Confidence intervals for the difference of marginal probabilities in clustered matched-pair binary data

Although there are several available test statistics to assess the difference of marginal probabilities in clustered matched‐pair binary data, associated confidence intervals (CIs) are not readily available. Herein, the construction of corresponding CIs is proposed, and the performance of each CI is investigated. The results from Monte Carlo simulation study indicate that the proposed CIs perform well in maintaining the nominal coverage probability: for small to medium numbers of clusters, the intracluster correlation coefficient‐adjusted McNemar statistic and its associated Wald or Score CIs are preferred; however, this statistic becomes conservative when the number of clusters is larger so that alternative statistics and their associated CIs are preferred. In practice, a combination of the intracluster correlation coefficient‐adjusted McNemar statistic with an alternative statistic is recommended. To illustrate the practical application, a real clustered matched‐pair collection of data is used to illustrate testing the difference of marginal probabilities and constructing the associated CIs. Copyright © 2012 John Wiley & Sons, Ltd.     

Testing homogeneity in clustered (longitudinal) count data regression model with over-dispersion

Clustered (longitudinal) count data arise in many bio-statistical practices in which a number of repeated count responses are observed on a number of individuals. The repeated observations may also represent counts over time from a number of individuals. One important problem that arises in practice is to test homogeneity within clusters (individuals) and between clusters (individuals). As data within clusters are observations of repeated responses, the count data may be correlated and/or over-dispersed. For over-dispersed count data with unknown over-dispersion parameter we derive two score tests by assuming a random intercept model within the framework of (i) the negative binomial mixed effects model and (ii) the double extended quasi-likelihood mixed effects model (Lee and Nelder, 2001). These two statistics are much simpler than a statistic derived by Jacqmin-Gadda and Commenges (1995) under the framework of the over-dispersed generalized linear model. The first statistic takes the over-dispersion more directly into the model and therefore is expected to do well when the model assumptions are satisfied and the other statistic is expected to be robust. Simulations show superior level property of the statistics derived under the negative binomial and double extended quasi-likelihood model assumptions. A data set is analyzed and a discussion is given.     

Testing the homogeneity of proportions for clustered binary data without knowing the correlation structure

A robust generalized score test for comparing groups of cluster binary data is proposed. This novel test is asymptotically valid for practically any underlying correlation configurations including the situation when correlation coefficients vary within or between clusters. This structure generally undermines the validity of the typical large sample properties of the method of maximum likelihood. Simulations and real data analysis are used to demonstrate the merit of this parametric robust method. Results show that our test is superior to two recently proposed test statistics advocated by other researchers.     

Adjusted homogeneity tests of odds ratios when data are clustered

Three modified tests for homogeneity of the odds ratio for a series of 2 × 2 tables are studied when the data are clustered. In the case of clustered data, the standard tests for homogeneity of odds ratios ignore the variance inflation caused by positive correlation among responses of subjects within the same cluster, and therefore have inflated Type I error. The modified tests adjust for the variance inflation in the three existing standard tests: Breslow–Day, Tarone and the conditional score test. The degree of clustering effect is measured by the intracluster correlation coefficient, ρ. A variance correction factor derived from ρ is then applied to the variance estimator in the standard tests of homogeneity of the odds ratio. The proposed tests are an application of the variance adjustment method commonly used in correlated data analysis and are shown to maintain the nominal significance level in a simulation study. Copyright © 2004 John Wiley & Sons, Ltd.     

Occupancy distributions for testing marginal homogeneity

In this paper different pairs of urns are considered. We are interested in the number of ways in which N balls can be placed into the urns so that differences and ratios between the number of balls in certain pairs of urns are the same.     

Testing the homogeneity of risk differences with sparse count data

ABSTRACT

In this paper, we consider testing the homogeneity of risk differences in independent binomial distributions especially when data are sparse. We point out some drawback of existing tests in either controlling a nominal size or obtaining powers through theoretical and numerical studies. The proposed test is designed to avoid the drawbacks of existing tests. We present the asymptotic null distribution and asymptotic power function for the proposed test. We also provide numerical studies including simulations and real data examples showing the proposed test has reliable results compared to existing testing procedures.     

Modeling proportions and marginal counts simultaneously for clustered multinomial data with random cluster sizes

Clustered multinomial data with random cluster sizes commonly appear in health, environmental and ecological studies. Traditional approaches for analyzing clustered multinomial data contemplate two assumptions. One of these assumptions is that cluster sizes are fixed, whereas the other demands cluster sizes to be positive. Randomness of the cluster sizes may be the determinant of the within-cluster correlation and between-cluster variation. We propose a baseline-category mixed model for clustered multinomial data with random cluster sizes based on Poisson mixed models. Our orthodox best linear unbiased predictor approach to this model depends only on the moment structure of unobserved distribution-free random effects. Our approach also consolidates the marginal and conditional modeling interpretations. Unlike the traditional methods, our approach can accommodate both random and zero cluster sizes. Two real-life multinomial data examples, crime data and food contamination data, are used to manifest our proposed methodology.     

Testing homogeneity in discrete mixtures

This paper introduces W-tests for assessing homogeneity in mixtures of discrete probability distributions. A W-test statistic depends on the data solely through parameter estimators and, if a penalized maximum likelihood estimation framework is used, has a tractable asymptotic distribution under the null hypothesis of homogeneity. The large-sample critical values are quantiles of a chi-square distribution multiplied by an estimable constant for which we provide an explicit formula. In particular, the estimation of large-sample critical values does not involve simulation experiments or random field theory. We demonstrate that W-tests are generally competitive with a benchmark test in terms of power to detect heterogeneity. Moreover, in many situations, the large-sample critical values can be used even with small to moderate sample sizes. The main implementation issue (selection of an underlying measure) is thoroughly addressed, and we explain why W-tests are well-suited to problems involving large and online data sets. Application of a W-test is illustrated with an epidemiological data set.     

Tests of marginal homogeneity and special cases

The analysis of two‐way contingency tables is common in clinical studies. In addition to summary counts and percentages, statistical tests or summary measures are often desired. If the data can be viewed as two categorical measurements on the same experimental unit (matched pair data) then a test of marginal homogeneity may be appropriate. The most common clinical example is the so called ‘shift table’ whereby a quantity is tested for change between two time points. The two principal marginal homogeneity tests are the Stuart Maxwell and Bhapkar tests. At present, SAS software does not compute either test directly (for tables with more than two categories) and a programmatic solution is required. Two examples of programmatic SAS code are found in the current literature. Although accurate in most instances, they fail to produce output for certain tables (‘special cases’). After summarizing the mathematics behind the two tests, a SAS macro is presented, which produces correct output for all tables. Finally, several examples are coded and presented with resultant output. Copyright © 2013 John Wiley & Sons, Ltd.     

Testing homogeneity of difference of two proportions for stratified correlated paired binary data

In ophthalmologic or otolaryngologic study, each subject may contribute paired organs measurements to the analysis. A number of statistical methods have been proposed on bilateral correlated data. In practice, it is important to detect confounding effect by treatment interaction, since ignoring confounding effect may lead to unreliable conclusion. Therefore, stratified data analysis can be considered to adjust the effect of confounder on statistical inference. In this article, we investigate and derive three test procedures for testing homogeneity of difference of two proportions for stratified correlated paired binary data in the basis of equal correlation model assumption. The performance of proposed test procedures is examined through Monte Carlo simulation. The simulation results show that the Score test is usually robust on type I error control with high power, and therefore is recommended among the three methods. One example from otolaryngologic study is given to illustrate the three test procedures.     

Testing for homogeneity in cross-lagged panel studies

Panel studies are statistical studies in which two or more variables are observed for two or more subjects at two or more points In time. Cross- lagged panel studies are those studies in which the variables are continuous and divide naturally into two effects or impacts of each set of variables on the other. If a regression approach is taken5 a regression structure Is formulated for the cross-lagged models This structure may assume that the regression parameters are homogeneous across waves and across subpopulations. Under such assumptions the methods of multivariate regression analysis can be adapted to make inferences about the parameters. These inferences are limited to the degree that homogeneity of the parameters Is 'supported b}T the data. We consider the problem of testing the hypotheses of homogeneity and consider the problem of making statistical inferences about the cross-effects should there be evidence against one of the homogeneity assumptions. We demonstrate the methods developed by applying then to two panel data sets.     

Testing homogeneity in a multivariate mixture model

Testing homogeneity is a fundamental problem in finite mixture models. It has been investigated by many researchers and most of the existing works have focused on the univariate case. In this article, the authors extend the use of the EM‐test for testing homogeneity to multivariate mixture models. They show that the EM‐test statistic asymptotically has the same distribution as a certain transformation of a single multivariate normal vector. On the basis of this result, they suggest a resampling procedure to approximate the P‐value of the EM‐test. Simulation studies show that the EM‐test has accurate type I errors and adequate power, and is more powerful and computationally efficient than the bootstrap likelihood ratio test. Two real data sets are analysed to illustrate the application of our theoretical results. The Canadian Journal of Statistics 39: 218–238; 2011 © 2011 Statistical Society of Canada     

Testing homogeneity of several covariance matrices and multi-sample sphericity for high-dimensional data under non-normality

A test for homogeneity of g ? 2 covariance matrices is presented when the dimension, p, may exceed the sample size, n_i, i = 1, …, g, and the populations may not be normal. Under some mild assumptions on covariance matrices, the asymptotic distribution of the test is shown to be normal when n_i, p → ∞. Under the null hypothesis, the test is extended for common covariance matrix to be of a specified structure, including sphericity. Theory of U-statistics is employed in constructing the tests and deriving their limits. Simulations are used to show the accuracy of tests.     

Measure of departure from marginal homogeneity using marginal odds for multi-way tables with ordered categories

For square contingency tables with ordered categories, this paper proposes a measure to represent the degree of departure from the marginal homogeneity model. It is expressed as the weighted sum of the power-divergence or Patil–Taillie diversity index, and is a function of marginal log odds ratios. The measure represents the degree of departure from the equality of the log odds that the row variable is i or below instead of i+1 or above and the log odds that the column variable is i or below instead of i+1 or above for every i. The measure is also extended to multi-way tables. Examples are given.     

Testing homogeneity in a heteroscedastic contaminated normal mixture

Large-scale simultaneous hypothesis testing appears in many areas. A well-known inference method is to control the false discovery rate. One popular approach is to model the z-scores derived from the individual t-tests and then use this model to control the false discovery rate. We propose a heteroscedastic contaminated normal mixture to describe the distribution of z-scores and design an EM-test for testing homogeneity in this class of mixture models. The proposed EM-test can be used to investigate whether a collection of z-scores has arisen from a single normal distribution or whether a heteroscedastic contaminated normal mixture is more appropriate. We show that the EM-test statistic has a shifted mixture of chi-squared limiting distribution. Simulation results show that the proposed testing procedure has accurate type-I error and significantly larger power than its competitors under a variety of model specifications. A real-data example is analysed to exemplify the application of the proposed method.     

Pseudo-likelihood inference for clustered binary data

The maximum likelihood procedure to estimate paraneters of a model has scveral attractive properties including the existence of the covariance matrix which yield asymptotic covariances: for a sample size N the asymptotics are in general of order 1/N. Here we give an asymptotic for the skewness of the distribution of the maximum likelihood estimator of a parameter; this is of order 1/ n2 and this expression is new. Applications relate to the parameters of (i) the Poisson, binomial, and normal density. (ii) the gamna density and (iii) the Beta debsity. Other application are being considered. The expression for the asymptotic skowness at one phase of the study tured out to be unusually complicated involving the asymptotic expressions for variance and bias. When these were identified a much simpler compact expression appeared which we now describe. The work is a much improved treatment of the subject described in Shenton and Bowman (Mariunm likelihood estimation in small samples, Griffin. 1977).     

Latent mixture modeling for clustered data

Statistics and Computing - This article proposes a mixture modeling approach to estimating cluster-wise conditional distributions in clustered (grouped) data. We adapt the mixture-of-experts model...     

Effects of correlation in modeling clustered binary data

A simulation study is conducted to determine the effects of varying correlation structures on two estimation procedures used to model clustered binary data; a parametric model, the beta-binomial, and a non-parametric model, the exchangeable binary. The simulations detected bias in estimation of the mean response parameter and the correlation parameter when assuming a parametric model. In addition it was found that variance parameters can be severely underestimated if the correlation structure is considered strictly a nuisance parameter.