Multiple Testing for Exploratory Research

Motivated by the practice of exploratory research, we formulate an approach to multiple testing that reverses the conventional roles of the user and the multiple testing procedure. Traditionally, the user chooses the error criterion, and the procedure the resulting rejected set. Instead, we propose to let the user choose the rejected set freely, and to let the multiple testing procedure return a confidence statement on the number of false rejections incurred. In our approach, such confidence statements are simultaneous for all choices of the rejected set, so that post hoc selection of the rejected set does not compromise their validity. The proposed reversal of roles requires nothing more than a review of the familiar closed testing procedure, but with a focus on the non-consonant rejections that this procedure makes. We suggest several shortcuts to avoid the computational problems associated with closed testing.Comment: Published in at http://dx.doi.org/10.1214/11-STS356 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Price Isn't Right: Shareholder Proposals as Opportunities for Institutional Investors to Restore Firm Value and Reduce Pharmaceutical Prices

Surging pharmaceutical prices in the United States create financial strain for patients, insurance companies, and state and federal governments. Regulatory delays and coverage denials due to product prices can also affect shareholders of pharmaceutical companies by depressing stock prices. While a number of industry leaders have acknowledged that dramatic price hikes can damage their businesses, many pharmaceutical companies have not demonstrated a willingness to scale back prices. This Note considers the use of shareholder proposals to address drug pricing policies at the company level. While shareholders of most companies are generally unable to address pricing policies, a carve-out created by the Securities and Exchange Commission allows shareholders of publicly traded pharmaceutical companies to do so. This Note studies how shareholders can use the carve-out to push for price restraint by either causing a company to include a price restraint proposal in its proxy materials and annual meeting or causing management to negotiate with proponent shareholders in order to convince the shareholders to withdraw their proposals. By evaluating the success of prior attempts to impact drug prices through shareholder proposals, this Note concludes that institutional investors are the linchpin of shareholder success, whether that success is through a vote at the annual meeting or a compromise at the negotiation table. This Note therefore calls on institutional investors to evaluate their portfolios and consider using shareholder proposals to unlock firm value and relieve the financial pressure created by rapidly rising drug prices

Freshwater Drum Spawning and Fecundity in the Upper Mississippi River

One hundred freshwater drum ovaries from 1981 collections were examined to provide spawning and fecundity information for the long-term fisheries monitoring program at the Quad Cities Nuclear Power Station. Objectives were to estimate freshwater drum fecundity in the Upper Mississippi River and relate sexual maturity to size or age. The mean fecundity estimate for ripe fish was 85,800 ova per female. Total estimated number of ova showed no relationship with length or weight, but there was a relationship with age. Mean number of ova for a given age group increased with age. Female freshwater drum in Pool 14 may become sexually mature at age 4, but females age 5 and older comprised over 95% of the 100 females representing the spawning population

Analyzing gene expression data in terms of gene sets: methodological issues

Motivation: Many statistical tests have been proposed in recent years for analyzing gene expression data in terms of gene sets, usually from Gene Ontology. These methods are based on widely different methodological assumptions. Some approaches test differential expression of each gene set against differential expression of the rest of the genes, whereas others test each gene set on its own. Also, some methods are based on a model in which the genes are the sampling units, whereas others treat the subjects as the sampling units. This article aims to clarify the assumptions behind different approaches and to indicate a preferential methodology of gene set testing. Results: We identify some crucial assumptions which are needed by the majority of methods. P-values derived from methods that use a model which takes the genes as the sampling unit are easily misinterpreted, as they are based on a statistical model that does not resemble the biological experiment actually performed. Furthermore, because these models are based on a crucial and unrealistic independence assumption between genes, the P-values derived from such methods can be wildly anti-conservative, as a simulation experiment shows. We also argue that methods that competitively test each gene set against the rest of the genes create an unnecessary rift between single gene testing and gene set testing. Contact: [email protected]

Robust testing in generalized linear models by sign flipping score contributions

Generalized linear models are often misspecified because of overdispersion, heteroscedasticity and ignored nuisance variables. Existing quasi-likelihood methods for testing in misspecified models often do not provide satisfactory type I error rate control. We provide a novel semiparametric test, based on sign flipping individual score contributions. The parameter tested is allowed to be multi-dimensional and even high dimensional. Our test is often robust against the mentioned forms of misspecification and provides better type I error control than its competitors. When nuisance parameters are estimated, our basic test becomes conservative. We show how to take nuisance estimation into account to obtain an asymptotically exact test. Our proposed test is asymptotically equivalent to its parametric counterpart