Census Transform Research Articles

A note on consistency of non‐parametric rank tests and related rank transformations

The extent to which rank transformations result in the same statistical decisions as their non-parametric counterparts is investigated. Simulations are presented using the Wilcoxon-Mann-Whitney test, the Wilcoxon signed-rank test and the Kruskal-Wallis test, together with the rank transformations and t and F tests corresponding to each of those non-parametric methods. In addition to Type I errors and power over all simulations, the study examines the consistency of the outcomes of the two methods on each individual sample. The results show how acceptance or rejection of the null hypothesis and differences in p-values of the test statistics depend in a regular and predictable way on sample size, significance level, and differences between means, for normal and various non-normal distributions.

Shoot organogenesis and plant regeneration in Pityopsis ruthii

Pityopsis ruthii is an endangered herbaceous perennial species from the United States. In vitro multiplication of this species can be valuable for germplasm conservation. Flower receptacles of P. ruthii were cultured on Murashige and Skoog medium (MS) supplemented with 11.4 μM indole-3-acetic acid (IAA) in combination with 2.2, 4.4 or 8.8 μM 6-benzyladenine (BA). Shoots were visible within 14–28 days and three plants were successfully rooted on MS medium supplemented with 5.7 μM IAA. A two tailed t-test for paired-variates revealed that shoot regeneration on MS medium amended with 11.4 μM IAA and 2.2 μM BA was significantly higher (P < 0.05) than on other treatments. Leaf explants were also cultured on MS not supplemented with growth regulators or supplemented with 11.4 μM IAA in combination with 0, 2.2, 4.4 or 8.8 μM BA. Shoots were visible within 21–35 days and one plant was successfully rooted on MS medium supplemented with 5.4 μM NAA. Shoot regeneration on MS medium augmented with 11.4 μM IAA and 2.2 μM BA was significantly higher (P < 0.05) than the other treatments according to analysis of variance (ANOVA) with a rank transformation. Hyperhydricity and rooting of shoots was problematic for explants derived from flower receptacles and leaf tissue, but viable plants were regenerated using both explants sources indicating the potential role for micropropagation in the ex situ conservation of the species.

Interim analyses from a randomised controlled trial to improve visual processing speed in older adults: the Iowa Healthy and Active Minds Study

ObjectivesThe Iowa Healthy and Active Minds Study is a four-arm randomised controlled trial of a visual processing speed training programme (Road Tour). This article presents the preplanned interim results immediately...

Misuse of Statistical Methods in 10 Leading Chinese Medical Journals in 1998 and 2008

Statistical methods are vital to biomedical research. Our aim was to find out whether progress has been made in the last decade in the use of statistical methods in Chinese medical research. We reviewed 10 leading Chinese medical journals published in 1998 and in 2008. Regarding statistical methods, using a multiple t-test for multiple group comparison was the most common error in the t-test in both years, which significantly decreased in 2008. In contingency tables, no significant level adjustment for multiple comparison significantly decreased in 2008. In ANOVA, over a quarter of articles misused the method of multiple pair-wise comparison in both years, and no significant difference was seen between the two years. In the rank transformation nonparametric test, the error of using multiple pair-wise comparison for multiple group comparison became less common. Many mistakes were found in the randomised controlled trial (56.3% in 1998; 67.9% in 2008), non- randomised clinical trial (57.3%; 58.6%), basic science study (72.9%; 65.5%), case study or case series study (48.4%; 47.2%), and cross-sectional study (57.1%; 44.2%). Progress has been made in the use of statistical methods in Chinese medical journals, but much is yet to be done.

CENTRIST: A Visual Descriptor for Scene Categorization

CENsus TRansform hISTogram (CENTRIST), a new visual descriptor for recognizing topological places or scene categories, is introduced in this paper. We show that place and scene recognition, especially for indoor environments, require its visual descriptor to possess properties that are different from other vision domains (e.g., object recognition). CENTRIST satisfies these properties and suits the place and scene recognition task. It is a holistic representation and has strong generalizability for category recognition. CENTRIST mainly encodes the structural properties within an image and suppresses detailed textural information. Our experiments demonstrate that CENTRIST outperforms the current state of the art in several place and scene recognition data sets, compared with other descriptors such as SIFT and Gist. Besides, it is easy to implement and evaluates extremely fast.

A Theory of Transformation Monoids: Combinatorics and Representation Theory

The aim of this paper is to develop a theory of finite transformation monoids and in particular to study primitive transformation monoids. We introduce the notion of orbitals and orbital digraphs for transformation monoids and prove a monoid version of D. Higman's celebrated theorem characterizing primitivity in terms of connectedness of orbital digraphs. A thorough study of the module (or representation) associated to a transformation monoid is initiated. In particular, we compute the projective cover of the transformation module over a field of characteristic zero in the case of a transitive transformation or partial transformation monoid. Applications of probability theory and Markov chains to transformation monoids are also considered and an ergodic theorem is proved in this context. In particular, we obtain a generalization of a lemma of P. Neumann, from the theory of synchronizing groups, concerning the partition associated to a transformation of minimal rank.

Variance heterogeneity analysis for detection of potentially interacting genetic loci: method and its limitations

BackgroundPresence of interaction between a genotype and certain factor in determination of a trait's value, it is expected that the trait's variance is increased in the group of subjects having this genotype. Thus, test of heterogeneity of variances can be used as a test to screen for potentially interacting single-nucleotide polymorphisms (SNPs). In this work, we evaluated statistical properties of variance heterogeneity analysis in respect to the detection of potentially interacting SNPs in a case when an interaction variable is unknown.ResultsThrough simulations, we investigated type I error for Bartlett's test, Bartlett's test with prior rank transformation of a trait to normality, and Levene's test for different genetic models. Additionally, we derived an analytical expression for power estimation. We showed that Bartlett's test has acceptable type I error in the case of trait following a normal distribution, whereas Levene's test kept nominal Type I error under all scenarios investigated. For the power of variance homogeneity test, we showed (as opposed to the power of direct test which uses information about known interacting factor) that, given the same interaction effect, the power can vary widely depending on the non-estimable direct effect of the unobserved interacting variable. Thus, for a given interaction effect, only very wide limits of power of the variance homogeneity test can be estimated. Also we applied Levene's approach to test genome-wide homogeneity of variances of the C-reactive protein in the Rotterdam Study population (n = 5959). In this analysis, we replicate previous results of Pare and colleagues (2010) for the SNP rs12753193 (n = 21, 799).ConclusionsScreening for differences in variances among genotypes of a SNP is a promising approach as a number of biologically interesting models may lead to the heterogeneity of variances. However, it should be kept in mind that the absence of variance heterogeneity for a SNP can not be interpreted as the absence of involvement of the SNP in the interaction network.

Fitness-Associated Sexual Reproduction in a Filamentous Fungus

Sex is a long-standing evolutionary enigma. Although the majority of eukaryotes reproduce sexually at least sometimes [1-3], the evolution of sex from an asexual ancestor has been difficult to explain because it requires sexually reproducing lineages to overcome the manifold costs of sex, including the destruction of favorable gene combinations created by selection [4, 5]. Conditions for the evolution of sex are much broader if individuals can reproduce either sexually or asexually (i.e., facultative sex) and allocate disproportionately more resources to sex when their fitness is low (fitness-associated-sex or FAS [6-10]). Although facultatively sexual organisms have been shown to engage in more sex when stressed [11], direct evidence for FAS is lacking. We provide evidence using 53 genotypes of the filamentous fungus Aspergillus nidulans in a reciprocal transplant experiment across three environments. Different genotypes achieved highest fitness in different environments and genotypes invested relatively more in sex in environments in which their fitness was lower, showing that allocation to sexual reproduction is a function of how well-adapted a genotype is to its environment. FAS in A. nidulans is unlikely to have evolved as a strategy to resist or avoid stress because asexual spores are more dispersive and equally resistant [12, 13].

A methodology for product reliability enhancement via saturated–unreplicated fractional factorial designs

Reliability enhancement constitutes an important component in product quality improvement. This work presents a methodology that unites the test effectiveness of Taguchi-type orthogonal arrays with the contrasting efficiency of order statistics at small sampling rates to create an optimization technique for improving reliability. The method relies on decoupling shape and scale effects and after a rank transformation, the super-ranking technique is applied to assign statistical significance to examined control factors. A case study based on aluminum milling operations is utilized to illustrate how the method presented here is adopted in screening through a can-stock product in order to achieve optimal levels of reliability.

Rank Transformation in Haseman-Elston Regression Using Scores for Location-Scale Alternatives

The Haseman-Elston method is a simple regression approach for detecting genetic linkage to quantitative traits in sib-pair studies. Although this method and especially the new extended Haseman-Elston approach are quite robust, there might be some loss of power for non-normally distributed traits. We propose using rank transformation techniques, which either combine the information on a trend in locations and in scales or detect a trend only for a subset of the trait variables for genetically different sibs under linkage. As this rank transformation is based on linear regression, no exact grouping of identity by descent proportions has to be assumed. Simulation results indicate a gain in power compared to recently suggested nonparametric methods.

Effects of normalization on quantitative traits in association test

BackgroundQuantitative trait loci analysis assumes that the trait is normally distributed. In reality, this is often not observed and one strategy is to transform the trait. However, it is not clear how much normality is required and which transformation works best in association studies.ResultsWe performed simulations on four types of common quantitative traits to evaluate the effects of normalization using the logarithm, Box-Cox, and rank-based transformations. The impact of sample size and genetic effects on normalization is also investigated. Our results show that rank-based transformation gives generally the best and consistent performance in identifying the causal polymorphism and ranking it highly in association tests, with a slight increase in false positive rate.ConclusionFor small sample size or genetic effects, the improvement in sensitivity for rank transformation outweighs the slight increase in false positive rate. However, for large sample size and genetic effects, normalization may not be necessary since the increase in sensitivity is relatively modest.

The Wilcoxon–Mann–Whitney test under scrutiny

The Wilcoxon-Mann-Whitney (WMW) test is often used to compare the means or medians of two independent, possibly nonnormal distributions. For this problem, the true significance level of the large sample approximate version of the WMW test is known to be sensitive to differences in the shapes of the distributions. Based on a wide ranging simulation study, our paper shows that the problem of lack of robustness of this test is more serious than is thought to be the case. In particular, small differences in variances and moderate degrees of skewness can produce large deviations from the nominal type I error rate. This is further exacerbated when the two distributions have different degrees of skewness. Other rank-based methods like the Fligner-Policello (FP) test and the Brunner-Munzel (BM) test perform similarly, although the BM test is generally better. By considering the WMW test as a two-sample T test on ranks, we explain the results by noting some undesirable properties of the rank transformation. In practice, the ranked samples should be examined and found to sufficiently satisfy reasonable symmetry and variance homogeneity before the test results are interpreted.

P02-205 Maintained attitudinal changes in nursing personnel after a brief training on suicide prevention

Aim:To verify whether nursing personnel working at a general hospital change their attitudes after a brief training course on suicide prevention and if these newly acquired attitudes persist over a 6-month time.Method:317 nursing personnel attended a 6-hour training program. They answered anonymously pre- and post-training the Suicide Behavior Attitude Questionnaire (SBAQ) which comprises 21 visual analogue scale items divided in three factorial sub-scales. The scores on each SBAQ sub-scale (dependent variable) were compared along the time using ANOVA for repeated measures with rank transformation. The time of the measurement and characteristics of the nursing staff were considered as independent variables.Results:There have been positive changes in the attitudes and these gains were significantly maintained at the 6-month follow-up evaluation. Improvement was in the Feelings and Professional Capacity factorial subscales (p = 0.0001 and 0.01, respectively). There was no change on the Right to Suicide subscale.Conclusion:It was possible to demonstrate positive changes in the attitudes of nursing personnel as assessed six months after a brief training course on suicide prevention. As attitudes influence the effectiveness of the health care personnel interventions our findings may have important implications for the development of suicide prevention programs.

Imaging research of normal ligamentous structures in the region of craniocervical junction

Objective To study the imaging characteristics of the ligaments in craniocervical junction (CCJ), and to optimize the examination methods and scanning sequences of the ligaments in this region. Methods Two groups of 51 healthy volunteers in each were selected to undergo CT and MRI examination respectively. The CT and MRI features of the ligaments in CCJ were assessed. Two senior imaging doctors compared the results of showing the ligaments in CCJ by several MRI sequences, including T1 WI ,T2 WI, proton density weighted imaging (PDWI), T2 * WI and short time inversion recovery (STIR) ,and proton density fat saturate (PDFSAT). Standard normal rank transformation was done according to the primary data,and then analysis of variance of repeated measurement was applied. Results CT and MRI could both demonstrate the ligaments (except the anterior atlantooccipital membrane only seen on MRI) and their adjoins in CCJ, while MRI had more advantages than CT. The display ratio of the anterior atlantooccipital membrane was 100% (51/51) by MRI. The display ratio of the apical ligament was 29.4%(15/51) by CT and 43.1% (22/51) by MRI. The posterior atlantooccipital membrane-dura complex,tectorial ligament-dura complex, transverse ligament, and alar ligament could be demonstrated clearly by CT and MRI, the display ratio was 100% respectively (51/51). The results of PDWi scored by two doctors were both 5.0, there were no significant differences between them (F = 0.000, P > 0.05), which were significantly higher than T, WI (M = 3.0), T2Wi (M = 3.0), T2 * WI (M = 1.0), STIR (M = 1.0), and PDFSAT(M = 3.0)(P < 0.01). Conclusion MRI was superior to CT in demonstrating the ligaments in CCJ. PDWI was the optimal MRI sequence. Imaging research of normal ligamentous structures in CCJ could provide valuable diagnostic and therapeutic information for evaluating the ligamentous diseases. Key words: Atlanto-occipital joint; Ligaments; Tomography, X-ray computed; Magneticresonance imaging

Decreasing gradient of antibiotic concentration in the lumen of catheters locked with vancomycin

The purpose of this study was to investigate if vancomycin concentration is maintained along the lumen of dialysis catheters after 48 h of lock therapy. Each lumen of nine catheters (three subclavian and six femoral) was locked with 2,500 mg/l of vancomycin for 48 h. After that period, the content of the lumen was aspirated with three different syringes of 0.4 ml each to measure the proximal, medial and distal vancomycin concentration. Vancomycin concentration was measured using a homogeneous particle-enhanced turbidimetric inhibition immunoassay. A non-parametric ANOVA, by means of a rank transformation on the antibiotic concentration, was used to assess the influence of the catheter segment (proximal, medial and distal) and the catheter type (femoral or subclavian). A significant decrease in vancomycin concentration from proximal to distal segments was observed (p < 0.001). In addition, the vancomycin concentration in subclavian catheters was significantly higher than in femoral catheters (p < 0.001). In our study there was a decreasing gradient in vancomycin concentration from proximal to distal segments of the catheter. This may explain the failure of antibiotic lock-therapy.

Correlative analyses of plasma cytokine/angiogenic factor (C/AF) profile, gender and outcome in a randomized, three-arm, phase II trial of first-line vandetanib (VAN) and/or carboplatin plus paclitaxel (CP) for advanced non-small cell lung cancer (NSCLC)

7593 Background: VAN (ZD6474) is an oral inhibitor of VEGFR, EGFR and RET. In a phase II trial, 181 patients with advanced NSCLC were randomized to 1st-line treatment with VAN, CP or VAN + CP. Progression free survival (PFS) was prolonged for VAN + CP vs CP (Heymach et al, submitted for ASCO 2007). Exploratory subgroup analyses suggest gender differences in PFS benefit for VAN + CP vs CP (HR 0.47 in females vs 1.05 in males). We performed exploratory analyses of plasma levels of 35 C/AFs to investigate gender differences and potential prognostic or predictive markers. Methods: Plasma was collected at baseline (n = 123; VAN 55, CP 32, VAN + CP 36), day (D) 8 (n = 104), D22 (n = 95), and D43 (n = 83). We used multiplex bead assays to measure 33 plasma C/AFs, including VEGF, basic FGF, EGF, HGF, E-selectin, ICAM-1, MMP-9, multiple chemokines and interleukins (IL). Osteopontin and sVEGFR-2 were measured by ELISA. Cox models were applied on PFS to identify prognostic/predictive markers after rank transformation and adjusted for covariates. Results: Significant gender differences in baseline C/AF levels were seen for IL-15, IL-1RA, IL-2R, MIG, and MIP-1A (all higher in females, all p = 0.022). Controlling for gender and treatment, high baseline E-selectin (p = .01), IL-6 (p = 0.018), and IL-2R (p = 0.008) were adverse prognostic indicators for PFS. Controlling for gender, the tests for treatment by factor interactions (to assess whether treatment effect was different in patients with low and high C/AF levels) were significant for baseline HGF (p = 0.04) and IL-2R (p = 0.008). For both HGF and IL- 2R, low levels were associated with prolonged PFS in the VAN arm, but were not associated with differences in the CP or VAN + CP arms. Significant changes in VEGF (rise) and sVEGFR-2 (decrease) occurred with treatment in the VAN arm; IL12, IL-1RA, MMP-9 and MCP-1 changed in the CP and VAN + CP arms. Conclusions: There are gender differences in PFS benefit from VAN and in plasma C/AF profile. Several C/AFs were of prognostic value, whereas low HGF and IL-2R were predictive of benefit in the VAN but not CP and VAN + CP arms. These gender differences and markers warrant further investigation. [Table: see text]

Environmental risk assessment in the Tuscany region: a proposal

AbstractIn this paper we present a first attempt to define a statistically coherent protocol for Environmental Risk Assessment (ERA), considered as a classification problem. Our approach moves from an idea developed in the pattern recognition literature. Several independent classifiers, each working on a subset of the covariates space, produce a set of corresponding units classifications. Then a gate, modulating the partial results, produces a final, combined classification. We propose a combined classification strategy based on rank transformations and Bayesian mixture classifiers. Although the use of Bayesian mixture models in classification problems is quite common in many fields of application, the novelty of our proposal concerns the use of truncated Gaussian components to model the behaviour of the rank variables in a multidimensional setting. We approach the general problem by partitioning the covariate space into several subspaces, each one representing one environmental dimension; we consider three environmental dimensions (Air, Water and Waste), represented by several pressure indicators. The evaluation of environmental risk for the Tuscany municipalities is our motivating example. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Andrews–Curtis groups and the Andrews–Curtis conjecture

For an integer n at least two and a positive integer m , let C( n,m ) denote the group of Andrews–Curtis transformations of rank ( n,m ) and let F denote the free group of rank n + m . A subgroup AC( n,m ) of Aut(F) is defined, and an anti-isomorphism AC( n,m ) to C( n,m ) is described. We solve the generalized word problem for AC( n,m ) in Aut(F) and discuss an associated reformulation of the Andrews–Curtis conjecture.

Gender differences in correlations among cardiovascular risk factors

Although the clustering of a few specific cardiovascular risk factors is known as the metabolic syndrome, sex-specific differences in correlations among risk factors have not been thoroughly examined. The analysis was undertaken to detect gender differences in correlations among cardio-vascular risk factors. Correlations among age, body mass index, systolic and diastolic blood pressures, and serum levels of fasting blood sugar (FBS), triglycerides (TG), high- and low-density lipoprotein cholesterol, high-sensitivity C-reactive protein (CRP), and uric acid were analyzed in apparently healthy Japanese men and women with TG<400 mg/dL and FBS<126 mg/dL. Among the 136 men and 136 women examined, the frequency of significant correlations was marginally higher in women than in men: 28/45 correlations versus 17/45 correlations, respectively (P=0.017). Of a total of 45 possible correlations, 5 were marginally or significantly stronger in women, whereas no correlations among these risk factors were marginally or significantly stronger in men (P=0.021). These gender differences were considerably attenuated after adjustment for age. However, a significant sex-specific difference was observed in the correlation between TG and rank transformation of CRP, even after adjustment for age (P<0.01). Correlations among cardiovascular risk factors were marginally stronger in women than in men. These results suggest that the existence of 1 additional risk factor may increase the risk of cardiovascular disease more steeply in women than in men.

Transformations of Count Data for Tests of Interaction in Factorial and Split-Plot Experiments

In applied entomological experiments, when the response is a count-type variable, certain transformation remedies such as the square root, logarithm (log), or rank transformation are often used to normalize data before analysis of variance. In this study, we examine the usefulness of these transformations by reanalyzing field-collected data from a split-plot experiment and by performing a more comprehensive simulation study of factorial and split-plot experiments. For field-collected data, significant interactions were dependent upon the type of transformation. For the simulation study, Poisson distributed errors were used for a 2 by 2 factorial arrangement, in both randomized complete block and split-plot settings. Various sizes of main effects were induced, and type I error rates and powers of the tests for interaction were examined for the raw response values, log-, square root-, and rank-transformed responses. The aligned rank transformation also was investigated because it has been shown to perform well in testing interactions in factorial arrangements. We found that for testing interactions, the untransformed response and the aligned rank response performed best (preserved nominal type I error rates), whereas the other transformations had inflated error rates when main effects were present. No evaluations of the tests for main effects or simple effects have been conducted. Potentially these transformations will still be necessary when performing these tests.