Genome scan meta-analysis of schizophrenia and bipolar disorder, part II: Schizophrenia

Schizophrenia is a common disorder with high heritability and a 10-fold increase in risk to siblings of probands. Replication has been inconsistent for reports of significant genetic linkage. To assess evidence for linkage across studies, rank-based genome scan meta-analysis (GSMA) was applied to data from 20 schizophrenia genome scans. Each marker for each scan was assigned to 1 of 120 30-cM bins, with the bins ranked by linkage scores (1 = most significant) and the ranks averaged across studies (R-avg) and then weighted for sample size (rootN[affected cases]). A permutation test was used to compute the probability of observing, by chance, each bin's average rank (P-AvgRnk) or of observing it for a bin with the same place (first, second, etc.) in the order of average ranks in each permutation (P-ord). The GSMA produced significant genomewide evidence for linkage on chromosome 2q (P-AvgRnk

Network effects, network structure and consumer interaction in mobile telecommunications in Europe and Asia

This paper estimates the importance of (tariff-mediated) network effects and the impact of a consumer's social network on her choice of mobile phone provider. The study uses network data obtained from surveys of students in several European and Asian countries. We use the Quadratic Assignment Procedure, a non-parametric permutation test, to adjust for the particular error structure of network data. We find that respondents strongly coordinate their choice of mobile phone providers, but only if their provider induces network effects. This suggests that this coordination depends on network effects rather than on information contagion or pressure to conform to the social environment.

Methods of Regularities Searching Based on Optimal Partitioning

The purpose of discussed optimal valid partitioning (OVP) methods is uncovering of ordinal or continuous explanatory variables effect on outcome variables of different types. The OVP approach is based on searching partitions of explanatory variables space that in the best way separate observations with different levels of outcomes. Partitions of single variables ranges or two-dimensional admissible areas for pairs of variables are searched inside corresponding families. Statistical validity associated with revealed regularities is estimated with the help of permutation test repeating search of optimal partition for each permuted dataset. Method for output regularities selection is discussed that is based on validity evaluating with the help of two types of permutation tests.

QTLs mapping for primary metabolites responsible of the organoleptic and nutritional characteristics of strawberry (Fragaria x ananassa)

The cultivated strawberry (Fragaria x ananassa) is the berry fruit most consumed worldwide and is well-known for its delicate flavour and nutritional properties. However, fruit quality attributes have been lost or reduced after years of traditional breeding focusing mainly on agronomical traits. To face the obstacles encountered in the improvement of cultivated crops, new technological tools, such as genomics and high throughput metabolomics, are becoming essential for the identification of genetic factors responsible of organoleptic and nutritive traits. Integration of “omics” data will allow a better understanding of the molecular and genetic mechanisms underlying the accumulation of metabolites involved in the flavour and nutritional value of the fruit. To identify genetic components affecting/controlling? fruit metabolic composition, here we present a quantitative trait loci (QTL) analysis using a 95 F1 segregating population derived from genotypes ‘1392’, selected for its superior flavour, and ‘232’ selected based in high yield (Zorrilla-Fontanesi et al., 2011; Zorrilla-Fontanesi et al., 2012). Metabolite profiling was performed on red stage strawberry fruits using gas chromatography hyphenated to time-of-flight mass spectrometry, which is a rapid and highly sensitive approach, allowing a good coverage of the central pathways of primary metabolism. Around 50 primary metabolites, including sugars, sugars derivatives, amino and organic acids, were detected and quantified after analysis in each individual of the population. QTL mapping was performed on the ‘232’ x ‘1392’ population separately over two successive years, based on the integrated linkage map (Sánchez-Sevilla et al., 2015). First, significant associations between metabolite content and molecular markers were identified by the non-parametric test of Kruskal-Wallis. Then, interval mapping (IM), as well as the multiple QTL method (MQM) allowed the identification of QTLs in octoploid strawberry. A permutation test established LOD thresholds for each metabolite and year. A total of 132 QTLs were detected in all the linkage groups over the two years for 42 metabolites out of 50. Among them, 4 (9.8%) QTLs for sugars, 9 (25%) for acids and 7 (12.7%) for amino acids were stable and detected in the two successive years. We are now studying the QTLs regions in order to find candidate genes to explain differences in metabolite content in the different individuals of the population, and we expect to identify associations between genes and metabolites which will help us to understand their role in quality traits of strawberry fruit.

A versatile gene-based test for genome-wide association studies

We have derived a versatile gene-based test for genome-wide association studies (GWAS). Our approach, called VEGAS (versatile gene-based association study), is applicable to all GWAS designs, including family-based GWAS, meta-analyses of GWAS on the basis of summary data, and DNA-pooling-based GWAS, where existing approaches based on permutation are not possible, as well as singleton data, where they are. The test incorporates information from a full set of markers (or a defined subset) within a gene and accounts for linkage disequilibrium between markers by using simulations from the multivariate normal distribution. We show that for an association study using singletons, our approach produces results equivalent to those obtained via permutation in a fraction of the computation time. We demonstrate proof-of-principle by using the gene-based test to replicate several genes known to be associated on the basis of results from a family-based GWAS for height in 11,536 individuals and a DNA-pooling-based GWAS for melanoma in approximately 1300 cases and controls. Our method has the potential to identify novel associated genes; provide a basis for selecting SNPs for replication; and be directly used in network (pathway) approaches that require per-gene association test statistics. We have implemented the approach in both an easy-to-use web interface, which only requires the uploading of markers with their association p-values, and a separate downloadable application.

Permutation Tests for Classification

We introduce and explore an approach to estimating statistical significance of classification accuracy, which is particularly useful in scientific applications of machine learning where high dimensionality of the data and the small number of training examples render most standard convergence bounds too loose to yield a meaningful guarantee of the generalization ability of the classifier. Instead, we estimate statistical significance of the observed classification accuracy, or the likelihood of observing such accuracy by chance due to spurious correlations of the high-dimensional data patterns with the class labels in the given training set. We adopt permutation testing, a non-parametric technique previously developed in classical statistics for hypothesis testing in the generative setting (i.e., comparing two probability distributions). We demonstrate the method on real examples from neuroimaging studies and DNA microarray analysis and suggest a theoretical analysis of the procedure that relates the asymptotic behavior of the test to the existing convergence bounds.

Permutation-based stochastic ordering using pairwise comparisons

The topic of this work concerns nonparametric permutation-based methods aiming to find a ranking (stochastic ordering) of a given set of groups (populations), gathering together information from multiple variables under more than one experimental designs. The problem of ranking populations arises in several fields of science from the need of comparing G>2 given groups or treatments when the main goal is to find an order while taking into account several aspects. As it can be imagined, this problem is not only of theoretical interest but it also has a recognised relevance in several fields, such as industrial experiments or behavioural sciences, and this is reflected by the vast literature on the topic, although sometimes the problem is associated with different keywords such as: "stochastic ordering", "ranking", "construction of composite indices" etc., or even "ranking probabilities" outside of the strictly-speaking statistical literature. The properties of the proposed method are empirically evaluated by means of an extensive simulation study, where several aspects of interest are let to vary within a reasonable practical range. These aspects comprise: sample size, number of variables, number of groups, and distribution of noise/error. The flexibility of the approach lies mainly in the several available choices for the test-statistic and in the different types of experimental design that can be analysed. This render the method able to be tailored to the specific problem and the to nature of the data at hand. To perform the analyses an R package called SOUP (Stochastic Ordering Using Permutations) has been written and it is available on CRAN.

Power Calculations for Preclinical Studies Using a K-Sample Rank Test and the Lehmann Alternative Hypothesis

Power calculations in a small sample comparative study, with a continuous outcome measure, are typically undertaken using the asymptotic distribution of the test statistic. When the sample size is small, this asymptotic result can be a poor approximation. An alternative approach, using a rank based test statistic, is an exact power calculation. When the number of groups is greater than two, the number of calculations required to perform an exact power calculation is prohibitive. To reduce the computational burden, a Monte Carlo resampling procedure is used to approximate the exact power function of a k-sample rank test statistic under the family of Lehmann alternative hypotheses. The motivating example for this approach is the design of animal studies, where the number of animals per group is typically small.

A Novel Range Test

In a range test, one party holds a ciphertext and needs to test whether the message encrypted in the ciphertext is within a certain interval range. In this paper, a range test protocol is proposed, where the party holding the ciphertext asks another party holding the private key of the encryption algorithm to help him. These two parties run the protocol to implement the test. The test returns TRUE if and only if the encrypted message is within the certain interval range. If the two parties do not conspire, no information about the encrypted message is revealed from the test except what can be deduced from the test result. Advantages of the new protocol over the existing related techniques are that it achieves correctness, soundness, °exibility, high e±ciency and privacy simultaneously.