# Ratio Test (ratio + test)

Distribution by Scientific Domains
Distribution within Mathematics and Statistics

Kinds of Ratio Test

 generalized likelihood ratio test likelihood ratio test

## Selected Abstracts

### A Conditional Likelihood Ratio Test for Structural Models

ECONOMETRICA, Issue 4 2003
Marcelo J. Moreira
This paper develops a general method for constructing exactly similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reduced-form covariance matrix. These tests are shown to be similar under weak-instrument asymptotics when the reduced-form covariance matrix is estimated and the errors are non-normal. The conditional test based on the likelihood ratio statistic is particularly simple and has good power properties. Like the score test, it is optimal under the usual local-to-null asymptotics, but it has better power when identification is weak. [source]

### Decision Theory Applied to an Instrumental Variables Model

ECONOMETRICA, Issue 3 2007
Gary Chamberlain
This paper applies some general concepts in decision theory to a simple instrumental variables model. There are two endogenous variables linked by a single structural equation; k of the exogenous variables are excluded from this structural equation and provide the instrumental variables (IV). The reduced-form distribution of the endogenous variables conditional on the exogenous variables corresponds to independent draws from a bivariate normal distribution with linear regression functions and a known covariance matrix. A canonical form of the model has parameter vector (,, ,, ,), where ,is the parameter of interest and is normalized to be a point on the unit circle. The reduced-form coefficients on the instrumental variables are split into a scalar parameter ,and a parameter vector ,, which is normalized to be a point on the (k,1)-dimensional unit sphere; ,measures the strength of the association between the endogenous variables and the instrumental variables, and ,is a measure of direction. A prior distribution is introduced for the IV model. The parameters ,, ,, and ,are treated as independent random variables. The distribution for ,is uniform on the unit circle; the distribution for ,is uniform on the unit sphere with dimension k-1. These choices arise from the solution of a minimax problem. The prior for ,is left general. It turns out that given any positive value for ,, the Bayes estimator of ,does not depend on ,; it equals the maximum-likelihood estimator. This Bayes estimator has constant risk; because it minimizes average risk with respect to a proper prior, it is minimax. The same general concepts are applied to obtain confidence intervals. The prior distribution is used in two ways. The first way is to integrate out the nuisance parameter ,in the IV model. This gives an integrated likelihood function with two scalar parameters, ,and ,. Inverting a likelihood ratio test, based on the integrated likelihood function, provides a confidence interval for ,. This lacks finite sample optimality, but invariance arguments show that the risk function depends only on ,and not on ,or ,. The second approach to confidence sets aims for finite sample optimality by setting up a loss function that trades off coverage against the length of the interval. The automatic uniform priors are used for ,and ,, but a prior is also needed for the scalar ,, and no guidance is offered on this choice. The Bayes rule is a highest posterior density set. Invariance arguments show that the risk function depends only on ,and not on ,or ,. The optimality result combines average risk and maximum risk. The confidence set minimizes the average,with respect to the prior distribution for ,,of the maximum risk, where the maximization is with respect to ,and ,. [source]

### Testing for separability of space,time covariances

ENVIRONMETRICS, Issue 8 2005
Matthew W. Mitchell
Abstract Separable space,time covariance models are often used for modeling in environmental sciences because of their computational benefits. Unfortunately, there are few formal statistical tests for separability. We adapt a likelihood ratio test based on multivariate repeated measures to the spatio,temporal context. We apply this test to an environmental monitoring data set. Copyright © 2005 John Wiley & Sons, Ltd. [source]

### Design of change detection algorithms based on the generalized likelihood ratio test

ENVIRONMETRICS, Issue 8 2001
Giovanna Capizzi
Abstract A design procedure for detecting additive changes in a state-space model is proposed. Since the mean of the observations after the change is unknown, detection algorithms based on the generalized likelihood ratio test, GLR, and on window-limited type GLR, are considered. As Lai (1995) pointed out, it is very difficult to find a satisfactory choice of both window size and threshold for these change detection algorithms. The basic idea of this article is to estimate, through the stochastic approximation of Robbins and Monro, the threshold value which satisfies a constraint on the mean between false alarms, for a specified window size. A convenient stopping rule, based on the first passage time of an F -statistic below a fixed boundary, is used to terminate the iterative approximation. Then, the window size which produces the most desirable out-of-control ARL, for a fixed value of the in-control ARL, can be selected. These change detection algorithms are applied to detect biases on the measurements of ozone, recorded from one monitoring site of Bologna (Italy). Comparisons of the ARL profiles reveal that the full-GLR scheme provides much more protection than the window-limited GLR schemes against small shifts in the process, but the modified window-limited GLR provides more protection against large shifts. Copyright © 2001 John Wiley & Sons, Ltd. [source]

### Sequential methods and group sequential designs for comparative clinical trials

FUNDAMENTAL & CLINICAL PHARMACOLOGY, Issue 5 2003
Véronique Sébille
Abstract Comparative clinical trials are performed to assess whether a new treatment has superior efficacy than a placebo or a standard treatment (one-sided formulation) or whether two active treatments have different efficacies (two-sided formulation) in a given population. The reference approach is the single-stage design and the statistical test is performed after inclusion and evaluation of a predetermined sample size. In practice, the single-stage design is sometimes difficult to implement because of ethical concerns and/or economic reasons. Thus, specific early termination procedures have been developed to allow repeated statistical analyses to be performed on accumulating data and stop the trial as soon as the information is sufficient to conclude. Two main different approaches can be used. The first one is derived from strictly sequential methods and includes the sequential probability ratio test and the triangular test. The second one is derived from group sequential designs and includes Peto, Pocock, and O'Brien and Fleming methods, , and , spending functions, and one-parameter boundaries. We review all these methods and describe the bases on which they rely as well as their statistical properties. We also compare these methods and comment on their advantages and drawbacks. We present software packages which are available for the planning, monitoring and analysis of comparative clinical trials with these methods and discuss the practical problems encountered when using them. The latest versions of all these methods can offer substantial sample size reductions when compared with the single-stage design not only in the case of clear efficacy but also in the case of complete lack of efficacy of the new treatment. The software packages make their use quite simple. However, it has to be stressed that using these methods requires efficient logistics with real-time data monitoring and, apart from survival studies or long-term clinical trials with censored endpoints, is most appropriate when the endpoint is obtained quickly when compared with the recruitment rate. [source]

### Differential parental transmission of markers in RUNX2 among cleft case-parent trios from four populations

GENETIC EPIDEMIOLOGY, Issue 6 2008
Jae Woong Sull
Abstract Isolated cleft lip with or without cleft palate (CL/P) is among the most common human birth defects, with a prevalence around 1 in 700 live births. The Runt-related transcription factor 2 (RUNX2) gene has been suggested as a candidate gene for CL/P based largely on mouse models; however, no human studies have focused on RUNX2 as a risk factor for CL/P. This study examines the association between markers in RUNX2 and isolated, nonsyndromic CL/P using a case-parent trio design, while considering parent-of-origin effects. Case-parent trios from four populations (77 from Maryland, 146 from Taiwan, 35 from Singapore, and 40 from Korea) were genotyped for 24 single nucleotide polymorphisms (SNPs) in the RUNX2 gene. We performed the transmission disequilibrium test on individual SNPs. Parent-of-origin effects were assessed using the transmission asymmetry test and the parent-of-origin likelihood ratio test (PO-LRT). When all trios were combined, the transmission asymmetry test revealed a block of 11 SNPs showing excess maternal transmission significant at the P<0.01 level, plus one SNP (rs1934328) showing excess paternal transmission (P=0.002). For the 11 SNPs showing excess maternal transmission, odds ratios of being transmitted to the case from the mother ranged between 3.00 and 4.00. The parent-of-origin likelihood ratio tests for equality of maternal and paternal transmission were significant for three individual SNPs (rs910586, rs2819861, and rs1934328). Thus, RUNX2 appears to influence risk of CL/P through a parent-of-origin effect with excess maternal transmission. Genet. Epidemiol. 2008. © 2008 Wiley-Liss, Inc. [source]

### An efficient adaptive algorithm for edge detection based on the likelihood ratio test

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 4 2002
A. De Santis
Abstract The edge detection problem in blurred and noisy 2-D signals is dealt with. An adaptive signal processing algorithm is proposed which marks edge points according to an hypothesis test which compares the likelihoods of two models describing the local signal behaviour in the two cases of absence/presence of an edge. The two models are identified by a regularized least squares estimation algorithm, obtaining a numerically efficient procedure, quite robust with respect to additive noise and blurr perturbation. No global thresholding or data prefiltering is required. Copyright © 2002 John Wiley & Sons, Ltd. [source]

### Modelling of small-angle X-ray scattering data using Hermite polynomials

JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 4 2001
A. K. Swain
A new algorithm, called the term-selection algorithm (TSA), is derived to treat small-angle X-ray scattering (SAXS) data by fitting models to the scattering intensity using weighted Hermite polynomials. This algorithm exploits the orthogonal property of the Hermite polynomials and introduces an error-reduction ratio test to select the correct model terms or to determine which polynomials are to be included in the model and to estimate the associated unknown coefficients. With no a priori information about particle sizes, it is possible to evaluate the real-space distribution function as well as three- and one-dimensional correlation functions directly from the models fitted to raw experimental data. The success of this algorithm depends on the choice of a scale factor and the accuracy of orthogonality of the Hermite polynomials over a finite range of SAXS data. An algorithm to select a weighted orthogonal term is therefore derived to overcome the disadvantages of the TSA. This algorithm combines the properties and advantages of both weighted and orthogonal least-squares algorithms and is numerically more robust for the estimation of the parameters of the Hermite polynomial models. The weighting feature of the algorithm provides an additional degree of freedom to control the effects of noise and the orthogonal feature enables the reorthogonalization of the Hermite polynomials with respect to the weighting matrix. This considerably reduces the error in orthogonality of the Hermite polynomials. The performance of the algorithm has been demonstrated considering both simulated data and experimental data from SAXS measurements of dewaxed cotton fibre at different temperatures. [source]

### Cryptic differentiation and geographic variation in genetic diversity of Hall's Babbler Pomatostomus halli

JOURNAL OF AVIAN BIOLOGY, Issue 2 2001
Grant I. Miura
Sequence variation was examined in domain I of the mitochondrial control region in three Queensland populations of Hall's Babbler Pomatostomus halli, a geographically restricted, monotypic songbird in eastern Australia. Surprisingly, we found that domain I sequences were strongly differentiated into two major clades differing by 3.29%. These two clades exhibited nearly complete geographic concordance with northern and southern populations, except for two haplotypes which were sampled in the north of the range but were phylogenetically allied to the southern clade. We also found a seven-fold higher level of genetic diversity in the northern than in the southern populations. Neutrality and molecular clock tests suggested that selection or differences in substitution rates were not responsible for this difference in diversity. However, a maximum likelihood analysis of gene flow between the north and south suggested that the difference in diversity could be due to both greater population size in the north and asymmetric gene flow dominated by south to north dispersal events. A likelihood ratio test rejected a model in which population sizes were equal and rates of gene flow symmetric, and came close to rejecting a model in which only population sizes were constrained to be equal. These results suggest that different population sizes and asymmetric gene flow could be a major source of differences in genetic variation between populations of Hall's Babbler, although ecological and biogeographic causes for these differences are obscure. [source]

### Single-season heteroscedasticity in time series

JOURNAL OF FORECASTING, Issue 3 2007
Yorghos Tripodis
Abstract We consider seasonal time series in which one season has variance that is different from all the others. This behaviour is evident in indices of production where variability is highest for the month with the lowest level of production. We show that when one season has different variability from others there are constraints on the seasonal models that can be used; neither dummy and trigonometric models are effective in modelling this type of behaviour. We define a general model that provides an appropriate representation of single-season heteroscedasticity and suggest a likelihood ratio test for the presence of periodic variance in one season.,,Copyright © 2007 John Wiley & Sons, Ltd. [source]

### Sample Size Determination for Categorical Responses

JOURNAL OF FORENSIC SCIENCES, Issue 1 2009
Dimitris Mavridis Ph.D.
Abstract:, Procedures are reviewed and recommendations made for the choice of the size of a sample to estimate the characteristics (sometimes known as parameters) of a population consisting of discrete items which may belong to one and only one of a number of categories with examples drawn from forensic science. Four sampling procedures are described for binary responses, where the number of possible categories is only two, e.g., licit or illicit pills. One is based on priors informed from historical data. The other three are sequential. The first of these is a sequential probability ratio test with a stopping rule derived by controlling the probabilities of type 1 and type 2 errors. The second is a sequential variation of a procedure based on the predictive distribution of the data yet to be inspected and the distribution of the data that have been inspected, with a stopping rule determined by a prespecified threshold on the probability of a wrong decision. The third is a two-sided sequential criterion which stops sampling when one of two competitive hypotheses has a probability of being accepted which is larger than another prespecified threshold. The fifth procedure extends the ideas developed for binary responses to multinomial responses where the number of possible categories (e.g., types of drug or types of glass) may be more than two. The procedure is sequential and recommends stopping when the joint probability interval or ellipsoid for the estimates of the proportions is less than a given threshold in size. For trinomial data this last procedure is illustrated with a ternary diagram with an ellipse formed around the sample proportions. There is a straightforward generalization of this approach to multinomial populations with more than three categories. A conclusion provides recommendations for sampling procedures in various contexts. [source]

### Design for model parameter uncertainty using nonlinear confidence regions

AICHE JOURNAL, Issue 8 2001
William C. Rooney
An accurate method presented accounts for uncertain model parameters in nonlinear process optimization problems. The model representation is considered in terms of algebraic equations. Uncertain quantity parameters are often discretized into a number of finite values that are then used in multiperiod optimization problems. These discrete values usually range between some lower and upper bound that can be derived from individual confidence intervals. Frequently, more than one uncertain parameter is estimated at a time from a single set of experiments. Thus, using simple lower and upper bounds to describe these parameters may not be accurate, since it assumes the parameters are uncorrelated. In 1999 Rooney and Biegler showed the importance of including parameter correlation in design problems by using elliptical joint confidence regions to describe the correlation among the uncertain model parameters. In chemical engineering systems, however, the parameter estimation problem is often highly nonlinear, and the elliptical confidence regions derived from these problems may not be accurate enough to capture the actual model parameter uncertainty. In this work, the description of model parameter uncertainty is improved by using confidence regions derived from the likelihood ratio test. It captures the nonlinearities efficiently and accurately in the parameter estimation problem. Several examples solved show the importance of accurately capturing the actual model parameter uncertainty at the design stage. [source]

### Sequential case series analysis for pharmacovigilance

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES A (STATISTICS IN SOCIETY), Issue 1 2009
Mounia N. Hocine
Summary., The self-controlled case series method is used to evaluate drug safety, particularly the safety of paediatric vaccines with respect to rare adverse reactions. We propose a group sequential version of the method for prospective surveillance of drug safety. We focus on the surveillance of new vaccines. We develop methods that are based on the sequential probability ratio test applied at predetermined surveillance intervals, using both simple and composite alternative hypotheses. We investigate the properties of the methods analytically in a simple setting and by simulations in more realistic scenarios. The methods are applied to data on influenza vaccine and Bell's palsy, and to data on measles, mumps and rubella vaccine and bleeding disorders. [source]

### Correlating two continuous variables subject to detection limits in the context of mixture distributions

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 5 2005
Haitao Chu
Summary., In individuals who are infected with human immunodeficiency virus (HIV), distributions of quantitative HIV ribonucleic acid measurements may be highly left censored with an extra spike below the limit of detection LD of the assay. A two-component mixture model with the lower component entirely supported on [0, LD] is recommended to model the extra spike in univariate analysis better. Let LD1 and LD2 be the limits of detection for the two HIV viral load measurements. When estimating the correlation coefficient between two different measures of viral load obtained from each of a sample of patients, a bivariate Gaussian mixture model is recommended to model the extra spike on [0, LD1] and [0, LD2] better when the proportion below LD is incompatible with the left-hand tail of a bivariate Gaussian distribution. When the proportion of both variables falling below LD is very large, the parameters of the lower component may not be estimable since almost all observations from the lower component are falling below LD. A partial solution is to assume that the lower component's entire support is on [0, LD1]×[0, LD2]. Maximum likelihood is used to estimate the parameters of the lower and higher components. To evaluate whether there is a lower component, we apply a Monte Carlo approach to assess the p -value of the likelihood ratio test and two information criteria: a bootstrap-based information criterion and a cross-validation-based information criterion. We provide simulation results to evaluate the performance and compare it with two ad hoc estimators and a single-component bivariate Gaussian likelihood estimator. These methods are applied to the data from a cohort study of HIV-infected men in Rio de Janeiro, Brazil, and the data from the Women's Interagency HIV oral study. These results emphasize the need for caution when estimating correlation coefficients from data with a large proportion of non-detectable values when the proportion below LD is incompatible with the left-hand tail of a bivariate Gaussian distribution. [source]

### A feasibility study of daytime fog and low stratus detection with TERRA/AQUA-MODIS over land

METEOROLOGICAL APPLICATIONS, Issue 2 2006
Jörg Bendix
Abstract A scheme for the detection of fog and low stratus over land during daytime based on data of the MODIS (Moderate Resolution Imaging Spectroradiometer) instrument is presented. The method is based on an initial threshold test procedure in the MODIS solar bands 1,7 (0.62,2.155µm). Fog and low stratus detection generally relies on the definition of minimum and maximum fog and low stratus properties, which are converted to spectral thresholds by means of radiative transfer calculations (RTC). Extended sensitivity studies reveal that thresholds mainly depend on the solar zenith angle and, hence, illumination-dependent threshold functions are developed. Areas covered by snow, ice and mid-/high-level clouds as well as bright/hazy land surfaces are omitted from the initial classification result by means of a subsequent cloud-top height test based on MODIS IR band 31 (at 12 µm) and a NIR/VIS ratio test. The validation of the final fog and low stratus mask generally shows a satisfactory performance of the scheme. Validation problems occur due to the late overpass time of the TERRA platform and the time lag between SYNOP and satellite observations. Apparent misclassifications are mainly found at the edge of the fog layers, probably due to over- or underestimation of fog and low stratus cover in the transition zone from fog to haze. Copyright © 2006 Royal Meteorological Society. [source]

### The Likelihood Ratio Test for the Rank of a Cointegration Submatrix,

OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 2006
Paolo Paruolo
Abstract This paper proposes a likelihood ratio test for rank deficiency of a submatrix of the cointegrating matrix. Special cases of the test include the one of invalid normalization in systems of cointegrating equations, the feasibility of permanent,transitory decompositions and of subhypotheses related to neutrality and long-run Granger noncausality. The proposed test has a chi-squared limit distribution and indicates the validity of the normalization with probability one in the limit, for valid normalizations. The asymptotic properties of several derived estimators of the rank are also discussed. It is found that a testing procedure that starts from the hypothesis of minimal rank is preferable. [source]

### Evaluating, Comparing and Combining Density Forecasts Using the KLIC with an Application to the Bank of England and NIESR ,Fan' Charts of Inflation,

OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 2005
James Mitchell
Abstract This paper proposes and analyses the Kullback,Leibler information criterion (KLIC) as a unified statistical tool to evaluate, compare and combine density forecasts. Use of the KLIC is particularly attractive, as well as operationally convenient, given its equivalence with the widely used Berkowitz likelihood ratio test for the evaluation of individual density forecasts that exploits the probability integral transforms. Parallels with the comparison and combination of point forecasts are made. This and related Monte Carlo experiments help draw out properties of combined density forecasts. We illustrate the uses of the KLIC in an application to two widely used published density forecasts for UK inflation, namely the Bank of England and NIESR ,fan' charts. [source]

### Is x-height a better indicator of legibility than type size for drug labels?

PACKAGING TECHNOLOGY AND SCIENCE, Issue 5 2003
Laura Bix
Abstract In 1999 the US Food and Drug Administration published a regulation in an attempt to ensure the legibility of OTC drugs, specifying, among other things, a minimum type size of 6 points. This is problematic because different typefaces of the same size vary widely in type heights and, presumably, legibility. We hypothesized that specifying a minimum x-height, the height of the lowercase x, would produce more consistent legibility than the minimum type size specified within the regulation. Twenty-six subjects viewed two groups of typefaces using the Lockhart Legibility Instrument to quantify legibility. The first group contained typefaces that were all 6 points, but, by nature of their design, varied greatly in their x-heights. The second group was made from the same set of typefaces, but these were manipulated so that their x-heights were equal to the average x-height of group 1. A likelihood ratio test indicated that the group that varied in x-height, group 1, produced significantly more variable results than the group with equal x-heights, group 2. This indicates that specifying a minimum type size may not be the best approach for producing consistent legibility. Copyright © 2003 John Wiley & Sons, Ltd. [source]

### Adaptive charting schemes based on double sequential probability ratio tests

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 1 2009
Yan Li
Abstract Sequential probability ratio test (SPRT) control charts are shown to be able to detect most shifts in the mean or proportion substantially faster than conventional charts such as CUSUM charts. However, they are limited in applications because of the absence of the upper bound on the sample size and possibly large sample numbers during implementation. The double SPRT (2-SPRT) control chart, which applies a 2-SPRT at each sampling point, is proposed in this paper to solve some of the limitations of SPRT charts. Approximate performance measures of the 2-SPRT control chart are obtained by the backward method with the Gaussian quadrature in a computer program. On the basis of two industrial examples and simulation comparisons, we conclude that the 2-SPRT chart is competitive in that it is more sensitive and economical for small shifts and has advantages in administration because of fixed sampling points and a proper upper bound on the sample size. Copyright © 2008 John Wiley & Sons, Ltd. [source]

### Binomial Mixture Model-based Association Tests under Genetic Heterogeneity

ANNALS OF HUMAN GENETICS, Issue 6 2009
Hui Zhou
Summary Most of the existing association tests for population-based case-control studies are based on comparing the mean genotype scores between the case and control groups, which may not be efficient under genetic heterogeneity. Given that most common diseases are genetically heterogeneous, caused by mutations in multiple loci, it may be beneficial to fully account for genetic heterogeneity in an association test. Here we first propose a binomial mixture model for such a purpose and develop a corresponding mixture likelihood ratio test (MLRT) for a single locus. We also consider two methods to combine single-locus-based MLRTs across multiple loci in linkage disequilibrium to boost power when causal SNPs are not genotyped. We show with a wide spectrum of numerical examples that under genetic heterogeneity the proposed tests are more powerful than some commonly used association tests. [source]

### European Mathematical Genetics Meeting, Heidelberg, Germany, 12th,13th April 2007

ANNALS OF HUMAN GENETICS, Issue 4 2007
Article first published online: 28 MAY 200

### Contribution of a haplotype in the HLA region to anti,cyclic citrullinated peptide antibody positivity in rheumatoid arthritis, independently of HLA,DRB1

ARTHRITIS & RHEUMATISM, Issue 12 2009
Objective To examine the risk of anti,cyclic citrullinated peptide (anti-CCP) antibody positivity in rheumatoid arthritis (RA) patients carrying certain haplotypes in the HLA region. Methods A total of 1,389 Japanese patients with RA were genotyped for 30 single-nucleotide polymorphisms (SNPs) in the HLA region using commercial oligonucleotide arrays (from Perlegen or Affymetrix) as well as for HLA,DRB1 alleles using a sequence-specific polymerase chain reaction method. Stepwise logistic regression was used to select from among the 30 SNPs the ones that represented a risk of anti-CCP antibody positivity. Haplotypes of the selected SNPs were inferred using an expectation-maximization algorithm. Associations of individual SNPs were evaluated with the Cochran-Armitage test for trend. DRB1 alleles and haplotypes were evaluated with the chi-square test. Heterogeneities of risks among the shared epitope (SE) and non-SE HLA,DRB1 alleles were examined using the exact test. Haplotype associations that were independent of individual HLA,DRB1 alleles were evaluated using the likelihood ratio test. Results Significant associations were found for 9 SNPs (smallest P value being 2.4 × 10,8) and in 4 HLA,DRB1 alleles (smallest P value being 2.0 × 10,10 in DRB1*0405). Stepwise logistic regression selected 4 SNPs (rs9262638, rs7775228, rs4713580, and rs9277359). Among the 16 inferred haplotypes of these 4 SNPs, 6 indicated significant associations (smallest P value being 1.9 × 10,11). Risks among SE and non-SE alleles were significantly heterogeneous (P = 0.0095 and P = 9.8 × 10,9, respectively), indicating the importance of stratification with individual DRB1 alleles rather than SE alleles. Conditional analysis of the risk associated with individual DRB1 alleles identified a risk haplotype that was independent of DRB1 (odds ratio 2.00 [95% confidence interval 1.44,2.79], P = 2.6 × 10,5). Conclusion Heterogeneous risks of anti-CCP antibody positivity were confirmed among SE and non-SE alleles in our patient population. A risk haplotype in the HLA region that is independent of HLA,DRB1 was confirmed. [source]

### Association of a specific ERAP1/ARTS1 haplotype with disease susceptibility in ankylosing spondylitis

ARTHRITIS & RHEUMATISM, Issue 5 2009
W. P. Maksymowych
Objective Alterations in antigen processing have been proposed to play a significant role in the pathogenesis of ankylosing spondylitis (AS). A non,major histocompatibility complex gene encoding an endoplasmic reticulum aminopeptidase, ERAP1, has been implicated recently. This study assessed 13 coding single-nucleotide polymorphisms (SNPs) from 5 genes involved in antigen processing (ERAP1, TAP1, TAP2, LMP2, and LMP7) in 3 Canadian cohorts of patients with AS, to address the possibility of gene interactions in disease susceptibility. Methods The study involved 992 AS cases and 1,437 controls from 3 centers (472 cases and 451 controls from Alberta, 138 cases and 392 controls from Newfoundland, and 382 cases and 594 controls from Toronto). Most of the patients with AS and healthy, unrelated controls were Caucasians of northern European descent. Single-marker and haplotype associations were determined using an allelic likelihood ratio test in UNPHASED, version 3.0.12, and the WHAP program, respectively. P values for significance of haplotype associations were calculated using a permutation test. Results A specific ERAP1 haplotype, rs27044/10050860/30187-CCT, was strongly associated with increased risk of AS in all 3 case,control cohorts (pooled odds ratio [OR] 1.81, 95% confidence interval [95% CI] 1.46,2.24; P = 7 × 10,8), while a second specific ERAP1 haplotype, rs30187/26618/26653-CTG, reduced the disease risk (pooled OR 0.77, 95% CI 0.67,0.88; P = 9 × 10,5). Significant associations were also noted for 3 ERAP1 SNP variants (rs10050860, rs30187, and rs26653), although no significant haplotype interaction between ERAP1 and TAP/LMP loci was evident. Conclusion These data indicate that an AS disease locus may reside on a specific ERAP1 haplotype, and its effect is not multiplicative with contributions from TAP and LMP genes. [source]

### POISSON VERSUS BINOMIAL: APPOINTMENT OF JUDGES TO THE U.S. SUPREME COURT

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2010
Vassilly Voinov
Summary The problem of discriminating between the Poisson and binomial models is discussed in the context of a detailed statistical analysis of the number of appointments of the U.S. Supreme Court justices from 1789 to 2004. Various new and existing tests are examined. The analysis shows that both simple Poisson and simple binomial models are equally appropriate for describing the data. No firm statistical evidence in favour of an exponential Poisson regression model was found. Two attendant results were obtained by simulation: firstly, that the likelihood ratio test is the most powerful of those considered when testing for the Poisson versus binomial and, secondly, that the classical variance test with an upper-tail critical region is biased. [source]

### Testing the Ratio of Two Poisson Rates

BIOMETRICAL JOURNAL, Issue 2 2008
Kangxia Gu
Abstract In this paper we compare the properties of four different general approaches for testing the ratio of two Poisson rates. Asymptotically normal tests, tests based on approximate p -values, exact conditional tests, and a likelihood ratio test are considered. The properties and power performance of these tests are studied by a Monte Carlo simulation experiment. Sample size calculation formulae are given for each of the test procedures and their validities are studied. Some recommendations favoring the likelihood ratio and certain asymptotic tests are based on these simulation results. Finally, all of the test procedures are illustrated with two real life medical examples. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

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

BIOMETRICAL JOURNAL, Issue 3 2004
Seung-Ho Kang
Abstract 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) [source]

### Statistical Inference For Risk Difference in an Incomplete Correlated 2 × 2 Table

BIOMETRICAL JOURNAL, Issue 1 2003
Nian-Sheng Tang
Abstract In some infectious disease studies and 2-step treatment studies, 2 × 2 table with structural zero could arise in situations where it is theoretically impossible for a particular cell to contain observations or structural void is introduced by design. In this article, we propose a score test of hypotheses pertaining to the marginal and conditional probabilities in a 2 × 2 table with structural zero via the risk/rate difference measure. Score test-based confidence interval will also be outlined. We evaluate the performance of the score test and the existing likelihood ratio test. Our empirical results evince the similar and satisfactory performance of the two tests (with appropriate adjustments) in terms of coverage probability and expected interval width. Both tests consistently perform well from small- to moderate-sample designs. The score test however has the advantage that it is only undefined in one scenario while the likelihood ratio test can be undefined in many scenarios. We illustrate our method by a real example from a two-step tuberculosis skin test study. [source]

### A Robust Genome-Wide Scan Statistic of the Wellcome Trust Case,Control Consortium

BIOMETRICS, Issue 4 2009
Jungnam Joo
Summary In genome-wide association (GWA) studies, test statistics that are efficient and robust across various genetic models are preferable, particularly for studying multiple diseases in the Wellcome Trust Case,Control Consortium (WTCCC, 2007,,Nature,447, 661,678). A new test statistic, the minimum of the p-values of the trend test and Pearson's test, was considered by the WTCCC. It is referred to here as MIN2. Because the minimum of two p-values is no longer a valid p-value itself, the WTCCC only used it to rank single nucleotide polymorphisms (SNPs) but did not report the p-values of the associated SNPs when MIN2 was used for ranking. Given its importance in practice, we derive the asymptotic null distribution of MIN2, study some of its analytical properties related to GWA studies, and compare it with existing methods (the trend test, Pearson's test, MAX3, and the constrained likelihood ratio test [CLRT]) by simulations across a wide range of possible genetic models: the recessive (REC), additive (ADD), multiplicative (MUL), dominant (DOM), and overdominant models. The results show that MAX3 and CLRT have greater efficiency robustness than other tests when the REC, ADD/MUL, and DOM models are possible, whereas Pearson's test and MIN2 have greater efficiency robustness if the possible genetic models also include the overdominant model. We conclude that robust tests (MAX3, MIN2, CLRT, and Pearson's test) are preferable to a single trend test for initial GWA studies. The four robust tests are applied to more than 100 SNPs associated with 11 common diseases identified by the two WTCCC GWA studies. [source]

### Nonparametric Functional Mapping of Quantitative Trait Loci

BIOMETRICS, Issue 1 2009
Jie Yang
Summary Functional mapping is a useful tool for mapping quantitative trait loci (QTL) that control dynamic traits. It incorporates mathematical aspects of biological processes into the mixture model-based likelihood setting for QTL mapping, thus increasing the power of QTL detection and the precision of parameter estimation. However, in many situations there is no obvious functional form and, in such cases, this strategy will not be optimal. Here we propose to use nonparametric function estimation, typically implemented with B-splines, to estimate the underlying functional form of phenotypic trajectories, and then construct a nonparametric test to find evidence of existing QTL. Using the representation of a nonparametric regression as a mixed model, the final test statistic is a likelihood ratio test. We consider two types of genetic maps: dense maps and general maps, and the power of nonparametric functional mapping is investigated through simulation studies and demonstrated by examples. [source]

### Comparison of Properties of Tests for Assessing Tumor Clonality

BIOMETRICS, Issue 4 2008
Irina Ostrovnaya
Summary In a recent article Begg et al. (2007, Biometrics 63, 522,530) proposed a statistical test to determine whether or not a diagnosed second primary tumor is biologically independent of the original primary tumor, by comparing patterns of allelic losses at candidate genetic loci. The proposed concordant mutations test is a conditional test, an adaptation of Fisher's exact test, that requires no knowledge of the marginal mutation probabilities. The test was shown to have generally good properties, but is susceptible to anticonservative bias if there is wide variation in mutation probabilities between loci, or if the individual mutation probabilities of the parental alleles for individual patients differ substantially from each other. In this article, a likelihood ratio test is derived in an effort to address these validity issues. This test requires prespecification of the marginal mutation probabilities at each locus, parameters for which some information will typically be available in the literature. In simulations this test is shown to be valid, but to be considerably less efficient than the concordant mutations test for sample sizes (numbers of informative loci) typical of this problem. Much of the efficiency deficit can be recovered, however, by restricting the allelic imbalance parameter estimate to a prespecified range, assuming that this parameter is in the prespecified range. [source]