Decomposition of $\rm R\times C$ contingency table chi -square: Application to binned DNA fragment size data and population structure analysis

The purpose of this research is to develop a new statistical method to determine the minimum set of rows (R) in a R x C contingency table of discrete data that explains the dependence of observations. The statistical power of the method will be empirically determined by computer simulation to judge its efficiency over the presently existing methods. The method will be applied to data on DNA fragment length variation at six VNTR loci in over 72 populations from five major racial groups of human (total sample size is over 15,000 individuals; each sample having at least 50 individuals). DNA fragment lengths grouped in bins will form the basis of studying inter-population DNA variation within the racial groups are significant, will provide a rigorous re-binning procedure for forensic computation of DNA profile frequencies that takes into account intra-racial DNA variation among populations. ^

A unified approach for representing rows and columns in contingency tables

By using suitable parameters, we present a uni¯ed aproach for describing four methods for representing categorical data in a contingency table. These methods include: correspondence analysis (CA), the alternative approach using Hellinger distance (HD), the log-ratio (LR) alternative, which is appropriate for compositional data, and the so-called non-symmetrical correspondence analysis (NSCA). We then make an appropriate comparison among these four methods and some illustrative examples are given. Some approaches based on cumulative frequencies are also linked and studied using matrices. Key words: Correspondence analysis, Hellinger distance, Non-symmetrical correspondence analysis, log-ratio analysis, Taguchi inertia

Statnote 7: chi-square contingency tables

When the data are counts or the frequencies of particular events and can be expressed as a contingency table, then they can be analysed using the chi-square distribution. When applied to a 2 x 2 table, the test is approximate and care needs to be taken in analysing tables when the expected frequencies are small either by applying Yate’s correction or by using Fisher’s exact test. Larger contingency tables can also be analysed using this method. Note that it is a serious statistical error to use any of these tests on measurement data!

The relationship between chronic disease self-efficacy and nutritional status, functional ability and quality of life in older adults at risk of hospital readmission

Background and significance: Older adults with chronic diseases are at increasing risk of hospital admission and readmission. Approximately 75% of adults have at least one chronic condition, and the odds of developing a chronic condition increases with age. Chronic diseases consume about 70% of the total Australian health expenditure, and about 59% of hospital events for chronic conditions are potentially preventable. These figures have brought to light the importance of the management of chronic disease among the growing older population. Many studies have endeavoured to develop effective chronic disease management programs by applying social cognitive theory. However, limited studies have focused on chronic disease self-management in older adults at high risk of hospital readmission. Moreover, although the majority of studies have covered wide and valuable outcome measures, there is scant evidence on examining the fundamental health outcomes such as nutritional status, functional status and health-related quality of life. Aim: The aim of this research was to test social cognitive theory in relation to self-efficacy in managing chronic disease and three health outcomes, namely nutritional status, functional status, and health-related quality of life, in older adults at high risk of hospital readmission. Methods: A cross-sectional study design was employed for this research. Three studies were undertaken. Study One examined the nutritional status and validation of a nutritional screening tool; Study Two explored the relationships between participants. characteristics, self-efficacy beliefs, and health outcomes based on the study.s hypothesized model; Study Three tested a theoretical model based on social cognitive theory, which examines potential mechanisms of the mediation effects of social support and self-efficacy beliefs. One hundred and fifty-seven patients aged 65 years and older with a medical admission and at least one risk factor for readmission were recruited. Data were collected from medical records on demographics, medical history, and from self-report questionnaires. The nutrition data were collected by two registered nurses. For Study One, a contingency table and the kappa statistic was used to determine the validity of the Malnutrition Screening Tool. In Study Two, standard multiple regression, hierarchical multiple regression and logistic regression were undertaken to determine the significant influential predictors for the three health outcome measures. For Study Three, a structural equation modelling approach was taken to test the hypothesized self-efficacy model. Results: The findings of Study One suggested that a high prevalence of malnutrition continues to be a concern in older adults as the prevalence of malnutrition was 20.6% according to the Subjective Global Assessment. Additionally, the findings confirmed that the Malnutrition Screening Tool is a valid nutritional screening tool for hospitalized older adults at risk of readmission when compared to the Subjective Global Assessment with high sensitivity (94%), and specificity (89%) and substantial agreement between these two methods (k = .74, p < .001; 95% CI .62-.86). Analysis data for Study Two found that depressive symptoms and perceived social support were the two strongest influential factors for self-efficacy in managing chronic disease in a hierarchical multiple regression. Results of multivariable regression models suggested advancing age, depressive symptoms and less tangible support were three important predictors for malnutrition. In terms of functional status, a standard regression model found that social support was the strongest predictor for the Instrumental Activities of Daily Living, followed by self-efficacy in managing chronic disease. The results of standard multiple regression revealed that the number of hospital readmission risk factors adversely affected the physical component score, while depressive symptoms and self-efficacy beliefs were two significant predictors for the mental component score. In Study Three, the results of the structural equation modelling found that self-efficacy partially mediated the effect of health characteristics and depression on health-related quality of life. The health characteristics had strong direct effects on functional status and body mass index. The results also indicated that social support partially mediated the relationship between health characteristics and functional status. With regard to the joint effects of social support and self-efficacy, social support fully mediated the effect of health characteristics on self-efficacy, and self-efficacy partially mediated the effect of social support on functional status and health-related quality of life. The results also demonstrated that the models fitted the data well with relative high variance explained by the models, implying the hypothesized constructs under discussion were highly relevant, and hence the application for social cognitive theory in this context was supported. Conclusion: This thesis highlights the applicability of social cognitive theory on chronic disease self-management in older adults at risk of hospital readmission. Further studies are recommended to validate and continue to extend the development of social cognitive theory on chronic disease self-management in older adults to improve their nutritional and functional status, and health-related quality of life.

Study of leukemia inhibitory factor polymorphism within an Australian multiple sclerosis population

OBJECTIVE: To examine a polymorphism within the 3' untranslated region of the leukemia inhibitory factor gene for an association with multiple sclerosis within an Australian case-control population. METHODS: A test group of 121 unrelated multiple sclerosis patients, of Caucasian origin, and 121 controls, matched for ethnicity, sex and age (+/-5 years) were included in the study. The LIF 3' UTR StuI polymorphism was genotyped by restriction fragment length polymorphism analysis. Statistical analysis of genotype and allele frequencies included Hardy-Weinberg law and conventional contingency table analysis incorporating the standard chi-squared test for independence. RESULTS: Allelic and genotype frequencies did not demonstrate a significant association between the case and control groups for the tested LIF 3' UTR StuI polymorphism. CONCLUSION: The results indicate that the LIF 3' UTR StuI polymorphism is not associated with multiple sclerosis, however we cannot exclude the hypothesis that other polymorphic alleles of LIF could be implicated in MS susceptibility.

No role for estrogen receptor 1 gene intron 1 Pvu II and exon 4 C325G polymorphisms in migraine susceptibility

Background We have previously reported an association between the estrogen receptor 1 (ESR1) gene exon 8 G594A polymorphism and migraine susceptibility in two independent Australian cohorts. In this paper we report results of analysis of two further single nucleotide polymorphisms (SNPs) in the ESR1 gene in the same study group, the T/C Pvu II SNP in intron 1 and the C325G SNP in exon 4, as well as results of linkage disequilibrium (LD) analysis on these markers. Methods We investigated these variants by case-control association analysis in a cohort of 240 migraineurs and 240 matched controls. The SNPs were genotyped using specific restriction enzyme assays. Results were analysed using contingency table methods incorporating the chi-squared statistic. LD results are presented as D' statistics with associated P values. Results We found no evidence for association of the Pvu II T/C polymorphism and the C325G polymorphism and migraine susceptibility and no evidence for LD between these two SNPs and the previously implicated exon 8 G594A marker. Conclusion We have found no role for the polymorphisms in intron 1 and exon 4 with migraine susceptibility. To further investigate our previously implicated exon 8 marker, we suggest the need for studies with a high density of polymorphisms be undertaken, with particular focus on markers in LD with the exon 8 marker.

Association analysis of a highly polymorphic CAG Repeat in the human potassium channel gene KCNN3 and migraine susceptibility

Background Migraine is a polygenic multifactorial disease, possessing environmental and genetic causative factors with multiple involved genes. Mutations in various ion channel genes are responsible for a number of neurological disorders. KCNN3 is a neuronal small conductance calcium-activated potassium channel gene that contains two polyglutamine tracts, encoded by polymorphic CAG repeats in the gene. This gene plays a critical role in determining the firing pattern of neurons and acts to regulate intracellular calcium channels. Methods The present association study tested whether length variations in the second (more 3') polymorphic CAG repeat in exon 1 of the KCNN3 gene, are involved in susceptibility to migraine with and without aura (MA and MO). In total 423 DNA samples from unrelated individuals, of which 202 consisted of migraine patients and 221 non-migraine controls, were genotyped and analysed using a fluorescence labelled primer set on an ABI310 Genetic Analyzer. Allele frequencies were calculated from observed genotype counts for the KCNN3 polymorphism. Analysis was performed using standard contingency table analysis, incorporating the chi-squared test of independence and CLUMP analysis. Results Overall, there was no convincing evidence that KCNN3 CAG lengths differ between Caucasian migraineurs and controls, with no significant difference in the allelic length distribution of CAG repeats between the population groups (P = 0.090). Also the MA and MO subtypes did not differ significantly between control allelic distributions (P > 0.05). The prevalence of the long CAG repeat (>19 repeats) did not reach statistical significance in migraineurs (P = 0.15), nor was there a significant difference between the MA and MO subgroups observed compared to controls (P = 0.46 and P = 0.09, respectively), or between MA vs MO (P = 0.40). Conclusion This association study provides no evidence that length variations of the second polyglutamine array in the N-terminus of the KCNN3 channel exert an effect in the pathogenesis of migraine.

Non-inherited maternal HLA alleles are associated with rheumatoid arthritis

Background. Rheumatoid arthritis (RA) is strongly associated with a series of HLA-DRB1 alleles that encode a conserved sequence of amino acids (70Q/R K/R R A A74) in the DRβ1 chain, known as the shared epitope (SE). However 30% of patients are negative for DRB1*04 and 15% are SE-negative. Exposure to these alleles as non-inherited maternal antigens (NIMA) might explain this discrepancy. We undertook a family study to investigate the role of NIMA in RA. Methods. One hundred families, including the RA proband and both parents, were recruited. HLA-DRB1 genotyping was performed using an allele-specific polymerase chain reaction by standard methods. The frequencies of NIMA and non-inherited paternal antigens (NIPA) were compared using contingency tables and a two-tailed P test. We then reviewed four previously published studies of NIMA in RA and conducted an analysis of the combined data Results. We identified 36 families in which the proband was DRB1*04-negative and 13 in which the proband lacked the SE. There was an excess of DRB1*04 and SE NIMA (P=0.05) compared with NIPA. Combined analysis with previous studies showed that 53/231 mothers (23%) versus 25/205 fathers (12%) had a non-inherited DRB1*04 (P=0.003) and 30/99 mothers versus 18/101 fathers had a non-inherited SE allele (P=0.03). Conclusion. A role for HLA NIMA in RA is suggested by these results.

Evaluation of Precipitation Retrievals From Orbital Data Products of TRMM Over a Subtropical Basin in India

The spatial error structure of daily precipitation derived from the latest version 7 (v7) tropical rainfall measuring mission (TRMM) level 2 data products are studied through comparison with the Asian precipitation highly resolved observational data integration toward evaluation of the water resources (APHRODITE) data over a subtropical region of the Indian subcontinent for the seasonal rainfall over 6 years from June 2002 to September 2007. The data products examined include v7 data from the TRMM radiometer Microwave Imager (TMI) and radar precipitation radar (PR), namely, 2A12, 2A25, and 2B31 (combined data from PR and TMI). The spatial distribution of uncertainty from these data products were quantified based on performance metrics derived from the contingency table. For the seasonal daily precipitation over a subtropical basin in India, the data product of 2A12 showed greater skill in detecting and quantifying the volume of rainfall when compared with the 2A25 and 2B31 data products. Error characterization using various error models revealed that random errors from multiplicative error models were homoscedastic and that they better represented rainfall estimates from 2A12 algorithm. Error decomposition techniques performed to disentangle systematic and random errors verify that the multiplicative error model representing rainfall from 2A12 algorithm successfully estimated a greater percentage of systematic error than 2A25 or 2B31 algorithms. Results verify that although the radiometer derived 2A12 rainfall data is known to suffer from many sources of uncertainties, spatial analysis over the case study region of India testifies that the 2A12 rainfall estimates are in a very good agreement with the reference estimates for the data period considered.

The performance and persistence of exchange-traded funds: evidence for iShares MSCI country-specific ETFs

The aim of this paper is to investigate the performance and persistence of 20 iShares MSCI country-specific exchange-traded funds (ETFs) in comparison with S&P 500 index over the period July 2001 to June 2006. There are several studies analysing mutual funds performance in past years, but very little is known about ETFs. In our analysis the Sharpe, Treynor and Sortino ratios are used as risk-adjusted performance measures. To evaluate performance persistence and therefore if there is any relationship among past performance and future performance, we apply to the Spearman Rank Correlation Coefficient and the Winner-loser Contingency Table. The main findings are at two levels. First, ETFs can beat the U.S. market index based on risk-adjusted performance measures. Second, there is evidence of ETFs performance persistence based on annual return.

Genes involved in the metabolism of fatty acids and risk for Crohn's disease in children: a candidate gene study

Contexte - La prévalence de la maladie de Crohn (MC), une maladie inflammatoire chronique du tube digestif, chez les enfants canadiens se situe parmi les plus élevées au monde. Les interactions entre les réponses immunes innées et acquises aux microbes de l'hôte pourraient être à la base de la transition de l’inflammation physiologique à une inflammation pathologique. Le leucotriène B4 (LTB4) est un modulateur clé de l'inflammation et a été associé à la MC. Nous avons postulé que les principaux gènes impliqués dans la voie métabolique du LTB4 pourrait conférer une susceptibilité accrue à l'apparition précoce de la MC. Dans cette étude, nous avons exploré les associations potentielles entre les variantes de l'ADN des gènes ALOX5 et CYP4F2 et la survenue précoce de la MC. Nous avons également examiné si les gènes sélectionnés montraient des effets parent-d'origine, influençaient les phénotypes cliniques de la MC et s'il existait des interactions gène-gène qui modifieraient la susceptibilité à développer la MC chez l’enfant. Méthodes – Dans le cadre d’une étude de cas-parents et de cas-témoins, des cas confirmés, leurs parents et des contrôles ont été recrutés à partir de trois cliniques de gastro-entérologie à travers le Canada. Les associations entre les polymorphismes de remplacement d'un nucléotide simple (SNP) dans les gènes CYP4F2 et ALOX5 ont été examinées. Les associations allélique et génotypiques ont été examinées à partir d’une analyse du génotype conditionnel à la parenté (CPG) pour le résultats cas-parents et à l’aide de table de contingence et de régression logistique pour les données de cas-contrôles. Les interactions gène-gène ont été explorées à l'aide de méthodes de réduction multi-factorielles de dimensionnalité (MDR). Résultats – L’étude de cas-parents a été menée sur 160 trios. L’analyse CPG pour 14 tag-SNP (10 dans la CYP4F2 et 4 dans le gène ALOX5) a révélé la présence d’associations alléliques ou génotypique significatives entre 3 tag-SNP dans le gène CYP4F2 (rs1272, p = 0,04, rs3093158, p = 0.00003, et rs3093145, p = 0,02). Aucune association avec les SNPs de ALOX5 n’a pu être démontrée. L’analyse de l’haplotype de CYP4F2 a montré d'importantes associations avec la MC (test omnibus p = 0,035). Deux haplotypes (GAGTTCGTAA, p = 0,05; GGCCTCGTCG, p = 0,001) montraient des signes d'association avec la MC. Aucun effet parent-d'origine n’a été observé. Les tentatives de réplication pour trois SNPs du gene CYP4F2 dans l'étude cas-témoins comportant 225 cas de MC et 330 contrôles suggèrent l’association dans un de ceux-ci (rs3093158, valeur non-corrigée de p du test unilatéral = 0,03 ; valeur corrigée de p = 0.09). La combinaison des ces deux études a révélé des interactions significatives entre les gènes CYP4F2, ALOX et NOD2. Nous n’avons pu mettre en évidence aucune interaction gène-sexe, de même qu’aucun gène associé aux phénotypes cliniques de la MC n’a pu être identifié. Conclusions - Notre étude suggère que la CYP4F2, un membre clé de la voie métabolique LTB4 est un gène candidat potentiel pour MC. Nous avons également pu mettre en évidence que les interactions entre les gènes de l'immunité adaptative (CYP4F2 et ALOX5) et les gènes de l'immunité innée (NOD2) modifient les risques de MC chez les enfants. D'autres études sur des cohortes plus importantes sont nécessaires pour confirmer ces conclusions.

Comparing correspondence analysis and the log-ratio alternative for representing categorical data

We compare correspondance análisis to the logratio approach based on compositional data. We also compare correspondance análisis and an alternative approach using Hellinger distance, for representing categorical data in a contingency table. We propose a coefficient which globally measures the similarity between these approaches. This coefficient can be decomposed into several components, one component for each principal dimension, indicating the contribution of the dimensions to the difference between the two representations. These three methods of representation can produce quite similar results. One illustrative example is given

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table has n rows and m columns and all probabilities are non-null. This kind of table can be seen as an element in the simplex of n · m parts. In this context, the marginals are identified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclidean elements of the Aitchison geometry of the simplex can also be translated into the table of probabilities: subspaces, orthogonal projections, distances. Two important questions are addressed: a) given a table of probabilities, which is the nearest independent table to the initial one? b) which is the largest orthogonal projection of a row onto a column? or, equivalently, which is the information in a row explained by a column, thus explaining the interaction? To answer these questions three orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independent two-way tables and fully dependent tables representing row-column interaction. An important result is that the nearest independent table is the product of the two (row and column)-wise geometric marginal tables. A corollary is that, in an independent table, the geometric marginals conform with the traditional (arithmetic) marginals. These decompositions can be compared with standard log-linear models. Key words: balance, compositional data, simplex, Aitchison geometry, composition, orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure, contingency table