Exact Test of Uniform Association in a 2 × 3 Table

In a similar approach to Fisher's exact test of independence (null association) for a 2 × 2 table, this note gives an exact test of uniform association for a 2 × 3 table.     

Alternatives to the Chi-Square Test of Homogeneity in 2×2 Tables and to Fisher's Exact Test

In comparing two independent binomial proportions by modified X² tests: Gart's modified likelihood-ratio, Overall and Starbuck's “tailored F”, Pearson's adjusted X²[=X² multiplied by (n - 1)/n] and its skewness-corrected version proposed by Berchtold, it was found that the last two have error probabilities that in the mean are close to the significance level.     

Normal Approximation of a Discrete Distribution on Exact Test of Uniform Association in a 2 × 3 Table

For the analysis of 2 × 3 tables, TOMIZAWA (1993) considered an exact test of uniform association, which is an extension of independence, and then derived a discrete distribution. This paper gives a normal approximation of the discrete distribution and describes that the normalized statistic can test a one-sided hypothesis on the uniform association. Also it points out that the square of the normalized test statistic is equal to the Pearson's chi-squared statistic for testing the uniform association.     

The Power Function of the Test for ‘No Three Factor Interaction’ in 2×2×2 Contingency Tables

Three approximations to the power function of the chi-square test for the hypotheses of ‘no three factor interaction’ in a 2 × 2 × 2 contingency table are introduced and compared. The first method is based on the sampling distribution of the logarithm of the odds ratio, the second-on the non-central X² distribution and the third—on the conditional distribution of a cell entry. The last method is found to provide the closest approximation under various alternative hypotheses and sample sizes.     

On Conditions for Validity of the Approximations to Fisher's Exact Test

A 2 × 2 table is analyzed from the conditional viewpoint, using Fisher's exact test, for which there is abundant software nowadays (StatXact, SPSS with the module “Exact Test”, …). Nevertheless, because it is well-nigh impossible to work the test out “by hand”, it is customary in many books to analyze the table, in an approximate fashion, by using the classic chi-square test with the appropriate continuity correction, and this is what many researchers do in practice. Unfortunately little research has been carried out on the validity conditions of the test (remember the classic advice that the minimum expected quantity E should be larger than or equal to 5), so that it is applied indiscriminately with the obvious danger of obtaining erroneous results. In this paper the exact validity conditions (which depend not only on E, but also on the real P-value, on the size of the sample, on the number of tails of the test and on the continuity correction used) are determined, showing that the classic condition E > 5 can be either very strict or quite liberal (depending on the circumstances) and it can even be necessary for the test to have E > 20. A similar study is made of the case of using the binomial approximation, while the Poisson approximation is also discussed. The article ends with a list of rules and precautions to be borne in mind by researchers using the approximate methods. The strict rules are complex enough to make the researcher want to use the exact test, but simplified (and conservative) rules are also given for those unable to do so.     

On analytical methods and inferences for 2×2 contingency table data using wildlife examples

The 2×2 contingency table is a common analytical method for wildlife studies, but inappropriate analyses and inferences are not uncommon. Issues of concern are presented for selecting the appropriate test for analyzing these data sets. These include the choice of test relative to experimental or sampling design and breadth of intended inferences, the careful statement of hypotheses, and analyses with small sample sizes. Examples from the wildlife literature are used to reinforce the statistical concepts.     

A Comparison of the Three Conditional Exact Tests in Two‐way Contingency Tables Using the Unconditional Exact Power

The conditional exact tests of homogeneity of two binomial proportions are often used in small samples, because the exact tests guarantee to keep the size under the nominal level. The Fisher's exact test, the exact chi‐squared test and the exact likelihood ratio test are popular and can be implemented in software StatXact. In this paper we investigate which test is the best in small samples in terms of the unconditional exact power. In equal sample cases it is proved that the three tests produce the same unconditional exact power. A symmetry of the unconditional exact power is also found. In unequal sample cases the unconditional exact powers of the three tests are computed and compared. In most cases the Fisher's exact test turns out to be best, but we characterize some cases in which the exact likelihood ratio test has the highest unconditional exact power. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Second Order Efficiency of Estimators Derived by Generalised χ2 Distance Functions

Taylor (1953) proposed a distance function in connection with the logit χ² estimator. For product (associated) multinomial distributions, he showed that minimization of the distance function yields BAN estimators. Aithal (1986) and Rao (1989) considered a modified version of Taylor's distance function and showed that a member belonging to this class leads to a second order efficient estimator. In this paper we consider Taylor's distance function and show that a member belonging to this class produces a second order efficient estimator. In addition to the above two, the m.l. estimator is also second order efficient. In order to compare these three second order efficient estimators, the small sample variances of the estimators are estimated through a simulation study. The results indicate that the variance of the m.l. estimator is the smallest in most of the cases.     

On the Equivalence of the Information-Theoretic Transmission-Measure to the Common χ2 Statistic

The results of a simulation study are presented in which the χ²-and the information theoretic approach to association measurement were compared to one another. It could be shown that neither the maximal values nor the minimal values obtainable for a given sample size coincide in all cases. The underlying association concepts are defined; implications are discussed.     

Some New Aspects of 2 × 2 Table Measures and Their Applications

The paper deals with the analysis of 2 × 2 table measures and describes several new possibilities for applying them. An estimate is given for HELLMICH's asymmetric K-measure and a possible extension of the contingency concept in a special 2×2 case is presented. The concept introduced and the recommended computer application of the 2×2 table measures is supported by new results obtained for the relationship between jaw joint pains and noises examined earlier by F. SCHMID and C. ZSCHEGE. With a larger number of observations the opportunity arises for a deeper analysis of this dental problem using path analysis. The plan of evaluation and the conncetion between the variables examined is illustrated by a path-diagram. The association tables determined on the basis of the (C) values introduced during the examination of jaw joint disturbances using association analysis draw attention to the special role of the left side of mastication. The paper raises ideas for further generalisations and indicates where further research is needed.     

Jeffreys' Likelihood Ratio for the 2×2-Table — A Monte Carlo Study —

Jeffreys' approach for analyzing a 2×2-table is discussed via a Monte Carlo study. The main findings are reported.     

One- and Two-Sample Tests of Kendall's τ

Several methods of testing general one-sample and two-sample hypotheses of Kendall's τ are discussed. The performance of these procedures in typical situations likely to occur in practice was investigated by numerous Monte Carlo experiments. The common one-sample test (H₀: τ = 0) based on the permutational variance performs very similar to bootstrap or jackknife testing for true τ near zero. For true |τ| perhaps greater than 0.4 and moderate sample sizes bootstrap techniques are the methods of choice.     

The role of calcium in apoptosis induced by 7β‐hydroxycholesterol and cholesterol‐5β,6β‐epoxide

Oxysterols, such as 7β‐hydroxy‐cholesterol (7β‐OH) and cholesterol‐5β,6β‐epoxide (β‐epoxide), may have a central role in promoting atherogenesis. This is thought to be predominantly due to their ability to induce apoptosis in cells of the vascular wall and in monocytes/macrophages. Although there has been extensive research regarding the mechanisms through which oxysterols induce apoptosis, much remains to be clarified. Given that experimental evidence has long associated alterations of calcium (Ca²⁺) homeostasis to apoptotic cell death, the aim of the present study was to determine the influence of intracellular Ca²⁺ changes on apoptosis induced by 7β‐OH and β‐epoxide. Ca²⁺ responses in differentiated U937 cells were assessed by epifluorescence video microscopy, using the ratiometric dye fura‐2. Over 15‐min exposure of differentiated U937 cells to 30 μM of 7β‐OH induced a slow but significant rise in fura‐2 ratio. The Ca²⁺ channel blocker nifedipine and the chelating agent EGTA blocked the increase in cytoplasmic Ca²⁺. Moreover, dihydropyridine (DHP) binding sites identified with BODIPY‐FLX‐DHP were blocked following pretreatment with nifedipine, indicating that the influx of Ca²⁺ occurred through L‐type channels. However, following long‐term incubation with 7β‐OH, elevated levels of cytoplasmic Ca²⁺ were not maintained and nifedipine did not provide protection against apoptotic cell death. Our results indicate that the increase in Ca²⁺ may be an initial trigger of 7β‐OH–induced apoptosis, but following chronic exposure to the oxysterol, the influence of Ca²⁺ on apoptotic cell death appears to be less significant. In contrast, Ca²⁺ did not appear to be involved in β‐epoxide–induced apoptosis. © 2009 Wiley Periodicals, Inc. J Biochem Mol Toxicol 23:324–332, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jbt.20295     

ω‐Turn: A novel β‐turn mimic in globular proteins stabilized by main‐chain to side‐chain CH···O interaction

Mimicry of structural motifs is a common feature in proteins. The 10‐membered hydrogen‐bonded ring involving the main‐chain C?O in a β‐turn can be formed using a side‐chain carbonyl group leading to Asx‐turn. We show that the N? H component of hydrogen bond can be replaced by a C^γ‐H group in the side chain, culminating in a nonconventional C? H···O interaction. Because of its shape this β‐turn mimic is designated as ω‐turn, which is found to occur ～three times per 100 residues. Three residues (i to i + 2) constitute the turn with the C? H···O interaction occurring between the terminal residues, constraining the torsion angles ?_{i + 1}, ψ_{i + 1}, ?_{i + 2} and χ′_{1(i + 2)} (using the interacting C^γ atom). Based on these angles there are two types of ω‐turns, each of which can be further divided into two groups. C^β‐branched side‐chains, and Met and Gln have high propensities to occur at i + 2; for the last two residues the carbonyl oxygen may participate in an additional interaction involving the S and amino group, respectively. With Cys occupying the i + 1 position, such turns are found in the metal‐binding sites. N‐linked glycosylation occurs at the consensus pattern Asn‐Xaa‐Ser/Thr; with Thr at i + 2, the sequence can adopt the secondary structure of a ω‐turn, which may be the recognition site for protein modification. Location between two β‐strands is the most common occurrence in protein tertiary structure, and being generally exposed ω‐turn may constitute the antigenic determinant site. It is a stable scaffold and may be used in protein engineering and peptide design. Proteins 2015; 83:203–214. © 2014 Wiley Periodicals, Inc.     

HLA‐DQ7 β1 and β2 derived peptides as immunomodulators

Modulation of protein–protein interactions involved in the immune system by using small molecular mimics of the contact interfaces may lead to the blockage of the autoimmune response and the development of drugs for immunotherapy. The nonpolymorphic β‐regions, exposed to the microenvironment, of the modeled HLA‐DQ7, which is genetically linked to autoimmune diseases, were determined. Peptides 132–141 and 58–67, located at the β₁ and β₂ domains of HLA‐DQ7, respectively, were tested for their involvement in the interactions with CD4⁺ T lymphocytes. Linear, cyclic, and dimeric analogs that mimic the exposed surfaces of HLA‐DQ7 were designed and synthesized. Their immunosuppressory activities, found in the secondary, humoral immune response to sheep erythrocytes (SRBC) in mice in vitro, ranged from 11% to 53%. The significance of the total charge of the peptides, the pattern of the hydrogen bonding, and the presence of secondary structure were investigated in relation to the immunomodulatory effect of the peptides. Two dimeric analogs of the HLA‐DQ7 58–67 fragment, consisting of the two monomers covalently linked by a polyethylene glycol (PEG) spacer, able to mimic the superdimers, were also synthesized and studied. As the 58–67 segment is located at the β₁ region of HLA‐DQ7, close to the major histocompatibility complex (MHC) groove, one may assume that the 58–67 peptide could accommodate the association between T‐cell receptor (TCR) and human leukocyte antigen (HLA) by activating a co‐stimulatory molecule of the TCR/HLA interaction. This hypothesis is supported by the confocal laser image of the fluorescein‐labeled 58–67 peptide and by the fact that it is an immunostimulator at low concentration. Copyright © 2009 European Peptide Society and John Wiley & Sons, Ltd.     

Further crystallographic evidence of NH· · ·π (system) and CO· · ·π (system) interactions: The structures of bis(diarylhydrazonecarbonyl)methylene derivatives [{ArPhCNNH—C(O)}2CH2] (Ar = Ph, 2‐C5H4N, 2‐C4H3S)

In this study are reported the syntheses of three bis(diarylhydrazonecarbonyl)methylene derivatives [{ArPhCNNH C(O)}₂CH₂] [Ar = 2 C₅H₄N (5), C₆H₅ (6), and 2‐C₄H₃S (7)], obtained by condensation of corresponding hydrazones with carbon suboxide, C₃O₂. The solid‐state self‐assembly of these carbonyl derivatives, giving rise to polymeric and dimeric networks, is described. In the formation of these structural features, in addition to N—H· · ·OC intermolecular hydrogen bonds, stabilizing intramolecular NH· · · π (systems) and intermolecular CO· · ·π (systems) interactions also seem to play an important role. Solution ¹H‐nmr data of compounds 5–7 indicate that the polymeric and dimeric structures are not maintained in solution and show the occurrence of keto‐enolic equilibria. © 1999 John Wiley & Sons, Inc. Biopoly 49: 541–549, 1999     

The β‐sheet breakers and π‐stacking

Fibrillation of β‐amyloid is recognized as a key process leading to the development of Alzheimer's disease. Small peptides called β‐sheet breakers were found to inhibit the process of β‐amyloid fibrillation and to dissolve amyloid fibrils in vitro, in vivo, and in cell culture studies [1,2]. The mechanism by which peptide inhibition takes place remains elusive and a detailed model needs to be established. Here, we present new insights into the possible role of consecutive Phe residues, present in the structure of β‐sheet breakers, supported by the results obtained by means of MD simulations. We performed a 30‐ns MD of two β‐sheet breakers: iAβ5 (LPFFD) and iAβ6 (LPFFFD) which have two and three consecutive Phe residues, respectively. We have found that Phe rings in these peptides tend to form stacked conformations. For one of the peptides – iAβ6 – the calculated electrostatic contribution to free energy of one of the conformers with three rings stacked (c2) is significantly lower than that corresponding to the unstacked one (c1), two rings stacked (c0) and second conformer with three rings stacked (c3). This may favor the interaction of the c2 conformer with the target on amyloid fibril. We hypothesize that the mechanism of inhibition of amyloidogenesis by β‐sheet breaker involves competition among π‐stacked Phe residues of the inhibitor and π‐stacking within the β‐amyloid fibril. iAβ6 may be a promising candidate for a lead compound of amyloidogenesis inhibitors. Copyright © 2013 European Peptide Society and John Wiley & Sons, Ltd.     

Development and validation of a high-performance liquid chromatography assay for the quantitative determination of 7-oxo-dehydroepiandrosterone-3β-sulfate in human plasma

A new, simple, reproducible and reliable high-performance liquid chromatography method with ultraviolet absorbance detection at 240 nm was developed and validated for the determination of 7-oxo-dehydroepiandrosterone-3β-sulfate in human plasma. The method was based upon solid-phase (C₁₈) extraction of plasma after addition of 17β-hydroxy-3β-methoxyandrost-5-en-7-one as internal standard. Using 1 ml of plasma for extraction, the detection limit of the assay was 3 ng/ml. The standard curve was linear over the concentration range 10–1000 ng/ml. Stored at −20°C for about 4 months at various concentrations in plasma, 7-oxo-dehydroepiandrosterone-3β-sulfate did not reveal any appreciable degradation. Also included herein is a method for the simultaneous detection and determination of 7-oxo-dehydroepiandrosterone and 7-oxo-dehydroepiandrosterone-3β-acetate in plasma.     

Dehydroepiandrosterone 7α-hydroxylation in human tissues: Possible interference with type 1 11β-hydroxysteroid dehydrogenase-mediated processes

Dehydroepiandrosterone (DHEA) is 7α-hydroxylated by the cytochome P450 7B1 (CYP7B1) in the human brain and liver. This produces 7α-hydroxy-DHEA that is a substrate for 11β-hydroxysteroid dehydrogenase type 1 (11β-HSD1) which exists in the same tissues and carries out the inter-conversion of 7α- and 7β-hydroxy-DHEA through a 7-oxo-intermediary. Since the role of 11β-HSD1 is to transform the inactive cortisone into active cortisol, its competitive inhibition by 7α-hydroxy-DHEA may support the paradigm of native anti-glucocorticoid arising from DHEA. Therefore, our objective was to use human tissues to assess the presences of both CYP7B1 and 11β-HSD1. Human skin was selected then and used to test its ability to produce 7α-hydroxy-DHEA, and to test the interference of 7α- and 7β-hydroxy-DHEA and 7-oxo-DHEA with the 11β-HSD1-mediated oxidoreduction of cortisol and cortisone. Immuno-histochemical studies showed the presence of both CYP7B1 and 11β-HSD1 in the liver, skin and tonsils. DHEA was readily 7α-hydroxylated when incubated using skin slices. A S9 fraction of dermal homogenates containing the 11β-HSD1 carried out the oxidoreduction of cortisol and cortisone. Inhibition of the cortisol oxidation by 7α-hydroxy-DHEA and 7β-hydroxy-DHEA was competitive with a K_i at 1.85 ± 0.495 and 0.255 ± 0.005 μM, respectively. Inhibition of cortisone reduction by 7-oxo-DHEA was of a mixed type with a K_i at 1.13 ± 0.15 μM. These findings may support the previously proposed native anti-glucocorticoid paradigm and suggest that the 7α-hydroxy-DHEA production is a key for the fine tuning of glucocorticoid levels in tissues.