Testing hypotheses about interclass correlations from familial data

Testing problems concerning interclass correlations from familial data are considered in the case where the number of siblings varies among families. Under the assumption of multivariate normality, two test procedures are proposed for testing the hypothesis that an interclass correlation is equal to a specified value. To compare the properties of the tests, including a likelihood ratio test, Monte Carlo experiments are performed. Several test statistics are derived for testing whether two variables about a parent and child are uncorrelated. The proposed tests are compared with previous test procedures, using Monte Carlo simulation. A general procedure for finding confidence intervals for interclass correlations is also derived.     

A Modified Chi-Square Test for Testing Equality of Two Multinomial Populations Against an Ordering Restricted Alternative

A modified chi-square test for testing the equality of two multinomial populations against an ordering restricted alternative in one sample and two sample cases is constructed. The relation between a concept of dependence called dependence by chi-square and stochastic ordering is established. A tabulation of the asymptotic distribution of the test statistic under the null hypothesis is given. Simulations are used to compare the power of this test with the power of the likelihood ratio test of stochastic ordering of the two multinomial populations.     

On the finite sample distribution of the likelihood ratio statistic for testing heterogeneity in meta-analysis

In meta-analysis, hypothesis testing is one of the commonly used approaches for assessing whether heterogeneity exists in effects between studies. The literature concluded that the Q-statistic is clearly the best choice and criticized the performance of the likelihood ratio test in terms of the type I error control and power. However, all the criticism for the likelihood ratio test is based on the use of a mixture of two chi-square distributions with 0 and 1 degrees of freedom, which is justified only asymptotically. In this study, we develop a novel method to derive the finite sample distribution of the likelihood ratio test and restricted likelihood ratio test statistics for testing the zero variance component in the random effects model for meta-analysis. We also extend this result to the heterogeneity test when metaregression is applied. A numerical study shows that the proposed statistics have superior performance to the Q-statistic, especially when the number of studies collected for meta-analysis is small to moderate.     

Some goodness-of-fit methods for the Poisson plus added zeros distribution

Methods for making inferences about the Poisson plus added zeros distribution and the truncated Poisson distribution are presented and illustrated with bacteriological data. Some of the methods are designed for testing the compatibility of the zero frequency with the Poisson distribution, whereas others are given for testing the goodness of fit for the truncated Poisson. In particular, a modified form of the Fisher index of dispersion is presented which is suitable for the truncated case. It is shown that the use of the usual expression of the index of dispersion for testing the adequacy of the truncated Poisson is not correct and leads to accepting inadequate fits more frequently than expected on the basis of test of significance. Furthermore, three test statistics are presented for testing the compatability of the zero frequency with the Poisson distribution. The results of the simulation show that two test statistics, one due to Cochran (W. G. Cochran, Biometrics 10:417-451, 1954) and the other to Rao and Chakravarti (C. R. Rao and I. M. Chakravarti, Biometrics 12:264-282, 1956), are preferable to those from the likelihood ratio test.     

The Residual Likelihood Ratio Test for the Variance Ratio in a Linear Model with Two Variance Components

Residual maximum likelihood has proved to be a successful approach to the estimation of variance components. In this paper, its counterpart in testing, the residual likelihood ratio test, is applied to testing the ratio of two variance components. The test is compared with the Wald test and the locally most powerful invariant test.     

Some goodness-of-fit methods for the Poisson plus added zeros distribution.

Methods for making inferences about the Poisson plus added zeros distribution and the truncated Poisson distribution are presented and illustrated with bacteriological data. Some of the methods are designed for testing the compatibility of the zero frequency with the Poisson distribution, whereas others are given for testing the goodness of fit for the truncated Poisson. In particular, a modified form of the Fisher index of dispersion is presented which is suitable for the truncated case. It is shown that the use of the usual expression of the index of dispersion for testing the adequacy of the truncated Poisson is not correct and leads to accepting inadequate fits more frequently than expected on the basis of test of significance. Furthermore, three test statistics are presented for testing the compatability of the zero frequency with the Poisson distribution. The results of the simulation show that two test statistics, one due to Cochran (W. G. Cochran, Biometrics 10:417-451, 1954) and the other to Rao and Chakravarti (C. R. Rao and I. M. Chakravarti, Biometrics 12:264-282, 1956), are preferable to those from the likelihood ratio test.     

Application of urinary mutagen testing to detect workplace hazardous exposure and bladder cancer

The objectives of this biochemical epidemiologic case-control study were to evaluate urinary mutagen testing for occupational exposure assessment, and for possible screening for bladder cancer in the workplace. Thirty-seven patients (19 bladder cancer cases and 18 controls) completed a questionnaire. Two urine samples, i.e. a work sample taken while at work, and a home sample, were requested from each patient. Twenty-six patients (17 cases and 9 controls) gave a total of 47 24-h urine samples for mutagenicity testing by the Ames test. A positive Ames test was found to be associated significantly with current occupation with hazardous exposure (odds ratio = 3.7, 95%CI 1.1–12.9), and non-significantly with bladder cancer (odds ratio = 1.8, 95%CI 0.5–7.1). Our results show that the urinary Ames test has the potential of being used as a surveillance for current workplace hazardous exposure (sensitivity = 52%, specificity = 77%, positive predictive value = 72%, negative predictive value = 59%, positive likelihood ratio = 2.3), but not as a screening test for bladder cancer cases (sensitivity = 42%, specificity = 71%, positive predictive value = 3%, negative predictive value = 98%, positive likelihood ratio = 1.5).     

Comparison of several independent population means when their samples contain log-normal and possibly zero observations

In this paper, we consider the problem of testing the mean equality of several independent populations that contain log-normal and possibly zero observations. We first showed that the currently used methods in statistical practice, including the nonparametric Kruskal-Wallis test, the standard ANOVA F-test and its two modified versions, the Welch test and the Brown-Forsythe test, could have poor Type I error control. Then we propose a likelihood ratio test that is shown to have much better Type I error control than the existing methods. Finally, we analyze two real data sets that motivated our study using the proposed test.     

Testing association between candidate-gene markers and phenotype in related individuals, by use of estimating equations.

Association studies are one of the major strategies for identifying genetic factors underlying complex traits. In samples of related individuals, conventional statistical procedures are not valid for testing association, and maximum likelihood (ML) methods have to be used, but they are computationally demanding and are not necessarily robust to violations of their assumptions. Estimating equations (EE) offer an alternative to ML methods, for estimating association parameters in correlated data. We studied through simulations the behavior of EE in a large range of practical situations, including samples of nuclear families of varying sizes and mixtures of related and unrelated individuals. For a quantitative phenotype, the power of the EE test was comparable to that of a conventional ML test and close to the power expected in a sample of unrelated individuals. For a binary phenotype, the power of the EE test decreased with the degree of clustering, as did the power of the ML test. This result might be partly explained by a modeling of the correlations between responses that is less efficient than that in the quantitative case. In small samples (< 50 families), the variance of the EE association parameter tended to be underestimated, leading to an inflation of the type I error. The heterogeneity of cluster size induced a slight loss of efficiency of the EE estimator, by comparison with balanced samples. The major advantages of the EE technique are its computational simplicity and its great flexibility, easily allowing investigation of gene-gene and gene-environment interactions. It constitutes a powerful tool for testing genotype-phenotype association in related individuals.     

Bayesian Insight into a Robust Test for Linear Contrast Based on Asymmetric Censored Samples

A robust test for linear contrast using modified maximum likelihood estimators based on symmetrically censored samples proposed by Tiku (1973, 1982a) is studied in this paper from the Bayesian point of view. The effects of asymmetric censoring on this testing procedure is investigated and a good approximation to its posterior distribution in this case is worked out. We also present an example which illustrates the method of obtaining the highest posterior density interval for the linear combination of the unknown location parameters.     

On the mechanical behaviour of carotid artery plaques: the influence of curve-fitting experimental data on numerical model results

Computational models of diseased arteries are advancing rapidly, and a need exists to develop more accurate material models of human atherosclerotic plaques. However, intact samples for in vitro mechanical testing are not readily available. Most plaque samples are harvested from carotid endarterectomies where the geometries are not suitable for the boundary parameters necessary for classical uniaxial tensile testing. Experimental studies of biological tissue, particularly human plaque tissue, have not specified the minimum width-to-length (WL) ratio necessary for appropriate tensile testing. This study proposes either tensile or planar shear testing on whole specimen samples depending on the WL ratio. However, a “grey-area” of WL ratios exists which are unsuitable for either test, between 0.5:1 and 4:1 WL ratio. Eighteen plaque samples are investigated in this study, and according to classical approaches, two of the plaque samples have WL ratios suitable for tensile testing and four are suitable for planar shear testing. The remaining twelve samples fall in the grey-area of WL ratio. The study analyses which test method is suitable for the samples in this grey-area and what effect using the incorrect test method has on results from a computational model. The study highlights that tissues above a WL ratio of 2:1 are suitable for planar shear testing, and samples below 1:1 are more suited for tensile testing. Therefore, the “grey-area” can be reduced with certain limitations applied by the minor strain assumption which need to be taken into account during experimental testing. This study also demonstrates the influence of curve-fitting experimental results using tensile- and planar shear–based boundary parameters from eighteen plaque samples.     

Bootstrap Restricted Likelihood Ratio Test for the Detection of Rare Variants

In this paper the detection of rare variants association with continuous phenotypes of interest is investigated via the likelihood-ratio based variance component test under the framework of linear mixed models. The hypothesis testing is challenging and nonstandard, since under the null the variance component is located on the boundary of its parameter space. In this situation the usual asymptotic chisquare distribution of the likelihood ratio statistic does not necessarily hold. To circumvent the derivation of the null distribution we resort to the bootstrap method due to its generic applicability and being easy to implement. Both parametric and nonparametric bootstrap likelihood ratio tests are studied. Numerical studies are implemented to evaluate the performance of the proposed bootstrap likelihood ratio test and compare to some existing methods for the identification of rare variants. To reduce the computational time of the bootstrap likelihood ratio test we propose an effective approximation mixture for the bootstrap null distribution. The GAW17 data is used to illustrate the proposed test.     

Detecting differential expression in microarray data: comparison of optimal procedures

Background  

Many procedures for finding differentially expressed genes in microarray data are based on classical or modified t-statistics. Due to multiple testing considerations, the false discovery rate (FDR) is the key tool for assessing the significance of these test statistics. Two recent papers have generalized two aspects: Storey et al. (2005) have introduced a likelihood ratio test statistic for two-sample situations that has desirable theoretical properties (optimal discovery procedure, ODP), but uses standard FDR assessment; Ploner et al. (2006) have introduced a multivariate local FDR that allows incorporation of standard error information, but uses the standard t-statistic (fdr2d). The relationship and relative performance of these methods in two-sample comparisons is currently unknown.     

A likelihood-based approach to estimating and testing for isolation by distance

Simple regression of genetic similarities between pairs of populations on their corresponding geographic distances is frequently used to detect the presence of isolation by distance (IBD). However, these pairwise values are obviously not independent and there is no parametric procedure for estimating and testing for the IBD intercepts and slopes based on standard regression theory. Nonparametric tests, such as the Mantel test, and resampling techniques, such as bootstrapping, have been exploited with limited success. Here, I describe a likelihood-based analysis to allow for simultaneously detecting patterns of correlated residuals and estimating and testing for the presence of IBD. It is shown, through the analysis of two molecular datasets in pine species, that different covariance structures of the residuals exist. More over, the likelihood ratio tests under these covariance structures are less sensitive to the presence of IBD than the Mantel test and the simple regression analysis but more sensitive than the bootstrap and jackknife samples over independent populations or population pairs. Because the likelihood analysis directly models and accounts for nonindependence of residuals, it should legitimately detect the presence of IBD, thereby allowing for accurate inferences about evolutionary and demographic processes influencing the extent and patterns of IBD.     

Goodness-of-fit in generalized nonlinear mixed-effects models

In recent years, generalized linear and nonlinear mixed-effects models have proved to be powerful tools for the analysis of unbalanced longitudinal data. To date, much of the work has focused on various methods for estimating and comparing the parameters of mixed-effects models. Very little work has been done in the area of model selection and goodness-of-fit, particularly with respect to the assumed variance-covariance structure. In this paper, we present a goodness-of-fit statistic which can be used in a manner similar to the R2 criterion in linear regression for assessing the adequacy of an assumed mean and variance-covariance structure. In addition, we introduce an approximate pseudo-likelihood ratio test for testing the adequacy of the hypothesized convariance structure. These methods are illustrated and compared to the usual normal theory likelihood methods (Akaike's information criterion and the likelihood ratio test) using three examples. Simulation results indicate the pseudo-likelihood ratio test compares favorably with the standard normal theory likelihood ratio test, but both procedures are sensitive to departures from normality.     

Relationships among somatic cell count, California mastitis test, impedance and bacteriological status of milk in goats and sheep in early lactation

The objectives of this trial were to evaluate and compare the test characteristics of a number of indirect tests of bacteriological status of the milk from goats and sheep and to assess the affect of varying levels of prevalence of infection on the performance of those tests.The somatic cell count, California mastitis test (CMT) score, electrical impedance and the bacteriological status of 220 and 262 milk samples from the glands of lactating dairy goats and sheep, respectively, were determined. The sensitivity and specificity of indirect tests in predicting the bacteriological status were compared by analyzing the areas under the receiver operating characteristic curve and calculating the likelihood ratio at various cut-off values.Bacteria were isolated from 17.7 and 4.6% of glands from goats and sheep, respectively. Somatic cell count was a better predictor of bacteriological status than either the CMT score or impedance in both goats and sheep. However, knowledge of the CMT score in both sheep and goats and the impedance in goats increases the likelihood of predicting the presence of a bacterial pathogen compared to no testing at all (P<0.05). Knowledge of the age and days postpartum of the animals at the time of testing did not increase the probability that infection status could be predicted. Variation in cut-off levels to predict infection status reported in the literature may be due to variation in the prevalence of infection in the populations studied. Use of likelihood ratio allows comparison of tests over a range of prevalence’s as likelihood ratios are independent of prevalence. The prevalence of infection within a herd should be considered when selecting a cut-off value for indirect testing for the presence of bacteria in milk of small ruminants.     

Simple Methods for Testing the Molecular Evolutionary Clock Hypothesis

Simple statistical methods for testing the molecular evolutionary clock hypothesis are developed which can be applied to both nucleotide and amino acid sequences. These methods are based on the chi-square test and are applicable even when the pattern of substitution rates is unknown and/or the substitution rate varies among different sites. Furthermore, some of the methods can be applied even when the outgroup is unknown. Using computer simulations, these methods were compared with the likelihood ratio test and the relative rate test. The results indicate that the powers of the present methods are similar to those of the likelihood ratio test and the relative rate test, in spite of the fact that the latter two tests assume that the pattern of substitution rates follows a certain model and that the substitution rate is the same among different sites, while such assumptions are not necessary to apply the present methods. Therefore, the present methods might be useful.     

A hybrid omnibus test for generalized semiparametric single‐index models with high‐dimensional covariate sets

Numerous statistical methods have been developed for analyzing high‐dimensional data. These methods often focus on variable selection approaches but are limited for the purpose of testing with high‐dimensional data. They are often required to have explicit‐likelihood functions. In this article, we propose a “hybrid omnibus test” for high‐dicmensional data testing purpose with much weaker requirements. Our hybrid omnibus test is developed under a semiparametric framework where a likelihood function is no longer necessary. Our test is a version of a frequentist‐Bayesian hybrid score‐type test for a generalized partially linear single‐index model, which has a link function being a function of a set of variables through a generalized partially linear single index. We propose an efficient score based on estimating equations, define local tests, and then construct our hybrid omnibus test using local tests. We compare our approach with an empirical‐likelihood ratio test and Bayesian inference based on Bayes factors, using simulation studies. Our simulation results suggest that our approach outperforms the others, in terms of type I error, power, and computational cost in both the low‐ and high‐dimensional cases. The advantage of our approach is demonstrated by applying it to genetic pathway data for type II diabetes mellitus.     

Sample size calculations for noninferiority trials with Poisson distributed count data

Clinical trials with Poisson distributed count data as the primary outcome are common in various medical areas such as relapse counts in multiple sclerosis trials or the number of attacks in trials for the treatment of migraine. In this article, we present approximate sample size formulae for testing noninferiority using asymptotic tests which are based on restricted or unrestricted maximum likelihood estimators of the Poisson rates. The Poisson outcomes are allowed to be observed for unequal follow‐up schemes, and both the situations that the noninferiority margin is expressed in terms of the difference and the ratio are considered. The exact type I error rates and powers of these tests are evaluated and the accuracy of the approximate sample size formulae is examined. The test statistic using the restricted maximum likelihood estimators (for the difference test problem) and the test statistic that is based on the logarithmic transformation and employs the maximum likelihood estimators (for the ratio test problem) show favorable type I error control and can be recommended for practical application. The approximate sample size formulae show high accuracy even for small sample sizes and provide power values identical or close to the aspired ones. The methods are illustrated by a clinical trial example from anesthesia.     

A comparison of methods to estimate cross-environment genetic correlations

Advanced techniques for quantitative genetic parameter estimation may not always be necessary to answer broad genetic questions. However, simpler methods are often biased, and the extent of this determines their usefulness. In this study we compare family mean correlations to least squares and restricted error maximum likelihood (REML) variance component approaches to estimating cross-environment genetic correlations. We analysed empirical data from studies where both types of estimates were made, and from studies in our own laboratories. We found that the agreement between estimates was better when full-sib rather than half-sib estimates of cross-environment genetic correlations were used and when mean family size increased. We also note biases in REML estimation that may be especially important when testing to see if correlations differ from 0 or 1. We conclude that correlations calculated from family means can be used to test for the presence of genetic correlations across environments, which is sufficient for some research questions. Variance component approaches should be used when parameter estimation is the objective, or if the goal is anything other than determining broad patterns.