The goal of this paper is to illustrate how two significance indices-the frequentist p-value and Bayesian e-valuehave a straight mathematical relationship. We calculate these indices for standard statistical situations in which sharp null hypotheses are being tested. The p-value considered here is based on the likelihood ratio statistic. The existence of a functional relationship between these indices could surprise readers because they are computed in different spaces: p-values in the sample space and e-values in the parameter space.

Abstract:The main objective of this paper is to find the relation between the adaptive significance level presented here and the sample size. We statisticians know of the inconsistency, or paradox, in the current classical tests of significance that are based on p-value statistics that are compared to the canonical significance levels (10%, 5%, and 1%): "Raise the sample to reject the null hypothesis" is the recommendation of some ill-advised scientists! This paper will show that it is possible to eliminate this problem of significance tests. We present here the beginning of a larger research project. The intention is to extend its use to more complex applications such as survival analysis, reliability tests, and other areas. The main tools used here are the Bayes factor and the extended Neyman-Pearson Lemma.

This article argues that researchers do not need to completely abandon the p-value, the best-known significance index, but should instead stop using significance levels that do not depend on sample sizes. A testing procedure is developed using a mixture of frequentist and Bayesian tools, with a significance level that is a function of sample size, obtained from a generalized form of the Neyman-Pearson Lemma that minimizes a linear combination of α, the probability of rejecting a true null hypothesis, and β, the probability of failing to reject a false null, instead of fixing α and minimizing β. The resulting hypothesis tests do not violate the Likelihood Principle and do not require any constraints on the dimensionalities of the sample space and parameter space. The procedure includes an ordering of the entire sample space and uses predictive probability (density) functions, allowing for testing of both simple and compound hypotheses. Accessible examples are presented to highlight specific characteristics of the new tests.

Summary 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.

Abstract: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.

Abstract:The search of alternative compounds to control tropical diseases such as schistosomiasis has pointed to secondary metabolites derived from natural sources. Piper species are candidates in strategies to control the transmission of schistosomiasis due to their production of molluscicidal compounds. A new benzoic acid derivative and three flavokawains from Piper diospyrifolium, P. cumanense and P. gaudichaudianum displayed significant activities against Biomphalaria glabrata snails. Additionally, "in silico" studies OPEN ACCESSMolecules 2014, 19 5206 were performed using docking assays and Molecular Interaction Fields to evaluate the physical-chemical differences among the compounds in order to characterize the observed activities of the test compounds against Biomphalaria glabrata snails.

The first step in statistical reliability studies of coherent systems is the estimation of the reliability of each system component. For the cases of parallel and series systems the literature is abundant. It seems that the present paper is the first that presents the general case of component inferences in coherent systems. The failure time model considered here is the three-parameter Weibull distribution. Furthermore, neither independence nor identically distributed failure times are required restrictions. The proposed model is general in the sense that it can be used for any coherent system, from the simplest to the more complex structures.It can be considered for all kinds of censored data; including interval-censored data. An important property obtained for the Weibull model is the fact that the posterior distributions are proper, even for non-informative priors. Using several simulations, the excellent performance of the model is illustrated. As a real example, boys' first use of marijuana is considered to show the efficiency of the solution even when censored data occurs.

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.