The F test for comparing two normal variances: correct and incorrect calculation of the two-sided p-value?

This article illustrates that not all statistical software packages are correctly calculating a p-value for the classical F test comparison of two independent Normal variances. This is illustrated with a simple example, and the reasons why are discussed. Eight different software packages are considered.

Sequentially testing for a gene-drug interaction in a genomewide analysis

Assaying a large number of genetic markers from patients in clinical trials is now possible in order to tailor drugs with respect to efficacy. The statistical methodology for analysing such massive data sets is challenging. The most popular type of statistical analysis is to use a univariate test for each genetic marker, once all the data from a clinical study have been collected. This paper presents a sequential method for conducting an omnibus test for detecting gene-drug interactions across the genome, thus allowing informed decisions at the earliest opportunity and overcoming the multiple testing problems from conducting many univariate tests. We first propose an omnibus test for a fixed sample size. This test is based on combining F-statistics that test for an interaction between treatment and the individual single nucleotide polymorphism (SNP). As SNPs tend to be correlated, we use permutations to calculate a global p-value. We extend our omnibus test to the sequential case. In order to control the type I error rate, we propose a sequential method that uses permutations to obtain the stopping boundaries. The results of a simulation study show that the sequential permutation method is more powerful than alternative sequential methods that control the type I error rate, such as the inverse-normal method. The proposed method is flexible as we do not need to assume a mode of inheritance and can also adjust for confounding factors. An application to real clinical data illustrates that the method is computationally feasible for a large number of SNPs. Copyright (c) 2007 John Wiley & Sons, Ltd.

Candidate genes for obesity-susceptibility show enriched association within a large genome-wide association study for BMI

Before the advent of genome-wide association studies (GWASs), hundreds of candidate genes for obesity-susceptibility had been identified through a variety of approaches. We examined whether those obesity candidate genes are enriched for associations with body mass index (BMI) compared with non-candidate genes by using data from a large-scale GWAS. A thorough literature search identified 547 candidate genes for obesity-susceptibility based on evidence from animal studies, Mendelian syndromes, linkage studies, genetic association studies and expression studies. Genomic regions were defined to include the genes ±10 kb of flanking sequence around candidate and non-candidate genes. We used summary statistics publicly available from the discovery stage of the genome-wide meta-analysis for BMI performed by the genetic investigation of anthropometric traits consortium in 123 564 individuals. Hypergeometric, rank tail-strength and gene-set enrichment analysis tests were used to test for the enrichment of association in candidate compared with non-candidate genes. The hypergeometric test of enrichment was not significant at the 5% P-value quantile (P = 0.35), but was nominally significant at the 25% quantile (P = 0.015). The rank tail-strength and gene-set enrichment tests were nominally significant for the full set of genes and borderline significant for the subset without SNPs at P < 10(-7). Taken together, the observed evidence for enrichment suggests that the candidate gene approach retains some value. However, the degree of enrichment is small despite the extensive number of candidate genes and the large sample size. Studies that focus on candidate genes have only slightly increased chances of detecting associations, and are likely to miss many true effects in non-candidate genes, at least for obesity-related traits.

Analyses of single nucleotide polymorphisms in selected nutrient-sensitive genes in weight-regain prevention: the DIOGENES study

BACKGROUND: Differences in the interindividual response to dietary intervention could be modified by genetic variation in nutrient-sensitive genes. OBJECTIVE: This study examined single nucleotide polymorphisms (SNPs) in presumed nutrient-sensitive candidate genes for obesity and obesity-related diseases for main and dietary interaction effects on weight, waist circumference, and fat mass regain over 6 mo. DESIGN: In total, 742 participants who had lost ≥ 8% of their initial body weight were randomly assigned to follow 1 of 5 different ad libitum diets with different glycemic indexes and contents of dietary protein. The SNP main and SNP-diet interaction effects were analyzed by using linear regression models, corrected for multiple testing by using Bonferroni correction and evaluated by using quantile-quantile (Q-Q) plots. RESULTS: After correction for multiple testing, none of the SNPs were significantly associated with weight, waist circumference, or fat mass regain. Q-Q plots showed that ALOX5AP rs4769873 showed a higher observed than predicted P value for the association with less waist circumference regain over 6 mo (-3.1 cm/allele; 95% CI: -4.6, -1.6; P/Bonferroni-corrected P = 0.000039/0.076), independently of diet. Additional associations were identified by using Q-Q plots for SNPs in ALOX5AP, TNF, and KCNJ11 for main effects; in LPL and TUB for glycemic index interaction effects on waist circumference regain; in GHRL, CCK, MLXIPL, and LEPR on weight; in PPARC1A, PCK2, ALOX5AP, PYY, and ADRB3 on waist circumference; and in PPARD, FABP1, PLAUR, and LPIN1 on fat mass regain for dietary protein interaction. CONCLUSION: The observed effects of SNP-diet interactions on weight, waist, and fat mass regain suggest that genetic variation in nutrient-sensitive genes can modify the response to diet. This trial was registered at clinicaltrials.gov as NCT00390637.

Meta-analysis of the INSIG2 association with obesity including 74,345 individuals: does heterogeneity of estimates relate to study design?

The INSIG2 rs7566605 polymorphism was identified for obesity (BMI> or =30 kg/m(2)) in one of the first genome-wide association studies, but replications were inconsistent. We collected statistics from 34 studies (n = 74,345), including general population (GP) studies, population-based studies with subjects selected for conditions related to a better health status ('healthy population', HP), and obesity studies (OB). We tested five hypotheses to explore potential sources of heterogeneity. The meta-analysis of 27 studies on Caucasian adults (n = 66,213) combining the different study designs did not support overall association of the CC-genotype with obesity, yielding an odds ratio (OR) of 1.05 (p-value = 0.27). The I(2) measure of 41% (p-value = 0.015) indicated between-study heterogeneity. Restricting to GP studies resulted in a declined I(2) measure of 11% (p-value = 0.33) and an OR of 1.10 (p-value = 0.015). Regarding the five hypotheses, our data showed (a) some difference between GP and HP studies (p-value = 0.012) and (b) an association in extreme comparisons (BMI> or =32.5, 35.0, 37.5, 40.0 kg/m(2) versus BMI<25 kg/m(2)) yielding ORs of 1.16, 1.18, 1.22, or 1.27 (p-values 0.001 to 0.003), which was also underscored by significantly increased CC-genotype frequencies across BMI categories (10.4% to 12.5%, p-value for trend = 0.0002). We did not find evidence for differential ORs (c) among studies with higher than average obesity prevalence compared to lower, (d) among studies with BMI assessment after the year 2000 compared to those before, or (e) among studies from older populations compared to younger. Analysis of non-Caucasian adults (n = 4889) or children (n = 3243) yielded ORs of 1.01 (p-value = 0.94) or 1.15 (p-value = 0.22), respectively. There was no evidence for overall association of the rs7566605 polymorphism with obesity. Our data suggested an association with extreme degrees of obesity, and consequently heterogeneous effects from different study designs may mask an underlying association when unaccounted for. The importance of study design might be under-recognized in gene discovery and association replication so far.

A genome wide association study of mathematical ability reveals an association at chromosome 3q29, a locus associated with autism and learning difficulties: a preliminary study

Mathematical ability is heritable, but few studies have directly investigated its molecular genetic basis. Here we aimed to identify specific genetic contributions to variation in mathematical ability. We carried out a genome wide association scan using pooled DNA in two groups of U.K. samples, based on end of secondary/high school national academic exam achievement: high (n = 419) versus low (n = 183) mathematical ability while controlling for their verbal ability. Significant differences in allele frequencies between these groups were searched for in 906,600 SNPs using the Affymetrix GeneChip Human Mapping version 6.0 array. After meeting a threshold of p<1.5×10-5, 12 SNPs from the pooled association analysis were individually genotyped in 542 of the participants and analyzed to validate the initial associations (lowest p-value 1.14 ×10-6). In this analysis, one of the SNPs (rs789859) showed significant association after Bonferroni correction, and four (rs10873824, rs4144887, rs12130910 rs2809115) were nominally significant (lowest p-value 3.278 × 10-4). Three of the SNPs of interest are located within, or near to, known genes (FAM43A, SFT2D1, C14orf64). The SNP that showed the strongest association, rs789859, is located in a region on chromosome 3q29 that has been previously linked to learning difficulties and autism. rs789859 lies 1.3 kbp downstream of LSG1, and 700 bp upstream of FAM43A, mapping within the potential promoter/regulatory region of the latter. To our knowledge, this is only the second study to investigate the association of genetic variants with mathematical ability, and it highlights a number of interesting markers for future study.

A pooled genome-wide association study of Asperger Syndrome

Asperger Syndrome (AS) is a neurodevelopmental condition characterized by impairments in social interaction and communication, alongside the presence of unusually repetitive, restricted interests and stereotyped behaviour. Individuals with AS have no delay in cognitive and language development. It is a subset of Autism Spectrum Conditions (ASC), which are highly heritable and has a population prevalence of approximately 1%. Few studies have investigated the genetic basis of AS. To address this gap in the literature, we performed a genome-wide pooled DNA association study to identify candidate loci in 612 individuals (294 cases and 318 controls) of Caucasian ancestry, using the Affymetrix GeneChip Human Mapping version 6.0 array. We identified 11 SNPs that had a p-value below 1x10-5. These SNPs were independently genotyped in the same sample. Three of the SNPs (rs1268055, rs7785891 and rs2782448) were nominally significant, though none remained significant after Bonferroni correction. Two of our top three SNPs (rs7785891 and rs2782448) lie in loci previously implicated in ASC. However, investigation of the three SNPs in the ASC genome-wide association dataset from the Psychiatric Genomics Consortium indicated that these three SNPs were not significantly associated with ASC. The effect sizes of the variants were modest, indicating that our study was not sufficiently powered to identify causal variants with precision.

Training on the use of a bespoke continuing professional development framework improves the quality of CPD records

BACKGROUND: Using continuing professional development (CPD) as part of the revalidation of pharmacy professionals has been proposed in the UK but not implemented. We developed a CPD Outcomes Framework (‘the framework’) for scoring CPD records, where the score range was -100 to +150 based on demonstrable relevance and impact of the CPD on practice. OBJECTIVE: This exploratory study aimed to test the outcome of training people to use the framework, through distance-learning material (active intervention), by comparing CPD scores before and after training. SETTING: Pharmacy professionals were recruited in the UK in Reading, Banbury, Southampton, Kingston-upon-Thames and Guildford in 2009. METHOD: We conducted a randomised, double-blinded, parallel-group, before and after study. The control group simply received information on new CPD requirements through the post; the active intervention group also received the framework and associated training. Altogether 48 participants (25 control, 23 active) completed the study. All participants submitted CPD records to the research team before and after receiving the posted resources. The records (n=226) were scored blindly by the researchers using the framework. A subgroup of CPD records (n=96) submitted first (before-stage) and rewritten (after-stage) were analysed separately. MAIN OUTCOME MEASURE: Scores for CPD records received before and after distributing group-dependent material through the post. RESULTS: Using a linear-regression model both analyses found an increase in CPD scores in favour of the active intervention group. For the complete set of records, the effect was a mean difference of 9.9 (95% CI = 0.4 to 19.3), p-value = 0.04. For the subgroup of rewritten records, the effect was a mean difference of 17.3 (95% CI = 5.6 to 28.9), p-value = 0.0048. CONCLUSION: The intervention improved participants’ CPD behaviour. Training pharmacy professionals to use the framework resulted in better CPD activities and CPD records, potentially helpful for revalidation of pharmacy professionals. IMPACT: • Using a bespoke Continuing Professional Development outcomes framework improves the value of pharmacy professionals’ CPD activities and CPD records, with the potential to improve patient care. • The CPD outcomes framework could be helpful to pharmacy professionals internationally who want to improve the quality of their CPD activities and CPD records. • Regulators and officials across Europe and beyond can assess the suitability of the CPD outcomes framework for use in pharmacy CPD and revalidation in their own setting.

Improving power and accuracy of genome-wide association studies via a multi-locus mixed linear model methodology

Genome-wide association studies (GWAS) have been widely used in genetic dissection of complex traits. However, common methods are all based on a fixed-SNP-effect mixed linear model (MLM) and single marker analysis, such as efficient mixed model analysis (EMMA). These methods require Bonferroni correction for multiple tests, which often is too conservative when the number of markers is extremely large. To address this concern, we proposed a random-SNP-effect MLM (RMLM) and a multi-locus RMLM (MRMLM) for GWAS. The RMLM simply treats the SNP-effect as random, but it allows a modified Bonferroni correction to be used to calculate the threshold p value for significance tests. The MRMLM is a multi-locus model including markers selected from the RMLM method with a less stringent selection criterion. Due to the multi-locus nature, no multiple test correction is needed. Simulation studies show that the MRMLM is more powerful in QTN detection and more accurate in QTN effect estimation than the RMLM, which in turn is more powerful and accurate than the EMMA. To demonstrate the new methods, we analyzed six flowering time related traits in Arabidopsis thaliana and detected more genes than previous reported using the EMMA. Therefore, the MRMLM provides an alternative for multi-locus GWAS.

An integral equation method for a boundary value problem arising in unsteady water wave problems

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’s

Does changing the taxonomical resolution alter the value of soil macroinvertebrates as bioindicators of metal pollution?

Ecological indicators are taxa that are affected by, and indicate effects of, anthropogenic environmental stress or disturbance on ecosystems. There is evidence that some species of soil macrofauna (i.e. diameter > 2 min) constitute valuable biological indicators of certain types of soil perturbations. This study aims to determine which level of taxonomic resolution, (species, family or ecological group) is the best to identify indicator of soil disturbance. Macrofauna were sampled in a set of sites encompassing different land-use systems (e.g. forests, pastures, crops) and different levels of pollution. Indicator taxa were sought using the IndVal index proposed by Dufrene and Legendre [Dufrene, M., Legendre, P., 1997. Species assemblages and indicator species: the need for a flexible asymetrical approach. Ecological Monographs 67, 345-3661. This approach is based on a hierarchical typology of sites. The index value changes along the typology and decreases (increases) for generalist (specialist) faunal units (species, families or ecological groups). Of the 327 morphospecies recorded, 19 were significantly associated with a site type or a group of sites (5.8%). Similarly, species were aggregated to form 59 families among which 17 (28.8%) displayed a significant indicator value. Gathering species into 28 broad ecological assemblages led to 14 indicator groups (50%). Beyond the simple proportion of units having significant association with a given level of the site typology, the proportion of specialist and generalist groups changed dramatically when the level of taxonomic resolution was altered. At the species level 84% of the indicator units were specialist, whereas this proportion decreased to 70 and 43% when families and ecological groups were considered. Because specialist groups are the most interesting type of indicators either in terms of conservation or for management purposes we come to the conclusion that the species level is the most accurate taxonomic level in bioindication studies although it requires a high amount of labour and operator knowledge and is time-consuming. (c) 2005 Published by Elsevier Ltd.

Students’ perception of the safety and value of a herbal vs. a conventional medicine for treating insomnia

University students suffer from variable sleep patterns including insomnia;[1] furthermore, the highest incidence of herbal use appears to be among college graduates.[2] Our objective was to test the perception of safety and value of herbal against conventional medicine for the treatment of insomnia in a non-pharmacy student population. We used an experimental design and bespoke vignettes that relayed the same effectiveness information to test our hypothesis that students would give higher ratings of safety and value to herbal product compared to conventional medicine. We tested another hypothesis that the addition of side-effect information would lower people’s perception of the safety and value of the herbal product to a greater extent than it would with the conventional medicine.

Interdisciplinarity: perceptions of the value of computer-supported collaborative work in design for the built environment

This paper presents the findings from a study into the current exploitation of computer-supported collaborative working (CSCW) in design for the built environment in the UK. The research is based on responses to a web-based questionnaire. Members of various professions, including civil engineers, architects, building services engineers, and quantity surveyors, were invited to complete the questionnaire. The responses reveal important trends in the breadth and size of project teams at the same time as new pressures are emerging regarding team integration and efficiency. The findings suggest that while CSCW systems may improve project management (e.g., via project documentation) and the exchange of information between team members, it has yet to significantly support those activities that characterize integrated collaborative working between disparate specialists. The authors conclude by combining the findings with a wider discussion of the application of CSCW to design activity-appealing for CSCW to go beyond multidisciplinary working to achieve interdisciplinary working.

A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.