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Chi-square Distribution (chi-square + distribution)
Selected AbstractsCentralizing the non-central chi-square: a new method to correct for population stratification in genetic case-control association studiesGENETIC EPIDEMIOLOGY, Issue 4 2006Prakash Gorroochurn Abstract We present a new method, the ,-centralization (DC) method, to correct for population stratification (PS) in case-control association studies. DC works well even when there is a lot of confounding due to PS. The latter causes overdispersion in the usual chi-square statistics which then have non-central chi-square distributions. Other methods approach the non-centrality indirectly, but we deal with it directly, by estimating the non-centrality parameter , itself. Specifically: (1) We define a quantity ,, a function of the relevant subpopulation parameters. We show that, for relatively large samples, , exactly predicts the elevation of the false positive rate due to PS, when there is no true association between marker genotype and disease. (This quantity , is quite different from Wright's FST and can be large even when FST is small.) (2) We show how to estimate ,, using a panel of unlinked "neutral" loci. (3) We then show that ,2 corresponds to , the non-centrality parameter of the chi-square distribution. Thus, we can centralize the chi-square using our estimate of ,; this is the DC method. (4) We demonstrate, via computer simulations, that DC works well with as few as 25,30 unlinked markers, where the markers are chosen to have allele frequencies reasonably close (within ±.1) to those at the test locus. (5) We compare DC with genomic control and show that where as the latter becomes overconservative when there is considerable confounding due to PS (i.e. when , is large), DC performs well for all values of ,. Genet. Epidemiol. 2006. © 2006 Wiley-Liss, Inc. [source] A New Method for Constructing Confidence Intervals for the Index CpmQUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 7 2004Michael Perakis Abstract In the statistical literature on the study of the capability of processes through the use of indices, Cpm appears to have been one of the most widely used capability indices and its estimation has attracted much interest. In this article, a new method for constructing approximate confidence intervals or lower confidence limits for this index is suggested. The method is based on an approximation of the non-central chi-square distribution, which was proposed by Pearson. Its coverage appears to be more satisfactory compared with that achieved by any of the two most widely used methods that were proposed by Boyles, in situations where one is interested in assessing a lower confidence limit for Cpm. This is supported by the results of an extensive simulation study. Copyright © 2004 John Wiley & Sons, Ltd. [source] A Class of Multiplicity Adjusted Tests for Spatial Clustering Based on Case,Control Point DataBIOMETRICS, Issue 1 2007Toshiro Tango Summary A class of tests with quadratic forms for detecting spatial clustering of health events based on case,control point data is proposed. It includes Cuzick and Edwards's test statistic (1990, Journal of theRoyal Statistical Society, Series B52, 73,104). Although they used the property of asymptotic normality of the test statistic, we show that such an approximation is generally poor for moderately large sample sizes. Instead, we suggest a central chi-square distribution as a better approximation to the asymptotic distribution of the test statistic. Furthermore, not only to estimate the optimal value of the unknown parameter on the scale of cluster but also to adjust for multiple testing due to repeating the procedure by changing the parameter value, we propose the minimum of the profile p-value of the test statistic for the parameter as an integrated test statistic. We also provide a statistic to estimate the areas or cases which make large contributions to significant clustering. The proposed methods are illustrated with a data set concerning the locations of cases of childhood leukemia and lymphoma and another on early medieval grave site locations consisting of affected and nonaffected grave sites. [source] Evaluation of the Clinical Anatomy Program in the Medical School of Porto by two cohorts of studentsCLINICAL ANATOMY, Issue 1 2002M.A.F. Tavares Abstract The discipline of Clinical Anatomy, as introduced in the Medical School of Porto in academic year 1995/96, involved major changes in the way we teach anatomy to medical students, by adopting a clinically oriented approach. A questionnaire was designed to evaluate the opinion of second-year medical students enrolled in the program concerning main aspects of the discipline in two consecutive years; 84% of the students returned the questionnaire in 1996/97, and 70% in 1997/98. Students were asked about the level of their approval of the organization of the discipline, the role of the teaching staff, lectures, practical sessions, educational media, and continuous and summative assessments. For items replicated in both academic years, the means of the sum of scores in each year were compared (Student's t -distribution). Whenever a significant difference was found, changes in individual items were tested (chi-square distribution). The evaluation of the discipline in each of the two years was highly favorable for most of the parameters analyzed. Clin. Anat. 15:56,61, 2002. © 2002 Wiley-Liss, Inc. [source] Centralizing the non-central chi-square: a new method to correct for population stratification in genetic case-control association studiesGENETIC EPIDEMIOLOGY, Issue 4 2006Prakash Gorroochurn Abstract We present a new method, the ,-centralization (DC) method, to correct for population stratification (PS) in case-control association studies. DC works well even when there is a lot of confounding due to PS. The latter causes overdispersion in the usual chi-square statistics which then have non-central chi-square distributions. Other methods approach the non-centrality indirectly, but we deal with it directly, by estimating the non-centrality parameter , itself. Specifically: (1) We define a quantity ,, a function of the relevant subpopulation parameters. We show that, for relatively large samples, , exactly predicts the elevation of the false positive rate due to PS, when there is no true association between marker genotype and disease. (This quantity , is quite different from Wright's FST and can be large even when FST is small.) (2) We show how to estimate ,, using a panel of unlinked "neutral" loci. (3) We then show that ,2 corresponds to , the non-centrality parameter of the chi-square distribution. Thus, we can centralize the chi-square using our estimate of ,; this is the DC method. (4) We demonstrate, via computer simulations, that DC works well with as few as 25,30 unlinked markers, where the markers are chosen to have allele frequencies reasonably close (within ±.1) to those at the test locus. (5) We compare DC with genomic control and show that where as the latter becomes overconservative when there is considerable confounding due to PS (i.e. when , is large), DC performs well for all values of ,. Genet. Epidemiol. 2006. © 2006 Wiley-Liss, Inc. [source] Investigation of Gibbs sampling conditions to estimate variance components from Japanese Black carcass field dataANIMAL SCIENCE JOURNAL, Issue 5 2009Aisaku ARAKAWA ABSTRACT The genetic evaluation using the carcass field data in Japanese Black cattle has been carried out employing an animal model, implementing the restricted maximum likelihood (REML) estimation of additive genetic and residual variances. Because of rapidly increasing volumes of the official data sets and therefore larger memory spaces required, an alternative approach like the REML estimation could be useful. The purpose of this study was to investigate Gibbs sampling conditions for the single-trait variance component estimation using the carcass field data. As prior distributions, uniform and normal distributions and independent scaled inverted chi-square distributions were used for macro-environmental effects, breeding values, and the variance components, respectively. Using the data sets of different sizes, the influences of Gibbs chain length and thinning interval were investigated, after the burn-in period was determined using the coupling method. As would be expected, the chain lengths had obviously larger effects on the posterior means than those of thinning intervals. The posterior means calculated using every 10th sample from 90 000 of samples after 10 000 samples discarded as burn-in period were all considered to be reasonably comparable to the corresponding estimates by REML. [source] Global Tests for LinkageBIOMETRICAL JOURNAL, Issue 1 2009Rachid el Galta Abstract To test for global linkage along a genome or in a chromosomal region, the maximum over the marker locations of mean alleles shared identical by descent of affected relative pairs, Zmax, can be used. Feingold et al. (1993) derived a Gaussian approximation to the distribution of the Zmax. As an alternative we propose to sum over the observed marker locations along the chromosomal region of interest. Two test statistics can be derived. (1) The likelihood ratio statistic (LR) and (2) the corresponding score statistic. The score statistic appears to be the average mean IBD over all available marker locations. The null distribution of the LR and score tests are asymptotically a 50: 50 mixture of chi-square distributions of null and one degree of freedom and a normal distribution, respectively. We compared empirically the type I error and power of these two new test statistics and Zmax along a chromosome and in a candidate region. Two models were considered, namely (1) one disease locus and (2) two disease loci. The new test statistics appeared to have reasonable type I error. Along the chromosome, for both models we concluded that for very small effect sizes, the score test has slightly more power than the other test statistics. For large effect sizes, the likelihood ratio statistic was comparable to and sometimes performed better than Zmax and both test statistics performed much better than the score test. For candidate regions of about 30 cM, all test statistics were comparable when only one disease-locus existed and the score and likelihood ratio statistics had somewhat better power than Zmax when two disease loci existed (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||