On the probability of correct selection for large k populations, with application to microarray data

One frontier of modern statistical research is the problems arising from data sets with extremely large k (>1000) populations, e.g. microarray and neuroimaging data. For many such problems the focus shifts from testing for significance to selecting, filtering, or screening. Classical Ranking and Selection Methodology (RSM) studied the probability of correct selection (PCS). PCS is the probability that the "best" (t = 1) of k populations is truly selected, according to some specified criteria of best. This paper extends and adapts two selection goals from the RSM literature that are suitable for large k problems (d-best and G-best selection). It is then shown how estimation of PCS for selecting multiple (t > 1) populations with d-best and G-best selection can be implemented to provide a useful measure of the quality of a given selection. A simulation study and the application of the proposed method to a benchmark microarray data set show it is an effective and versatile tool for assessing the probability that a particular gene selection or gene filtering step truly obtains the best genes. Moreover, the proposed method is fully general and may be applied to any such extremely large k problem.     

Releve ranking based on a sum of squares criterion

Summary When a very large number of phytosociological types have to be compared, a reduction of the number of relevés is desirable. In this paper a method of relevé selection from given phytosociological tables is suggested. The method is based on a sum of squares criterion. The advantage, in comparison with other selection procedures, is that this method provides a means on the basis of which the efficiency of a relevé selection can be objectively measured.Contribution from the Working Group for Data-Processing in Phytosociology, International Society for Vegetation Science.The work was completed at the Department of Plant Sciences of the University of Western Ontario, London, Canada. We wish to thank Prof. L. Orlóci for the hospitality and the helpful discussions. The work was supported by Italian C.N.R., within the project Promozione qualità dell'ambiente subproject Metodologie matematiche e basi di dati.     

Drop-the-losers design: normal case

Drop-the-losers designs are statistical designs which have two stages of a trial separated by a data based decision. In the first stage k experimental treatments and a control are administered. During a transition period, the empirically best experimental treatment is selected for continuation into the second phase, along with the control. At the study's end, inference focuses on the comparison of the selected treatment with the control using both stages' data. Traditional methods used to make inferences based on both stages' data can yield tests with higher than advertised levels of significance and confidence intervals with lower than advertised confidence. For normally distributed data, methods are provided to correct these deficiencies, providing confidence intervals with accurate levels of confidence. Drop-the-losers designs are particularly applicable to biopharmaceutical clinical trials where they can allow Phase II and Phase III clinical trials to be conducted under a single protocol with the use of all available data.     

Covariate Adjustment and Ranking Methods to Identify Regions with High and Low Mortality Rates

Summary Identifying regions with the highest and lowest mortality rates and producing the corresponding color‐coded maps help epidemiologists identify promising areas for analytic etiological studies. Based on a two‐stage Poisson–Gamma model with covariates, we use information on known risk factors, such as smoking prevalence, to adjust mortality rates and reveal residual variation in relative risks that may reflect previously masked etiological associations. In addition to covariate adjustment, we study rankings based on standardized mortality ratios (SMRs), empirical Bayes (EB) estimates, and a posterior percentile ranking (PPR) method and indicate circumstances that warrant the more complex procedures in order to obtain a high probability of correctly classifying the regions with the upper 100γ% and lower 100γ% of relative risks for γ= 0.05, 0.1 , and 0.2. We also give analytic approximations to the probabilities of correctly classifying regions in the upper 100γ% of relative risks for these three ranking methods. Using data on mortality from heart disease, we found that adjustment for smoking prevalence has an important impact on which regions are classified as high and low risk. With such a common disease, all three ranking methods performed comparably. However, for diseases with smaller event counts, such as cancers, and wide variation in event counts among regions, EB and PPR methods outperform ranking based on SMRs.     

Prioritization of natural habitats: A methodological framework applied to the French Mediterranean

Long-term preservation of habitats has become a cornerstone of modern conservation policies. As resources allocated to conservation actions are often limited, developing relevant prioritizing methods is necessary. Although many studies have been published on species prioritization, habitats have been the subject of less research. This study aims to develop a simple prioritization method suitable for habitats and appropriate to any typology. We analyzed literature to select criteria that would be the most accurate to rank habitats. Our final method consists in calculating a score based on four criteria: legal obligation, territorial responsibility, conservation condition and an extra criterion designed to fit local interests and objectives. The method is applied on habitats listed in Annex I of the Habitats Directive (92/43/EEC) on the territory of RESEDA-Flore, a network of stakeholders involved in the conservation of Mediterranean flora. Results highlight that dune habitats show the highest conservation values, while rocky habitats and caves obtain relatively low scores. At the top of the ranking, Mediterranean temporary ponds (3170), Dunes with Pinus pinea and/or Pinus pinaster forests (2270) and Coastal dunes with Juniperus spp. (2250) appear to be a high priority. These results can be used to design and implement habitat conservation strategies in the French Mediterranean.     

Use of the Maximum Likelihood Method in the Analysis of Phenotypic Stability

The stability variance is an important estimator of phenotypic stability of genotypes. It may be estimated by method of moments and by maximum likelihood. We demonstrate by Monte Carlo simulation that, given a sufficient number of environments, maximum likelihood estimates (MLE's) are slightly better if ranking of genotypes is the experimenter's major aim. A likelihood ratio test is available for different hypotheses.     

Blinded predictions of binding modes and energies of HSP90-α ligands for the 2015 D3R grand challenge

In the framework of the 2015 D3R inaugural grand challenge, blind binding pose and affinity predictions were performed for a set of 180 ligands of the Heat Shock Protein HSP90-α protein, a relevant cancer target. Spectral clustering was used to rapidly identify alternative binding site conformations in publicly available crystallographic HSP90-α structures. Subsequently, multiple docking and scoring protocols employing the software Autodock Vina and rDock were applied to predict binding modes and rank order ligands. Alchemical free energy calculations were performed with the software FESetup and Sire/OpenMM to predict binding affinities for three congeneric series subsets. Some of the protocols used here were ranked among the top submissions according to most of the evaluation metrics. Docking performance was excellent, but the scoring results were disappointing. A critical assessment of the results is reported, as well as suggestions for future similar competitions.