Independence In Contingency Tables Research Articles

Trends and variation in treatment of early breast cancer in European certified breast centres: an EUSOMA-based analysis

BackgroundPractice indicators (PI) measure provided care making use of real-world data. This study describes trends and variations in adjuvant treatment of early breast cancer (EBC) using the European Society of Breast Cancer Specialists (EUSOMA) database. MethodsThe analysis was conducted on anonymous cumulative data registered by 56 certified breast centres, which all entered at least 500 new diagnoses in the database in the 10-year period 2010–2019. Practice trends of radiotherapy, endocrine treatment, chemotherapy, and anti-HER2 therapy were evaluated. The association with age group (<50, 50–69, ≥70) and geographical area of the centre (Northern, Central, Southern Europe; NE, CE, SE) was assessed with the Pearson Chi2 test for independence in contingency tables. ResultsIn total, 150,150 patients with EBC were selected. Overall, radiotherapy was administered more frequently in NE centres, and conversely, endocrine, chemo-, and anti-HER2 therapy were used more frequently in SE centres (p<0.001). 46.9% of the pN1 patients received postmastectomy radiotherapy, with significant differences by age and geographical region (p < 0.001). Adjuvant endocrine treatment for endocrine-sensitive carcinoma in situ was administered in 46.1%, with a decreasing trend during the study period (58.5–34.5%; p < 0.001). Anti-HER2 therapy was delivered in 75.6% of all patients with HER2BC T1a/bN0, patients older than 70 received anti-HER2 in 67.6% in SE compared to 31.3% in NE centres. ConclusionImportant variations in EBC management between European certified breast centres have been demonstrated. PI using real-world data can help to monitor, evaluate, and eventually guide and align good clinical practice in the management of breast cancer.

Flight Delay Causes at Selected Visegrad Group International Airports

The aim of this article is to analyse the flight delay causes at base airports (Prague, Brno, Ostrava, Budapest, Bratislava, Katowice, and Warsaw), with a special focus on a selected airline company operating in the central European region. To process the data, methods of multivariable statistics, namely tests of independence in contingency tables, the Kruskal-Wallis testing, cluster analysis, and correspondence analysis were used. Apparently, both charter and scheduled flights have the same percentage of delayed flights, delays occur most frequently in June, and Boeing 737-800 reported delays more frequently than Airbus A320. The research has shown that the highest number of delayed flights occurs in Budapest, the lowest number in Katowice. During the night, short delays occur most often, long delays most frequently arise in the evening. The most common cause for longer delays is technical maintenance or an aircraft defect and previously delayed flights. The flight dispatch by supplier companies is the source accounting only for rather short delays. Overall, the delayed flights frequency increases with the size of the city and the airport.

On the Existence of Uniformly Most Powerful Bayesian Tests With Application to Non-Central Chi-Squared Tests.

Uniformly most powerful Bayesian tests (UMPBT's) are an objective class of Bayesian hypothesis tests that can be considered the Bayesian counterpart of classical uniformly most powerful tests. Because the rejection regions of UMPBT's can be matched to the rejection regions of classical uniformly most powerful tests (UMPTs), UMPBT's provide a mechanism for calibrating Bayesian evidence thresholds, Bayes factors, classical significance levels and p-values. The purpose of this article is to expand the application of UMPBT's outside the class of exponential family models. Specifically, we introduce sufficient conditions for the existence of UMPBT's and propose a unified approach for their derivation. An important application of our methodology is the extension of UMPBT's to testing whether the non-centrality parameter of a chi-squared distribution is zero. The resulting tests have broad applicability, providing default alternative hypotheses to compute Bayes factors in, for example, Pearson's chi-squared test for goodness-of-fit, tests of independence in contingency tables, and likelihood ratio, score and Wald tests.

New Equivalence Tests for Approximate Independence in Contingency Tables

We introduce new equivalence tests for approximate independence in two-way contingency tables. The critical values are calculated asymptotically. The finite sample performance of the tests is improved by means of the bootstrap. An estimator of boundary points is developed to make the bootstrap based tests statistically efficient and computationally feasible. We compare the performance of the proposed tests for different table sizes by simulation. Then we apply the tests to real data sets.

A Note on Karl Pearson’s 1900 Chi-Squared Test: Two Derivations of the Asymptotic Distribution, and Uses in Goodness of Fit and Contingency Tests of Independence, and a Comparison with the Exact Sample Variance Chi-Square Result

Karl Pearson’s chi-squared test is widely known and used, both as a goodness-of-fit test for hypothesized distributions or frequencies, and in tests of independence in contingency tables. The test was introduced in Pearson (1900), but the derivation in that paper is almost incomprehensible. Two derivations of the asymptotic distribution are given here. The first uses joint characteristic functions, and the second uses a multivariate central limit theorem. Goodness-of-fit tests and contingency table tests of independence are discussed, and the asymptotic chi-square distribution result for Pearson’s test statistic is compared and contrasted with the exact chi-square result for the sample variance estimator.

Independence in Contingency Tables Using Simplicial Geometry

Frequently, contingency tables are generated in a multinomial sampling. Multinomial probabilities are then organized in a table assigning probabilities to each cell. A probability table can be viewed as an element in the simplex. The Aitchison geometry of the simplex identifies independent probability tables as a linear subspace. An important consequence is that, given a probability table, the nearest independent table is obtained by orthogonal projection onto the independent subspace. The nearest independent table is identified as that obtained by the product of geometric marginals, which do not coincide with the standard marginals, except in the independent case. The original probability table is decomposed into orthogonal tables, the independent and the interaction tables. The underlying model is log-linear, and a procedure to test independence of a contingency table, based on a multinomial simulation, is developed. Its performance is studied on an illustrative example.

Testing for independence in J×K contingency tables with complex sample survey data.

The test of independence of row and column variables in a (J×K) contingency table is a widely used statistical test in many areas of application. For complex survey samples, use of the standard Pearson chi-squared test is inappropriate due to correlation among units within the same cluster. Rao and Scott (1981, Journal of the American Statistical Association 76, 221-230) proposed an approach in which the standard Pearson chi-squared statistic is multiplied by a design effect to adjust for the complex survey design. Unfortunately, this test fails to exist when one of the observed cell counts equals zero. Even with the large samples typical of many complex surveys, zero cell counts can occur for rare events, small domains, or contingency tables with a large number of cells. Here, we propose Wald and score test statistics for independence based on weighted least squares estimating equations. In contrast to the Rao-Scott test statistic, the proposed Wald and score test statistics always exist. In simulations, the score test is found to perform best with respect to type I error. The proposed method is motivated by, and applied to, post surgical complications data from the United States' Nationwide Inpatient Sample (NIS) complex survey of hospitals in 2008.

Oral Health-related Quality of Life in Czech Population

The purpose of this study was to assess the oral health-related quality of life in Czech population. Data were collected from 1,380 subjects aged 30 to 69 years attending the Department of Dentistry, Medical Faculty of Charles University in Hradec Králové or attending three private dental practitioners collaborating on the study. Oral health-related quality of life was measured with the Oral Health Impact Profile (OHIP-14) questionnaire that was translated to Czech. The OHIP-14 scores were assessed in relation to chosen clinical and sociodemographic characteristics and oral health behaviour. Statistical analyses included descriptive analyses, the Mann-Whitney test, the Kolmogorov-Smirnov test and the Kruskal-Wallis test using the NCSS 2007 program. The chi2 test of independence in contingency tables or Fisher's exact test was used for qualitative data. Internal reliability for the 14 items overall was very high (Cronbach's ac = 0.924). The two most frequently scored items using the answer other than "never" during the last year were "painful aching" (62% of subjects) and "uncomfortable to eat" (44.4%), representing subdomain physical pain. The domain of social disability was reported least frequently. The OHIP-14 was significantly associated with dental status, dental behaviour, income and age. The findings of this study do suggest that the culturally adapted OHIP-14 version may be a good research instrument to be considered for use in measuring the impact of oral problems on the quality of life in Czech population.

Assessing Robustness of Intrinsic Tests of Independence in Two-Way Contingency Tables

For testing nested hypotheses from a Bayesian standpoint, a desirable condition is that the prior for the alternative model concentrates mass around the smaller, or null, model. For testing independence in contingency tables, the intrinsic priors satisfy this requirement. Furthermore, the degree of concentration of the priors is controlled by a discrete parameter, t, the training sample size, which plays an important role in the resulting answer. In this article we report on the robustness of the tests of independence for small or moderate sample sizes in contingency tables with respect to intrinsic priors with different degrees of concentration around the null. We compare these tests to frequentist tests and other robust Bayes tests. For large sample sizes, robustness is achieved because the intrinsic Bayesian tests are consistent. Examples using real and simulated data are given. Supplemental materials (technical details and data sets) are available online.

Can a significance test be genuinely Bayesian?

The Full Bayesian Significance Test, FBST, is extensively reviewed. Its test statistic, a genuine Bayesian measure of evidence, is discussed in detail. Its behavior in some problems of statistical inference like testing for independence in contingency tables is discussed.

One message for all? Framing public health messages to recognize diversity

Abstract This study investigates the influence of framing messages as either a “gain” or a “loss” to encourage eligible women to participate in a population-based program to screen for breast cancer in New Zealand. In the first phase, self-completion questionnaire surveys were distributed to a random sample of 1085 women who had experienced a screening mammogram, which included an invitation to participate in focus group or individual interviews. The data from the survey questionnaire were quantitatively analyzed using SPPS to conduct χ 2 -tests for independence in contingency tables. Qualitative analysis of the survey and focus group interview material was carried out using an interpretive phenomenology approach of hermeneutic analysis [Ricoeur, P. (1981). Hermeneutics and the human sciences (J. B. Thompson, Trans., & Ed.). Cambridge: Cambridge University Press]. As the first New Zealand study of the screening mammography program to stratify by ethnicity, this research has indicated that some ethnic minority groups respond differently to the mainstream population to framed messages about the desirability of participating in a screening mammogram. Questions which arise from the differing responses to framed communication reflect the crucial importance of recognizing the information needs of diverse populations in any communication strategy, which indicates the important need for future research in this area.

Theory &amp; Methods: Analysis of Contingency Tables with Clustered Observations

A new approach is presented for testing independence in contingency tables with clustered observations. The approach is based on the framework of generalized linear mixed models. Under the multinomial logistic link function, the category counts are modelled with random cluster effects and a modified likelihood ratio statistic is used for testing independence. The method is applicable to multi‐way tables, and can accommodate multiple levels of clustering. It is illustrated using a benchmark dataset.

Directional tests for one-sided alternatives in multivariate models

Consider one-sided testing problems for a multivariate exponential family model. Through conditioning or other considerations, the problem oftentimes reduces to testing a null hypothesis that the natural parameter is a zero vector against the alternative that the natural parameter lies in a closed convex cone $\mathscr{C}$. The problems include testing homogeneity of parameters, testing independence in contingency tables, testing stochastic ordering of distributions and many others. A test methodology is developed that directionalizes the usual test procedures such as likelihood ratio, chi square, Fisher, and so on. The methodology can be applied to families of tests where the family is indexed by a size parameter so as to enable nonrandomized testing by $p$-values. For discrete models, a refined family of tests provides a refined grid for better testing by $p$-values. The tests have essential monotonicity properties that are required for admissibility and for desirable power properties. Two examples are given.

Tests of Independence in Contingency Tables with Small Samples: A Comparison of Statistical Power

The chi-square test of independence is a frequently used nonparametric test. Although the Type I error estimates for small-sample chi-square statistics applied to 2 x 2 tables have been relatively thoroughly studied, the Type II error rate (or power) has not been as extensively investigated. Additionally, most of the previous research has been limited to 2 x 2 tables and has not been extended to tables of larger dimensions. The objectives of the present research were (a) to investigate the small-sample power of several statistical tests in 2 x 2 and 3 x 3 contingency tables, and (b) to examine the Type I error rates for these tests under studied conditions. Various marginal distributions, sample sizes, and effect sizes were examined.

Algorithm AS 301: The Computation of a Bayes Factor Against Independence in Contingency Tables

Algorithm AS 301: The Computation of a Bayes Factor Against Independence in Contingency Tables

Tests for independence in contingency tables with ordered categories

Consider an r × c contingency table under the full multinomial model where each category is ordered. The problem is to test the null hypothesis of independence against the alternative that all local log odds ratios are nonnegative with a least one local log odds ratio positive. We find the class of all tests that are simultaneously exact, unbiased, and admissible. The problem is of considerable interest to social scientists. Some discussion of specific tests is given.

Prediction versus Independence in Contingency Tables

SummaryAlthough Chi‐square analysis of contingency tables is almost always taught in introductory courses students often show little understanding. The authors here introduce a method to remedy this.

The Robustness and Sensitivity of the Mixed-Dirichlet Bayesian Test for "Independence" in Contingency Tables

A mixed-Dirichlet prior was previously used to model the hypotheses of independence and dependence in contingency tables, thus leading to a Bayesian test for independence. Each Dirichlet has a main hyperparameter $\kappa$ and the mixing is attained by assuming a hyperprior for $\kappa$. This hyperparameter can be regarded as a flattening or shrinking constant. We here review the method, generalize it and check the robustness and sensitivity with respect to variations in the hyperpriors and in their hyperhyperparameters. The hyperpriors examined included generalized log-Students with various numbers of degrees of freedom $\nu$. When $\nu$ is as large as 15 this hyperprior approximates a log-normal distribution and when $\nu = 1$ it is a log-Cauchy. Our experiments caused us to recommend the log-Cauchy hyperprior (or of course any distribution that closely approximates it). The user needs to judge values for the upper and lower quartiles, or any two quantiles, of $\kappa$, but we find that the outcome is robust with respect to fairly wide variations in these judgments.

THE CHOICE OF CELLS IN CHI–SQUARE TESTS

AbstractThe choice of cells in chi–square goodness of fit tests is a classical problem. Some recent results in this area are discussed. It is shown that the likelihood ratio of alternatives w.r.t. null distributions plays a key role when judging different procedures. The discussion centers on the case of a simple hypothesis, but location–scale models and tests of independence in contingency tables are also considered.

On Asymptotic Power and Efficiency of Tests of Independence in Contingency Tables with Ordered Classifications

Abstract Asymptotic power formulas for tests of independence against simple association models in I × J contingency tables with ordered categories are presented. Yates's score correlation test and Spearman's tied rank correlation test are compared with a likelihood ratio test proposed by S. J. Haberman for testing independence in log-linear models with ordered classifications. Asymptotic power and relative efficiencies are derived under local alternatives that need not be included in the likelihood model assumed by Haberman's procedure. Some computations for real and fictitious data are presented.