Tapabrata Maiti

An improved empirical bayes approach to estimating differential gene expression in microarray time-course data: BETR (Bayesian Estimation of Temporal Regulation)

BackgroundMicroarray gene expression time-course experiments provide the opportunity to observe the evolution of transcriptional programs that cells use to respond to internal and external stimuli. Most commonly used methods for identifying differentially expressed genes treat each time point as independent and ignore important correlations, including those within samples and between sampling times. Therefore they do not make full use of the information intrinsic to the data, leading to a loss of power.ResultsWe present a flexible random-effects model that takes such correlations into account, improving our ability to detect genes that have sustained differential expression over more than one time point. By modeling the joint distribution of the samples that have been profiled across all time points, we gain sensitivity compared to a marginal analysis that examines each time point in isolation. We assign each gene a probability of differential expression using an empirical Bayes approach that reduces the effective number of parameters to be estimated.ConclusionsBased on results from theory, simulated data, and application to the genomic data presented here, we show that BETR has increased power to detect subtle differential expression in time-series data. The open-source R package betr is available through Bioconductor. BETR has also been incorporated in the freely-available, open-source MeV software tool available from http://www.tm4.org/mev.html.

Nonparametric estimation of mean-squared prediction error in nested-error regression models

Nested-error regression models are widely used for analyzing clustered data. For example, they are often applied to two-stage sample surveys, and in biology and econometrics. Prediction is usually the main goal of such analyses, and mean-squared prediction error is the main way in which prediction performance is measured. In this paper we suggest a new approach to estimating mean-squared prediction error. We introduce a matched-moment, double-bootstrap algorithm, enabling the notorious underestimation of the naive mean-squared error estimator to be substantially reduced. Our approach does not require specific assumptions about the distributions of errors. Additionally, it is simple and easy to apply. This is achieved through using Monte Carlo simulation to implicitly develop formulae which, in a more conventional approach, would be derived laboriously by mathematical arguments.

A comparative study of the bias corrected estimates in logistic regression

Logistic regression is frequently used in many areas of applied statistics. The maximum likelihood estimates (MLE) of the logistic regression parameters are usually computed using the iterative Newton—Raphson method. It is well known that these estimates are biased. Several methods are proposed to correct the bias of these estimates. Among them Firth (1993) and Cordeiro and McCullagh (1991) proposed two promising methods. The conditional exact method (CMLE) is popular for small-sample estimates, and is available in many software packages. In this article we compare these methods in terms of their bias. In general, our extensive simulations show that the methods proposed by Cordeiro and McCullagh and by Firth work well, though Cordeiro and McCullagh is slightly better in our simulations. In case of separation, Firth or CMLE can be used; however, a judicious approach is required when there is a wide variation in results. Two real data analyses are given exhibiting these properties. The data analysis also includes bootstrap results.

Current Methods for Recurrent Events Data With Dependent Termination: A Bayesian Perspective

There has been a recent surge of interest in modeling and methods for analyzing recurrent events data with risk of termination dependent on the history of the recurrent events. To aid future users in understanding the implications of modeling assumptions and modeling properties, we review the state-of-the-art statistical methods and present novel theoretical properties, identifiability results, and practical consequences of key modeling assumptions of several fully specified stochastic models. After introducing stochastic models with 2 noninformative termination process, we focus on a class of models that allows both negative and positive association between the risk of termination and the rate of recurrent events through a frailty variable. We also discuss the relationship, as well as the major differences between these models in terms of their motivations and physical interpretations. We discuss associated Bayesian methods based on Markov chain Monte Carlo tools, and novel model diagnostic tools to perform inference based on fully specified models. We demonstrate the usefulness of the current methodology through an analysis of a data set from a clinical trial. Finally, we explore possible future extensions and limitations of the methodology.

Sequential Bayesian Prediction and Adaptive Sampling Algorithms for Mobile Sensor Networks

In this technical note, we formulate a fully Bayesian approach for spatio-temporal Gaussian process regression such that multifactorial effects of observations, measurement noise and prior distributions are all correctly incorporated in the predictive distribution. Using discrete prior probabilities and compactly supported kernels, we provide a way to design sequential Bayesian prediction algorithms in which exact predictive distributions can be computed in constant time as the number of observations increases. For a special case, a distributed implementation of sequential Bayesian prediction algorithms has been proposed for mobile sensor networks. An adaptive sampling strategy for mobile sensors, using the maximum a posteriori (MAP) estimation, has been proposed to minimize the prediction error variances. Simulation results illustrate the practical usefulness of the proposed theoretically-correct algorithms.

Hierarchical Bayesian Neural Networks: An Application to a Prostate Cancer Study

Prostate cancer is one of the most common cancers in American men. Management depends on the staging of prostate cancer. Only cancers that are confined to organs of origin are potentially curable. The article considers a hierarchical Bayesian neural network approach for posterior prediction probabilities of certain features indicative of non-organ-confined prostate cancer. The Bayesian procedure is implemented by an application of the Markov chain Monte Carlo numerical integration technique. For the problem at hand, the hierarchical Bayesian neural network approach is shown to be superior to the approach based on hierarchical Bayesian logistic regression model as well as the classical feedforward neural networks.

Efficient Bayesian spatial prediction with mobile sensor networks using Gaussian Markov random fields

In this paper, we consider the problem of predicting a large scale spatial field using successive noisy measurements obtained by mobile sensing agents. The physical spatial field of interest is discretized and modeled by a Gaussian Markov random field (GMRF) with unknown hyperparameters. From a Bayesian perspective, we design a sequential prediction algorithm to exactly compute the predictive inference of the random field. The prediction algorithm correctly takes into account the uncertainty in hyperparameters in a Bayesian way and also is scalable to be usable for the mobile sensor networks with limited resources. An adaptive sampling strategy is also designed for mobile sensing agents to find the most informative locations in taking future measurements in order to minimize the prediction error and the uncertainty in hyperparameters simultaneously. The effectiveness of the proposed algorithms is illustrated by a numerical experiment.

Bias reduction in conditional logistic regression

We employ a general bias preventive approach developed by Firth (Biometrika 1993; 80:27-38) to reduce the bias of an estimator of the log-odds ratio parameter in a matched case-control study by solving a modified score equation. We also propose a method to calculate the standard error of the resultant estimator. A closed-form expression for the estimator of the log-odds ratio parameter is derived in the case of a dichotomous exposure variable. Finite sample properties of the estimator are investigated via a simulation study. Finally, we apply the method to analyze a matched case-control data from a low birthweight study.

Analyzing 2000–2010 Childhood Age-Adjusted Cancer Rates in Florida: A Spatial Clustering Approach

In this work, we apply a Bayesian hierarchical model that uses spatial clustering techniques to data from the Florida Association of Pediatric Tumor Programs (FAPTP) for the period 2000–2010. The goal is to determine whether there are statistically significant childhood cancer clusters at the Zip Code Tabulation Area (ZCTA) level of geography. The model provides estimates of the uncertainty associated with the clustering configurations, which is typically lacking in classical analyses of large datasets where a unique clustering representation can be insufficient. The model also allows covariate adjustment for known risk factors, bringing further relevant information, and it produces clusters that are spatially contiguous, enabling simple interpretation. The output clustering map is able to capture such patterns as the high-risk area that appear in the Southwest, Northeast, and Northwest Florida, which is consistent with the previous studies, but with finer details and deeper insight into year-specific features. New findings from the latest data, from 2008 to 2010, were also obtained and investigated. Our post-hoc validation of the clusters provides evidence for concluding that areas of elevated risk exist.

Bias Reduction and a Solution for Separation of Logistic Regression with Missing Covariates

Logistic regression is an important statistical procedure used in many disciplines. The standard software packages for data analysis are generally equipped with this procedure where the maximum likelihood estimates of the regression coefficients are obtained iteratively. It is well known that the estimates from the analyses of small- or medium-sized samples are biased. Also, in finding such estimates, often a separation is encountered in which the likelihood converges but at least one of the parameter estimates diverges to infinity. Standard approaches of finding such estimates do not take care of these problems. Moreover, the missingness in the covariates adds an extra layer of complexity to the whole process. In this article, we address these three practical issues--bias, separation, and missing covariates by means of simple adjustments. We have applied the proposed technique using real and simulated data. The proposed method always finds a solution and the estimates are less biased. A SAS macro that implements the proposed method can be obtained from the authors.