Parametric and nonparametric FDR estimation revisited

Nonparametric and parametric approaches have been proposed to estimate false discovery rate under the independent hypothesis testing assumption. The parametric approach has been shown to have better performance than the nonparametric approaches. In this article, we study the nonparametric approaches and quantify the underlying relations between parametric and nonparametric approaches. Our study reveals the conservative nature of the nonparametric approaches, and establishes the connections between the empirical Bayes method and p-value-based nonparametric methods. Based on our results, we advocate using the parametric approach, or directly modeling the test statistics using the empirical Bayes method.     

Multiple testing with discrete data: Proportion of true null hypotheses and two adaptive FDR procedures

We consider multiple testing with false discovery rate (FDR) control when p values have discrete and heterogeneous null distributions. We propose a new estimator of the proportion of true null hypotheses and demonstrate that it is less upwardly biased than Storey's estimator and two other estimators. The new estimator induces two adaptive procedures, that is, an adaptive Benjamini–Hochberg (BH) procedure and an adaptive Benjamini–Hochberg–Heyse (BHH) procedure. We prove that the adaptive BH (aBH) procedure is conservative nonasymptotically. Through simulation studies, we show that these procedures are usually more powerful than their nonadaptive counterparts and that the adaptive BHH procedure is usually more powerful than the aBH procedure and a procedure based on randomized p‐value. The adaptive procedures are applied to a study of HIV vaccine efficacy, where they identify more differentially polymorphic positions than the BH procedure at the same FDR level.     

Comparison of design strategies for a three‐arm clinical trial with time‐to‐event endpoint: Power,time‐to‐analysis,and operational aspects

To optimize resources, randomized clinical trials with multiple arms can be an attractive option to simultaneously test various treatment regimens in pharmaceutical drug development. The motivation for this work was the successful conduct and positive final outcome of a three‐arm randomized clinical trial primarily assessing whether obinutuzumab plus chlorambucil in patients with chronic lympocytic lymphoma and coexisting conditions is superior to chlorambucil alone based on a time‐to‐event endpoint. The inference strategy of this trial was based on a closed testing procedure. We compare this strategy to three potential alternatives to run a three‐arm clinical trial with a time‐to‐event endpoint. The primary goal is to quantify the differences between these strategies in terms of the time it takes until the first analysis and thus potential approval of a new drug, number of required events, and power. Operational aspects of implementing the various strategies are discussed. In conclusion, using a closed testing procedure results in the shortest time to the first analysis with a minimal loss in power. Therefore, closed testing procedures should be part of the statistician's standard clinical trials toolbox when planning multiarm clinical trials.     

Molecular phylogenies in the genus Mus: Comparative analysis of electrophoretic, scnDNA hybridization, and mtDNA RFLP data

In this paper, we present data on murid rodents obtained by three major techniques used in biochemical systematics today: protein electrophoresis, scnDNA hybridization and mtDNA RFLP. The data have been analysed by both phenetic and cladistic methods and results of the three techniques were compared with one another. Four clear major levels of divergence (or nodes) can be recognized by all methods. Node 1 groups four subspecies of M. musculus ( domesticus, bactrianus, castaneus and musculus ). Node 2 groups four species: M. musculus, M. spretus, M. spicilegus and M. spretoides . Node 3 groups the stem of node 2 and three strictly Oriental species ( M. caroli, M. cervicolor and M. cookii ) Node 4 groups the previous lineages with Oriental Pyromys and Coelomys and the Ethiopian Nannomys . However, the relationships within each level cannot be resolved without ambiguity. We argue that this is not due to the resolutive power of our methods, but to a biological reality, that is successive adaptive radiations marked by quasi-simultaneous speciation events linked with geographical colonization. Our estimation of divergence time between different taxa showed that the genus Mus is very young. The youngest 'bona fide' species are 1.1 Myr old, or even less than 0.3 Myr if one takes into consideration the two sibling species M. spicilegus and M. spretoides . It appears that mtDNA evolves three to six times faster than scnDNA. The zoogeographical history of the genus can be reconstructed as a séries of adaptative radiations leading to the present day distribution of the Palaearctic, Oriental, and Ethiopian groups of taxa.     

Resampling-based empirical Bayes multiple testing procedures for controlling generalized tail probability and expected value error rates: focus on the false discovery rate and simulation study

This article proposes resampling-based empirical Bayes multiple testing procedures for controlling a broad class of Type I error rates, defined as generalized tail probability (gTP) error rates, gTP (q,g) = Pr(g (V(n),S(n)) > q), and generalized expected value (gEV) error rates, gEV (g) = E [g (V(n),S(n))], for arbitrary functions g (V(n),S(n)) of the numbers of false positives V(n) and true positives S(n). Of particular interest are error rates based on the proportion g (V(n),S(n)) = V(n) /(V(n) + S(n)) of Type I errors among the rejected hypotheses, such as the false discovery rate (FDR), FDR = E [V(n) /(V(n) + S(n))]. The proposed procedures offer several advantages over existing methods. They provide Type I error control for general data generating distributions, with arbitrary dependence structures among variables. Gains in power are achieved by deriving rejection regions based on guessed sets of true null hypotheses and null test statistics randomly sampled from joint distributions that account for the dependence structure of the data. The Type I error and power properties of an FDR-controlling version of the resampling-based empirical Bayes approach are investigated and compared to those of widely-used FDR-controlling linear step-up procedures in a simulation study. The Type I error and power trade-off achieved by the empirical Bayes procedures under a variety of testing scenarios allows this approach to be competitive with or outperform the Storey and Tibshirani (2003) linear step-up procedure, as an alternative to the classical Benjamini and Hochberg (1995) procedure.     

Complete mitochondrial genomes from four subspecies of common chaffinch (Fringilla coelebs): New inferences about mitochondrial rate heterogeneity,neutral theory,and phylogenetic relationships within the order Passeriformes

We describe whole mitochondrial genome sequences from four subspecies of the common chaffinch (Fringilla coelebs), and compare them to 31 publicly available mitochondrial genome sequences from other Passeriformes. Rates and patterns of mitochondrial gene evolution are analyzed at different taxonomic levels within this avian order, and evidence is adduced for and against the nearly neutral theory of molecular evolution and the role of positive selection in shaping genetic variation of this small but critical genome. We find evidence of mitochondrial rate heterogeneity in birds as in other vertebrates, likely due to differences in mutational pressure across the genome. Unlike in gadine fish and some of the human mitochondrial work we do not observe strong support for the nearly neutral theory of molecular evolution; instead evidence from molecular clocks, distribution of dN/dS ratios at different levels of the taxonomic hierarchy and in different lineages, McDonald–Kreitman tests within Fringillidae, and site-specific tests of selection within Passeriformes, all point to a role for positive selection, especially for the complex I NADH dehydrogenase genes. The protein-coding mitogenome phylogeny of the order Passeriformes is broadly consistent with previously-reported molecular findings, but provides support for a sister relationship between the superfamilies Muscicapoidea and Passeroidea on a short basal internode of the Passerida where relationships have been difficult to resolve. An unexpected placement of the Paridae (represented by Hume's groundpecker) within the Muscicapoidea was observed. Consistent with other molecular studies the mtDNA phylogeny reveals paraphyly within the Muscicapoidea and a sister relationship of Fringilla with Carduelis rather than Emberiza.