Adriano Polpo

Reliability Nonparametric Bayesian Estimation in Parallel Systems

Relevant results for (sub-)distribution functions related to parallel systems are discussed. The reverse hazard rate is defined using the product integral. Consequently, the restriction of absolute continuity for the involved distributions can be relaxed. The only restriction is that the sets of discontinuity points of the parallel distributions have to be disjointed. Nonparametric Bayesian estimators of all survival (sub-)distribution functions are derived. Dual to the series systems that use minimum life times as observations, the parallel systems record the maximum life times. Dirichlet multivariate processes forming a class of prior distributions are considered for the nonparametric Bayesian estimation of the component distribution functions, and the system reliability. For illustration, two striking numerical examples are presented.

Semiparametric Bayesian Survival Analysis using Models with Log-linear Median

We present a novel semiparametric survival model with a log-linear median regression function. As a useful alternative to existing semiparametric models, our large model class has many important practical advantages, including interpretation of the regression parameters via the median and the ability to address heteroscedasticity. We demonstrate that our modeling technique facilitates the ease of prior elicitation and computation for both parametric and semiparametric Bayesian analysis of survival data. We illustrate the advantages of our modeling, as well as model diagnostics, via a reanalysis of a small-cell lung cancer study. Results of our simulation study provide further support for our model in practice.

Statistical analysis for weibull distributions in presence of right and left censoring

Series system reliability is based on the minimum life time of its components. Its dual, the parallel system, is based on maximum. Here, we consider the statistical analysis of both, series and parallel, systems where the components follow the Weibull parametric model. Our perspective is Bayesian. Due to the mathematical complexity, to obtain the posterior distribution we use the Metropolis-Hasting simulation method. Based on this posterior, we evaluated the evidence of the Full Bayesian Significance Test (FBST) for comparing the reliabilities of the components. The reason for using FBST is the fact that we are testing precise hypotheses. We also compute the probability of a particular component be responsible for the system failure. An example illustrates the methodology.

Nonparametric Bayesian Estimation of Reliabilities in a Class of Coherent Systems

Usually, methods evaluating system reliability require engineers to quantify the reliability of each of the system components. For series and parallel systems, there are limited options to handle the estimation of each components reliability. This study examines the reliability estimation of complex problems of two classes of coherent systems: series-parallel, and parallel-series. In both of the cases, the component reliabilities may be unknown. We developed estimators for reliability functions at all levels of the system (component and system reliabilities). The main assumption required is that, for all the distributions of the components of a particular system, the sets of discontinuity points have to be disjoint. Nonparametric Bayesian estimators of all sub-distribution and distribution functions are derived, and a Dirichlet multivariate process as a prior distribution is considered for the nonparametric Bayesian estimation of all distributions. For illustration, two simulated numerical examples are presented. The estimators are s-consistent, and one may observe from the examples that they have good performance. Our estimator can accommodate continuous failure distributions, as well as distributions with mass points.

Reliability analysis in series systems: An empirical comparison between Bayesian and classical estimators

In Reliability Analysis, coherent systems represent a most important structure. In many situations systems are arranged in a series configuration, meaning that the systems failure is determined by the first component to fail. A problem of fundamental importance is to estimate the survival function parameters for each component, which allows the specification of adequate maintainance policies. However, reliability data for series systems are usually censored, in the sense that one only has information about the first component to fail. In this work, we focus on two components series systems. We discuss and compare, via numerical experiments on simulated datasets, the performances of three estimation methods: Bayesian, Frequetist maximum likelihood and nonparametric Kaplan-Meier estimators. The results of simulation study suggest that maximum likelihood and Bayesian estimatorss are roughly equivalent, while Kaplan-Meier underperforms the other two.

A Simple Proof for the Multinomial Version of the Representation Theorem

In this work we present a demonstration for the multinomial version of de Finetti’s Representation Theorem. We use characteristic functions, following his first demonstration for binary random quantities, but simplify the argument through forward operators.

Transform both sides model: A parametric approach

A parametric regression model for right-censored data with a log-linear median regression function and a transformation in both response and regression parts, named parametric Transform-Both-Sides (TBS) model, is presented. The TBS model has a parameter that handles data asymmetry while allowing various different distributions for the error, as long as they are unimodal symmetric distributions centered at zero. The discussion is focused on the estimation procedure with five important error distributions (normal, double-exponential, Students t, Cauchy and logistic) and presents properties, associated functions (that is, survival and hazard functions) and estimation methods based on maximum likelihood and on the Bayesian paradigm. These procedures are implemented in TBSSurvival, an open-source fully documented R package. The use of the package is illustrated and the performance of the model is analyzed using both simulated and real data sets.

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.

A Set of miRNAs, Their Gene and Protein Targets and Stromal Genes Distinguish Early from Late Onset ER Positive Breast Cancer

Breast cancer (BC) in young adult patients (YA) has a more aggressive biological behavior and is associated with a worse prognosis than BC arising in middle aged patients (MA). We proposed that differentially expressed miRNAs could regulate genes and proteins underlying aggressive phenotypes of breast tumors in YA patients when compared to those arising in MA patients. Objective: Using integrated expression analyses of miRs, their mRNA and protein targets and stromal gene expression, we aimed to identify differentially expressed profiles between tumors from YA-BC and MA-BC. Methodology and Results: Samples of ER+ invasive ductal breast carcinomas, divided into two groups: YA-BC (35 years or less) or MA-BC (50–65 years) were evaluated. Screening for BRCA1/2 status according to the BOADICEA program indicated low risk of patients being carriers of these mutations. Aggressive characteristics were more evident in YA-BC versus MA-BC. Performing qPCR, we identified eight miRs differentially expressed (miR-9, 18b, 33b, 106a, 106b, 210, 518a-3p and miR-372) between YA-BC and MA-BC tumors with high confidence statement, which were associated with aggressive clinicopathological characteristics. The expression profiles by microarray identified 602 predicted target genes associated to proliferation, cell cycle and development biological functions. Performing RPPA, 24 target proteins differed between both groups and 21 were interconnected within a network protein-protein interactions associated with proliferation, development and metabolism pathways over represented in YA-BC. Combination of eight mRNA targets or the combination of eight target proteins defined indicators able to classify individual samples into YA-BC or MA-BC groups. Fibroblast-enriched stroma expression profile analysis resulted in 308 stromal genes differentially expressed between YA-BC and MA-BC. Conclusion: We defined a set of differentially expressed miRNAs, their mRNAs and protein targets and stromal genes that distinguish early onset from late onset ER positive breast cancers which may be involved with tumor aggressiveness of YA-BC.

Ordering Quantiles through Confidence Statements

This work proposes Quor, a simple yet effective nonparametric method to compare independent samples with respect to corresponding quantiles of their populations. The method is solely based on the order statistics of the samples, and independence is its only requirement. All computations are performed using exact distributions with no need for any asymptotic considerations, and yet can be run using a fast quadratic-time dynamic programming idea. Computational performance is essential in high-dimensional domains, such as gene expression data. We describe the approach and discuss on the most important assumptions, building a parallel with assumptions and properties of widely used techniques for the same problem. Experiments using real data from biomedical studies are performed to empirically compare Quor and other methods in a classification task over a selection of high-dimensional data sets.Ranking variables according to their relevance to predict an outcome is an important task in biomedicine. For instance, such ranking can be used for selecting a smaller number of genes for then applying other sophisticated experiments only on genes identified as important. A nonparametric method called Quor is designed to provide a confidence value for the order of arbitrary quantiles of different populations using independent samples. This confidence may provide insights about possible differences among groups and yields a ranking of importance for the variables. Computations are efficient and use exact distributions with no need for asymptotic considerations. Experiments with simulated data and with multiple real -omics data sets are performed, and they show advantages and disadvantages of the method. Quor has no assumptions but independence of samples, thus it might be a better option when assumptions of other methods cannot be asserted. The software is publicly available on CRAN.