Some further remarks "on testing hypotheses concerning standardized mortality ratios"

In testing the equality of any k standardized mortality ratios from p(?k) populations, Kupper and Kleinbaum (1971) pointed out that different test procedures are required for the two situations where the standard population is chosen independently of the p populations and where the standard is formed by pooling all p populations. Unfortunately, the test they propose for the latter situation is applicable only when k = p. The purpose of this paper is to describe an alternative procedure based on the general theories of Wald (1943) and Neyman (1949) which can be used if the standard is a pooled one even when k < p.     

Robust Umbrella Tests for a Generalized Behrens-Fisher Problem

This paper is concerned with testing for umbrella alternatives in a k-sample location problem when the underlying populations have possibly different shapes. Following CHEN and WOLFE (1990b), rank-based modifications of the HETTMANSPERGER-NORTON (1987) tests are considered for both the settings where the peak of the umbrella is known and where it is unknown. The proposed procedures are exactly distribution-free when the continuous populations are identical with any shape. Moreover, the modified test for peak-known umbrella alternatives remains asymptotically distribution-free when the continuous populations are assumed to be symmetric, even if they differ in shapes. Comparative results of a Monte Carlo study are presented.     

Simultaneous Selection of Extreme Populations: A Subset Selection Approach

The problem of selecting a “best” (largest mean, or smallest mean) population from a collection of k independent populations was formulated and solved by Bechhofer (1954). Gupta (1965) solved another important problem, that of selecting a subset of populations containing the “best” population from the original collection of populations. Since then many variations of the problem have been considered. Tong (1969) and Lewis (1980) have investigated the problem of selecting extreme populations (populations with a largest, and populations with a smallest, mean) with respect to one and two standard populations, respectively. In this paper we study the selection of extreme populations in absence of any standard population. We formulate subset-selection procedures when variances are known and equal, and also in the most general case when they are unknown and unequal. Nonexistence of a single-stage procedure is noted for this latter case (even if variances are equal). A two-stage procedure and some of its associated properties are discussed. Tables needed for application are provided, as is a worked example.     

A Simple Algorithm for Finding All k-Edge-Connected Components

The problem of finding k-edge-connected components is a fundamental problem in computer science. Given a graph G = (V, E), the problem is to partition the vertex set V into {V ₁, V ₂,…, V _h}, where each V _i is maximized, such that for any two vertices x and y in V _i, there are k edge-disjoint paths connecting them. In this paper, we present an algorithm to solve this problem for all k. The algorithm preprocesses the input graph to construct an Auxiliary Graph to store information concerning edge-connectivity among every vertex pair in O(Fn) time, where F is the time complexity to find the maximum flow between two vertices in graph G and n = ∣V∣. For any value of k, the k-edge-connected components can then be determined by traversing the auxiliary graph in O(n) time. The input graph can be a directed or undirected, simple graph or multigraph. Previous works on this problem mainly focus on fixed value of k.     

ON THE MEASURE OF EXCITABILITY

Recent time-intensity data by Rushton (1932) on the sciatic nerve of the frog are shown to provide additional support to the writer''s suggestion (1932, a) that integrals of the equation See PDF for Equation where V is the applied voltage, p is the local excitatory process and K and k are constants adequately represent the just effective direct current stimuli when the threshold value of p is made a linear function of the voltage of the form h ± α V where h and α are constants. The measurement of excitability is discussed and it is shown that the criteria for "true" measurements are not likely to be found by the agreement of the data with canonical time-intensity functions as suggested by Lapicque (1931) but rather in the establishing of standard experimental conditions. These conditions may permit the use of chronaxie as a measure of excitability, but it seems more likely that the constant k of the above equation will have to be adopted. There is sufficient evidence to cast considerable doubt on the validity of any conclusions drawn from the existing measurements of chronaxie although those derived through a particular technique may be valid. The problem requires a thorough experimental investigation in terms of integrals of the above equation.     

Accurate Computation of Survival Statistics in Genome-Wide Studies

A key challenge in genomics is to identify genetic variants that distinguish patients with different survival time following diagnosis or treatment. While the log-rank test is widely used for this purpose, nearly all implementations of the log-rank test rely on an asymptotic approximation that is not appropriate in many genomics applications. This is because: the two populations determined by a genetic variant may have very different sizes; and the evaluation of many possible variants demands highly accurate computation of very small p-values. We demonstrate this problem for cancer genomics data where the standard log-rank test leads to many false positive associations between somatic mutations and survival time. We develop and analyze a novel algorithm, Exact Log-rank Test (ExaLT), that accurately computes the p-value of the log-rank statistic under an exact distribution that is appropriate for any size populations. We demonstrate the advantages of ExaLT on data from published cancer genomics studies, finding significant differences from the reported p-values. We analyze somatic mutations in six cancer types from The Cancer Genome Atlas (TCGA), finding mutations with known association to survival as well as several novel associations. In contrast, standard implementations of the log-rank test report dozens-hundreds of likely false positive associations as more significant than these known associations.     

A Simple Construction Procedure for Eesolvable Incomplete Block Designs for any Number of Treatments

A simple, straightforward procedure, which requires no special tables or generators, is presented for constructing resolvable incomplete block designs for v=pk, v=p²k, …, treatments, for k≥p, in incomplete blocks of size k. Also, it is shown, how to obtain incomplete block designs for any v in blocks of size k and k+1. The procedure allows construction of balanced incomplete block designs for p = k a prime number. For p = n not a prime number, incomplete block designs can be obtained by the procedure, but are not balanced. However, for p_s being the smallest prime factor of n, p_s + 1 for v = n², p_s²+ p_s + 1 for v = n³, …, arrangements can be obtained for which the occurrence of any treatment pair in the blocks is either zero or one. This is called a zero-one concurrence design. Procedures are described for obtaining additional zero-one concurrence arrangements. It is shown that the efficiency of these designs is maximum. Both intra-block and inter-block analyses are described.     

Population genetic structure of Sagittaria natans (Alismataceae), an endangered species in China,revealed by nuclear SSR loci analyses

Sagittaria natans (Alismataceae) is an endangered aquatic herb in China. The nuclear microsatellite (SSR) loci variation of the 11 extant populations of S. natans was investigated in the present study. A relative high level of genetic diversity was found in this species. The Wilcoxon’s signed rank tests did not indicate a recent bottleneck in any of the populations. The Analysis of molecular variance (AMOVA) showed a low level of population differentiation (FST = 0.284) among the populations of S. natans. This result was supported by STRUCTURE analysis (K = 1), the NJ analyses and Mantel test (r = ?0.0221, p > 0.5). The genetic structure could be contributed to an earlier period of more pronounced gene flow when the species had a more continuous distribution. The results of this study could be used as the basis for conservation guidelines for the management of this endangered species in China.     

Simulation of Interstitial Fluid Flow in Ligaments: Comparison among Stokes,Brinkman and Darcy Models

In this paper, we use Stokes, Brinkman and Darcy equations to approximate the porous continuum media of ligament tissues respectively, simulate the flow field with FLUENT software, and study the shear stress on the cell surface due to the interstitial fluid flow. Since the Brinkman equation approaches Stokes equation well in high hydraulic permeability (k_p) condition (k_p ≥1.0×10^-8 m² in our numerical simulation), and it is an approximation to Darcy model in low k_p condition (k_p ≤5.0×10^-12 m² in our numerical simulation), we used the Brinkman model to simulate the interstitial fluid flow in the ligament where k_p is approximately 1.0×10^-16 m². It shows k_p and anisotropic property have a little effect on the flow field, but have a great effect on the shear stress on the membrane of interstitial cells (τ_cell). There is a linear relationship between τ_cell and , when k_p =1.0×10^-16 m² and the maximum τ_cell (τ_cell,max) is approximately 10 Pa. The anisotropic property will affect τ_cell''s distribution on the cell surface. When k_x/k_y>1, low τ_cell dominates the cell, while when k_x/k_y<1, high τ_cell dominants the cell.     

Testing for Treatment Effects on Subsets of Endpoints

Multiple endpoints are tested to assess an overall treatment effect and also to identify which endpoints or subsets of endpoints contributed to treatment differences. The conventional p‐value adjustment methods, such as single‐step, step‐up, or step‐down procedures, sequentially identify each significant individual endpoint. Closed test procedures can also detect individual endpoints that have effects via a step‐by‐step closed strategy. This paper proposes a global‐based statistic for testing an a priori number, say, r of the k endpoints, as opposed to the conventional approach of testing one (r = 1) endpoint. The proposed test statistic is an extension of the single‐step p‐value‐based statistic based on the distribution of the smallest p‐value. The test maintains strong control of the FamilyWise Error (FWE) rate under the null hypothesis of no difference in any (sub)set of r endpoints among all possible combinations of the k endpoints. After rejecting the null hypothesis, the individual endpoints in the sets that are rejected can be tested further, using a univariate test statistic in a second step, if desired. However, the second step test only weakly controls the FWE. The proposed method is illustrated by application to a psychosis data set.     

An efficient Fmoc strategy for the rapid synthesis of peptide para-nitroanilides

A new strategy has been developed for the rapid synthesis ofpeptide para-nitroanilides (pNA). The method involves derivatization of commercially available tritylchloride resin(TCP-resin) with 1,4-phenylenediamine, subsequent coupling withdesired amino acids by the standard Fmoc protocol, and oxidationof the intermediate para-aminoanilides (pAA) with Oxone®. This procedure allows easy assembly of the desired para-aminoanilides (pAA) on standard resin and efficient oxidation and purification of the corresponding para-nitroanilides (pNA). The method allows easy access to any desired peptide para-nitroanilides, which are useful substrates for the characterization and study of proteolytic enzymes.     

ON THE RELATION OF DIRECT CURRENTS TO CONDENSER DISCHARGES AS STIMULI

Data on the electrical stimulation of sciatic-gastrocnemius preparations of the frog by both direct currents and condenser discharges at the same time are discussed in relation to the validity of the differential equation See PDF for Equation where p is the local excitatory process, V the stimulating current or voltage, and K and k are constants. It is concluded that the constant k is the same whether it is derived from the data of the one stimulus or the other when the same fibres are being stimulated.     

Prognostic Significance of the Metabolic Marker Hexokinase-2 in Various Solid Tumors: A Meta-Analysis

ObjectiveRecently, numerous studies have reported that hexokinase-2 (HK2) is aberrantly expressed in cancer, indicating that HK2 plays a pivotal role in the development and progression of cancer. However, its prognostic significance in solid tumor remains unclear. Accordingly, we performed a meta-analysis to assess the prognostic value of HK2 in solid tumor.MethodsEligible studies were identified using PubMed, Embase, and Web of Science databases. Pooled hazard ratios (HRs) with 95% confidence intervals (CIs) for overall survival (OS) or progression-free survival (PFS)/disease-free survival (DFS)/relapse-free survival (RFS) were estimated with random effects or fixed effects models, respectively. Subgroup analysis was also performed according to patients’ ethnicities, tumor types, detection methods, and analysis types.ResultsData from 21 included studies with 2532 patients were summarized. HK2 overexpression was significantly associated with worse OS (pooled HR = 1.90, 95% CI = 1.51–2.38, p < 0.001) and PFS (pooled HR = 2.91, 95% CI = 2.02–4.22, p < 0.001) in solid tumor. As to a specific form of cancer, the negative effect of HK2 on OS was observed in hepatocellular carcinoma (pooled HR = 2.06, 95% CI = 1.67–2.54, p < 0.001), gastric cancer (pooled HR = 1.72, 95% CI = 1.09–2.71, p = 0.020), colorectal cancer (pooled HR = 2.89, 95% CI = 1.62–5.16, p < 0.001), but not in pancreatic cancer (pooled HR = 1.13, 95% CI = 0.28–4.66, p = 0.864). No publication bias was found in the included studies for OS (Begg’s test, p = 0.325; Egger’s test, p = 0.441).ConclusionIn this meta-analysis, we identified that elevated HK2 expression was significantly associated with shorter OS and PFS in patients with solid tumor, but the association varies according to cancer type.     

Crowding Effects on Association Reactions at Membranes

The effect of macromolecular crowding on the binding of ligands to a receptor near membranes is studied using Brownian dynamics simulations. The receptor is modeled as a reactive patch on a hard surface and the ligands and crowding agents are modeled as spheres that interact via a steep repulsive interaction potential. When a ligand collides with the patch, it reacts with probability p_rxn. The association rate constant (k_∞) can be decomposed into contributions from diffusion-limited (k_D) and reaction-limited (k_R) rates, i.e., 1/k_∞ = 1/k_D + 1/k_R. The simulations show that k_D is a nonmonotonic function of the volume fraction of crowding agents for receptors of small sizes. k_R is always an increasing function of the volume fraction of crowding agents, and the association rate constant k_∞ determined from both contributions has a qualitatively different dependence on the macromolecular crowding for high and low values of the reaction probability p_rxn. The simulation results are used to predict the velocity of the membrane protrusion driven by actin filament elongation. Based on the simple model where the protrusive force on the membrane is generated by the intercalation of actin monomers between the membrane and actin filament ends, we predict that crowding increases the local concentration of actin monomers near the filament ends and hence accelerates the membrane protrusion.     

Improved power of familywise error rate procedures for discrete data under dependency

In many applications where it is necessary to test multiple hypotheses simultaneously, the data encountered are discrete. In such cases, it is important for multiplicity adjustment to take into account the discreteness of the distributions of the p‐values, to assure that the procedure is not overly conservative. In this paper, we review some known multiple testing procedures for discrete data that control the familywise error rate, the probability of making any false rejection. Taking advantage of the fact that the exact permutation or exact pairwise permutation distributions of the p‐values can often be determined when the sample size is small, we investigate procedures that incorporate the dependence structure through the exact permutation distribution and propose two new procedures that incorporate the exact pairwise permutation distributions. A step‐up procedure is also proposed that accounts for the discreteness of the data. The performance of the proposed procedures is investigated through simulation studies and two applications. The results show that by incorporating both discreteness and dependency of p‐value distributions, gains in power can be achieved.     

Simultaneous Comparisons of Multiple Treatments to Two (or More) Control

DUNNETT (1955) developed a procedure simultaneously comparing k treatments to one control with an exact overall type I error of α when all sampling distributions are normal. Sometimes it is desirable to compare k treatments to m≧2 controls, in particular to two controls. For instance, several new therapies (e.g., pain relievers) could be compared to two standard therapies (e.g., Aspirin and Tylenol). Alternatively, a standard therapy could be very expensive, difficult to apply and/or have bad side effects, making it useful to compare each new therapy to both standard therapy and no therapy (Placebo). Dunnett's method is expanded here to give comparisons of mean values for k treatments to mean values for m≧2 controls at an exact overall type I error of α when all sampling distributions are normal. Tabled values needed to make exact simultaneous comparisons at α = .05 are given for m = 2. An application is made to an example from the literature.     

Multiple liquid-liquid partition: II. Theory of Martin-Synge distribution (MSD)

The theory of Martin-Synge distribution (MSD) was refined, with special attention being focused upon the derivation of the separation functions. The separation function for the fundamental distribution of MSD was obtained in the form v = t²(αk₁ + 1)(αk₁ + β)[(αk₁ + 1)^1/2 + (αk₁ + β)^1/2]²/αk₁(β ? 1)², where ν is the number of aliquots v_m driven through the apparatus, t the abscissa of the standard normal distribution, α = v_m/v₈ the phase ratio, β = k₁/k₂≥ 1 the separation factor, and k₁ the partition coefficient of the more rapidly moving component; ν was shown to have minima at given αk₁ values. The separation function of the single withdrawal of MSD was presented in the form N = u + 1 = t²(2αk₁ + β + 1)²/(β ? 1)²+ 1, where N is the number of partition units; N is minimal when αk₁ = 0. The elution volumes and standard deviations of the two compounds to be separated were mathematically analyzed in a manner similar to that previously presented when dealing with the theory of counter-current distribution (CCD). As in CCD, the elution volumes in MSD were found to have minima at given αk₁ values. However, the standard deviations of the elution curves also have minima in respect to αk₁ in MSD, which is a different situation as compared to CCD. The selection of optimal operating conditions was found to be more critical in MSD than in CCD.     

Use of known Coefficients of Variation in the Estimation of the Common mean of two Normal Populations

The problem of estimating the common mean of two normal populations N(?, a1?2) and N(?, a2?2) where the coefficients of variation of two populations respectively, are known constants, on the basis of two independent random samples, one from each population, is considered. The minimum mean square estimator is proposed. It is also shown that the proposed estimator is Best Asymptotic Normal (BAN) estimator. It is pointed out that the result can be generalized to k population problem. It is remarked that the same method works, also for the problem of estimating the common standard deviation of k normal populations when coefficients of variation are known.     

Gametic Frequency of Second Chromosomes of the T-007 Type in a Natural Population of DROSOPHILA MELANOGASTER in Texas

The T-007 second chromosome, which was isolated from a natural population of Drosophila melanogaster in south Texas in 1970, is known to show, when made heterozygous in males with a standard cn bw second chromosome, a transmission frequency (k) of 0.35—much lower than the theoretically expected 0.5. Natural populations of this species in Texas contain second chromosomes that, against the standard cn bw genetic background, are associated with distorted transmission frequencies comparable to that of the T-007 chromosome. In order to explain how such chromosomes can persist in natural populations in nontrivial frequencies, it has been postulated that, although such chromosomes show reduced k values when tested under the genetic background of a laboratory stock such as cn bw, they may show, on the average, k values larger than 0.5 under natural genetic backgrounds. If this were true, the frequency of chromosomes of the T-007 type (T chromosomes) should be higher in male than in female gametes under natural genetic backgrounds. The present study was conducted to examine this possibility. The results clearly showed that the frequency of such chromosomes was much higher among male than among female gametes, and that the transmission frequency of this type of chromosome was higher than 0.5 under natural genetic backgrounds. These results suggest that T chromosomes behave like Segregation Distorter (SD) chromosomes in natural populations of this species in Texas. A possible relationship between T-007 and SD chromosomes is suggested.