and a real example are used to illustrate the proposed methodologies.

Identifying significant covariates for anti‐HIV treatment response: Mechanism‐based differential equation models and empirical semiparametric regression models

In this paper, the mechanism-based ordinary differential equation (ODE) model and the flexible semiparametric regression model are employed to identify the significant covariates for antiretroviral response in AIDS clinical trials. We consider the treatment effect as a function of three factors (or covariates) including pharmacokinetics, drug adherence and susceptibility. Both clinical and simulated data examples are given to illustrate these two different kinds of modeling approaches. We found that the ODE model is more powerful to model the mechanism-based nonlinear relationship between treatment effects and virological response biomarkers. The ODE model is also better in identifying the significant factors for virological response, although it is slightly liberal and there is a trend to include more factors (or covariates) in the model. The semiparametric mixed-effects regression model is very flexible to fit the virological response data, but it is too liberal to identify correct factors for the virological response; sometimes it may miss the correct factors. The ODE model is also biologically justifiable and good for predictions and simulations for various biological scenarios. The limitations of the ODE models include the high cost of computation and the requirement of biological assumptions that sometimes may not be easy to validate. The methodologies reviewed in this paper are also generally applicable to studies of other viruses such as hepatitis B virus or hepatitis C virus.

Semiparametric Inference in Generalized Mixed Effects Models

Summary The paper presents a study of the generalized partially linear model including random effects in its linear part. We propose an estimator that combines likelihood approaches for mixed effects models, with kernel methods. Following the methodology of Härdle and co-workers, we introduce a test for the hypothesis of a parametric mixed effects model against the alternative of a semiparametric mixed effects model. The critical values are estimated by using a bootstrap procedure. The asymptotic theory for the methods is provided, as are the results of a simulation study. These verify the feasibility and the excellent behaviour of the methods for samples of even moderate size. The usefulness of the methodology is illustrated with an application in which the objective is to estimate forest coverage in Galicia, Spain.

Semiparametric Inference in Generalized Mixed Effects Models

The paper presents a study of the generalized partially linear model including random effects in its linear part. We propose an estimator that combines like-lihood approaches for mixed effects models, with kernel methods. Following the methodology of Hardle et al (1998), we introduce a test for the hypothesis of a parametric mixed effects model against the alternative of a semiparametric mixed effects model. The critical values are estimated using a bootstrap procedure. The asymptotic theory for the methods is provided, as are the results of a simulation study. These verify the feasibility and the excellent behavior of the methods for samples of even moderate size. The usefulness of the methodology is illustrated with an application in which the objective is to estimate forest coverage in Galicia, Spain.