A Bayesian approach for mixed effects state-space models under skewness and heavy tails.

Human immunodeficiency virus (HIV) dynamics have been the focus of epidemiological and biostatistical research during the past decades to understand the progression of acquired immunodeficiency syndrome (AIDS) in the population. Although there are several approaches for modeling HIV dynamics, one of the most popular is based on Gaussian mixed-effects models because of its simplicity from the implementation and interpretation viewpoints. However, in some situations, Gaussian mixed-effects models cannot (a) capture serial correlation existing in longitudinal data, (b) deal with missing observations properly, and (c) accommodate skewness and heavy tails frequently presented in patients' profiles. For those cases, mixed-effects state-space models (MESSM) become a powerful tool for modeling correlated observations, including HIV dynamics, because of their flexibility in modeling the unobserved states and the observations in a simple way. Consequently, our proposal considers an MESSM where the observations' error distribution is a skew-t. This new approach is more flexible and can accommodate data sets exhibiting skewness and heavy tails. Under the Bayesian paradigm, an efficient Markov chain Monte Carlo algorithm is implemented. To evaluate the properties of the proposed models, we carried out some exciting simulation studies, including missing data in the generated data sets. Finally, we illustrate our approach with an application in the AIDS Clinical Trial Group Study 315 (ACTG-315) clinical trial data set.

Prostate Cancer Diagnosis in the Clinic Using an 8-Protein Biomarker Panel.

The inability to distinguish aggressive from indolent prostate cancer is a longstanding clinical problem. Prostate specific antigen (PSA) tests and digital rectal exams cannot differentiate these forms. Because only ∼10% of diagnosed prostate cancer cases are aggressive, existing practice often results in overtreatment including unnecessary surgeries that degrade patients' quality of life. Here, we describe a fast microfluidic immunoarray optimized to determine 8-proteins simultaneously in 5 µL of blood serum for prostate cancer diagnostics. Using polymeric horseradish peroxidase (poly-HRP, 400 HRPs) labels to provide large signal amplification and limits of detection in the sub-fg mL-1 range, a protocol was devised for the optimization of the fast, accurate assays of 100-fold diluted serum samples. Analysis of 130 prostate cancer patient serum samples revealed that some members of the protein panel can distinguish aggressive from indolent cancers. Logistic regression was used to identify a subset of the panel, combining biomarker proteins ETS-related gene protein (ERG), insulin-like growth factor-1 (IGF-1), pigment epithelial-derived factor (PEDF), and serum monocyte differentiation antigen (CD-14) to predict whether a given patient should be referred for biopsy, which gave a much better predictive accuracy than PSA alone. This represents the first prostate cancer blood test that can predict which patients will have a high biopsy Gleason score, a standard pathology score used to grade tumors.

Comparisons of zero-augmented continuous regression models from a Bayesian perspective.

The two-part model and the Tweedie model are two essential methods to analyze the positive continuous and zero-augmented responses. Compared with other continuous zero-augmented models, the zero-augmented gamma model (ZAG) demonstrates its performance on the mass zeros data. In this article, we compare the Bayesian model for continuous data of excess zeros by considering the ZAG and Tweedie model. We model the mean of both models in a logarithmic scale and the probability of zero within the zero-augmented model in a logit scale. As previous researchers employed different priors in Bayesian settings for the Tweedie model, by conducting a sensitivity analysis, we select the optimal priors for Tweedie model. Furthermore, we present a simulation study to evaluate the performance of two models in the comparison and apply them to a dataset about the daily fish intake and blood mercury levels from National Health and Nutrition Examination Survey. According to the Watanabe-Akaike information criterion and leave-one-out cross-validation criterion, the Tweedie model provides higher predictive accuracy for the positive continuous and zero-augmented data.

On Posterior Properties of the Two Parameter Gamma Family of Distributions.

The gamma distribution has been extensively used in many areas of applications. In this paper, considering a Bayesian analysis we provide necessary and sufficient conditions to check whether or not improper priors lead to proper posterior distributions. Further, we also discuss sufficient conditions to verify if the obtained posterior moments are finite. An interesting aspect of our findings are that one can check if the posterior is proper or improper and also if its posterior moments are finite by looking directly in the behavior of the proposed improper prior. To illustrate our proposed methodology these results are applied in different objective priors.

Categorical Data Analysis Using a Skewed Weibull Regression Model.

In this paper, we present a Weibull link (skewed) model for categorical response data arising from binomial as well as multinomial model. We show that, for such types of categorical data, the most commonly used models (logit, probit and complementary log-log) can be obtained as limiting cases. We further compare the proposed model with some other asymmetrical models. The Bayesian as well as frequentist estimation procedures for binomial and multinomial data responses are presented in detail. The analysis of two datasets to show the efficiency of the proposed model is performed.

Canonical variate regression.

In many fields, multi-view datasets, measuring multiple distinct but interrelated sets of characteristics on the same set of subjects, together with data on certain outcomes or phenotypes, are routinely collected. The objective in such a problem is often two-fold: both to explore the association structures of multiple sets of measurements and to develop a parsimonious model for predicting the future outcomes. We study a unified canonical variate regression framework to tackle the two problems simultaneously. The proposed criterion integrates multiple canonical correlation analysis with predictive modeling, balancing between the association strength of the canonical variates and their joint predictive power on the outcomes. Moreover, the proposed criterion seeks multiple sets of canonical variates simultaneously to enable the examination of their joint effects on the outcomes, and is able to handle multivariate and non-Gaussian outcomes. An efficient algorithm based on variable splitting and Lagrangian multipliers is proposed. Simulation studies show the superior performance of the proposed approach. We demonstrate the effectiveness of the proposed approach in an [Formula: see text] intercross mice study and an alcohol dependence study.

Flexible link functions in nonparametric binary regression with Gaussian process priors.

In many scientific fields, it is a common practice to collect a sequence of 0-1 binary responses from a subject across time, space, or a collection of covariates. Researchers are interested in finding out how the expected binary outcome is related to covariates, and aim at better prediction in the future 0-1 outcomes. Gaussian processes have been widely used to model nonlinear systems; in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes. A critical issue in modeling binary response data is the appropriate choice of link functions. Commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness. To address this limitation, we propose a flexible binary regression model which combines a generalized extreme value link function with a Gaussian process prior on the latent structure. Bayesian computation is employed in model estimation. Posterior consistency of the resulting posterior distribution is demonstrated. The flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples. Empirical results show that the proposed model outperforms a set of alternative models, which only have either a Gaussian process prior on the latent regression function or a Dirichlet prior on the link function.

Latent Class Analysis of Incomplete Data via an Entropy-Based Criterion.

Latent class analysis is used to group categorical data into classes via a probability model. Model selection criteria then judge how well the model fits the data. When addressing incomplete data, the current methodology restricts the imputation to a single, pre-specified number of classes. We seek to develop an entropy-based model selection criterion that does not restrict the imputation to one number of clusters. Simulations show the new criterion performing well against the current standards of AIC and BIC, while a family studies application demonstrates how the criterion provides more detailed and useful results than AIC and BIC.

A flexible cure rate model for spatially correlated survival data based on generalized extreme value distribution and Gaussian process priors.

Our present work proposes a new survival model in a Bayesian context to analyze right-censored survival data for populations with a surviving fraction, assuming that the log failure time follows a generalized extreme value distribution. Many applications require a more flexible modeling of covariate information than a simple linear or parametric form for all covariate effects. It is also necessary to include the spatial variation in the model, since it is sometimes unexplained by the covariates considered in the analysis. Therefore, the nonlinear covariate effects and the spatial effects are incorporated into the systematic component of our model. Gaussian processes (GPs) provide a natural framework for modeling potentially nonlinear relationship and have recently become extremely powerful in nonlinear regression. Our proposed model adopts a semiparametric Bayesian approach by imposing a GP prior on the nonlinear structure of continuous covariate. With the consideration of data availability and computational complexity, the conditionally autoregressive distribution is placed on the region-specific frailties to handle spatial correlation. The flexibility and gains of our proposed model are illustrated through analyses of simulated data examples as well as a dataset involving a colon cancer clinical trial from the state of Iowa.

BAYESIAN SPATIAL-TEMPORAL MODELING OF ECOLOGICAL ZERO-INFLATED COUNT DATA.

A Bayesian hierarchical model is developed for count data with spatial and temporal correlations as well as excessive zeros, uneven sampling intensities, and inference on missing spots. Our contribution is to develop a model on zero-inflated count data that provides flexibility in modeling spatial patterns in a dynamic manner and also improves the computational efficiency via dimension reduction. The proposed methodology is of particular importance for studying species presence and abundance in the field of ecological sciences. The proposed model is employed in the analysis of the survey data by the Northeast Fisheries Sciences Center (NEFSC) for estimation and prediction of the Atlantic cod in the Gulf of Maine - Georges Bank region. Model comparisons based on the deviance information criterion and the log predictive score show the improvement by the proposed spatial-temporal model.

Entropy-based clustering of embryonic stem cells using digital holographic microscopy.

Embryonic stem (ES) cells are an important factor in the development of cell-based therapeutic strategies. In this work, the use of digital holographic interferometric microscopy and statistical identification for automatic discrimination of ES cells and fibroblast (FB) cells is discussed in detail. The proposed algorithm first reduces the complex data structure to lower dimensions. Then, based on asymptotic normality, model-based clustering and linear discriminant analysis are applied to the transformed data to obtain the classification between ES and FB cells. The proposed algorithm is robust because it does not depend on parametric assumptions and can be extended to the classification of other cell image data. Experimental results are presented to demonstrate the performance of the system.

Fully semiparametric Bayesian approach for modeling survival data with cure fraction.

In this paper, we consider a piecewise exponential model (PEM) with random time grid to develop a full semiparametric Bayesian cure rate model. An elegant mechanism enjoying several attractive features for modeling the randomness of the time grid of the PEM is assumed. To model the prior behavior of the failure rates of the PEM we assume a hierarchical modeling approach that allows us to control the degree of parametricity in the right tail of the survival curve. Properties of the proposed model are discussed in detail. In particular, we investigate the impact of assuming a random time grid for the PEM on the estimation of the cure fraction. We further develop an efficient collapsed Gibbs sampler algorithm for carrying out posterior computation. A Bayesian diagnostic method for assessing goodness of fit and performing model comparisons is briefly discussed. Finally, we illustrate the usefulness of the new methodology with the analysis of a melanoma clinical trial that has been discussed in the literature.

Bayesian Modeling with Spatial Curvature Processes.

Spatial process models are widely used for modeling point-referenced variables arising from diverse scientific domains. Analyzing the resulting random surface provides deeper insights into the nature of latent dependence within the studied response. We develop Bayesian modeling and inference for rapid changes on the response surface to assess directional curvature along a given trajectory. Such trajectories or curves of rapid change, often referred to as wombling boundaries, occur in geographic space in the form of rivers in a flood plain, roads, mountains or plateaus or other topographic features leading to high gradients on the response surface. We demonstrate fully model based Bayesian inference on directional curvature processes to analyze differential behavior in responses along wombling boundaries. We illustrate our methodology with a number of simulated experiments followed by multiple applications featuring the Boston Housing data; Meuse river data; and temperature data from the Northeastern United States.

Updating categorical soil maps using limited survey data by Bayesian Markov chain cosimulation.

Updating categorical soil maps is necessary for providing current, higher-quality soil data to agricultural and environmental management but may not require a costly thorough field survey because latest legacy maps may only need limited corrections. This study suggests a Markov chain random field (MCRF) sequential cosimulation (Co-MCSS) method for updating categorical soil maps using limited survey data provided that qualified legacy maps are available. A case study using synthetic data demonstrates that Co-MCSS can appreciably improve simulation accuracy of soil types with both contributions from a legacy map and limited sample data. The method indicates the following characteristics: (1) if a soil type indicates no change in an update survey or it has been reclassified into another type that similarly evinces no change, it will be simply reproduced in the updated map; (2) if a soil type has changes in some places, it will be simulated with uncertainty quantified by occurrence probability maps; (3) if a soil type has no change in an area but evinces changes in other distant areas, it still can be captured in the area with unobvious uncertainty. We concluded that Co-MCSS might be a practical method for updating categorical soil maps with limited survey data.

Assessing intervention efficacy on high-risk drinkers using generalized linear mixed models with a new class of link functions.

Unhealthy alcohol use is one of the leading causes of morbidity and mortality in the United States. Brief interventions with high-risk drinkers during an emergency department (ED) visit are of great interest due to their possible efficacy and low cost. In a collaborative study with patients recruited at 14 academic ED across the United States, we examined the self-reported number of drinks per week by each patient following the exposure to a brief intervention. Count data with overdispersion have been mostly analyzed with generalized linear mixed models (GLMMs), of which only a limited number of link functions are available. Different choices of link function provide different fit and predictive power for a particular dataset. We propose a class of link functions from an alternative way to incorporate random effects in a GLMM, which encompasses many existing link functions as special cases. The methodology is naturally implemented in a Bayesian framework, with competing links selected with Bayesian model selection criteria such as the conditional predictive ordinate (CPO). In application to the ED intervention study, all models suggest that the intervention was effective in reducing the number of drinks, but some new models are found to significantly outperform the traditional model as measured by CPO. The validity of CPO in link selection is confirmed in a simulation study that shared the same characteristics as the count data from high-risk drinkers. The dataset and the source code for the best fitting model are available in Supporting Information.

Ultrasensitive detection of cancer biomarkers in the clinic by use of a nanostructured microfluidic array.

Multiplexed biomarker protein detection holds unrealized promise for clinical cancer diagnostics due to lack of suitable measurement devices and lack of rigorously validated protein panels. Here we report an ultrasensitive electrochemical microfluidic array optimized to measure a four-protein panel of biomarker proteins, and we validate the protein panel for accurate oral cancer diagnostics. Unprecedented ultralow detection into the 5-50 fg·mL(-1) range was achieved for simultaneous measurement of proteins interleukin 6 (IL-6), IL-8, vascular endothelial growth factor (VEGF), and VEGF-C in diluted serum. The immunoarray achieves high sensitivity in 50 min assays by using off-line protein capture by magnetic beads carrying 400,000 enzyme labels and ~100,000 antibodies. After capture of the proteins and washing to inhibit nonspecific binding, the beads are magnetically separated and injected into the array for selective capture by antibodies on eight nanostructured sensors. Good correlations with enzyme-linked immunosorbent assays (ELISA) for protein determinations in conditioned cancer cell media confirmed the accuracy of this approach. Normalized means of the four protein levels in 78 oral cancer patient serum samples and 49 controls gave clinical sensitivity of 89% and specificity of 98% for oral cancer detection, demonstrating high diagnostic utility. The low-cost, easily fabricated immunoarray provides a rapid serum test for diagnosis and personalized therapy of oral cancer. The device is readily adaptable to clinical diagnostics of other cancers.

Skew-normal/independent linear mixed models for censored responses with applications to HIV viral loads.

Often in biomedical studies, the routine use of linear mixed-effects models (based on Gaussian assumptions) can be questionable when the longitudinal responses are skewed in nature. Skew-normal/elliptical models are widely used in those situations. Often, those skewed responses might also be subjected to some upper and lower quantification limits (QLs; viz., longitudinal viral-load measures in HIV studies), beyond which they are not measurable. In this paper, we develop a Bayesian analysis of censored linear mixed models replacing the Gaussian assumptions with skew-normal/independent (SNI) distributions. The SNI is an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal, skew-t, skew-slash, and skew-contaminated normal distributions as special cases. The proposed model provides flexibility in capturing the effects of skewness and heavy tail for responses that are either left- or right-censored. For our analysis, we adopt a Bayesian framework and develop a Markov chain Monte Carlo algorithm to carry out the posterior analyses. The marginal likelihood is tractable, and utilized to compute not only some Bayesian model selection measures but also case-deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated with a simulation study as well as an HIV case study involving analysis of longitudinal viral loads.

Estimation of COVID-19 mortality in the United States using Spatio-temporal Conway Maxwell Poisson model.

Spatio-temporal Poisson models are commonly used for disease mapping. However, after incorporating the spatial and temporal variation, the data do not necessarily have equal mean and variance, suggesting either over- or under-dispersion. In this paper, we propose the Spatio-temporal Conway Maxwell Poisson model. The advantage of Conway Maxwell Poisson distribution is its ability to handle both under- and over-dispersion through controlling one special parameter in the distribution, which makes it more flexible than Poisson distribution. We consider data from the pandemic caused by the SARS-CoV-2 virus in 2019 (COVID-19) that has threatened people all over the world. Understanding the spatio-temporal pattern of the disease is of great importance. We apply a spatio-temporal Conway Maxwell Poisson model to data on the COVID-19 deaths and find that this model achieves better performance than commonly used spatio-temporal Poisson model.

Genetic diversity of microsatellite loci in hierarchically structured populations.

Microsatellite loci are widely used for investigating patterns of genetic variation within and among populations. Those patterns are in turn determined by population sizes, migration rates, and mutation rates. We provide exact expressions for the first two moments of the allele frequency distribution in a stochastic model appropriate for studying microsatellite evolution with migration, mutation, and drift under the assumption that the range of allele sizes is bounded. Using these results, we study the behavior of several measures related to Wright's F(ST), including Slatkin's R(ST). Our analytical approximations for F(ST) and R(ST) show that familiar relationships between N(e)m and F(ST) or R(ST) hold when the migration and mutation rates are small. Using the exact expressions for F(ST) and R(ST), our numerical results show that, when the migration and mutation rates are large, these relationships no longer hold. Our numerical results also show that the diversity measures most closely related to F(ST) depend on mutation rates, mutational models (stepwise versus two-phase), migration rates, and population sizes. Surprisingly, R(ST) is relatively insensitive to the mutation rates and mutational models. The differing behaviors of R(ST) and F(ST) suggest that properties of the among-population distribution of allele frequencies may allow the roles of mutation and migration in producing patterns of diversity to be distinguished, a topic of continuing investigation.

A Beta-mixture model for assessing genetic population structure.

An important fraction of recently generated molecular data is dominant markers. They contain substantial information about genetic variation but dominance makes it impossible to apply standard techniques to calculate measures of genetic differentiation, such as F-statistics. In this article, we propose a new Bayesian beta-mixture model that more accurately describes the genetic structure from dominant markers and estimates multiple F(ST) s from the sample. The model also has important application for codominant markers and single-nucleotide polymorphism (SNP) data. The number of F(ST) is assumed unknown beforehand and follows a random distribution. The reversible jump algorithm is used to estimate the unknown number of multiple F(ST) s. We evaluate the performance of three split proposals and the overall performance of the proposed model based on simulated dominant marker data. The model could reliably identify and estimate a spectrum of degrees of genetic differentiation present in multiple loci. The estimates of F(ST) s also incorporate uncertainty about the magnitude of within-population inbreeding coefficient. We illustrate the method with two examples, one using dominant marker data from a rare orchid and the other using codominant marker data from human populations.