On generalized bonferroni means

In this paper we investigate modeling capabilities of Bonferroni means and their generalizations. We will show that weighted Bonferroni means can model the concepts of hard and soft partial conjunction, and lead to several interesting special cases, with quite an intuitive interpretation.

Generalized Bonferroni mean operators in multi-criteria aggregation

In this paper we provide a systematic investigation of a family of composed aggregation functions which generalize the Bonferroni mean. Such extensions of the Bonferroni mean are capable of modeling the concepts of hard and soft partial conjunction and disjunction as well as that of k-tolerance and k-intolerance. There are several interesting special cases with quite an intuitive interpretation for application.

On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts

Extensions of aggregation functions to Atanassov orthopairs (often referred to as intuitionistic fuzzy sets or AIFS) usually involve replacing the standard arithmetic operations with those defined for the membership and non-membership orthopairs. One problem with such constructions is that the usual choice of operations has led to formulas which do not generalize the aggregation of ordinary fuzzy sets (where the membership and non-membership values add to 1). Previous extensions of the weighted arithmetic mean and ordered weighted averaging operator also have the absorbent element 〈1,0〉, which becomes particularly problematic in the case of the Bonferroni mean, whose generalizations are useful for modeling mandatory requirements. As well as considering the consistency and interpretability of the operations used for their construction, we hold that it is also important for aggregation functions over higher order fuzzy sets to exhibit analogous behavior to their standard definitions. After highlighting the main drawbacks of existing Bonferroni means defined for Atanassov orthopairs and interval data, we present two alternative methods for extending the generalized Bonferroni mean. Both lead to functions with properties more consistent with the original Bonferroni mean, and which coincide in the case of ordinary fuzzy values.

Defining Bonferroni means over lattices

In the face of mass amounts of information and the need for transparent and fair decision processes, aggregation functions are essential for summarizing data and providing overall evaluations. Although families such as weighted means and medians have been well studied, there are still applications for which no existing aggregation functions can capture the decision makers' preferences. Furthermore, extensions of aggregation functions to lattices are often needed to model operations on L-fuzzy sets, interval-valued and intuitionistic fuzzy sets. In such cases, the aggregation properties need to be considered in light of the lattice structure, as otherwise counterintuitive or unreliable behavior may result. The Bonferroni mean has recently received attention in the fuzzy sets and decision making community as it is able to model useful notions such as mandatory requirements. Here, we consider its associated penalty function to extend the generalized Bonferroni mean to lattices. We show that different notions of dissimilarity on lattices can lead to alternative expressions.

Using linear programming for weights identification of generalized bonferroni means in R

The generalized Bonferroni mean is able to capture some interaction effects between variables and model mandatory requirements. We present a number of weights identification algorithms we have developed in the R programming language in order to model data using the generalized Bonferroni mean subject to various preferences. We then compare its accuracy when fitting to the journal ranks dataset.

A generalization of the Bonferroni mean based on partitions

The mean defined by Bonferroni in 1950 (known by the same name) averages all non-identical product pairs of the inputs. Its generalizations to date have been able to capture unique behavior that may be desired in some decision-making contexts such as the ability to model mandatory requirements. In this paper, we propose a composition that averages conjunctions between the respective means of a designated subset-size partition. We investigate the behavior of such a function and note the relationship within a given family as the subset size is changed. We found that the proposed function is able to more intuitively handle multiple mandatory requirements or mandatory input sets.

When to use the Bonferroni correction

PURPOSE: The Bonferroni correction adjusts probability (p) values because of the increased risk of a type I error when making multiple statistical tests. The routine use of this test has been criticised as deleterious to sound statistical judgment, testing the wrong hypothesis, and reducing the chance of a type I error but at the expense of a type II error; yet it remains popular in ophthalmic research. The purpose of this article was to survey the use of the Bonferroni correction in research articles published in three optometric journals, viz. Ophthalmic & Physiological Optics, Optometry & Vision Science, and Clinical & Experimental Optometry, and to provide advice to authors contemplating multiple testing. RECENT FINDINGS: Some authors ignored the problem of multiple testing while others used the method uncritically with no rationale or discussion. A variety of methods of correcting p values were employed, the Bonferroni method being the single most popular. Bonferroni was used in a variety of circumstances, most commonly to correct the experiment-wise error rate when using multiple 't' tests or as a post-hoc procedure to correct the family-wise error rate following analysis of variance (anova). Some studies quoted adjusted p values incorrectly or gave an erroneous rationale. SUMMARY: Whether or not to use the Bonferroni correction depends on the circumstances of the study. It should not be used routinely and should be considered if: (1) a single test of the 'universal null hypothesis' (Ho ) that all tests are not significant is required, (2) it is imperative to avoid a type I error, and (3) a large number of tests are carried out without preplanned hypotheses.

Patterns of reporting to child protection services in Canada by healthcare and nonhealthcare professionals

Background: All Canadian jurisdictions require certain professionals to report suspected or observed child maltreatment. This study examined the types of maltreatment, level of harm and child functioning issues, controlling for family socioeconomic status, age and gender of the child reported by healthcare and non-healthcare professionals. Methods: We conducted chi-square analyses and logistic regression on a national child welfare sample from the 2003 Canadian Incidence Study of Reported Child Abuse and Neglect (CIS-2003) and compared the differences in professional reporting with its previous cycle (CIS-1998) using Bonferroni-corrected confidence intervals. Results: Our analysis of CIS-2003 data revealed that the majority of substantiated child maltreatment is reported to service agencies by non-healthcare professionals (57%), followed by non-professionals (33%) and healthcare professionals (10%). The number of professional reports increased 2.5 times between CIS-1998 and CIS-2003, while non-professionals’ increased 1.7 times. Of the total investigations, professional reports represented 59% in CIS-1998 and 67% in CIS-2003 (p<0.001). Compared to non-healthcare professionals, healthcare professionals more often reported younger children, children who experienced neglect and emotional maltreatment and those assessed as suffering harm and child functioning issues, but less often exposure to domestic violence. Conclusion: The results indicate that healthcare professionals played an important role in identifying children in need of protection considering harm and other child functioning issues. The authors discuss the reasons why underreporting is likely to remain an issue.

Impacts of traditional husbandry practices on exploitable levels of genetic diversity in cultured 'Tra' catfish (Pangasianodon hypophthalmus) in the Mekong Delta, Vietnam

Sutchi catfish (Pangasianodon hypophthalmus) – known more universally by the Vietnamese name ‘Tra’ is an economically important freshwater fish in the Mekong Delta in Vietnam that constitutes an important food resource. Artificial propagation technology for Tra catfish has only recently been developed along the main branches of the Mekong River where more than 60% of the local human population participate in fishing or aquaculture. Extensive support for catfish culture in general, and that of Tra (P. hypophthalmus) in particular, has been provided by the Vietnamese government to increase both the scale of production and to develop international export markets. In 2006, total Vietnamese catfish exports reached approximately 286,602 metric tons (MT) and were valued at 736.87 $M with a number of large new export destinations being developed. Total value of production from catfish culture has been predicted to increase to approximately USD 1 billion by 2020. While freshwater catfish culture in Vietnam has a promising future, concerns have been raised about long-term quality of fry and the effectiveness of current brood stock management practices, issues that have been largely neglected to date. In this study, four DNA markers (microsatellite loci: CB4, CB7, CB12 and CB13) that were developed specifically for Tra (P. hypophthalmus) in an earlier study were applied to examine the genetic quality of artificially propagated Tra fry in the Mekong Delta in Vietnam. The goals of the study were to assess: (i) how well available levels of genetic variation in Tra brood stock used for artificial propagation in the Mekong Delta of Vietnam (breeders from three private hatcheries and Research Institute of Aquaculture No2 (RIA2) founders) has been conserved; and (ii) whether or not genetic diversity had declined significantly over time in a stock improvement program for Tra catfish at RIA2. A secondary issue addressed was how genetic markers could best be used to assist industry development. DNA was extracted from fins of catfish collected from the two main branches of the Mekong River inf Vietnam, three private hatcheries and samples from the Tra improvement program at RIA2. Study outcomes: i) Genetic diversity estimates for Tra brood stock samples were similar to, and slightly higher than, wild reference samples. In addition, the relative contribution by breeders to fry in commercial private hatcheries strongly suggest that the true Ne is likely to be significantly less than the breeder numbers used; ii) in a stock improvement program for Tra catfish at RIA2, no significant differences were detected in gene frequencies among generations (FST=0.021, P=0.036>0.002 after Bonferroni correction); and only small differences were observed in alleles frequencies among sample populations. To date, genetic markers have not been applied in the Tra catfish industry, but in the current project they were used to evaluate the levels of genetic variation in the Tra catfish selective breeding program at RIA2 and to undertake genetic correlations between genetic marker and trait variation. While no associations were detected using only four loci, they analysis provided training in the practical applications of the use of molecular markers in aquaculture in general, and in Tra culture, in particular.

The 3D kinematics of the single leg flat and decline squat

Background: Pre-participation screening is commonly used to measure and assess potential intrinsic injury risk. The single leg squat is one such clinical screening measure used to assess lumbopelvic stability and associated intrinsic injury risk. With the addition of a decline board, the single leg decline squat (SLDS) has been shown to reduce ankle dorsiflexion restrictions and allowed greater sagittal plane movement of the hip and knee. On this basis, the SLDS has been employed in the Cricket Australia physiotherapy screening protocols as a measure of lumbopelvic control in the place of the more traditional single leg flat squat (SLFS). Previous research has failed to demonstrate which squatting technique allows for a more comprehensive assessment of lumbopelvic stability. Tenuous links are drawn between kinematics and hip strength measures within the literature for the SLS. Formal evaluation of subjective screening methods has also been suggested within the literature. Purpose: This study had several focal points namely 1) to compare the kinematic differences between the two single leg squatting conditions, primarily the five key kinematic variables fundamental to subjectively assess lumbopelvic stability; 2) determine the effect of ankle dorsiflexion range of motion has on squat kinematics in the two squat techniques; 3) examine the association between key kinematics and subjective physiotherapists’ assessment; and finally 4) explore the association between key kinematics and hip strength. Methods: Nineteen (n=19) subjects performed five SLDS and five SLFS on each leg while being filmed by an 8 camera motion analysis system. Four hip strength measures (internal/external rotation and abd/adduction) and ankle dorsiflexion range of motion were measured using a hand held dynamometer and a goniometer respectively on 16 of these subjects. The same 16 participants were subjectively assessed by an experienced physiotherapist for lumbopelvic stability. Paired samples t-tests were performed on the five predetermined kinematic variables to assess the differences between squat conditions. A Bonferroni correction for multiple comparisons was used which adjusted the significance value to p = 0.005 for the paired t-tests. Linear regressions were used to assess the relationship between kinematics, ankle range of motion and hip strength measures. Bivariate correlations between hip strength measures and kinematics and pelvic obliquity were employed to investigate any possible relationships. Results: 1) Significant kinematic differences between squats were observed in dominant (D) and non-dominant (ND) end of range hip external rotation (ND p = <0.001; D p = 0.004) and hip adduction kinematics (ND p = <0.001; D p = <0.001). With the mean angle, only the non-dominant leg observed significant differences in hip adduction (p = 0.001) and hip external rotation (p = <0.001); 2) Significant linear relationships were observed between clinical measures of ankle dorsiflexion and sagittal plane kinematic namely SLFS dominant ankle (p = 0.006; R2 = .429), SLFS non-dominant knee (p = 0.015; R2 = .352) and SLFS non-dominant ankle (p = 0.027; R2 = .305) kinematics. Only the dominant ankle (p = 0.020; R2 = .331) was found to have a relationship with the decline squat. 3) Strength measures had tenuous associations with the subjective assessments of lumbopelvic stability with no significant relationships being observed. 4) For the non-dominant leg, external rotation strength and abduction strength were found to be significantly correlated with hip rotation kinematics (Newtons r = 0.458 p = 0.049; Normalised for bodyweight: r = 0.469; p = 0.043) and pelvic obliquity (normalised for bodyweight: r = 0.498 p = 0.030) respectively for the SLFS only. No significant relationships were observed in the dominant leg for either squat condition. Some elements of the hip strength screening protocols had linear relationships with kinematics of the lower limb, particularly the sagittal plane movements of the knee and ankle. Strength measures had tenuous associations with the subjective assessments of lumbopelvic stability with no significant relationships being observed; Discussion: The key finding of this study illustrated that kinematic differences can occur at the hip without significant kinematic differences at the knee as a result of the introduction of a decline board. Further observations reinforce the role of limited ankle dorsiflexion range of motion on sagittal plane movement of the hip and knee and in turn multiplanar kinematics of the lower limb. The kinematic differences between conditions have clinical implications for screening protocols that employ frontal plane movement of the knee as a guide for femoral adduction and rotation. Subjects who returned stronger hip strength measurements also appeared to squat deeper as characterised by differences in sagittal plane kinematics of the knee and ankle. Despite the aforementioned findings, the relationship between hip strength and lower limb kinematics remains largely tenuous in the assessment of the lumbopelvic stability using the SLS. The association between kinematics and the subjective measures of lumbopelvic stability also remain tenuous between and within SLS screening protocols. More functional measures of hip strength are needed to further investigate these relationships. Conclusion: The type of SLS (flat or decline) should be taken into account when screening for lumbopelvic stability. Changes to lower limb kinematics, especially around the hip and pelvis, were observed with the introduction of a decline board despite no difference in frontal plane knee movements. Differences in passive ankle dorsiflexion range of motion yielded variations in knee and ankle kinematics during a self-selected single leg squatting task. Clinical implications of removing posterior ankle restraints and using the knee as a guide to illustrate changes at the hip may result in inaccurate screening of lumbopelvic stability. The relationship between sagittal plane lower limb kinematics and hip strength may illustrate that self-selected squat depth may presumably be a useful predictor of the lumbopelvic stability. Further research in this area is required.

Association study of the calcitonin gene-related polypeptide-alpha (CALCA) and the receptor activity modifying 1 (RAMP1) genes with migraine

Migraine is a common neurovascular brain disorder characterised by recurrent attacks of severe headache that may be accompanied by various neurological symptoms. Migraine is thought to result from activation of the trigeminovascular system followed by vasodilation of pain-producing intracranial blood vessels and activation of second-order sensory neurons in the trigeminal nucleus caudalis. Calcitonin gene-related peptide (CGRP) is a mediator of neurogenic inflammation and the most powerful vasodilating neuropeptide, and has been implicated in migraine pathophysiology. Consequently, genes involved in CGRP synthesis or CGRP receptor genes may play a role in migraine and/or increase susceptibility. This study investigates whether variants in the gene that encodes CGRP, calcitonin-related polypeptide alpha (CALCA) or in the gene that encodes a component of its receptor, receptor activity modifying protein 1 (RAMP1), are associated with migraine pathogenesis and susceptibility. The single nucleotide polymorphisms (SNPs) rs3781719 and rs145837941 in the CALCA gene, and rs3754701 and rs7590387 at the RAMP1 locus, were analysed in an Australian Caucasian population of migraineurs and matched controls. Although we find no significant association of any of the SNPs tested with migraine overall, we detected a nominally significant association (p = 0.031) of the RAMP1 rs3754701 variant in male migraine subjects, although this is non-significant after Bonferroni correction for multiple testing.

Polymorphisms in inflammation pathway genes and endometrial cancer risk

BACKGROUND Experimental and epidemiologic evidence have suggested that chronic inflammation may play a critical role in endometrial carcinogenesis. METHODS To investigate this hypothesis, a two-stage study was carried out to evaluate single-nucleotide polymorphisms (SNP) in inflammatory pathway genes in association with endometrial cancer risk. In stage I, 64 candidate pathway genes were identified and 4,542 directly genotyped or imputed SNPs were analyzed among 832 endometrial cancer cases and 2,049 controls, using data from the Shanghai Endometrial Cancer Genetics Study. Linkage disequilibrium of stage I SNPs significantly associated with endometrial cancer (P < 0.05) indicated that the majority of associations could be linked to one of 24 distinct loci. One SNP from each of the 24 loci was then selected for follow-up genotyping. Of these, 21 SNPs were successfully designed and genotyped in stage II, which consisted of 10 additional studies including 6,604 endometrial cancer cases and 8,511 controls. RESULTS Five of the 21 SNPs had significant allelic odds ratios (ORs) and 95% confidence intervals (CI) as follows: FABP1, 0.92 (0.85-0.99); CXCL3, 1.16 (1.05-1.29); IL6, 1.08 (1.00-1.17); MSR1, 0.90 (0.82-0.98); and MMP9, 0.91 (0.87-0.97). Two of these polymorphisms were independently significant in the replication sample (rs352038 in CXCL3 and rs3918249 in MMP9). The association for the MMP9 polymorphism remained significant after Bonferroni correction and showed a significant association with endometrial cancer in both Asian- and European-ancestry samples. CONCLUSIONS These findings lend support to the hypothesis that genetic polymorphisms in genes involved in the inflammatory pathway may contribute to genetic susceptibility to endometrial cancer. Impact statement: This study adds to the growing evidence that inflammation plays an important role in endometrial carcinogenesis.

Functional impairments characterising mild, moderate and severe hallux valgus

Objective Hallux valgus has been linked to functional disability and increased falls risk, but mechanisms underpinning functional disability are unclear. This study investigated functional performance, muscle strength and plantar pressures in adults with mild, moderate, and severe HV compared to controls, while considering the influence of foot pain. Methods Sixty adults with hallux valgus (classified as mild, moderate and severe on dorsalplantar radiographs) and 30 controls participated. Measures included: hallux plantarflexion and abduction strength, walking performance, postural sway and forefoot plantar pressures. Multiple analysis of covariance and pairwise comparisons (p<0.05, Bonferroni adjustment) were used to investigate differences between groups, adjusting for age, sex, body mass index and foot pain. Results Hallux plantarflexion and abduction strength was significantly reduced in those with moderate (mean differences: plantarflexion -45.8N, abduction -12.3N, p<0.001) and severe hallux valgus (plantarflexion -50.1N, p<0.001; abduction -11.2N, p=0.01) compared to controls. A significant reduction in hallux peak pressure and pressure-time integral was evident in moderate (peak pressure -90.8kPa, p<0.001) and severe hallux valgus (peak pressure -106.2kPa, p<0.001) compared to controls. Those with severe hallux valgus also demonstrated increased mediolateral postural sway in single leg stance compared to controls (3.5cm, p=0.01). Conclusion Moderate to severe hallux valgus is associated with reduced hallux plantar pressures and strength measures, while relatively normal function compared to controls was found in those with mild deformity. Greater understanding of specific functional deficits associated with different stages of hallux valgus will help inform clinical management and future research.

Is retinal shape different in Asians and Caucasians? Estimation from peripheral refraction and peripheral eye length methods

Purpose:Race appears to be associated with myopiogenesis, with East Asians showing high myopia prevalence. Considering structural variations in the eye, it is possible that retinal shapes are different between races. The purpose of this study was to quantify and compare retinal shapes between racial groups using peripheral refraction (PR) and peripheral eye lengths (PEL). Methods:A Shin-Nippon SRW5000 autorefractor and a Haag-Streit Lenstar LS900 biometer measured PR and PEL, respectively, along horizontal (H) and vertical (V) fields out to ±35° in 5° steps in 29 Caucasian (CA), 16 South Asian (SA) and 23 East Asian (EA) young adults (spherical equivalent range +0.75D to –5.00D in all groups). Retinal vertex curvature Rv and asphericity Q were determined from two methods: a) PR (Dunne): The Gullstrand-Emsley eye was modified according to participant’s intraocular lengths and anterior cornea curvature. Ray-tracing was performed at each angle through the stop, altering cornea asphericity until peripheral astigmatism matched experimental measurements. Retinal curvature and hence retinal co-ordinate intersection with the chief ray were altered until sagittal refraction matched its measurement. b) PEL: Ray-tracing was performed at each angle through the anterior corneal centre of curvature of the Gullstrand-Emsley eye. Ignoring lens refraction, retinal co-ordinates relative to the fovea were determined from PEL and trigonometry. From sets of retinal co-ordinates, conic retinal shapes were fitted in terms of Rv and Q. Repeated-measures ANOVA were conducted on Rv and Q, and post hoc t-tests with Bonferroni correction were used to compare races. Results:In all racial groups both methods showed greater Rv for the horizontal than for the vertical meridian and greater Rv for myopes than emmetropes. Rv was greater in EA than in CA (P=0.02), with Rv for SA being intermediate and not significantly different from CA and EA. The PEL method provided larger Rv than the PR method: PEL: EA vs CA 87±13 vs 83±11 m-1 (H), 79±13 vs 72±14 m-1 (V); PR: EA vs CA 79±10 vs 67±10 m-1 (H), 71±17 vs 66±12 m-1 (V). Q did not vary significantly with race. Conclusions:Estimates of Rv, but not of Q, varied significantly with race. The greater Rv found in EA than in CA and the comparatively high prevalence rate of myopia in many Asian countries may be related.