Test for linear trend in 2 x K ordered tables with open-ended categories

A method of evaluating trend (positive or negative) in 2 x K ordered tables is suggested for cases in which the scores for the first (K-1) categories are known a priori but the score for the last category is not known. Such a category is termed as open-ended category in this paper. Ordered tables with an open-ended category are often encountered while evaluating the Cochran-Armitage-Mantel (CAM) trend. In the present paper, the distribution of the test statistic is presented and simulations are carried out to check the asymptotics. The method is then exemplified by an existing data set.     

A logistic model for trend in 2 x 2 x kappa tables with applications to meta-analyses

There recently has been an increased interest in examining the relationship between the baseline (control) risk of an adverse outcome and the magnitude of the treatment effect (Brand and Kragt, 1992, Statistics in Medicine 11, 2077-2082; Davey Smith, Song, and Sheldon, 1993, The British Medical Journal 306, 1367-1373; Senn, 1994, Statistics in Medicine 13, 293-294). To facilitate such an examination, we propose a logistic model in which the relationship between the treatment effect, as measured by the log odds ratio, and the baseline risk is specified parametrically. This procedure is founded on a product-binomial likelihood and generates maximum likelihood estimates of the baseline event rates and two parameters characterizing the trend in the treatment effect. We fit this model to data from a meta-analysis involving the treatment of women at risk of preterm labor and contrast our findings with those of an earlier analysis.     

Graphic determination of significance of 2 X 2 contingency tables.

There are several techniques available for determining the significance of differences in proportions, or frequencies in the 2 X 2 contingency tables. All of these techniques have their limitations. A method is proposed which overcomes some of these limitations. The method is applicable for the situation where the two samples being compared are independently selected and contain the same number of Ss. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Convex hull test for ordered categorical data

When testing for stochastic order in ordered 2 x J contingency tables, it is common to select the cutoff required to declare significance so as to ensure that the size of the test is exactly alpha conditionally on the margins. It is valid, however, to use the margins to select not only the cutoff but also the form of the test. Linear rank tests, which are locally most powerful and frequently used in practice, suffer from the drawback that they may have power as low as zero to detect some alternatives of interest when the margins satisfy certain conditions. The Smirnov and convex hull tests are shown, through exact conditional power calculations and simulations, to avoid this drawback. The convex hull test is also admissible and palindromic invariant and minimizes the required significance level to have limiting power of one as the alternative moves away from the null in any direction.     

Measurement precision in test score and item response models.

The population-dependent concept of reliability is used in test score models such as classical test theory and the binomial error model, whereas in item response models, the population-independent concept of information is used. Reliability and information apply to both test score and item response models. Information is a conditional definition of precision, that is, the precision for a given subject; reliability is an unconditional definition, that is, the precision for a population of subjects. Information and reliability do not distinguish test score and item response models. The main distinction is that the parameters are specific for the test and the subject in test score models, whereas in item response models, the item parameters are separated from the subject parameters. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The test of homogeneity for 2?×?2 contingency tables: A review of and some personal opinions on the controversy.

The 2?×?2 table has received an enormous amount of attention in the research literature. Most studies have focused on Type I error rates and the power of the chi-square statistic, but some have been more concerned with the theoretical justification behind methods of analysis. Little consensus has been achieved in either area. The reason for this is that 2 basic inferential paradigms that underlie much of the work in 2?×?2 tables are incompatible. Thus, empirical studies of Type I error rates of the chi-square test within the Neyman–Pearson framework are considered irrelevant by advocates of R. A. Fisher's exact test. Both approaches are described in this article. G. A. Barnard's (1947) test is shown to be theoretically superior to the chi-square test and all of its corrected cousins. However, Fisher's exact test is advocated as the most rational choice. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An exact unconditional test for the 2?×?2 comparative trial.

A 1-sided exact test, based on the unconditional distribution of the common Z statistic, is proposed for the hypothesis of equal stress probabilities in a 2?×?2 comparative trials contingency table. The need for an exact test is justified by the fact that the Type I error probabilities of the large-sample (normal) test may turn out to be more than twice the nominal significance level. Power comparisons reveal that the new test performs considerably better than Fisher's exact test and, in some cases, is even more powerful than the randomized conditional test. (6 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Molecular biologic screening test (PCR) for fragile X syndrome

Fragile X syndrome is the most common inherited from of familial mental retardation. It is caused by an expanded CGG repeat in the first exon of the fragile X mental retardation gene. A polymerase chain reaction based technique was used for the identification of full mutations among men. According to our conditions full mutations failed to amplify. An internal control was used at a CG rich region 147 bp upstream of the polymorphic region. The bands were visualised on silver stained polyacrylamide gels. From the 57 individuals studied molecular analysis was performed on 38 males and 16 females. From the 26 males with suspected fragile X syndrome 9 males resulted in no amplification of the 500 kb product, all having a positive cytogenetic result for fragile X syndrome. One cytogeneticly positive male had normal results by molecular studies suggesting a different mutation. All control males had normal results. The results on the 16 females studied were inconclusive. We suggest that our method is highly sensitive and specific for screening males for fragile X syndrome.     

Small-sample tests for homogeneity of response probabilities in 2?×?2 contingency tables.

Classical tests of significance for homogeneity of response probabilities in 2?×?2 tables tend to have actual Type I error probabilities that differ substantially from the theoretical alpha level. Fisher's exact test and chi-square with Yates's (1934) correction for continuity have severely conservative biases, whereas the Pearson chi-square is frequently nonconservative. A z test proposed by Haber (1986) has the advantage of never producing nonconservative results while evidencing only modest conservative bias in most cases. We show several other new tests to have actual Type I error probabilities that vary more closely about theoretical alpha levels. They avoid the conservative biases of the Fisher, Yates, and Haber tests and are less often nonconservative than is the Pearson chi-square. We present computational formulas. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A sample size correction for Pearson chi-square in 2?×?2 contingency tables.

A test statistic that is asymptotically equivalent to the Pearson chi-square, but which is more conservative by a factor of (N?–?1)/N, is proposed for use with small samples when testing for homogeneity of response probabilities in 2?×?2 tables. Evaluation of this test statistic indicates that it produces actual Type I error probabilities that are less often and less seriously nonconservative than the Pearson chi-square, although it does not result in the severely conservative bias previously reported for Yates's correction or Fisher's exact probability test. Other recent evaluations of bias in the Pearson chi-square test for 2?×?2 tables have resulted in conflicting recommendations, primarily because the evaluations have been based on different assumptions concerning the degree of experimenter control over marginal frequencies. Three conditions of control over the marginal frequencies are identified, and the results of exact probability evaluations for the Pearson chi-square under different assumptions are discussed. (9 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An optimality score for the neurologic examination of the term newborn

We describe the application of a revised version of the Dubowitz neurologic examination of the newborn in 224 low-risk, term newborn infants. The method has been updated by eliminating less useful items and including new items evaluating general movements and patterns of distribution of tone. An optimality score is included to make the evaluation more quantitative and for comparison with sequential examinations with neurophysiologic and imaging findings. The score is based on the distribution of the scores for each item in the population of low-risk term infants. We defined not only the most common pattern for each item but also the variability of the findings by using 10th and 5th centiles. Because most of the items assessing tone and the Moro reflex varied with gestational age between 37 and 42 weeks, the changes were incorporated in the scoring system. The total optimality score was the sum of the optimality scores of individual items. Although the association of 4 or more deviant scores was found in less than 10% of our infants, deviant results on 1 or 2 single items could be observed in a third of this normal population, suggesting that isolated deviant signs have little diagnostic value. In contrast, an abnormal distribution of tone patterns, which we have commonly observed in infants with brain lesions, was not found in this cohort.     

Understanding and testing for heterogeneity across 2 x 2 tables: application to meta-analysis

A question of interest in a meta-analysis is whether the studies considered are homogeneous. This paper addresses two forms of heterogeneity. Additive heterogeneity occurs when a particular treatment performs differently in different studies. Interactive heterogeneity occurs when the relative performance of two treatments varies with the study. This paper discusses the use and calculation of Bayes factors to test for both forms of heterogeneity. I consider three hierarchical models. One exhibits both forms of heterogeneity, a second exhibits only additive heterogeneity, and the third model has neither form of heterogeneity. I use a method based on bridge sampling for calculating the Bayes factors between the models. I consider two examples: in one both forms of heterogeneity seem to be present and in the other there seems to be additive heterogeneity but not interactive heterogeneity.     

A test for linear trend in constant hazards and its application to a problem in occupational health

A score test is derived for testing a linear trend in constant hazards. The test is applied to prove the attenuation of healthy worker effects in the analysis of occupational mortality.     

Testing for association in 2?×?2 contingency tables with very small sample sizes.

Applied statistics textbooks generally recommend the use of the chi-square tests of homogeneity and independence with 2?×?2 contingency tables only when the expected frequency of each cell is 5 or more. Recent research has shown this rule-of-thumb criterion to be unnecessarily restrictive, but has not explored the accuracy of the chi-square tests when the total number of observations is less than 20 or when the expected frequencies fall well below one—the primary issues considered in this article. The chi-square tests of homogeneity and independence were found to provide reasonably accurate estimates of Type I error probability for N?≥?8. Certain alternatives to the chi-square tests are considered. (61 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A PCR-based test suitable for screening for fragile X syndrome among mentally retarded males

Ever since the identification of the genetic cause of fragile X syndrome as the expansion of an unstable trinucleotide sequence, several diagnostic strategies have evolved from molecular studies. However, we still lack a simple test suitable for population screening. We have therefore developed a nonisotopic polymerase chain reaction (PCR)-based technique for the identification of fragile X full mutations among men, with easy visualization of the PCR products on silver-stained polyacrylamide gels. The technique consists of PCR amplification with primers that flank the trinucleotide repeats, with a product of 557 bp for the (CGG)29 allele. Conditions were established such that full mutations failed to amplify and were thus identified with 98% sensitivity compared with Southern blot analysis. To produce an indispensable internal control we added to the reaction a third primer, internal to this fragment, allowing the multiplex amplification of a monomorphic band corresponding to a CG-rich stretch 147 bp upstream of the polymorphic region. In trials involving 41 patients and 74 controls, the PCR-based test here described showed specificity of more than 98.6%, accuracy of 99% and a sensitivity of 98%. Thus, although not suitable for medical diagnosis, it constitutes a useful tool for screening for the fragile X syndrome in populations of mentally retarded males.