Bayesian estimation in animal breeding using the Dirichlet process prior for correlated random effects

In the case of the mixed linear model the random effects are usually assumed to be normally distributed in both the Bayesian and classical frameworks. In this paper, the Dirichlet process prior was used to provide nonparametric Bayesian estimates for correlated random effects. This goal was achieved by providing a Gibbs sampler algorithm that allows these correlated random effects to have a nonparametric prior distribution. A sampling based method is illustrated. This method which is employed by transforming the genetic covariance matrix to an identity matrix so that the random effects are uncorrelated, is an extension of the theory and the results of previous researchers. Also by using Gibbs sampling and data augmentation a simulation procedure was derived for estimating the precision parameter M associated with the Dirichlet process prior. All needed conditional posterior distributions are given. To illustrate the application, data from the Elsenburg Dormer sheep stud were analysed. A total of 3325 weaning weight records from the progeny of 101 sires were used.     

Bayesian Inference for Smoking Cessation with a Latent Cure State

Summary .  We present a Bayesian approach to modeling dynamic smoking addiction behavior processes when cure is not directly observed due to censoring. Subject-specific probabilities model the stochastic transitions among three behavioral states: smoking, transient quitting, and permanent quitting (absorbent state). A multivariate normal distribution for random effects is used to account for the potential correlation among the subject-specific transition probabilities. Inference is conducted using a Bayesian framework via Markov chain Monte Carlo simulation. This framework provides various measures of subject-specific predictions, which are useful for policy-making, intervention development, and evaluation. Simulations are used to validate our Bayesian methodology and assess its frequentist properties. Our methods are motivated by, and applied to, the Alpha-Tocopherol, Beta-Carotene Lung Cancer Prevention study, a large (29,133 individuals) longitudinal cohort study of smokers from Finland.     

Optimal Drift Correction for Superresolution Localization Microscopy with Bayesian Inference

Single-molecule-localization-based superresolution microscopy requires accurate sample drift correction to achieve good results. Common approaches for drift compensation include using fiducial markers and direct drift estimation by image correlation. The former increases the experimental complexity and the latter estimates drift at a reduced temporal resolution. Here, we present, to our knowledge, a new approach for drift correction based on the Bayesian statistical framework. The technique has the advantage of being able to calculate the drifts for every image frame of the data set directly from the single-molecule coordinates. We present the theoretical foundation of the algorithm and an implementation that achieves significantly higher accuracy than image-correlation-based estimations.     

Bayesian Framework for Causal Inference with Principal Stratification and Clusters

Statistics in Biosciences - In observational studies, principal stratification is a well-established method in causal analysis to adjust the treatment effect estimation for post-treatment...     

A powerful adaptive microbiome-based association test for microbial association signals with diverse sparsity levels

The dysbiosis of microbiome may have negative effects on a host phenotype. The microbes related to the host phenotype are regarded as microbial association signals. Recently, statistical methods based on microbiome-phenotype association tests have been extensively developed to detect these association signals. However, the currently available methods do not perform well to detect microbial association signals when dealing with diverse sparsity levels (i.e., sparse, low sparse, non-sparse). Actually, the real association patterns related to different host phenotypes are not unique. Here, we propose a powerful and adaptive microbiome-based association test to detect microbial association signals with diverse sparsity levels, designated as MiATDS. In particular, we define probability degree to measure the associations between microbes and the host phenotype and introduce the adaptive weighted sum of powered score tests by considering both probability degree and phylogenetic information. We design numerous simulation experiments for the task of detecting association signals with diverse sparsity levels to prove the performance of the method. We find that type I error rates can be well-controlled and MiATDS shows superior efficiency on the power. By applying to real data analysis, MiATDS displays reliable practicability too. The R package is available at https://github.com/XiaoyunHuang33/MiATDS.     

Bayesian Inference for the Ratio of the Means of Two Normal Populations with Unequal Variances

The problem of making inferences about the ratio of two normal means has been addressed, both from the frequentist and Bayesian perspectives, by several authors. Most of this work is concerned with the homoscedastic case. In contrast, the situation where the variances are not equal has received little attention. Cox (1985) deals, within the frequentist framework, with a model where the variances are related to the means. His results are mainly based on Fieller's theorem whose drawbacks are well known. In this paper we present a Bayesian analysis of this model and discuss some related problems. An agronomical example is used throughout to illustrate the methods.     

Semiparametric Bayesian estimation of quantile function for breast cancer survival data with cured fraction

Existing cure‐rate survival models are generally not convenient for modeling and estimating the survival quantiles of a patient with specified covariate values. This paper proposes a novel class of cure‐rate model, the transform‐both‐sides cure‐rate model (TBSCRM), that can be used to make inferences about both the cure‐rate and the survival quantiles. We develop the Bayesian inference about the covariate effects on the cure‐rate as well as on the survival quantiles via Markov Chain Monte Carlo (MCMC) tools. We also show that the TBSCRM‐based Bayesian method outperforms existing cure‐rate models based methods in our simulation studies and in application to the breast cancer survival data from the National Cancer Institute's Surveillance, Epidemiology, and End Results (SEER) database.     

A regularized estimation approach for case-cohort periodic follow-up studies with an application to HIV vaccine trials

This paper discusses regression analysis of the failure time data arising from case-cohort periodic follow-up studies, and one feature of such data, which makes their analysis much more difficult, is that they are usually interval-censored rather than right-censored. Although some methods have been developed for general failure time data, there does not seem to exist an established procedure for the situation considered here. To address the problem, we present a semiparametric regularized procedure and develop a simple algorithm for the implementation of the proposed method. In addition, unlike some existing procedures for similar situations, the proposed procedure is shown to have the oracle property, and an extensive simulation is conducted and it suggests that the presented approach seems to work well for practical situations. The method is applied to an HIV vaccine trial that motivated this study.     

Bayesian mapping of quantitative trait loci for multiple complex traits with the use of variance components

Complex traits important for humans are often correlated phenotypically and genetically. Joint mapping of quantitative-trait loci (QTLs) for multiple correlated traits plays an important role in unraveling the genetic architecture of complex traits. Compared with single-trait analysis, joint mapping addresses more questions and has advantages for power of QTL detection and precision of parameter estimation. Some statistical methods have been developed to map QTLs underlying multiple traits, most of which are based on maximum-likelihood methods. We develop here a multivariate version of the Bayes methodology for joint mapping of QTLs, using the Markov chain-Monte Carlo (MCMC) algorithm. We adopt a variance-components method to model complex traits in outbred populations (e.g., humans). The method is robust, can deal with an arbitrary number of alleles with arbitrary patterns of gene actions (such as additive and dominant), and allows for multiple phenotype data of various types in the joint analysis (e.g., multiple continuous traits and mixtures of continuous traits and discrete traits). Under a Bayesian framework, parameters--including the number of QTLs--are estimated on the basis of their marginal posterior samples, which are generated through two samplers, the Gibbs sampler and the reversible-jump MCMC. In addition, we calculate the Bayes factor related to each identified QTL, to test coincident linkage versus pleiotropy. The performance of our method is evaluated in simulations with full-sib families. The results show that our proposed Bayesian joint-mapping method performs well for mapping multiple QTLs in situations of either bivariate continuous traits or mixed data types. Compared with the analysis for each trait separately, Bayesian joint mapping improves statistical power, provides stronger evidence of QTL detection, and increases precision in estimation of parameter and QTL position. We also applied the proposed method to a set of real data and detected a coincident linkage responsible for determining bone mineral density and areal bone size of wrist in humans.     

Maximum likelihood estimation of variance components for a multivariate mixed model with equal design matrices

An algorithm is described for estimating variance and covariance components by restricted maximum likelihood for a multivariate mixed two-way classification with equal design matrices. The procedure involves a transformation to canonical scale, effectively reducing a q-variate analysis to q corresponding univariate analyses. A small numerical example is given as well as a large-scale practical application.     

A method for removal of low frequency components associated with head movements from dual-axis swallowing accelerometry signals

Head movements can greatly affect swallowing accelerometry signals. In this paper, we implement a spline-based approach to remove low frequency components associated with these motions. Our approach was tested using both synthetic and real data. Synthetic signals were used to perform a comparative analysis of the spline-based approach with other similar techniques. Real data, obtained data from 408 healthy participants during various swallowing tasks, was used to analyze the processing accuracy with and without the spline-based head motions removal scheme. Specifically, we analyzed the segmentation accuracy and the effects of the scheme on statistical properties of these signals, as measured by the scaling analysis. The results of the numerical analysis showed that the spline-based technique achieves a superior performance in comparison to other existing techniques. Additionally, when applied to real data, we improved the accuracy of the segmentation process by achieving a 27% drop in the number of false negatives and a 30% drop in the number of false positives. Furthermore, the anthropometric trends in the statistical properties of these signals remained unaltered as shown by the scaling analysis, but the strength of statistical persistence was significantly reduced. These results clearly indicate that any future medical devices based on swallowing accelerometry signals should remove head motions from these signals in order to increase segmentation accuracy.     

A Bayesian functional data model for surveys collected under informative sampling with application to mortality estimation using NHANES

Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non-Gaussian data and can be applied in multivariate settings. In addition, we make use of a variety of Bayesian modeling techniques to ensure that the model is fit in a computationally efficient manner. We illustrate the value of our approach through two simulation studies as well as an example of mortality estimation using NHANES data.     

Variance component estimation techniques compared for two mating designs with forest genetic architecture through computer simulation

Computer simulation was used to compare minimum variance quadratic estimation (MIVQUE), minimum norm quadratic unbiased estimation (MINQUE), restricted maximum likelihood (REML), maximum likelihood (ML), and Henderson's Method 3 (HM3) on the basis of variance among estimates, mean square error (MSE), bias and probability of nearness for estimation of both individual variance components and three ratios of variance components. The investigation also compared three procedures for dealing with negative estimates and included the use of both individual observations and plot means as the experimental unit of the analysis. The structure of data simulated (field design, mating designs, genetic architecture and imbalance) represented typical analysis problems in quantitative forest genetics. Results of comparing the estimation techniques demonstrated that: estimates of probability of nearness did not discriminate among techniques; bias was discriminatory among procedures for dealing with negative estimates but not among estimation techniques (except ML); sampling variance among estimates was discriminatory among procedures for dealing with negative estimates, estimation techniques and unit of observation; and MSE provided no additional information to variance of the estimates. HM3 and REML were the closest competitors under these criteria; however, REML demonstrated greater robustness to imbalance. Of the three negative estimate procedures, two are of practical significance and guidelines for their application are presented. Estimates from individual observations were always preferable to those from plot means over the experimental levels of this study.This is Journal Series NO. R-03768 of the Institute of Food and Agricultural Sciences     

Bayesian estimation of two-part joint models for a longitudinal semicontinuous biomarker and a terminal event with INLA: Interests for cancer clinical trial evaluation

Two-part joint models for a longitudinal semicontinuous biomarker and a terminal event have been recently introduced based on frequentist estimation. The biomarker distribution is decomposed into a probability of positive value and the expected value among positive values. Shared random effects can represent the association structure between the biomarker and the terminal event. The computational burden increases compared to standard joint models with a single regression model for the biomarker. In this context, the frequentist estimation implemented in the R package frailtypack can be challenging for complex models (i.e., a large number of parameters and dimension of the random effects). As an alternative, we propose a Bayesian estimation of two-part joint models based on the Integrated Nested Laplace Approximation (INLA) algorithm to alleviate the computational burden and fit more complex models. Our simulation studies confirm that INLA provides accurate approximation of posterior estimates and to reduced computation time and variability of estimates compared to frailtypack in the situations considered. We contrast the Bayesian and frequentist approaches in the analysis of two randomized cancer clinical trials (GERCOR and PRIME studies), where INLA has a reduced variability for the association between the biomarker and the risk of event. Moreover, the Bayesian approach was able to characterize subgroups of patients associated with different responses to treatment in the PRIME study. Our study suggests that the Bayesian approach using the INLA algorithm enables to fit complex joint models that might be of interest in a wide range of clinical applications.