Testing the ratio of two poisson rates

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.     

On the Comparison of Umbrella Pattern Treatment Means with a Control Mean

This paper is concerned with comparing several increasing dose levels (treatments) with a zero dose control when the prior information about the umbrella pattern treatment means is available. The problem of testing whether there is at least one treatment which is better than the control is considered. Multiple test procedures are then proposed for deciding treatments (if any) which are better than the control. Some approximate criticial values of the proposed tests are reported. The results of a Monte Carlo power study are presented.     

Semiparametric Bayes Multiple Testing: Applications to Tumor Data

Summary In National Toxicology Program (NTP) studies, investigators want to assess whether a test agent is carcinogenic overall and specific to certain tumor types, while estimating the dose‐response profiles. Because there are potentially correlations among the tumors, a joint inference is preferred to separate univariate analyses for each tumor type. In this regard, we propose a random effect logistic model with a matrix of coefficients representing log‐odds ratios for the adjacent dose groups for tumors at different sites. We propose appropriate nonparametric priors for these coefficients to characterize the correlations and to allow borrowing of information across different dose groups and tumor types. Global and local hypotheses can be easily evaluated by summarizing the output of a single Monte Carlo Markov chain (MCMC). Two multiple testing procedures are applied for testing local hypotheses based on the posterior probabilities of local alternatives. Simulation studies are conducted and an NTP tumor data set is analyzed illustrating the proposed approach.     

Testing Equality between Two Diagnostic Procedures in Paired‐Sample Ordinal Data

When a new diagnostic procedure is developed, it is important to assess whether the diagnostic accuracy of the new procedure is different from that of the standard procedure. For paired‐sample ordinal data, this paper develops two test statistics for testing equality of the diagnostic accuracy between two procedures without assuming any parametric models. One is derived on the basis of the probability of correctly identifying the case for a randomly selected pair of a case and a non‐case over all possible cutoff points, and the other is derived on the basis of the sensitivity and specificity directly. To illustrate the practical use of the proposed test procedures, this paper includes an example regarding the use of digitized and plain films for screening breast cancer. This paper also applies Monte Carlo simulation to evaluate the finite sample performance of the two statistics developed here and notes that they can perform well in a variety of situations. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Robust Umbrella Tests for a Generalized Behrens-Fisher Problem

This paper is concerned with testing for umbrella alternatives in a k-sample location problem when the underlying populations have possibly different shapes. Following CHEN and WOLFE (1990b), rank-based modifications of the HETTMANSPERGER-NORTON (1987) tests are considered for both the settings where the peak of the umbrella is known and where it is unknown. The proposed procedures are exactly distribution-free when the continuous populations are identical with any shape. Moreover, the modified test for peak-known umbrella alternatives remains asymptotically distribution-free when the continuous populations are assumed to be symmetric, even if they differ in shapes. Comparative results of a Monte Carlo study are presented.     

Some simple tests for spatial effects around putative sources of health risk

The need for tests dealing with different features of small area health data is less important with the increase in computation speed of computers and the access to MCMC methods. However there are many situations where exploratory testing could be useful and where MCMC methods are not readily usable or available. In this paper, a number of simple tests are derived for the logistic model for case events. This model assumes that a control disease is available and that the events have a binary label relating to case or control state. The tests are derived from likelihood considerations and Monte Carlo critical regions are examined. A simulated evaluation of the tests is presented in terms of Monte Carlo power. A data example is considered.     

Efficient statistical inference procedures for partially nonlinear models and their applications

Summary .   Motivated by an analysis of a real data set in ecology, we consider a class of partially nonlinear models where both a nonparametric component and a parametric component are present. We develop two new estimation procedures to estimate the parameters in the parametric component. Consistency and asymptotic normality of the resulting estimators are established. We further propose an estimation procedure and a generalized F -test procedure for the nonparametric component in the partially nonlinear models. Asymptotic properties of the newly proposed estimation procedure and the test statistic are derived. Finite sample performance of the proposed inference procedures are assessed by Monte Carlo simulation studies. An application in ecology is used to illustrate the proposed methods.     

Small-sample inference for the comparison of means of log-normal distributions

We propose a likelihood-based test for comparing the means of two or more log-normal distributions, with possibly unequal variances. A modification to the likelihood ratio test is needed when sample sizes are small. The performance of the proposed procedures is compared with the F-ratio test using Monte Carlo simulations.     

A simple test of the homogeneity of risk difference in sparse data: an application to a multicenter study

In this paper, we focus discussion on testing the homogeneity of risk difference for sparse data, in which we have few patients in each stratum, but a moderate or large number of strata. When the number of patients per treatment within strata is small (2 to 5 patients), none of test procedures proposed previously for testing the homogeneity of risk difference for sparse data can really perform well. On the basis of bootstrap methods, we develop a simple test procedure that can improve the power of the previous test procedures. Using Monte Carlo simulations, we demonstrate that the test procedure developed here can perform reasonable well with respect to Type I error even when the number of patients per stratum for each treatment is as small as two patients. We evaluate and study the power of the proposed test procedure in a variety of situations. We also include a comparison of the performance between the test statistics proposed elsewhere and the test procedure developed here. Finally, we briefly discuss the limitation of using the proposed test procedure. We use the data comparing two chemotherapy treatments in patients with multiple myeloma to illustrate the use of the proposed test procedure.     

A note on the tests for clustered matched-pair binary data

McNemar's test is used to assess the difference between two different procedures (treatments) using independent matched-pair data. For matched-pair data collected in clusters, the tests proposed by Durkalski et al. and Obuchowski are popular and commonly used in practice since these tests do not require distributional assumptions or assumptions on the structure of the within-cluster correlation of the data. Motivated by these tests, this note proposes a modified Obuchowski test and illustrates comparisons of the proposed test with the extant methods. An extensive Monte Carlo simulation study suggests that the proposed test performs well with respect to the nominal size, and has higher power; Obuchowski's test is most conservative, and the performance of the Durkalski's test varies between the modified Obuchowski test and the original Obuchowski's test. These results form the basis for our recommendation that (i) for equal cluster size, the modified Obuchowski test is always preferred; (ii) for varying cluster size Durkalski's test can be used for a small number of clusters (e.g. K < 50), whereas for a large number of clusters (e.g. K ≥ 50) the modified Obuchowski test is preferred. Finally, to illustrate practical application of the competing tests, two real collections of clustered matched-pair data are analyzed.     

The calculation and significance testing of genetic correlations across environments

Genetic correlations within a trait across environments (r_g) are important in the analysis of phenotypic plasticity. Not all methods are, however, equally reliable. An overview of all different methods for estimation of r_g with one generation data sets is given. Formulae for the relationship between causal variance components and family means are derived. When these formulae are used covariances derived from family means, thought to be incorrect, are exactly the same as those derived with the ANOVA method. The bias, precision and power of the different methods are compared with Monte Carlo simulations. For all methods bias is small and precision is high for the large balanced data sets analyzed here, except when the variance in one or both of the environments is close to 0. Significance testing causes more problems. Confidence intervals with or without z-transformation are not suitable for testing, nor is testing for g*e interaction in an ANOVA suitable for testing whether the r_g is different from 1. The F-test in a mixed model ANOVA and a likelihood ratio test in a REML-analysis can be used for testing a difference from 0 but not from 1 or other values. Jackknife and Bootstrap, however, are suitable tests both for differences with 0,1 and other values, though negative variances can make these tests difficult to apply.     

A Study of Distribution-free Tests for Umbrella Alternatives

In this paper we are concerned with test procedures for umbrella alternatives in the k-sample location problem. Distribution-free tests are considered for both cases where the peak of the umbrella is known or unknown. Comparative results of a Monte Carlo power study are presented.     

Rank-based tests for dose finding in nonmonotonic dose-response settings

Lim and Wolfe (1997, Biometrics 53, 410-418) proposed rank-based multiple test procedures for identifying the dose levels that are more effective than the zero-dose control in randomized complete block designs when it can be assumed that the efficacy of the increasing dose levels is monotonically increasing up to a point, followed by a monotonic decrease. Modifications of the Lim-Wolfe tests are suggested that provide more practical and powerful alternatives. Two numerical examples are illustrated and the results of a Monte Carlo power study are presented.     

Confidence Limits for the Intraclass Correlation in Compound-Poisson Sampling

When the underlying responses are discrete, the interval estimation of the intraclass correlation derived from the normality assumption is not strictly valid for use. This paper focuses the interval estimation on the intraclass correlation under the negative binomial distribution, that has been commonly applied in epidemiological or consumer purchasing behaviour studies. This paper develops two simple asymptotic interval estimation procedures in closed forms for the intraclass correlation. To evaluate the performance of these procedures, a Monte Carlo simulation is carried out for a variety of situations. An example about consumer purchasing behaviors is also included to illustrate the use of the two proposed interval estimation procedures.     

Testing for linkage under robust genetic models.

Robust genetic models are used to assess linkage between a quantitative trait and genetic variation at a specific locus using allele-sharing data. Little is known about the relative performance of different possible significance tests under these models. Under the robust variance components model approach there are several alternatives: standard Wald and likelihood ratio tests, a quasilikelihood Wald test, and a Monte Carlo test. This paper reports on the relative performance (significance level and power) of the robust sibling pair test and the different alternatives under the robust variance components model. Simulations show that (1) for a fixed sample size of nuclear families, the variance components model approach is more powerful than the robust sibling pair approach; (2) when the number of nuclear families is at least approximately 100 and heritability at the trait locus is moderate to high (>0.20) all tests based on the variance components model are equally effective; (3) when the number of nuclear families is less than approximately 100 or heritability at the trait locus is low (<0. 20), on balance, the Monte Carlo test provides the best power and is the most valid. The different testing procedures are applied to determine which are able to detect the known association between low density lipoprotein cholesterol and the common genotypes at the locus encoding apolipoprotein E. Results from this application show that the robust sibling pair method may be more effective in practice than that indicated by simulations.     

One-sided significance tests for generalized linear models under dichotomous response

Dichotomous response models are common in many experimental settings. Often, concomitant explanatory variables are recorded, and a generalized linear model, such as a logit model, is fit. In some cases, interest in specific model parameters is directed only at one-sided departures from some null effect. In these cases, procedures can be developed for testing the null effect against a one-sided alternative. These include Bonferroni-type adjustments of univariate Wald tests, and likelihood ratio tests that employ inequality-constrained multivariate theory. This paper examines such tests of significance. Monte Carlo evaluations are undertaken to examine the small-sample properties of the various procedures. The procedures are seen to perform fairly well, generally achieving their nominal sizes at total sample sizes near 100 experimental units. Extensions to the problem of one-sided tests against a control or standard are also considered.     

Bayesian inference for kappa from single and multiple studies

Cohen's kappa coefficient is a widely popular measure for chance-corrected nominal scale agreement between two raters. This article describes Bayesian analysis for kappa that can be routinely implemented using Markov chain Monte Carlo (MCMC) methodology. We consider the case of m > or = 2 independent samples of measured agreement, where in each sample a given subject is rated by two rating protocols on a binary scale. A major focus here is on testing the homogeneity of the kappa coefficient across the different samples. The existing frequentist tests for this case assume exchangeability of rating protocols, whereas our proposed Bayesian test does not make any such assumption. Extensive simulation is carried out to compare the performances of the Bayesian and the frequentist tests. The developed methodology is illustrated using data from a clinical trial in ophthalmology.     

Quadratic inference functions for varying-coefficient models with longitudinal data

Nonparametric smoothing methods are used to model longitudinal data, but the challenge remains to incorporate correlation into nonparametric estimation procedures. In this article, we propose an efficient estimation procedure for varying-coefficient models for longitudinal data. The proposed procedure can easily take into account correlation within subjects and deal directly with both continuous and discrete response longitudinal data under the framework of generalized linear models. The proposed approach yields a more efficient estimator than the generalized estimation equation approach when the working correlation is misspecified. For varying-coefficient models, it is often of interest to test whether coefficient functions are time varying or time invariant. We propose a unified and efficient nonparametric hypothesis testing procedure, and further demonstrate that the resulting test statistics have an asymptotic chi-squared distribution. In addition, the goodness-of-fit test is applied to test whether the model assumption is satisfied. The corresponding test is also useful for choosing basis functions and the number of knots for regression spline models in conjunction with the model selection criterion. We evaluate the finite sample performance of the proposed procedures with Monte Carlo simulation studies. The proposed methodology is illustrated by the analysis of an acquired immune deficiency syndrome (AIDS) data set.     

A Monte Carlo Test for Variance Homogeneity in Linear Models

A Monte Carlo procedure is proposed for testing homogeneity of variances in linear models. The method is applicable to a variety of common experimental designs. It is valid when errors are independently normally distributed. Under nonnormality the test is expected to behave robust in a similar fashion as Levene's test. Three examples are given to demonstrate the method.     

Test Statistics for Three-Factor Interaction in 2 × 2 × 2 Contingency Tables

A Monte Carlo simulation was conducted in order to determine the size and power of two proposed tests (the covariance and correlation tests) for three-factor interaction in 2 × 2 × 2 contingency tables. Results were compared to the log-odds ratio test statistic. Simulation showed the correlation test to be more conservative than the covariance test, but less so than the log-odds ratio test. However, the correlation test was the most powerful among the three tests.