Power-enhanced multiple decision functions controlling family-wise error and false discovery rates

Improved procedures, in terms of smaller missed discovery rates (MDR), for performing multiple hypotheses testing with weak and strong control of the family-wise error rate (FWER) or the false discovery rate (FDR) are developed and studied. The improvement over existing procedures such as the \v{S}id\'ak procedure for FWER control and the Benjamini--Hochberg (BH) procedure for FDR control is achieved by exploiting possible differences in the powers of the individual tests. Results signal the need to take into account the powers of the individual tests and to have multiple hypotheses decision functions which are not limited to simply using the individual $p$-values, as is the case, for example, with the \v{S}id\'ak, Bonferroni, or BH procedures. They also enhance understanding of the role of the powers of individual tests, or more precisely the receiver operating characteristic (ROC) functions of decision processes, in the search for better multiple hypotheses testing procedures. A decision-theoretic framework is utilized, and through auxiliary randomizers the procedures could be used with discrete or mixed-type data or with rank-based nonparametric tests. This is in contrast to existing $p$-value based procedures whose theoretical validity is contingent on each of these $p$-value statistics being stochastically equal to or greater than a standard uniform variable under the null hypothesis. Proposed procedures are relevant in the analysis of high-dimensional "large $M$, small $n$" data sets arising in the natural, physical, medical, economic and social sciences, whose generation and creation is accelerated by advances in high-throughput technology, notably, but not limited to, microarray technology.Comment: Published in at http://dx.doi.org/10.1214/10-AOS844 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bayes multiple decision functions

This paper deals with the problem of simultaneously making many M binary decisions based on one realization of a random data matrix X. M is typically large and X will usually have M rows associated with each of the M decisions to make, but for each row the data may be low dimensional. Such problems arise in many practical areas such as the biological and medical sciences, where the available dataset is from microarrays or other high-throughput technology and with the goal being to decide which among of many genes are relevant with respect to some phenotype of interest; in the engineering and reliability sciences; in astronomy; in education; and in business. A Bayesian decision-theoretic approach to this problem is implemented with the overall loss function being a cost-weighted linear combination of Type I and Type II loss functions. The class of loss functions considered allows for use of the false discovery rate (FDR), false nondiscovery rate (FNR), and missed discovery rate (MDR) in assessing the quality of decision. Through this Bayesian paradigm, the Bayes multiple decision function (BMDF) is derived and an efficient algorithm to obtain the optimal Bayes action is described. In contrast to many works in the literature where the rows of the matrix X are assumed to be stochastically independent, we allow a dependent data structure with the associations obtained through a class of frailty-induced Archimedean copulas. In particular, non-Gaussian dependent data structure, which is typical with failure-time data, can be entertained. The numerical implementation of the determination of the Bayes optimal action is facilitated through sequential Monte Carlo techniques. The theory developed could also be extended to the problem of multiple hypotheses testing, multiple classification and prediction, and high-dimensional variable selection. The proposed procedure is illustrated for the simple versus simple hypotheses setting and for the composite hypotheses setting through simulation studies. The procedure is also applied to a subset of a microarray data set from a colon cancer study

Bayes Multiple Binary Classifier - How to Make Decisions Like a Bayesian

This presentation will start by a general introduction of Bayesian statistics, which has become popular in the era of big data. Then we consider a two-class classification problem, where the goal is to predict the class membership of M units based on the values of high-dimensional categorical predictor variables as well as both the values of predictor variables and the class membership of other N independent units. We focus on applying generalized linear regression models with Boolean expressions of categorical predictors. We consider a Bayesian and decision-theoretic framework, and develop a general form of Bayes multiple binary classification functions with respect to a class of cost-weighted loss functions. In particular, the loss function pairs such as the proportions of false positives and false negatives, and (1-sensitivity) and (1-specificity), are considered. The results will be illustrated via simulations and on a Lupus diagnosis dataset

Returnee Entrepreneurs and the Performance Implications of Political and Business Relationships under Institutional Uncertainty

Acknowledgements We would like to thank the reviewers, the guest editor Bradley Barnes, and the editor in chief Naveen Donthu for the constructive comments. We are grateful with the financial support from the Broman Foundation for Research and Entrepreneurship, the National Natural Science Foundation of China (Grant No. 71772165), and the National Key Project of Philosophy and Social Science from Ministry of Education of the People’s Republic of China (Grant No. 17JZD018).Peer reviewedPostprin

Several parameters of generalized Mycielskians

AbstractThe generalized Mycielskians (also known as cones over graphs) are the natural generalization of the Mycielski graphs (which were first introduced by Mycielski in 1955). Given a graph G and any integer m⩾0, one can transform G into a new graph μm(G), the generalized Mycielskian of G. This paper investigates circular clique number, total domination number, open packing number, fractional open packing number, vertex cover number, determinant, spectrum, and biclique partition number of μm(G)

Novel insights into young adults’ perceived effectiveness of waterpipe tobacco-specific pictorial health warning labels in lebanon: Implications for tobacco control policy

This study aims to explore the perceived effectiveness of waterpipe (WP) tobacco specific health warning labels (HWLs) among young adult WP smokers and nonsmokers in Lebanon. Before participating in focus group discussions, participants (n = 66; WP smokers n = 30; nonsmokers n = 36; age 18–33) completed a brief survey to rate the effectiveness of 12 HWLs’ and rank them according to four risk themes (WP health effects, WP harm to others, WP-specific harm, and WP harm compared to cigarettes). Differences in HWLs ratings by WP smoking status were examined and the top-ranked HWL in each theme were identified. HWLs depicting mouth cancer and harm to babies were rated as the most effective by both WP smokers and non-smokers. WP smokers rated HWLs which depicted harm to children and infants as more effective than non-smokers. The top-ranked HWLs for perceived overall effectiveness were those depicting “oral cancer”, “harm to babies”, “orally transmitted diseases” and “mouth cancer”. HWLs depicting oral lesions and harm to babies were rated as most effective, while HWLs showing the harmful effects of WP secondhand smoke on infants and children were rated as less effective by nonsmokers compared to smokers. Our study provides evidence on the potential effectiveness of HWLs for further evaluation in Lebanon and the Eastern Mediterranean region. The results will inform and guide the development and implementation of tobacco control policy

Peripheral Ulcerative Keratitis Associated with Autoimmune Disease: Pathogenesis and Treatment

Peripheral ulcerative keratitis (PUK) is type of crescent-shaped inflammatory damage that occurs in the limbal region of the cornea. PUK is always combined with an epithelial defect and the destruction of the peripheral corneal stroma. PUK may have a connection to systemic conditions, such as long-standing rheumatoid arthritis (RA), systemic lupus erythematosus (SLE), Wegener granulomatosis (WG), relapsing polychondritis, classic polyarteritis nodosa and its variants, microscopic polyangiitis, and Churg-Strauss syndrome. However, the most common connection is with RA, which is also the focus of this review. The pathogenesis of PUK is still unclear. It is thought that circulating immune complexes and cytokines exert an important influence on the progression of this syndrome. Treatment is applied to inhibit certain aspects of PUK pathogenesis