Proposed genetic nomenclature rules for Tetrahymena thermophila,Paramecium primaurelia and Paramecium tetraurelia. The Seventh International Meeting on Ciliate Molecular Biology Genetics Nomenclature.

Ordered tetrad data yield information on chromatid interference, chiasma interference, and centromere locations. In this article, we show that the assumption of no chromatid interference imposes certain constraints on multilocus ordered tetrad probabilities. Assuming no chromatid interference, these constraints can be used to order markers under general chiasma processes. We also derive multilocus tetrad probabilities under a class of chiasma interference models, the chi-square models. Finally, we compare centromere map functions under the chi-square models with map functions proposed in the literature. Results in this article can be applied to order genetic markers and map centromeres using multilocus ordered tetrad data.     

The performances of the chi-square test and complexity measures for signal recognition in biological sequences

With large amounts of experimental data, modern molecular biology needs appropriate methods to deal with biological sequences. In this work, we apply a statistical method (Pearson's chi-square test) to recognize the signals appear in the whole genome of the Escherichia coli. To show the effectiveness of the method, we compare the Pearson's chi-square test with linguistic complexity on the complete genome of E. coli. The results suggest that Pearson's chi-square test is an efficient method for distinguishing genes (coding regions) form pseudogenes (noncoding regions). On the other hand, the performance of the linguistic complexity is much lower than the chi-square test method. We also use the Pearson's chi-square test method to determine which parts of the Open Reading Frame (ORF) have significant effect on discriminating genes form pseudogenes. Moreover, different complexity measures and Pearson's chi-square test applied on the genes with high value of Pearson's chi-square statistic. We also compute the measures on homologous of these genes. The results illustrate that there is a region near the start codon with high value of chi-square statistic and low complexity that is conserve between homologous genes.     

Pedigree data analysis with crossover interference

We propose a new method for calculating probabilities for pedigree genetic data that incorporates crossover interference using the chi-square models. Applications include relationship inference, genetic map construction, and linkage analysis. The method is based on importance sampling of unobserved inheritance patterns conditional on the observed genotype data and takes advantage of fast algorithms for no-interference models while using reweighting to allow for interference. We show that the method is effective for arbitrarily many markers with small pedigrees.     

Computing power and sample size for case-control association studies with copy number polymorphism: application of mixture-based likelihood ratio test

Recent studies suggest that copy number polymorphisms (CNPs) may play an important role in disease susceptibility and onset. Currently, the detection of CNPs mainly depends on microarray technology. For case-control studies, conventionally, subjects are assigned to a specific CNP category based on the continuous quantitative measure produced by microarray experiments, and cases and controls are then compared using a chi-square test of independence. The purpose of this work is to specify the likelihood ratio test statistic (LRTS) for case-control sampling design based on the underlying continuous quantitative measurement, and to assess its power and relative efficiency (as compared to the chi-square test of independence on CNP counts). The sample size and power formulas of both methods are given. For the latter, the CNPs are classified using the Bayesian classification rule. The LRTS is more powerful than this chi-square test for the alternatives considered, especially alternatives in which the at-risk CNP categories have low frequencies. An example of the application of the LRTS is given for a comparison of CNP distributions in individuals of Caucasian or Taiwanese ethnicity, where the LRTS appears to be more powerful than the chi-square test, possibly due to misclassification of the most common CNP category into a less common category.     

Note on the choice of statistic for testing hypotheses regarding seasonality

The Kolmogorov-Smirnov one-sample test and the Pearson chi-square test are discussed regarding their application for testing hypotheses of seasonality in births. This paper addresses some points mentioned in an earlier paper by McCullough and argues that the chi-square procedure may be the better test.     

A Modified Chi-Square Test for Testing Equality of Two Multinomial Populations Against an Ordering Restricted Alternative

A modified chi-square test for testing the equality of two multinomial populations against an ordering restricted alternative in one sample and two sample cases is constructed. The relation between a concept of dependence called dependence by chi-square and stochastic ordering is established. A tabulation of the asymptotic distribution of the test statistic under the null hypothesis is given. Simulations are used to compare the power of this test with the power of the likelihood ratio test of stochastic ordering of the two multinomial populations.     

Asymptotic Efficiency of the Chi-Square Test for Heterogeneity of Proportions in Some Sparse-Data Cases

We consider the problem of testing for heterogeneity of K proportions when K is not small and the binomial sample sizes may not be large. We assume that the binomial proportions are normally distributed with variance σ². The asymptotic relative efficiency (ARE) of the usual chi-square test is found relative to the likelihood-based tests for σ²=0. The chi-square test is found to have ARE = 1 when the binomial sample sizes are all equal and high relative efficiency for other cases. The efficiency is low only in cases where there is insufficient data to use the chi-square test.     

A disequilibrium coefficient approach to Hardy-Weinberg testing

A comparison was made of various tests for Hardy-Weinberg equilibrium, with emphasis on methods for multiple alleles. For an overall test of deviations from equilibrium, the classical chi-square goodness-of-fit test generally performs well, with continuity corrections needed for extreme gene frequencies or extreme departures from equilibrium. For small samples, probability tests are preferable and for multiple alleles these probability tests may be performed on a sample of all possible sets of genotypic frequencies having a fixed set of sample gene frequencies. Numerical work showed that the continuity-corrected chi-square was the most conservative test procedure, and the uncorrected chi-square the least conservative. With multiple alleles, a better appreciation of the nature of departures from equilibrium is given by the use of disequilibrium coefficients, defined for each heterozygote as the difference between observed and expected frequencies. Likelihood-ratio tests can be used to test each of these coefficients individually but a satisfactory procedure is to divide the squared estimate of each coefficient by its estimated variance and regard the ratio as a single-degree-of-freedom chi-square. Numerical studies confirmed the validity of this approach, which has the great advantage of not requiring solutions of nonlinear equations.     

Product Quality Research Institute evaluation of cascade impactor profiles of pharmaceutical aerosols: Part 2—Evaluation of a method for determining equivalence

The purpose of this article is to present the thought process, methods, and interim results of a PQRI Working Group, which was charged with evaluating the chi-square ratio test as a potential method for determining in vitro equivalence of aerodynamic particle size distribution (APSD) profiles obtained from cascade impactor measurements. Because this test was designed with the intention of being used as a tool in regulatory review of drug applications, the capability of the test to detect differences in APSD profiles correctly and consistently was evaluated in a systematic way across a designed space of possible profiles. To establish a “base line,” properties of the test in the simplest case of pairs of identical profiles were studied. Next, the test's performance was studied with pairs of profiles, where some difference was simulated in a systematic way on a single deposition site using realistic product profiles. The results obtained in these studies, which are presented in detail here, suggest that the chi-square ratio test in itself is not sufficient to determine equivalence of particle size distributions. This article, therefore, introduces the proposal to combine the chi-square ratio test with a test for impactor-sized mass based on Population Bioequivalence and describes methods for evaluating discrimination capabilities of the combined test. The approaches and results described in this article elucidate some of the capabilities and limitations of the original chi-square ratio test and provide rationale for development of additional tests capable of comparing APSD profiles of pharmaceutical aerosols. Published: January 19, 2007     

Testing Hypotheses about Occupancy Rates for Clustered Populations

The use of the Pearson chi-square statistic for testing hypotheses on biological populations is not appropriate when the individuals are distributed by clusters. In the case where the clusters are distributed independently of each other, we propose an asymptotically chi-square distributed test statistic taking into account the cluster size distribution. An example provided by European Corn Borer eggs data is used to illustrate the test procedure.     

Product quality research institute evaluation of cascade impactor profiles of pharmaceutical aerosols, part 3: Final report on a statistical procedure for determining equivalence

The purpose of this article is to report final results of the evaluation of a chi-square ratio test proposed by the US Food and Drug Administration (FDA) for demonstrating equivalence of aerodynamic particle size distribution (APSD) profiles of nasal and orally inhaled drug products. A working group of the Product Quality Research Institute previously published results demonstrating some limitations of the proposed test. In an effort to overcome the test's limited discrimination, the group proposed a supplemental test, a population bioequivalence (PBE) test for impactor-sized mass (ISM). In this final report the group compares the chi-square ratio test to the ISM-PBE test and to the combination of both tests. The basis for comparison is a set of 55 realistic scenarios of cascade impactor data, which were evaluated for equivalence by the statistical tests and independently by the group members. In many instances, the combined application of these 2 tests appeared to increase the discriminating ability of the statistical procedure compared with the chi-square ratio test alone. In certain situations the chi-square ratio test alone was sufficient to determine equivalence of APSD profiles, while in other situations neither of the tests alone nor their combination was adequate. This report describes all of these scenarios and results. In the end, the group did not recommend a statistical test for APSD profile equivalence. The group did not investigate other in vitro tests, in vivo issues, or other statistical tests for APSD profile comparisons. The studied tests are not intended for routine quality control of APSD.     

Estimating the size of closed populations using inverse multiple-recapture sampling

A log-linear model for estimating the size of a closed population is defined for inverse multiple-recapture sampling with dependent samples. Efficient estimators of the log-linear model parameters and the population size are obtained by the method of minimum chi-square. A chi-square test of the general linear hypothesis regarding the log-linear model parameters is defined.     

A note on permutation tests for variance components in multilevel generalized linear mixed models

In many applications of generalized linear mixed models to multilevel data, it is of interest to test whether a random effects variance component is zero. It is well known that the usual asymptotic chi-square distribution of the likelihood ratio and score statistics under the null does not necessarily hold. In this note we propose a permutation test, based on randomly permuting the indices associated with a given level of the model, that has the correct Type I error rate under the null. Results from a simulation study suggest that it is more powerful than tests based on mixtures of chi-square distributions. The proposed test is illustrated using data on the familial aggregation of sleep disturbance.     

A reduction factor in goodness-of-fit and independence tests for clustered and weighted observations

Situations often arise in a large-scale household survey where a complex probability sample of clusters rather than of individuals is drawn from a large population. Typically, the clusters of such complex samples include a number of correlated members. The responses of these members are then weighted to obtain estimates for the population. Such weighted data are commonly published by the National Center for Health Statistics and other U.S. federal agencies. Frequently, problems arise when such data are tested by usual chi-square test statistics for goodness of fit or independence. Researchers have discovered that the usual chi-square tests provide spuriously inflated results when applied to cluster samples and that new methods are required to correct such problems. This paper proposes a strategy for a goodness-of-fit or independence test based on correlated and weighted data arising in cluster samples, and provides a factor that validly reduces the inflation of the usual chi-square statistics. This method is applied to the chronic condition data collected from the St Paul-Minneapolis, Minnesota, primary sampling unit (PSU) during the 1975 National Health Interview Survey (NHIS). This analysis, together with simulation studies presented elsewhere, provides evidence that the usual chi-square statistics from such data can be corrected for the impacts of clustering and weighting by use of the proposed reduction factor.     

Principal axis analysis of gene frequency data

When a set of populations are compared in respect of gene frequencies, and the chi-square test of heterogeneity is found to be significant, it is pertinent to find out whether the heterogeneity can be explained by a few linear combinations of the gene frequencies, and the total heterogeneity chi-square value can be partitioned as the sum of heterogeneity chi-square values contributed by the linear combinations. The present report describes such a method, and the linear combination that explains the maximum heterogeneity is called the principal axis. An application of this method is presented to find clusters of 31 Mongoloid tribal populations of eastern India using ABO gene frequency data.     

Sample size requirement for detecting interference under the chi-square model.

The chi-square model (CHS) of recombination has been studied extensively, in recent years, for its ability of capturing the process and estimating the level of crossover interference. Exploration thus far shows that this model yields much better fits to human genetic data than Haldane's no-interference model, and the explicit level of interference can be easily estimated as well. This paper provides calculations of sample sizes required to detect interference under CHS for a variety of settings. Two data types, fully informative meioses and phase-unknown backcross families, are studied. Under each setting, we calculate the number of meioses/families needed to ensure that the expected log-likelihood difference between the chi(2) interference model and Haldane's no-interference model exceeds a prespecified threshold. It is found that joint consideration of multiple (more than three) markers dramatically reduces the number of meioses/families needed when compared to an analysis based on three-point data, a traditional setting for detecting interference using three-point tests. The results indicate that the numbers of meioses needed to detect interference under CHS are well within the reach of most genetic mapping studies.     

人工饲养条件下死亡恒河猴肺脏病理改变分析

目的观察人工饲养条件下实验恒河猴肺脏病理改变,探讨实验猴呼吸系统疾病分布规律和病理改变特点,丰富实验猴自发病变基本研究资料。方法对1998～2008年云南地区饲养的自然死亡的155只恒河猴（年龄2～20岁）的肺脏进行病理检查,按年龄分为幼年组、成年组、老年组,并对观察结果进行统计学分析。结果实验猴肺脏主要病变有大叶性肺炎、支气管肺炎、间质性肺炎、肺气肿、支气管扩张症、胸膜炎、肺肉芽肿性炎等12种,出现率最高的为支气管肺炎（18.71%）和大叶性肺炎（16.74%）。恒河猴肺脏病变在不同年龄阶段均有发生,老年猴组肺脏病变发生率最高,疾病类型和发生率在不同年组中分布不相同,统计学分析显示：支气管炎病变成年组发病率明显高于幼年组;肺气肿病变老年组明显高于成年组和幼年组,（P〈0.05）。结论人工饲养条件下死亡实验猴肺脏病变检出率较高,实验猴肺脏病变在不同年龄阶段存在差异,实验猴肺脏病理改变结果丰富了实验猴的基本研究资料,对实验猴的质量控制和相关动物实验有重要价值。     

Tests of Occupancy Rates for Clustered Populations: Case Where the Cluster Sizes are Known

A modified chi-squared statistic Z is proposed for testing hypotheses about category occupancy rates for individuals distributed by clusters, when the cluster sizes are observed. This statistic is the Pearson chi-square statistic based on the individuals' counts divided by 1 + M* where M* is the mean number of other individuals per cluster per individual. The kind of alternative hypothesis for which the Z-based test compares favourably in power with the Pearson chi-square test based on the cluster frequencies is given. However, we prove that this latter test is more powerful than the former one as long as the equidistribution of the random choice vectors is assumed.     

Patterns of recombination and MLH1 foci density along mouse chromosomes: modeling effects of interference and obligate chiasma

Crossover interference in meiosis is often modeled via stationary renewal processes. Here we consider a new model to incorporate the known biological feature of "obligate chiasma" whereby in most organisms each bivalent almost always has at least one crossover. The initial crossover is modeled as uniformly distributed along the chromosome, and starting from its position, subsequent crossovers are placed with forward and backward stationary renewal processes using a chi-square distribution of intercrossover distances. We used our model as well as the standard chi-square model to simulate the patterns of crossover densities along bivalents or chromatids for those having zero, one, two, or three or more crossovers; indeed, such patterns depend on the number of crossovers. With both models, simulated patterns compare very well to those found experimentally in mice, both for MLH1 foci on bivalents and for crossovers on genetic maps. However, our model provides a better fit to experimental data as compared to the standard chi-square model, particularly regarding the distribution of numbers of crossovers per chromosome. Finally, our model predicts an enhancement of the recombination rate near the extremities, which, however, explains only a part of the pattern observed in mouse.