Semiparametric Mixed Model Research Articles

A Bayesian semiparametric mixed effects proportional hazards model for clustered partly interval-censored data

Clustered partly interval-censored survival data naturally arise from many medical and epidemiological studies. We propose a Bayesian semiparametric approach for fitting a mixed effects proportional hazards (PH) model to clustered partly interval-censored data. The proposed method allows for not only a random intercept as most frailty models do for clustered survival data, but also random effects of covariates. We assume a normal prior for each random intercept/random effect, seeing the instability of a gamma prior for a frailty in this situation. Simulation studies with data generated from both mixed effects PH model and mixed effects accelerated failure times model are conducted, to evaluate the performance of the proposed method and compare it with the three methods currently available in the literature. The application of the proposed approach is illustrated through analyzing the progression-free survival data derived from a phase III metastatic colorectal cancer clinical trial.

Explaining transmission rate variations and forecasting epidemic spread in multiple regions with a semiparametric mixed effects SIR model.

The transmission rate is a central parameter in mathematical models of infectious disease. Its pivotal role in outbreak dynamics makes estimating the current transmission rate and uncovering its dependence on relevant covariates a core challenge in epidemiological research as well as public health policy evaluation. Here, we develop a method for flexibly inferring a time-varying transmission rate parameter, modeled as a function of covariates and a smooth Gaussian process (GP). The transmission rate model is further embedded in a hierarchy to allow information borrowing across parallel streams of regional incidence data. Crucially, the method makes use of optional vaccination data as a first step toward modeling of endemic infectious diseases. Computational techniques borrowed from the Bayesian spatial analysis literature enable fast and reliable posterior computation. Simulation studies reveal that the method recovers true covariate effects at nominal coverage levels. We analyze data from the COVID-19 pandemic and validate forecast intervals on held-out data. User-friendly software is provided to enable practitioners to easily deploy the method in public healthresearch.

Estimating subject-specific hazard functions

Abstract The central idea of this paper is to compare mean responses of several subjects in the presence of censoring and subject-specific variation. We develop a semiparametric mixed model for fitting subject-specific hazard curves to a set of censored failure times. A spline-based model and a mixed effects framework for smoothing are used. Efficient estimators of fixed parameters and predictors of the random components are derived and their asymptotic properties studied. This is a generalization of the method proposed by [Cai, T., Hyndman, R. J., & Wand, M. P. (2002). Mixed model-based hazard estimation. Journal of Computational and Graphical Statistics, 11(4), 784–798. https://doi.org/10.1198/106186002862] to incorporate additional subject-specific variation of the hazard function. The results are illustrated using two motivating examples.

Extending multivariate Student's- semiparametric mixed models for longitudinal data with censored responses and heavy tails.

This article extends the semiparametric mixed model for longitudinal censored data with Gaussian errors by considering the Student's -distribution. This model allows us to consider a flexible, functional dependence of an outcome variable over the covariates using nonparametric regression. Moreover, the proposed model takes into account the correlation between observations by using random effects. Penalized likelihood equations are applied to derive the maximum likelihood estimates that appear to be robust against outlying observations with respect to the Mahalanobis distance. We estimate nonparametric functions using smoothing splines under an EM-type algorithm framework. Finally, the proposed approach's performance is evaluated through extensive simulation studies and an application to two datasets from acquired immunodeficiency syndrome clinical trials.

A semi-parametric mixed model for short-term projection of daily COVID-19 incidence in Canada

During a pandemic, data are very “noisy” with enormous amounts of local variation in daily counts, compared with any rapid changes in trend. Accurately characterizing the trends and reliable predictions on future trajectories are important for planning and public situation awareness. We describe a semi-parametric statistical model that is used for short-term predictions of daily counts of cases and deaths due to COVID-19 in Canada, which are routinely disseminated to the public by Public Health Agency of Canada. The main focus of the paper is the presentation of the model. Performance indicators of our model are defined and then evaluated through extensive sensitivity analyses. We also compare our model with other commonly used models such as generalizations of logistic models for similar purposes. The proposed model is shown to describe the historical trend very well with excellent ability to predict the short-term trajectory.

Irregular identification of structural models with nonparametric unobserved heterogeneity

One of the most important empirical findings in microeconometrics is the pervasiveness of heterogeneity in economic behavior (cf. Heckman, 2001). This paper shows that cumulative distribution functions and quantiles of the nonparametric unobserved heterogeneity have an infinite efficiency bound in many structural economic models of interest. The paper presents general and precise conditions to prove such results. The usefulness of the theory is demonstrated with several relevant examples in economics, including, among others, the proportion of individuals with severe long term unemployment duration, Average Marginal Effects (AME) in a correlated random coefficient model without monotonicity, and the distribution and quantiles of random coefficients in linear, binary and the popular semiparametric Mixed Logit model.

Modelling trends of CD4 counts for patients on antiretroviral therapy (ART): a comprehensive health care clinic in Nairobi, Kenya

BackgroundIn resource-limited settings, changes in CD4 counts constitute an important component in patient monitoring and evaluation of treatment response as these patients do not have access to routine viral load testing. In this study, we quantified trends on CD4 counts in patients on highly active antiretroviral therapy (HAART) in a comprehensive health care clinic in Kenya between 2011 and 2017. We evaluated the rate of change in CD4 cell count in response to antiretroviral treatment. We further assessed factors that influenced time to treatment change focusing on baseline characteristics of the patients and different initial drug regimens used. This was a retrospective study involving 432 naïve HIV patients that had at least two CD4 count measurements for the period. The relationship between CD4 cell count and time was modeled using a semi parametric mixed effects model while the Cox proportional hazards model was used to assess factors associated with the first regimen change.ResultsMajority of the patients were females and the average CD4 count at start of treatment was 362.1 cell/mm^3. The CD4 count measurements increased nonlinearly over time and these trends were similar regardless of the treatment regimen administered to the patients. The change of logarithm CD4 cell count rises fast for in the first 450 days of antiretroviral initiation. The average time to first regimen change was 2142 days. Tenoforvir (TDF) based regimens had a lower drug substitution(aHR 0.2682, 95% CI:0.08263- 0.8706) compared to Zidovudine(AZT).ConclusionThe backbone used was found to be associated with regimen changes among the patients with fewer switches being observed, with the use of TDF when compared to AZT. There was however no significant difference between TDF and AZT in terms of the rate of change in logarithm CD4 count over time.

Regression analysis of intelligent education based on linear mixed effect model

In order to explore the regression effect of the intelligent education model, based on the linear mixed effect model, this paper constructs a regression analysis model based on the linear mixed effect model and studies the estimation algorithm of the linear mixed effect model under massive data. Moreover, this paper combines the three-step estimation method with the divide-and-conquer algorithm to propose a three-stage estimation algorithm. In addition, this paper studies the estimation algorithm of the semi-parametric mixed effect model under massive data, and combines the local linear least square method with the divide and conquer algorithm to obtain a new estimation algorithm. At the same time, this article extends the estimation algorithm to the semi-parametric mixed effect model under massive data to obtain a new estimation algorithm, so that the semi-parametric mixed model is also applicable under massive data. Finally, this paper constructs an intelligent education regression analysis model with data mining function based on actual needs, and designs experiments to verify the performance of the model. The research results show that the model constructed in this paper has a certain effect.

Multivariate t semiparametric mixed-effects model for longitudinal data with multiple characteristics

Semiparametric mixed-effects models (SMM) have received increasing attention in recent years because of the greater flexibility in analysing longitudinal trajectories. However, the normality assumption of SMM may be unrealistic when outliers occur in the data. This paper presents a semiparametric extension of the multivariate t linear mixed-effects model (MtLMM), called the multivariate t semiparametric mixed model (MtSMM). To be specific, the MtSMM incorporates a parametric linear function related to the fixed covariate effects and random effects which have a joint multivariate t distribution together with an arbitrary nonparametric smooth function to capture the unexpected patterns. A computationally analytical EM-based algorithm is developed for carrying out maximum likelihood estimation of the MtSMM. Simulation studies and a real example concerning the analysis of PBCseq data are used to investigate the empirical behaviour of the proposed methodology.

Cluster non-Gaussian functional data.

Gaussian distributions have been commonly assumed when clustering functional data. When the normality condition fails, biased results will follow. Additional challenges occur as the number of the clusters is often unknown a priori. This paper focuses on clustering non-Gaussian functional data without the prior information of the number of clusters. We introduce a semiparametric mixed normal transformation model to accommodate non-Gaussian functional data, and propose a penalized approach to simultaneously estimate the parameters, transformation function, and the number of clusters. The estimators are shown to be consistent and asymptotically normal. The practical utility of the methods is confirmed via simulations as well as an application of the analysis of Alzheimer's disease study. The proposed method yields much less classification error than the existing methods. Data used in preparation of this paper were obtained from the Alzheimer's Disease Neuroimaging Initiativedatabase.

Random forests for high-dimensional longitudinal data.

Random forests are one of the state-of-the-art supervised machine learning methods and achieve good performance in high-dimensional settings where p, the number of predictors, is much larger than n, the number of observations. Repeated measurements provide, in general, additional information, hence they are worth accounted especially when analyzing high-dimensional data. Tree-based methods have already been adapted to clustered and longitudinal data by using a semi-parametric mixed effects model, in which the non-parametric part is estimated using regression trees or random forests. We propose a general approach of random forests for high-dimensional longitudinal data. It includes a flexible stochastic model which allows the covariance structure to vary over time. Furthermore, we introduce a new method which takes intra-individual covariance into consideration to build random forests. Through simulation experiments, we then study the behavior of different estimation methods, especially in the context of high-dimensional data. Finally, the proposed method has been applied to an HIV vaccine trial including 17 HIV-infected patients with 10 repeated measurements of 20,000 gene transcripts and blood concentration of human immunodeficiency virus RNA. The approach selected 21 gene transcripts for which the association with HIV viral load was fully relevant and consistent with results observed during primary infection.

TESTING A PARAMETRIC TRANSFORMATION MODEL VERSUS A NONPARAMETRIC ALTERNATIVE

Despite an abundance of semiparametric estimators of the transformation model, no procedure has been proposed yet to test the hypothesis that the transformation function belongs to a finite-dimensional parametric family against a nonparametric alternative. In this article, we introduce a bootstrap test based on integrated squared distance between a nonparametric estimator and a parametric null. As a special case, our procedure can be used to test the parametric specification of the integrated baseline hazard in a semiparametric mixed proportional hazard model. We investigate the finite sample performance of our test in a Monte Carlo study. Finally, we apply the proposed test to Kennan’s strike durations data.

Kernel estimation in semiparametric mixed effect longitudinal modeling

HIV damages the immune system by targeting the CD4 cells. Hence CD4 count data modeling is important in the analysis of HIV infection. This paper considers a semiparametric mixed effects model for the analysis of CD4 longitudinal data. The model is a natural extension to the linear mixed and semiparametric models that uses parametric linear model to present the covariate effects and an arbitrary nonparametric smooth function to model the time effect and account for the within subject correlation using random effects. We approximate the nonparametric function by the profile kernel method, and make use of the weighted least squares to estimate the regression coefficients. Under some regularity conditions, the asymptotic normality of the resulting estimator is established and the performance is compared with the backfitting method. Although, two estimators share the same asymptotic variance matrix for independent data, it is shown that, backfitting often produces larger bias and variance than the profile-kernel method, asymptotically. Consequently, the use of backfitting method is no longer advised in semiparametric mixed effect longitudinal model. For practical implementation and also improve efficiency, the estimation of the covariance function is accomplished using an iterative algorithm. Performance of the proposed methods are compared through a simulation study and the analysis of CD4 data.

Analysis of generalized semiparametric mixed varying-coefficients models for longitudinal data.

The generalized semiparametric mixed varying-coefficient effects model for longitudinal data can accommodate a variety of link functions and flexibly model different types of covariate effects, including time-constant, time-varying, and covariate-varying effects. The time-varying effects are unspecified functions of time and the covariate-varying effects are nonparametric functions of a possibly time-dependent exposure variable. A semiparametric estimation procedure is developed that uses local linear smoothing and profile weighted least squares, which requires smoothing in the two different and yet connected domains of time and the time-dependent exposure variable. The asymptotic properties of the estimators of both nonparametric and parametric effects are investigated. In addition, hypothesis testing procedures are developed to examine the covariate effects. The finite-sample properties of the proposed estimators and testing procedures are examined through simulations, indicating satisfactory performances. The proposed methods are applied to analyze the ACTG 244 clinical trial to investigate the effects of antiretroviral treatment switching in HIV-infected patients before and after developing the T215Y antiretroviral drug resistance mutation.

Semiparametric Mixed Effects Models for Unsupervised Classification of Italian Schools

Summary The main purpose of the paper is to improve research on school effectiveness by applying a new strategy for uncovering subpopulations of schools that differ in terms of distribution of student outcomes. We propose a semiparametric mixed effects model with an expectation–maximization algorithm to estimate its parameters and we apply it to the Italian Institute for the Educational Evaluation of Instruction and Training data of 2013–2014 as a tool for the identification of latent subpopulations of schools. The semiparametric assumption provides the random effects of the mixed effects model to be distributed according to a discrete distribution with an (a priori) unknown number of support points. This modelling induces an automatic clustering of schools (the higher level of hierarchy), where schools within the same cluster share the same random effects. The latent subpopulations of schools identified may then be exploited through the use of multinomial models that include school level features. The novelties introduced by this paper are twofold: first, the semiparametric expectation–maximization algorithm is an innovative method that could be used in many classification problems; second, its application to education data represents a new approach to study school effectiveness.

A semi-parametric mixed models for longitudinally measured fasting blood sugar level of adult diabetic patients

BackgroundAt the diabetic clinic of Jimma University Specialized Hospital, health professionals provide regular follow-up to help people with diabetes live long and relatively healthy lives. Based on patient condition, they also provide interventions in the form of counselling to promote a healthy diet and physical activity and prescribing medicines. The main purpose of this study is to estimate the rate of change of fasting blood sugar (FBS) profile experienced by patients over time. The change may help to assess the effectiveness of interventions taken by the clinic to regulate FBS level, where rates of change close to zero over time may indicate the interventions are good regulating the level.MethodsIn the analysis of longitudinal data, the mean profile is often estimated by parametric linear mixed effects model. However, the individual and mean profile plots of FBS level for diabetic patients are nonlinear and imposing parametric models may be too restrictive and yield unsatisfactory results. We propose a semi-parametric mixed model, in particular using spline smoothing to efficiently analyze a longitudinal measured fasting blood sugar level of adult diabetic patients accounting for correlation between observations through random effects.ResultsThe semi-parametric mixed models had better fit than the linear mixed models for various variance structures of subject-specific random effects. The study revealed that the rate of change in FBS level in diabetic patients, due to the clinic interventions, does not continue as a steady pace but changes with time and weight of patients.ConclusionsThe proposed method can help a physician in clinical monitoring of diabetic patients and to assess the effect of intervention packages, such as healthy diet, physical activity and prescribed medicines, because individualized curve may be obtained to follow patient-specific FBS level trends.

A Joint Modeling Approach for Longitudinal Data with Informative Observation Times and a Terminal Event

In this article, we propose a new joint modeling approach for the analysis of longitudinal data with informative observation times and a dependent terminal event. We specify a semiparametric mixed effects model for the longitudinal process, a proportional rate frailty model for the observation process, and a proportional hazards frailty model for the terminal event. The association among the three related processes is modeled via two latent variables. Estimating equation approaches are developed for parameter estimation, and the asymptotic properties of the proposed estimators are established. The finite sample performance of the proposed estimators is examined through simulation studies, and an application to a medical cost study of chronic heart failure patients is illustrated.

Robust probabilistic classification applicable to irregularly sampled functional data

A robust probabilistic classifier for functional data is developed to predict class membership based on functional input measurements and to provide a reliable probability estimate for class membership. The method combines a Bayes classifier and semi-parametric mixed effects model with robust tuning parameter to make the method robust to outlying curves, and to improve the accuracy of the risk or uncertainty estimates, which is crucial in medical diagnostic applications. The approach applies to functional data with varying ranges and irregular sampling without making parametric assumptions on the within-curve covariance. Simulation studies evaluate the proposed method and competitors in terms of sensitivity to heavy tailed functional distributions and outlying curves. Classification performance is evaluated by both error rate and logloss, the latter of which imposes heavier penalties on highly confident errors than on less confident errors. Run-time experiments on the R implementation indicate that the proposed method scales well computationally. Illustrative applications include data from quantitative ultrasound analysis and phoneme recognition.

Geographical variation of overweight, obesity and related risk factors: Findings from the European Health Examination Survey in Luxembourg, 2013-2015.

The analyses of geographic variations in the prevalence of major chronic conditions, such as overweight and obesity, are an important public health tool to identify “hot spots” and inform allocation of funding for policy and health promotion campaigns, yet rarely performed. Here we aimed at exploring, for the first time in Luxembourg, potential geographic patterns in overweight/obesity prevalence in the country, adjusted for several demographic, socioeconomic, behavioural and health status characteristics. Data came from 720 men and 764 women, 25–64 years old, who participated in the European Health Examination Survey in Luxembourg (2013–2015). To investigate the geographical variation, geo-additive semi-parametric mixed model and Bayesian modelisations based on Markov Chain Monte Carlo techniques for inference were performed. Large disparities in the prevalence of overweight and obesity were found between municipalities, with the highest rates of obesity found in 3 municipalities located in the South-West of the country. Bayesian approach also underlined a nonlinear effect of age on overweight and obesity in both genders (significant in men) and highlighted the following risk factors: 1. country of birth for overweight in men born in a non-European country (Posterior Odds Ratio (POR): 3.24 [1.61–8.69]) and women born in Portugal (POR: 2.44 [1.25–4.43]), 2. low educational level (secondary or below) for overweight (POR: 1.66 (1.06–2.72)] and obesity (POR:2.09 [1.05–3.65]) in men, 3. single marital status for obesity in women (POR: 2.20 [1.24–3.91]), 4.fair (men: POR: 3.19 [1.58–6.79], women: POR: 2.24 [1.33–3.73]) to very bad health perception (men: POR: 15.01 [2.16–98.09]) for obesity, 5. sleeping more than 6 hours for obesity in unemployed men (POR: 3.66 [2.02–8.03]). Protective factors highlighted were: 1. single marital status against overweight (POR: [0.60 (0.38–0.96)]) and obesity (POR: 0.39 [0.16–0.84]) in men, 2. the fact to be widowed against overweight in women (POR: [0.30 (0.07–0.86)], as well as a non European country of birth (POR: 0.49 [0.19–0.98]), tertiary level of education (POR: 0.34 [0.18–0.64]), moderate alcohol consumption (POR: 0.54 [0.36–0.90]) and aerobic physical activity practice (POR: 0.44 [0.27–0.77]) against obesity in women. A double burden of environmental exposure due to historic mining and industrial activities and past economic vulnaribility in the South-West of the country may have participated to the higher prevalence of obesity found in this region. Other demographic, socioeconomic, behavioural and health status covariates could have been involved as well.

HIV EPIDEMIC HETEROGENEITY IN ZIMBABWE: EVIDENCE FROM SUCCESSIVE DEMOGRAPHIC AND HEALTH SURVEYS

Zimbabwe has one of the worst HIV epidemics in the world. This study investigated data from two successive Zimbabwe Demographic and Health Surveys (ZDHS) conducted in 2005-06 and 2010-11. A random representative sample of 30,000 men aged 15-59 and women aged 15-49 was selected from the two surveys. The HIV prevalence was mapped with a flexible, coherent regression framework using a geo-additive semi-parametric mixed model. HIV indicator prevalence maps were constructed at the regional level, and at the administrative level relevant for policy design, planning and decision-making. Substantial regional variation was found, not only in the burden of HIV, but also in its risk factors. The results suggest that responses/policies should vary at the regional level to ensure that the often diverse needs of populations across a country are met and incorporated into planning the HIV response. The use of geographically referenced data in two successive ZDHS provides crucial new insights into the spatial characteristics of the HIV epidemic in Zimbabwe. In particular, it highlights the HIV heterogeneity across Zimbabwe, with substantial regional variation, not only in the burden of HIV, but also in its risk factors.