Changes in expression site control and DNA modification in Trypanosoma brucei during differentiation of the bloodstream form to the procyclic form

The 2 x 2 table is an invaluable tool for displaying bivariate binary data. It is easy to find examples of correlated binary response in biopharmaceutical experiments and clinical research and analysis of these data is a current research topic. The most common hypothesis tested for 2 x 2 tables of correlated proportions is that of homogeneity of the marginal proportions or, equivalently, the hypothesis of table symmetry. The 2 x 2 table of correlated proportions is rich with information and we present a survey of some of the analyses relevant for these data. Using asymptotic theory, we develop estimators of relevant parameters and associated test statistics that are of interest. We discuss interval estimation using arguments proposed by Quesenberry and Hurst (1) and Goodman (2). These interval estimators do not rely on estimation of the covariance matrix and are not necessarily equivalent to those obtained using modified chi-square statistics.     

Bootstrapping correlation coefficients using univariate and bivariate sampling.

A new univariate sampling approach for bootstrapping correlation coefficients is proposed and evaluated. Bootstrapping correlations to define confidence intervals or to test hypotheses has previously relied on repeated bivariate sampling of observed (x,y) values to create an empirical sampling distribution. Bivariate sampling matches the logic of confidence interval construction, but hypothesis testing logic suggests that x and y should be sampled independently. This study uses Monte Carlo methods to compare the univariate bootstrap with 3 bivariate bootstrap procedures and with the traditional parametric procedure, using various sample sizes, population correlations, and population distributions. Results suggest that the univariate bootstrap is superior to other bootstrap procedures in many hypothesis testing settings, and even improves on parametric hypothesis testing in certain cases. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Modeling multivariate discrete failure time data

A bivariate discrete survival distribution that allows flexible modeling of the marginal distributions and yields a constant odds ratio at any grid point is proposed. The distribution can be extended to a multivariate distribution and is readily generalized to accommodate covariates in the marginal distributions and pairwise odds ratios. In addition, a pseudo-likelihood estimation procedure for estimating the regression coefficients in the marginal models and the association parameters in the pairwise odds ratios is presented. We evaluate the performance of the proposed estimation procedure through simulations. For bivariate data, pseudo-likelihood estimation of the association parameter has high efficiency. Loss of efficiency in the marginal regression coefficient estimates is small when the association is not strong. For both the marginal regression coefficients and the association parameter, coverage probabilities are close to the 95% nominal level. For multivariate data, the simulation results show that the parameter estimates are consistent. Coverage probability for the regression coefficient in the marginal model is close to the 95% nominal level but is slightly less than the nominal level for the association parameter. We illustrate the proposed methods using a subset of the Framingham Heart Study data where a significant positive association was found between the failure times of siblings.     

Notes on conditional confidence limits under inverse sampling

When the number of subjects in a two-by-two table is small or moderate, we may commonly use the exact conditional distribution with all marginals fixed to derive the conditional confidence limits on the underlying parameter. Under inverse sampling, in which we continue to sample subjects until we obtain exactly a pre-determined number of subjects failing into a specific category, this paper notes that derivation of a confidence interval, which has the coverage probability equal to or larger than a nominal 1-alpha confidence level, for relative risk and relative difference in cohort studies is straightforward. This paper further finds that, when the underlying disease is rare, we can similarly apply an inverse sampling to produce an approximate 1-alpha conditional confidence limits on attributable risk in case-control studies as well. When the number of subjects is small and the test statistic derived on the basis of large sample theory is not strictly adequate for use, this paper also presents an exact hypothesis testing procedure for the above parameters in the corresponding study designs.     

Families of smooth confidence bands for the survival function under the general random censorship model

Randomly right censored data often arise in industrial life testing and clinical trials. Several authors have proposed asymptotic confidence bands for the survival function when data are randomly censored on the right. All of these bands are based on the empirical estimator of the survival function. In this paper, families of asymptotic (1-alpha) 100% level confidence bands are developed from the smoothed estimate of the survival function under the general random censorship model. The new bands are compared to empirical bands, and it is shown that for small sample sizes, the smooth bands have a higher coverage probability than the empirical counterparts.     

Weighted kappa: Nominal scale agreement provision for scaled disagreement or partial credit.

A previously described coefficient of agreement for nominal scales, kappa, treats all disagreements equally. A generalization to weighted kappa (Kw) is presented. The Kw provides for the incorpation of ratio-scaled degrees of disagreement (or agreement) to each of the cells of the k * k table of joint nominal scale assignments such that disagreements of varying gravity (or agreements of varying degree) are weighted accordingly. Although providing for partial credit, Kw is fully chance corrected. Its sampling characteristics and procedures for hypothesis testing and setting confidence limits are given. Under certain conditions, Kw equals product-moment r. The use of unequal weights for symmetrical cells makes Kw suitable as a measure of validity. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A goodness-of-fit approach to inference procedures for the kappa statistic: confidence interval construction, significance-testing and sample size estimation

We propose a new procedure for constructing a confidence interval about the kappa statistic in the case of two raters and a dichotomous outcome. The procedure is based on a chi-square goodness-of-fit test as applied to a model frequently used for clustered binary data. The procedure provides coverage levels that are accurate in samples of smaller size than those required for other procedures. The procedure also has use for significance-testing and the planning of corresponding sample size requirements.     

Inference for odds ratio regression models with sparse dependent data

Suppose the number of 2 x 2 tables is large relative to the average table size, and the observations within a given table are dependent, as occurs in longitudinal or family-based case-control studies. We consider fitting regression models to the odds ratios using table-level covariates. The focus is on methods to obtain valid inferences for the regression parameters beta when the dependence structure is unknown. In this setting, Liang (1985, Biometrika 72, 678-682) has shown that inference based on the noncentral hypergeometric likelihood is sensitive to misspecification of the dependence structure. In contrast, estimating functions based on the Mantel-Haenszel method yield consistent estimators of beta. We show here that, under the estimating function approach, Wald's confidence interval for beta performs well in multiplicative regression models but unfortunately has poor coverage probabilities when an additive regression model is adopted. As an alternative to Wald inference, we present a Mantel-Haenszel quasi-likelihood function based on integrating the Mantel-Haenszel estimating function. A simulation study demonstrates that, in medium-sized samples, the Mantel-Haenszel quasi-likelihood approach yields better inferences than other methods under an additive regression model and inferences comparable to Wald's method under a multiplicative model. We illustrate the use of this quasi-likelihood method in a study of the familial risk of schizophrenia.     

Interpersonal preference and cognitive organization.

The paper describes "an empirical test of certain aspects of Heider's theory of cognitive organization." The method, procedures, and results are described and illustrated by tables. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Conditional logistic regression with sandwich estimators: application to a meta-analysis

Motivated by a meta-analysis of animal experiments on the effect of dietary fat and total caloric intake on mammary tumorigenesis, we explore the use of sandwich estimators of variance with conditional logistic regression. Classical conditional logistic regression assumes that the parameters are fixed effects across all clusters, while the sandwich estimator gives appropriate inferences for either fixed effects or random effects. However, inference using the standard Wald test with the sandwich estimator requires that each parameter is estimated using information from a large number of clusters. Since our example violates this condition, we introduce two modifications to the standard Wald test. First, we reduce the bias of the empirical variance estimator (the middle of the sandwich) by using standardized residuals. Second, we approximately account for the variance of these estimators by using the t-distribution instead of the normal distribution, where the degrees of freedom are estimated using Satterthwaite's approximation. Through simulations, we show that these sandwich estimators perform almost as well as classical estimators when the true effects are fixed and much better than the classical estimators when the true effects are random. We achieve simulated nominal coverage for these sandwich estimators even when some parameters are estimated from a small number of clusters.     

Combining 2 x 2 tables that contain structural zeros

When one cell or more of a contingency table is necessarily zero, the table is said to contain structural zeros. These structural voids may be inherent to the problem at hand, or, in some applications, they may be introduced intentionally through the experimental design. With data classified by a third stratification variable, one needs a method for analysing a set of independent 2 x 2 tables. We propose Cochran-Mantel-Haenszel type analyses that combine observations across strata. We also propose tests of hypotheses pertaining to the marginal and conditional probabilities.     

Large sample standard errors of kappa and weighted kappa.

2 statistics, kappa and weighted kappa, are available for measuring agreement between 2 raters on a nominal scale. Formulas for the standard errors of these 2 statistics are in error in the direction of overestimation, so that their use results in conservative significance tests and confidence intervals. Valid formulas for the approximate large-sample variances are given, and their calculation is illustrated using a numerical example. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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.     

Defining and testing hypotheses in multidimensional contingency tables.

Describes the log-linear model as a framework for analyzing effects in multidimensional contingency tables, i.e., tables of frequencies formed by 2 or more variables of classification. Variables are considered to have nominal categories. A general purpose analysis is proposed for such tables, similar to analysis of variance. 2 test procedures are considered: (a) maximum likelihood estimation of expected cell frequencies and associated chi-square tests, and (b) chi-square tests based on logarithms of adjusted cell frequencies. In addition, 2 multiple-comparison methods, related to the latter approach, are considered as supplementary or alternative procedures. (28 ref.) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The instance theory of automaticity: Why the Weibull?

It is shown that in order to derive the Weibull shape for the response time distribution in the instance theory of automaticity (G. D. Logan, 1988) by an asymptotic argument from the theory of extreme value statistics, it is necessary to determine the domain of attraction of the underlying parent distribution. An alternative, nonasymptotic characterization property equivalent to the power law of practice is presented here that gives a more feasible justification for the choice of the Weibull. This result leads to a different emphasis on the empirical conditions testing the theory. Some problems arising from the use of the asymptotic theory of extreme value statistics for the stochastic modeling of behavioral data are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Toward using confidence intervals to compare correlations.

Confidence intervals are widely accepted as a preferred way to present study results. They encompass significance tests and provide an estimate of the magnitude of the effect. However, comparisons of correlations still rely heavily on significance testing. The persistence of this practice is caused primarily by the lack of simple yet accurate procedures that can maintain coverage at the nominal level in a nonlopsided manner. The purpose of this article is to present a general approach to constructing approximate confidence intervals for differences between (a) 2 independent correlations, (b) 2 overlapping correlations, (c) 2 nonoverlapping correlations, and (d) 2 independent R2s. The distinctive feature of this approach is its acknowledgment of the asymmetry of sampling distributions for single correlations. This approach requires only the availability of confidence limits for the separate correlations and, for correlated correlations, a method for taking into account the dependency between correlations. These closed-form procedures are shown by simulation studies to provide very satisfactory results in small to moderate sample sizes. The proposed approach is illustrated with worked examples. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Statistical methods for mapping quantitative trait loci from a dense set of markers

Lander and Botstein introduced statistical methods for searching an entire genome for quantitative trait loci (QTL) in experimental organisms, with emphasis on a backcross design and QTL having only additive effects. We extend their results to intercross and other designs, and we compare the power of the resulting test as a function of the magnitude of the additive and dominance effects, the sample size and intermarker distances. We also compare three methods for constructing confidence regions for a QTL: likelihood regions, Bayesian credible sets, and support regions. We show that with an appropriate evaluation of the coverage probability a support region is approximately a confidence region, and we provide a theroretical explanation of the empirical observation that the size of the support region is proportional to the sample size, not the square root of the sample size, as one might expect from standard statistical theory.     

Type I error rate of the chi-square test in independence in R?×?C tables that have small expected frequencies.

Sampling experiments are reported that show that the uncorrected chi-square test of independence is exceptionally robust with respect to small expected frequencies in R?×?C contingency tables. In general, error rates that exceed .06 occurred only when both marginal probability distributions were extremely skewed and sample size was small. Nevertheless, the quality of the approximation of chi-square probabilities for exact multinomial probabilities was sometimes poor, although excessive errors in approximation by W. G. Cochran's (1952) criteria usually resulted from actual error rates being smaller, not larger, than the nominal level. A distinction is made between accuracy of approximation and control of the Type I error rate as considerations dictating the advisability of using an approximate test. (38 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Confidence intervals for the receiver operating characteristic area in studies with small samples

RATIONALE AND OBJECTIVES: The authors performed this study to address two practical questions. First, how large does the sample size need to be for confidence intervals (CIs) based on the usual asymptotic methods to be appropriate? Second, when the sample size is smaller than this threshold, what alternative method of CI construction should be used? MATERIALS AND METHODS: The authors performed a Monte Carlo simulation study where 95% CIs were constructed for the receiver operating characteristic (ROC) area and for the difference between two ROC areas for rating and continuous test results--for ROC areas of moderate and high accuracy--by using both parametric and nonparametric estimation methods. Alternative methods evaluated included several bootstrap CIs and CIs with the Student t distribution. RESULTS: For the difference between two ROC areas, CIs based on the asymptotic theory provided adequate coverage even when the sample size was very small (20 patients). In contrast, for a single ROC area, the asymptotic methods do not provide adequate CI coverage for small samples; for ROC areas of high accuracy, the sample size must be large (more than 200 patients) for the asymptotic methods to be applicable. The recommended alternative (bootstrap percentile, bootstrap t, or bootstrap bias-corrected accelerated method) depends on the estimation approach, format of the test results, and ROC area. CONCLUSION: Currently, there is not a single best alternative for constructing CIs for a single ROC area for small samples.