Nonparametric Mixed-effects Research Articles

A NONPARAMETRIC MIXED-EFFECTS MIXTURE MODEL FOR PATTERNS OF CLINICAL MEASUREMENTS ASSOCIATED WITH COVID-19.

Some patients with COVID-19 show changes in signs and symptoms such as temperature and oxygen saturation days before being positively tested for SARS-CoV-2, while others remain asymptomatic. It is important to identify these subgroups and to understand what biological and clinical predictors are related to these subgroups. This information will provide insights into how the immune system may respond differently to infection and can further be used to identify infected individuals. We propose a flexible nonparametric mixed-effects mixture model that identifies risk factors and classifies patients with biological changes. We model the latent probability of biological changes using a logistic regression model and trajectories in the latent groups using smoothing splines. We developed an EM algorithm to maximize the penalized likelihood for estimating all parameters and mean functions. We evaluate our methods by simulations and apply the proposed model to investigate changes in temperature in a cohort of COVID-19-infected hemodialysis patients.

Functional non-parametric mixed effects models for cytotoxicity assessment and clustering

A multitude of natural and synthetic chemicals are present in our environment.Through the study of a compound’s cytotoxicity, researchers can carefully set regulations regarding how much of a certain chemical in the ambient environment is tolerable. In the past, research has focused on point measurements such as the LD50. Instead, we consider entire time-dependent cellular response curves through the application of functional mixed effects models. We identify differences in such curves corresponding to the chemical’s mode of action—i.e. how the compound attacks human cells. Through such analysis, we identify curve features to be used for cluster analysis via application of both k-means and self organizing maps. The data is analyzed by making use of functional principal components as a data driven basis and separately by considering B-splines for identifying local-time features. Our analysis can be used to drastically speed up future cytotoxicity research.

MO920: SARS-COV-2 Neutralizing Antibody Response to Booster Vaccination in Patients on Hemodialysis

BACKGROUND AND AIMSSARS-CoV-2 antibody titers after two doses of vaccination decrease over time. Hemodialysis patients are especially vulnerable to COVID-19 as they are immunocompromised, putting them at higher risk of infection and poorer response to vaccines. Therefore, administrating the third dose (‘booster’) in these patients is key to reduce COVID-19 infections and prevent severe illness. Dialysis patients were among the first group of patients who received booster vaccinations. To study the humoral response to the third injection in this group, we collected serum from 33 patients on hemodialysis and measured neutralizing antibody titers against SARS-CoV-2 before and after their booster doses.METHODPatients were recruited from a dialysis center in New York City, NY from June to September 2021. Data on COVID-19 vaccination and demographics were collected upon enrollment. Blood samples were taken after enrollment. SARS-CoV-2 neutralization antibodies were assayed using the GenScript SARS-CoV-2 Surrogate Virus Neutralization Test Kit (Cat#L00847-A). Corresponding neutralizing antibody titers are presented as Unit/mL (U/mL).RESULTSA total of 33 in-center hemodialysis patients who had received three doses of vaccination were studied. Patients had a mean age of 61 years, 23 (70%) were male. Out of these, 31 (94%) patients received three doses of mRNA-1273 (Moderna), and two patients received the BNT162b2 (Pfizer BioNTech) vaccine. A total of 138 serum samples were analyzed (ranging from 156 days before to 85 days after the booster). Figure 1 shows the antibody titer distribution of all samples in these 33 patients. Each color indicates an individual patient. Each patient has up to 12 data points before and after the booster. The mean neutralizing antibody titers of all 48 data points pre-booster is 29.291 U/mL (range: 228–188.600). Seven days post-booster, the mean neutralizing antibody titer is 73.088 U/mL (range: 12.401–254.504). Mean titer is 169.826 U/mL (range: 17.830–375.046) at 14–28 days post-booster. After the peak time, we observe a decline of the titers. At 72–85 days, the mean titer is 72.179 (range: 33.702–204.382).We fitted a nonparametric mixed effects model with an adaptive spline and a random intercept for each subject to neutralizing antibody titers on the log10 scale. The estimate of the mean trajectory and its 95% confidence interval are shown in Fig. 2. The estimated peak time is 18.2 days with a 95% confidence interval (0–27.7).CONCLUSIONOur results suggest that hemodialysis patients have a strong humoral response to booster vaccination. Neutralizing antibody titers peak at 18 days post-booster and wane to an average of 42% of peak value after 10–12 weeks.FIGURE 1:Time-course of neutralizing antibody titers before and after booster vaccination. The colors identify individual hemodialysis patients.FIGURE 2:A nonparametric mixed effects model with an adaptive spline and a random intercept for each subject to neutralizing antibody titers. The red line indicates the average titer, and the gray area indicates the 95% confidence interval. The circles are means across all data points.

Bayesian nonparametric multivariate spatial mixture mixed effects models with application to American Community Survey special tabulations

Leveraging multivariate spatial dependence to improve the precision of estimates using American Community Survey data and other sample survey data has been a topic of recent interest among data users and federal statistical agencies. One strategy is to use a multivariate spatial mixed effects model with a Gaussian observation model and latent Gaussian process model. In practice, this works well for a wide range of tabulations. Nevertheless, in situations in which the data exhibit heterogeneity within or across geographies, and/or there is sparsity in the data, the Gaussian assumptions may be problematic and lead to underperformance. To remedy these situations, we propose a multivariate hierarchical Bayesian nonparametric mixed effects spatial mixture model to increase model flexibility. The number of clusters is chosen automatically in a data-driven manner. The effectiveness of our approach is demonstrated through a simulation study and motivating application of special tabulations for American Community Survey data.

Bayesian Change-Point Joint Models for Multivariate Longitudinal and Time-to-Event Data

Joint modeling of longitudinal and survival data is an active area of statistical research that has received much attention recently. Although it is a common practice to analyze complex longitudinal data using nonlinear mixed-effects (NLME) or nonparametric mixed-effects (NPME) models in literature, the following issues may standout: (i) In practice, the profile of each subject’s longitudinal response may follow a “broken-stick” like trajectory, indicating multiple phases of increase and/or decline in response trajectory. Such multiple phases (with random change-points) may be an important indicator to help quantify treatment effect and clinical diagnosis of a disease. To estimate random change-points, NLME or NPME models become a challenge. (ii) Many studies are often to collect data of multivariate longitudinal variables which may be significantly correlated, ignoring their correlation may lead to biased estimate and reduce efficiency. Moreover, the time-to-event may be dependent of the multivariate longitudinal measures and it is of importance to explore their association. (iii) Missing observations in the longitudinal responses are often encountered. The missing data are likely to be informative (nonignorable) and ignoring this phenomenon may result in inaccurate statistical inference. In this article, under a Bayesian framework we consider a piecewise joint model for multivariate longitudinal and time-to-event data to accurately estimate change rates of longitudinal trajectory patterns and timing of change-point which may be critical indicators to quantify the effect of longitudinal profile on the risk of an event. The proposed models and method are applied to analyze a longitudinal dataset arising from a diabetes study. Simulation studies are conducted to assess the performance of the proposed models under various scenarios.

A Bayesian non-parametric mixed-effects model of microbial growth curves.

Substantive changes in gene expression, metabolism, and the proteome are manifested in overall changes in microbial population growth. Quantifying how microbes grow is therefore fundamental to areas such as genetics, bioengineering, and food safety. Traditional parametric growth curve models capture the population growth behavior through a set of summarizing parameters. However, estimation of these parameters from data is confounded by random effects such as experimental variability, batch effects or differences in experimental material. A systematic statistical method to identify and correct for such confounding effects in population growth data is not currently available. Further, our previous work has demonstrated that parametric models are insufficient to explain and predict microbial response under non-standard growth conditions. Here we develop a hierarchical Bayesian non-parametric model of population growth that identifies the latent growth behavior and response to perturbation, while simultaneously correcting for random effects in the data. This model enables more accurate estimates of the biological effect of interest, while better accounting for the uncertainty due to technical variation. Additionally, modeling hierarchical variation provides estimates of the relative impact of various confounding effects on measured population growth.

Changes in the oral health-related quality of life in adult patients with intellectual disabilities after dental treatment under general anesthesia.

This study aimed to assess self- and proxy-rated changes in the oral health-related quality of life (OHRQoL) in adult patients with intellectual disabilities after dental treatment in general anesthesia. The OHRQoL in 52 adult patients with intellectual and developmental disabilities was assessed prior to dental treatment in general anesthesia (t0), 2 to 3 (t1) and 12weeks (t2) postoperatively. Therefore, patients and primary cargivers were surveyed using either the 5-item short form of the Oral Health Impact Profile translated into easy language (OHIP-G5-easy, self-rating, n = 27) or the 14-item short form of the Oral Health Impact Profile (OHIP-G14, proxy-rating, n = 51), respectively. OHIP-G5-easy and OHIP-G14 summary scores were statistically analyzed with non-parametric mixed effects models and spearman correlation (p < 0.05). Additionally, the effect of demographic, anamnestic, oral health and treatment factors on QHRQoL or on changes of OHRQoL were analyzed using univariate and multivariate ordinal logistic regressions (p < 0.05). Self- (t0: 5.8 ± 4.6, t1: 4.3 ± 5.9, t2: 2.0 ± 3.9) and proxy-ratings (t0: 18.8 ± 11.6, t1: 10.1 ± 11.2, t2: 2.7 ± 5.3) revealed a significant improvement of OHRQoL after dental treatment in general anesthesia. Data showed a moderate correlation (p < 0.001, rSp = 0.43). OHRQoL at baseline was affected by the etiology of cognitive impairment and by the periodontal status (OHIP-G14). Improvement of OHRQoL was associated with the etiology of cognitive impairment (OHIP-G14) and the extent of dental treatment (OHIP-G5-easy). Self- and proxy-ratings revealed a significant improvement of OHRQoL in patients with intellectual disabilities after dental treatment in general anesthesia. Assessment of OHRQoL promotes patient-centred care of adults with intellectual disabilities.

Maternal Weight after Childbirth versus Aging-Related Weight Changes

BackgroundPregnancy weight gain is believed to contribute to female overweight and obesity. However, most studies do not account for the changes in body weight expected to occur as women age. We examined the long-term weight trajectory of childbearing women relative to weight progression that could be expected in the absence of pregnancy. MethodsFrom the hospital records of 32,187 women with two births in Wisconsin during 2006 to 2013, we extracted the maternal weight at pregravid, delivery, and subsequent pregravid. We predicted the corresponding aging-progressed weights using a weight-for-age equation adjusted for sociodemographic variables. Nonparametric mixed effects models estimated the average maternal weight trajectory and the corresponding aging-related progression through 5 years after birth. ResultsThe estimated aging-related progression predicted a gradual annual weight increase of 1.94 pounds (95% confidence interval 1.90–1.98), from 152.79 pounds at pregravid to 163.76 pounds by 5 years after birth. Actual maternal weight followed a sinusoidal pattern: increasing during gestation, decreasing during the first postbirth year, converging with the aging-related progression during the second postbirth year, and then increasing at 2.89 pounds (95% confidence interval 2.23–3.55) annually and diverging upward from the aging-related progression to 168.03 pounds by 5 years after birth. ConclusionPregnancy weight gain did not contribute to the aging-related trend, but lifestyle changes of parenthood may later exacerbate the long-term trend.

Piecewise Mixture Modeling for Longitudinal Virologic Data With Heterogeneity, Nonnormality, and Missingness

ABSTRACTIt is a common practice to analyze complex longitudinal data that arise frequently in medical studies that use nonlinear mixed-effects (NLME) or nonparametric mixed-effects (NPME) models. However, the following issues may stand out in AIDS longitudinal data analysis: (i) In clinical practice, the profile of each subject’s virologic response may follow a “broken stick” like trajectory, indicating multiple phases of decline and increase in response. Such multiple phases (with change-points) may be an important indicator to help quantify treatment effect and improve management of patient care. To estimate change-points, NLME or NPME models become a challenge due to complicated structures of model formulations. (ii) A homogeneous population assumption in models may be unrealistically obscuring important features of between- and within-subject variations. (iii) Normality assumption for model errors may not always give robust and reliable results, in particular, if the data exhibit nonnormality. And (iv) the responses may be missing and the missingness may be nonignorable. When statistical inference is carried out in such settings, it is important to account for the effects of these data features; otherwise, erroneous or even misleading results may be produced. Inferential procedures can be complicated dramatically when data with heterogeneous, nonnormal (skewed) and missing characteristics are observed in conjunction with change-points as unknown parameters into models. There has been relatively little study concerning all these features simultaneously. There is a need to fill up this gap as longitudinal data do often have these features. In this article, our objectives are to study simultaneous impact of these data features by developing Bayesian modeling approach-based finite mixture of hierarchical change-point (FMHC) models with skew distributions, allowing estimates of both model parameters and class membership probabilities at population and individual levels. An HIV/AIDS clinical data example is analyzed to demonstrate the proposed methodologies, and to compare various scenarios-based potential models. Supplementary materials for this article are available online.

Efficient estimation of variance components in nonparametric mixed-effects models with large samples

Linear mixed-effects (LME) regression models are a popular approach for analyzing correlated data. Nonparametric extensions of the LME regression model have been proposed, but the heavy computation...

Bayesian nonparametric mixed-effects joint model for longitudinal-competing risks data analysis in presence of multiple data features.

Recently, the joint analysis of longitudinal and survival data has been an active research area. Most joint models focus on survival data with only one type of failure. The research on joint modeling of longitudinal and competing risks survival data is sparse. Even so, many joint models for this type of data assume parametric function forms for both longitudinal and survival sub-models, thus limits their use. Further, the common data features that are usually observed in practice, such as asymmetric distribution and missingness in response, measurement errors in covariate, need to be taken into account for reliable parameter estimation. The statistical inference is complicated when all these factors are considered simultaneously. In the article, driven by a motivating example, we assume nonparametric function forms for the varying coefficients in both longitudinal and competing risks survival sub-models. We propose a Bayesian nonparametric mixed-effects joint model for the analysis of longitudinal-competing risks data with asymmetry, missingness, and measurement errors. Simulation studies are conducted to assess the performance of the proposed method. We apply the proposed method to an AIDS dataset and compare a few candidate models under various settings. Some interesting results are reported.

A refined parameter estimating approach for HIV dynamic model

HIV dynamic models, a set of ordinary differential equations (ODEs), have provided new understanding of the pathogenesis of HIV infection and the treatment effects of antiviral therapies. However, to estimate parameters for ODEs is very challenging due to the complexity of this nonlinear system. In this article, we propose a comprehensive procedure to deal with this issue. In the proposed procedure, a series of cutting-edge statistical methods and techniques are employed, including nonparametric mixed-effects smoothing-based methods for ODE models and stochastic approximation expectation–maximization (EM) approach for mixed-effects ODE models. A simulation study is performed to validate the proposed approach. An application example from a real HIV clinical trial study is used to illustrate the usefulness of the proposed method.

Segmental modeling of changing immunologic response for CD4 data with skewness, missingness and dropout

In clinical practice, the profile of each subject's CD4 response from a longitudinal study may follow a ‘broken stick’ like trajectory, indicating multiple phases of increase and/or decline in response. Such multiple phases (changepoints) may be important indicators to help quantify treatment effect and improve management of patient care. Although it is a common practice to analyze complex AIDS longitudinal data using nonlinear mixed-effects (NLME) or nonparametric mixed-effects (NPME) models in the literature, NLME or NPME models become a challenge to estimate changepoint due to complicated structures of model formulations. In this paper, we propose a changepoint mixed-effects model with random subject-specific parameters, including the changepoint for the analysis of longitudinal CD4 cell counts for HIV infected subjects following highly active antiretroviral treatment. The longitudinal CD4 data in this study may exhibit departures from symmetry, may encounter missing observations due to various reasons, which are likely to be non-ignorable in the sense that missingness may be related to the missing values, and may be censored at the time of the subject going off study-treatment, which is a potentially informative dropout mechanism. Inferential procedures can be complicated dramatically when longitudinal CD4 data with asymmetry (skewness), incompleteness and informative dropout are observed in conjunction with an unknown changepoint. Our objective is to address the simultaneous impact of skewness, missingness and informative censoring by jointly modeling the CD4 response and dropout time processes under a Bayesian framework. The method is illustrated using a real AIDS data set to compare potential models with various scenarios, and some interested results are presented.

Posterior propriety in nonparametric mixed effects model

It is well known that spline smoothing estimator relates to the Bayesian estimate under partially informative normal prior. In this paper, we derive the conditions for the propriety of the posterior in the nonparametric mixed effects model under this class of partially informative normal prior for fixed effect with inverse gamma priors on the variance components and hierarchical priors for covariance matrix of random effect, then we explore the Gibbs sampling procedure.

Comparison of Mixed-Effects Models for Skew-Normal Responses with an Application to AIDS Data: A Bayesian Approach

The potency of antiretroviral agents in AIDS clinical trials can be assessed on the basis of a viral response such as viral decay rate or change in viral load (number of HIV RNA copies in plasma). Linear, nonlinear, and nonparametric mixed-effects models have been proposed to estimate such parameters in viral dynamic models. However, there are two critical questions that stand out: whether these models achieve consistent estimates for viral decay rates, and which model is more appropriate for use in practice. Moreover, one often assumes that a model random error is normally distributed, but this assumption may be unrealistic, obscuring important features of within- and among-subject variations. In this article, we develop a skew-normal (SN) Bayesian linear mixed-effects (SN-BLME) model, an SN Bayesian nonlinear mixed-effects (SN-BNLME) model, and an SN Bayesian semiparametric nonlinear mixed-effects (SN-BSNLME) model that relax the normality assumption by considering model random error to have an SN distribution. We compare the performance of these SN models, and also compare their performance with the corresponding normal models. An AIDS dataset is used to test the proposed models and methods. It was found that there is a significant incongruity in the estimated viral decay rates. The results indicate that SN-BSNLME model is preferred to the other models, implying that an arbitrary data truncation is not necessary. The findings also suggest that it is important to assume a model with an SN distribution in order to achieve reasonable results when the data exhibit skewness.

Bayesian semiparametric mixture Tobit models with left censoring, skewness, and covariate measurement errors

Common problems to many longitudinal HIV/AIDS, cancer, vaccine, and environmental exposure studies are the presence of a lower limit of quantification of an outcome with skewness and time-varying covariates with measurement errors. There has been relatively little work published simultaneously dealing with these features of longitudinal data. In particular, left-censored data falling below a limit of detection may sometimes have a proportion larger than expected under a usually assumed log-normal distribution. In such cases, alternative models, which can account for a high proportion of censored data, should be considered. In this article, we present an extension of the Tobit model that incorporates a mixture of true undetectable observations and those values from a skew-normal distribution for an outcome with possible left censoring and skewness, and covariates with substantial measurement error. To quantify the covariate process, we offer a flexible nonparametric mixed-effects model within the Tobit framework. A Bayesian modeling approach is used to assess the simultaneous impact of left censoring, skewness, and measurement error in covariates on inference. The proposed methods are illustrated using real data from an AIDS clinical study. .

비모수와 준모수 혼합모형을 이용한 소지역 추정

Semiparametric and nonparametric small area estimations have been studied to overcome a large variance due to a small sample size allocated in a small area. In this study, we investigate semiparametric and nonparametric mixed effect small area estimators using penalized spline and kernel smoothing methods respectively and compare their performances using labor statistics.

Vertical Density Profile Monitoring Using Mixed-effects Model

Profile monitoring is a recent field of research in Statistical Process Control (SPC) literature, which is attracting the interests of many researchers. This approach is used where process data follow a profile and the stability of this functional relationship is checked over time. We consider nonparametric mixed effect models for functional data to model the profile. Then, multivariate control charting is applied to identify mean shifts or shape changes in the profile.A real case study dealing with density measurements along the particleboard thickness (usually referred to as Vertical Densit y Profile -VDP) is taken as reference throughout the paper. Performance of the nonparametric approach is computed for a set of out- of-control scenarios. Our main conclusion is that nonparametric methods represent a flexible and effective solution to complex profile monitoring.

Nonlinear nonparametric mixed-effects models for unsupervised classification

In this work we propose a novel EM method for the estimation of nonlinear nonparametric mixed-effects models, aimed at unsupervised classification. We perform simulation studies in order to evaluate the algorithm performance and we apply this new procedure to a real dataset.

Segmental modeling of viral load changes for HIV longitudinal data with skewness and detection limits

Although it is a common practice to analyze complex HIV longitudinal data using nonlinear mixed-effects or nonparametric mixed-effects models in literature, the following issues may standout. (i) In clinical practice, the profile of each subject's viral response may follow a 'broken-stick'-like trajectory, indicating multiple phases of decline and increase in response. Such multiple phases (change points) may be an important indicator to help quantify treatment effect and improve management of patient care. To estimate change points, nonlinear mixed-effects or nonparametric mixed-effects models become a challenge because of complicated structures of model formulations. (ii) The commonly assumed distribution for model random errors is normal, but this assumption may unrealistically obscure important features of subject variations. (iii) The response observations (viral load) may be subject to left censoring due to a limit of detection. Inferential procedures can be complicated dramatically when data with asymmetric (skewed) characteristics and left censoring are observed in conjunction with change points as unknown parameters into models. There is relatively little work concerning all these features simultaneously. This article proposes segmental mixed-effects models with skew distributions for the response process (with left censoring) under a Bayesian framework. A real data example is used to illustrate the proposed methods.