BAMarray™: Java software for Bayesian analysis of variance for microarray data

Background  

DNA microarrays open up a new horizon for studying the genetic determinants of disease. The high throughput nature of these arrays creates an enormous wealth of information, but also poses a challenge to data analysis. Inferential problems become even more pronounced as experimental designs used to collect data become more complex. An important example is multigroup data collected over different experimental groups, such as data collected from distinct stages of a disease process. We have developed a method specifically addressing these issues termed Bayesian ANOVA for microarrays (BAM). The BAM approach uses a special inferential regularization known as spike-and-slab shrinkage that provides an optimal balance between total false detections and total false non-detections. This translates into more reproducible differential calls. Spike and slab shrinkage is a form of regularization achieved by using information across all genes and groups simultaneously.     

CART variance stabilization and regularization for high-throughput genomic data

MOTIVATION: mRNA expression data obtained from high-throughput DNA microarrays exhibit strong departures from homogeneity of variances. Often a complex relationship between mean expression value and variance is seen. Variance stabilization of such data is crucial for many types of statistical analyses, while regularization of variances (pooling of information) can greatly improve overall accuracy of test statistics. RESULTS: A Classification and Regression Tree (CART) procedure is introduced for variance stabilization as well as regularization. The CART procedure adaptively clusters genes by variances. Using both local and cluster wide information leads to improved estimation of population variances which improves test statistics. Whereas making use of cluster wide information allows for variance stabilization of data. AVAILABILITY: Sufficient details for our CART procedure are given so that the interested reader can program the method for themselves. The algorithm is also accessible within the Java software package BAMarray(TM), which is freely available to non-commercial users at www.bamarray.com. CONTACT: hemant.ishwaran@gmail.com.     

Random forests for genomic data analysis

Random forests (RF) is a popular tree-based ensemble machine learning tool that is highly data adaptive, applies to "large p, small n" problems, and is able to account for correlation as well as interactions among features. This makes RF particularly appealing for high-dimensional genomic data analysis. In this article, we systematically review the applications and recent progresses of RF for genomic data, including prediction and classification, variable selection, pathway analysis, genetic association and epistasis detection, and unsupervised learning.     

Estimating the prevalence of atrial fibrillation from a three‐class mixture model for repeated diagnoses

Atrial fibrillation (AF) is an abnormal heart rhythm characterized by rapid and irregular heartbeat, with or without perceivable symptoms. In clinical practice, the electrocardiogram (ECG) is often used for diagnosis of AF. Since the AF often arrives as recurrent episodes of varying frequency and duration and only the episodes that occur at the time of ECG can be detected, the AF is often underdiagnosed when a limited number of repeated ECGs are used. In studies evaluating the efficacy of AF ablation surgery, each patient undergoes multiple ECGs and the AF status at the time of ECG is recorded. The objective of this paper is to estimate the marginal proportions of patients with or without AF in a population, which are important measures of the efficacy of the treatment. The underdiagnosis problem is addressed by a three‐class mixture regression model in which a patient's probability of having no AF, paroxysmal AF, and permanent AF is modeled by auxiliary baseline covariates in a nested logistic regression. A binomial regression model is specified conditional on a subject being in the paroxysmal AF group. The model parameters are estimated by the Expectation‐Maximization (EM) algorithm. These parameters are themselves nuisance parameters for the purpose of this research, but the estimators of the marginal proportions of interest can be expressed as functions of the data and these nuisance parameters and their variances can be estimated by the sandwich method. We examine the performance of the proposed methodology in simulations and two real data applications.