Point and Interval Estimation in the Combination of Bioassay Results with Unequal Variances

Symmetric parallel‐line biological assays involve the estimation of (log) relative potencies. The class of p(≥ 2) combination of symmetric parallel line bioassays are considered in this study. A large sample test for the equality of the several potencies is developed. An estimator and a confidence interval are proposed for the common relative potency parameter. The asymptotic distribution of the proposed test‐statistic under the null hypothesis as well as under a contagious hypothesis is derived.     

Investigations on the Similarity of the Structure of Two Covariance Matrices for Some Blood Pressure Data

We have two sample covariance matrices of size p × p, where p is the number of variables denoting measurements of arterial blood pressure recorded in various positions and methods for women and men. The hypothesis on equality of the two covariance matrices was rejected and we want to find, why this happened and in which covariances the two matrices differ. In § 2 we explore the primary (observed) data looking for outliers and deviations from normality. We do it by drawing χ² plots. In § 3 we look for common principal components. We use here Flury's method. We find that the data for blood pressure systolic might have a common principal axes system (P≈?0.0866), while for blood pressure diastolic this is dubious (p≈?0.0112). The variances of the first principal component found for woman are a little larger than those for men, and this fact explains the rejection of the classical test ∑₁ = ∑₂ on the equality of the two covariance matrices. After applying a common rotation to the two covariance matrices we reduce them to a nearly diagonal form. Looking at the non diagonal elements we see which covariances do not fit into the model. In § 4 we repeat the calculations from § 3 for covariance matrices calculated from the same data using robust methods.     

A Test for the Equality of Variances in the Paired Case with Incomplete Data

A modification of the numbers of degrees of freedom which makes the F ratio test of the equality of two variances applicable also in the paired case with incomplete data is suggested. Monte Carlo simulation studies indicate that the suggested test is reasonably powerful in many cases.     

Rotation gene set testing for longitudinal expression data

Gene set analysis methods are popular tools for identifying differentially expressed gene sets in microarray data. Most existing methods use a permutation test to assess significance for each gene set. The permutation test's assumption of exchangeable samples is often not satisfied for time‐series data and complex experimental designs, and in addition it requires a certain number of samples to compute p‐values accurately. The method presented here uses a rotation test rather than a permutation test to assess significance. The rotation test can compute accurate p‐values also for very small sample sizes. The method can handle complex designs and is particularly suited for longitudinal microarray data where the samples may have complex correlation structures. Dependencies between genes, modeled with the use of gene networks, are incorporated in the estimation of correlations between samples. In addition, the method can test for both gene sets that are differentially expressed and gene sets that show strong time trends. We show on simulated longitudinal data that the ability to identify important gene sets may be improved by taking the correlation structure between samples into account. Applied to real data, the method identifies both gene sets with constant expression and gene sets with strong time trends.     

A remark on a paper by misra

MISRA (1978) sets confidence intervals for a double linear compound of multivariate normal regression coefficients by using ROY'S maximum root test criterion. The exact test statistic to be used is STUDENT'S t. The t statistic gives narrower confidence bounds than those given by ROY's maximum root statistic. A result given by MORRISON (1975, p. 18, equation 10) for profile analysis is also obtained by using the STUDENT'S t test.     

Distribution-free Estimation of a Monotonic pth Quantile Function

When analyzing biological data sets, a frequent problem is to estimate the pth quantile of a distribution, when that quantile is assumed to depend on a covariate; in the present paper the dependence of the quantile on the covariate is assumed to be monotonic. Some properties of an isotonic pth quantile regression, considered as an estimator of an increasing pth quantile function, are presented.     

Demerelate: calculating interindividual relatedness for kinship analysis based on codominant diploid genetic markers using R

The Demerelate package offers algorithms to calculate different interindividual relatedness measurements. Three different allele sharing indices, five pairwise weighted estimates of relatedness and four pairwise weighted estimates with sample size correction are implemented to analyse kinship structures within populations. Statistics are based on randomization tests; modelling relatedness coefficients by logistic regression, modelling relatedness with geographic distance by mantel correlation and comparing mean relatedness between populations using pairwise t‐tests. Demerelate provides an advance on previous software packages by including some estimators not available in R to date, along with F_IS, as well as combining analysis of relatedness and spatial structuring. An UPGMA tree visualizes genetic relatedness among individuals. Additionally, Demerelate summarizes information on data sets (allele vs. genotype frequencies; heterozygosity; F_IS values). Demerelate is – to our knowledge – the first R package implementing basic allele sharing indices such as Blouin's M_xy relatedness, the estimator of Wang corrected for sample size (wang_xy), estimators based on Morans I adapted to genetic relatedness as well as combining all estimators with geographic information. The R environment enables users to better understand relatedness within populations due to the flexibility of Demerelate of accepting different data sets as empirical data, reference data, geographical data and by providing intermediate results. Each statistic and tool can be used separately, which helps to understand the suitability of the data for relatedness analysis, and can be easily implemented in custom pipelines.     

Tables for Testing the Equality of Two Proportions when Prior Information on their Common Value May be Available

In testing the equality of two proportions, one may define a rejection point T? such that if the test statistic T (in this paper, the ordinary Pearsonian chi-squared) exceeds T? then the hypothesis may safely be rejected, whatever the common value p of the two proportions may be; and similarly define an acceptance point A? such that if T ≦ T? then one may safely accept. These points may be refined if prior information is available, for example that p must lie in the central interval (c, 1 – c) or one of the extremal intervals (v, w) and (1 – w, 1 – v). Smallsample tables are provided both for the unrestricted case and for situations where one has such prior information.     

Analysis of genetic association and epistasis interactions between circadian clock genes and symptom dimensions of bipolar affective disorder

Bipolar affective disorder (BD) is a severe psychiatric disorder characterized by periodic changes in mood from depression to mania. Disruptions of biological rhythms increase risk of mood disorders. Because clinical representation of disease is heterogeneous, homogenous sets of patients are suggested to use in the association analyses. In our study, we aimed to apply previously computed structure of bipolar disorder symptom dimension for analyses of genetic association. We based quantitative trait on: main depression, sleep disturbances, appetite disturbances, excitement and psychotic dimensions consisted of OPCRIT checklist items. We genotyped 42 polymorphisms from circadian clock genes: PER3, ARNTL, CLOCK and TIMELSSS from 511 patients BD (n?=?292 women and n?=?219 men). As quantitative trait we used clinical dimensions, described above. Genetic associations between alleles and quantitative trait were performed using applied regression models applied in PLINK. In addition, we used the Kruskal–Wallis test to look for associations between genotypes and quantitative trait. During second stage of our analyses, we used multidimensional scaling (multifactor dimensionality reduction) for quantitative trait to compute pairwise epistatic interactions between circadian gene variants. We found association between ARNTL variant rs11022778 main depression (p?=?0.00047) and appetite disturbances (p?=?0.004). In epistatic interaction analyses, we observed two locus interactions between sleep disturbances (p?=?0.007; rs11824092 of ARNTL and rs11932595 of CLOCK) as well as interactions of subdimension in main depression and ARNTL variants (p?=?0.0011; rs3789327, rs10766075) and appetite disturbances in depression and ARNTL polymorphism (p?=?7?×?10^?4; rs11022778, rs156243).     

Trimmed Weighted Simes' Test for Two One‐Sided Hypotheses With Arbitrarily Correlated Test Statistics

The two‐sided Simes test is known to control the type I error rate with bivariate normal test statistics. For one‐sided hypotheses, control of the type I error rate requires that the correlation between the bivariate normal test statistics is non‐negative. In this article, we introduce a trimmed version of the one‐sided weighted Simes test for two hypotheses which rejects if (i) the one‐sided weighted Simes test rejects and (ii) both p‐values are below one minus the respective weighted Bonferroni adjusted level. We show that the trimmed version controls the type I error rate at nominal significance level α if (i) the common distribution of test statistics is point symmetric and (ii) the two‐sided weighted Simes test at level 2α controls the level. These assumptions apply, for instance, to bivariate normal test statistics with arbitrary correlation. In a simulation study, we compare the power of the trimmed weighted Simes test with the power of the weighted Bonferroni test and the untrimmed weighted Simes test. An additional result of this article ensures type I error rate control of the usual weighted Simes test under a weak version of the positive regression dependence condition for the case of two hypotheses. This condition is shown to apply to the two‐sided p‐values of one‐ or two‐sample t‐tests for bivariate normal endpoints with arbitrary correlation and to the corresponding one‐sided p‐values if the correlation is non‐negative. The Simes test for such types of bivariate t‐tests has not been considered before. According to our main result, the trimmed version of the weighted Simes test then also applies to the one‐sided bivariate t‐test with arbitrary correlation.     

General description of Lake Peipsi-Pihkva

Neural networks and multiple linear regression models of the abundance of brown trout (Salmo trutta L.) on the mesohabitat scale were developed from combinations of physical habitat variables in 220 channel morphodynamic units (pools, riffles, runs, etc.) of 11 different streams in the central Pyrenean mountains. For all the 220 morphodynamic units, the determination coefficients obtained between the estimated and observed values of density or biomass were significantly higher for the neural network (r ² adjusted= 0.93 and r ² adjusted=0.92 (p<0.01) for biomass and density respectively with the neural network, against r ² adjusted=0.69 (p<0.01) and r ² adjusted = 0.54 (p<0.01) with multiple linear regression). Validation of the multivariate models and learning of the neural network developed from 165 randomly chosen channel morphodynamic units, was tested on the 55 other channel morphodynamic units. This showed that the biomass and density estimated by both methods were significantly related to the observed biomass and density. Determination coefficients were significantly higher for the neural network (r ² adjusted =0.72 (p<0.01) and 0.81 (p<0.01) for biomass and density respectively) than for the multiple regression model (r ² adjusted=0.59 and r ² adjusted=0.37 for biomass and density respectively). The present study shows the advantages of the backpropagation procedure with neural networks over multiple linear regression analysis, at least in the field of stochastic salmonid ecology.     

Comparison of Zinc Reduction with Platinum Reduction for Analysis of Deuterium‐Enriched Water Samples for the Doubly Labeled Water Technique

Objective: Isotope ratio mass spectrometry of hydrogen and oxygen is frequently used to determine total energy expenditure (TEE) using doubly labeled water. Conventionally, hydrogen isotope ratio is determined in hydrogen gas generated from water samples using zinc reduction. We compare this with a new automated platinum method to determine the ratios of hydrogen isotopes in deuterium‐enriched water samples. Research Methods and Procedures: The platinum method of sample preparation was compared with the zinc method in three ways: analytical variation in deuterium enrichment (within sample; n = 51), analytical variation in TEE estimates (within sample set; n = 10), and level of agreement of TEE estimates between both methods (n = 14). Results: For the zinc method, the standard deviation for multiple sets of triplicate ²H₂O sample analysis was ±4.36‰ and ±2.07‰ for platinum. The correlation between TEE estimates when sample sets were analyzed in duplicate was r = 0.89 for zinc and r = 0.83 for platinum. The intercept and slope of the regression line were significantly different from the line of identity for duplicate TEE estimates by zinc but were not different from the line of identity for platinum. After correction for the intra‐assay variation of each method, the correlation between zinc and platinum for TEE was 0.77, and the intercept, but not the slope, of the regression was significantly different from the line of identity. The mean difference between the zinc method and the platinum method was 56 kcal/day, and the 95% confidence interval was ?438 to 550 kcal/day. Discussion: These data suggest that the platinum method is at least as reliable as the zinc method as a sample preparation technique for isotope ratio mass spectrometry of deuterium‐enriched water samples. The platinum method is also less costly and less labor‐intensive than the zinc method.     

Bootstrap and Second‐Order Tests of Risk Difference

Summary Clinical trials data often come in the form of low‐dimensional tables of small counts. Standard approximate tests such as score and likelihood ratio tests are imperfect in several respects. First, they can give quite different answers from the same data. Second, the actual type‐1 error can differ significantly from nominal, even for quite large sample sizes. Third, exact inferences based on these can be strongly nonmonotonic functions of the null parameter and lead to confidence sets that are discontiguous. There are two modern approaches to small sample inference. One is to use so‐called higher order asymptotics ( Reid, 2003 , Annal of Statistics 31 , 1695–1731) to provide an explicit adjustment to the likelihood ratio statistic. The theory for this is complex but the statistic is quick to compute. The second approach is to perform an exact calculation of significance assuming the nuisance parameters equal their null estimate ( Lee and Young, 2005 , Statistic and Probability Letters 71 , 143–153), which is a kind of parametric bootstrap. The purpose of this article is to explain and evaluate these two methods, for testing whether a difference in probabilities p₂? p₁ exceeds a prechosen noninferiority margin δ₀ . On the basis of an extensive numerical study, we recommend bootstrap P‐values as superior to all other alternatives. First, they produce practically identical answers regardless of the basic test statistic chosen. Second, they have excellent size accuracy and higher power. Third, they vary much less erratically with the null parameter value δ₀ .     

Testing the Equality of Dependent Variances

The likelihood ratio test for testing equality of vgE;2 correlated variables is developed. In general, evaluation of the test statistic involves the iterative optimization of a likelihood function with 1 + v(v – 1)/2 parameters. The explicit form of the test statistic is derived in the bivariate case, and an iterative algorithm for determining the maximum likelihood estimates is suggested. A limited Monte Carlo study determines the behavior of the proposed procedure under the null hypothesis and variety of parameter values.     

Associations Between Season of Birth and the Risk of Lung Cancer: Epidemiological Findings From Hungary

Lung cancer is the leading cause of cancer deaths worldwide. Both incidence and mortality of lung cancer are especially high in Hungary. Several investigations suggested recently that month of birth (MOB) is associated with the risks of several nonmalignant disorders as well as some malignant disorders. Only a few studies investigated previously the association between MOB and risk of lung cancer, but they provided inconsistent results. We, therefore, decided to investigate this issue in a large sample of individuals who died from lung cancer. Accordingly, we determined the MOB-associated risk of death by lung cancer between the years 1970 and 2009 among all individuals born in Hungary between 1925 and 1934. The final sample included about two million people. A total of 61,904 deaths by lung cancer occurred in this sample during the period investigated. Using analysis of variance (ANOVA), we did not find significant association between MOB and risk of lung cancer death, either in the whole population investigated (F?=?1.492; p?=?.145) or in the female subpopulation (F?=?1.535; p?=?.129). However, those males born in late spring (May–June) had a lower risk of lung cancer development (F?=?2.577; p?=?.006). Results of the Edwards test also did not suggest consistent association between MOB and risk of lung cancer death in the whole investigated period (1925–1934) in any populations (i.e., whole population or male and female subpopulations). In conclusion, we did not find significant association between MOB and risk of lung cancer in our total sample (although results alluded to a weak association between MOB and risk of lung cancer development among males). The possible associations between MOB and the risk of lung cancer development (or smoking) would require confirmation (or refutation) in large studies from other populations. (Author correspondence: dome_peter@yahoo.co.uk)     

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.     

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.     

Factors associated with the oral health-related quality of life in elderly persons in dental clinic: validation of a Mandarin Chinese version of GOHAI

Gerodontology 2011; doi: 10.1111/j.1741‐2358.2009.00360.x
Factors associated with the oral health‐related quality of life in elderly persons in dental clinic: validation of a Mandarin Chinese version of GOHAI Objectives: To translate the original English version of Geriatric Oral Health Assessment Index (GOHAI) into Mandarin Chinese and assess its reliability and validity for use among the elderly in inland China and to explore the factors associated with oral health‐related quality of life (OHRQoL). Methods: The original English version of GOHAI was translated, back‐translated and cross‐culturally adapted. The psychometric properties of GOHAI‐M were assessed in a sample of 263 people aged 60 years and over and OHRQoL was examined in 221 subjects using GOHAI‐M. Multiple regression analysis was conducted. Results: Internal consistency of the GOHAI‐M was excellent (Cronbach’s α : 0.81). Split‐half reliability coefficient was 0.80, and item‐scale correlation coefficient ranged from 0.25 to 0.71. Self‐rated oral health was significantly associated with OHRQoL (r_s = 0.505, p < 0.01). The relation coefficient between GOHAI‐M and self‐perceived need for dental treatment and number of missing teeth were 0.231 and ?0.653, respectively (p < 0.05). Multiple regression analysis found that better OHRQoL was significantly associated with better self‐ratings of oral health (β = 0.497, p = 0.01), number of missing teeth (β = 0.187, p < 0.01) and life satisfaction (β = 0.132, p < 0.05). Conclusion: The Mandarin Chinese version of GOHAI demonstrates acceptable reliability and validity. OHRQoL is associated with self‐rated oral health, number of missing teeth and satisfaction with life.     

Testing the rate isomorphy hypothesis using five statistical methods

Abstract Organisms are said to be in developmental rate isomorphy when the proportions of developmental stage durations are unaffected by temperature. Comprehensive stage‐specific developmental data were generated on the cabbage beetle, Colaphellus bowringi Baly (Coleoptera: Chrysomelidae), at eight temperatures ranging from 16°C to 30°C (in 2°C increments) and five analytical methods were used to test the rate isomorphy hypothesis, including: (i) direct comparison of lower developmental thresholds with standard errors based on the traditional linear equation describing developmental rate as the linear function of temperature; (ii) analysis of covariance to compare the lower developmental thresholds of different stages based on the Ikemoto‐Takai linear equation; (iii) testing the significance of the slope item in the regression line of versus temperature, where p is the ratio of the developmental duration of a particular developmental stage to the entire pre‐imaginal developmental duration for one insect or mite species; (iv) analysis of variance to test for significant differences between the ratios of developmental stage durations to that of pre‐imaginal development; and (v) checking whether there is an element less than a given level of significance in the p‐value matrix of rotating regression line. The results revealed no significant difference among the lower developmental thresholds or among the aforementioned ratios, and thus convincingly confirmed the rate isomorphy hypothesis.