Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors

In many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors. The main goal of this paper is to consider inference on such models with error-prone observations and variances of the measurement errors changing across observations. We suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed. Aggregate data allow the estimation of the error variances. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed. Test statistics are proposed for testing hypotheses of interest. Further, we implement a simple graphical device that enables an assessment of the model`s goodness of fit. Results of simulations concerning the properties of the test statistics are reported. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease. Copyright (C) 2008 John Wiley & Sons, Ltd.

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

Methods for Equivalence and Noninferiority Testing

Classical hypothesis testing focuses on testing whether treatments have differential effects on outcome. However, sometimes clinicians may be more interested in determining whether treatments are equivalent or whether one has noninferior outcomes. We review the hypotheses for these noninferiority and equivalence research questions, consider power and sample size issues, and discuss how to perform such a test for both binary and survival outcomes. The methods are illustrated on 2 recent studies in hematopoietic cell transplantation.

Inference for a skew extension of the Grubbs model

In this paper, we discuss inferential aspects for the Grubbs model when the unknown quantity x (latent response) follows a skew-normal distribution, extending early results given in Arellano-Valle et al. (J Multivar Anal 96:265-281, 2005b). Maximum likelihood parameter estimates are computed via the EM-algorithm. Wald and likelihood ratio type statistics are used for hypothesis testing and we explain the apparent failure of the Wald statistics in detecting skewness via the profile likelihood function. The results and methods developed in this paper are illustrated with a numerical example.

A Bayesian approach to fuzzy hypotheses testing for the estimation of optimal age for vaccination against measles

Fuzzy Bayesian tests were performed to evaluate whether the mother`s seroprevalence and children`s seroconversion to measles vaccine could be considered as ""high"" or ""low"". The results of the tests were aggregated into a fuzzy rule-based model structure, which would allow an expert to influence the model results. The linguistic model was developed considering four input variables. As the model output, we obtain the recommended age-specific vaccine coverage. The inputs of the fuzzy rules are fuzzy sets and the outputs are constant functions, performing the simplest Takagi-Sugeno-Kang model. This fuzzy approach is compared to a classical one, where the classical Bayes test was performed. Although the fuzzy and classical performances were similar, the fuzzy approach was more detailed and revealed important differences. In addition to taking into account subjective information in the form of fuzzy hypotheses it can be intuitively grasped by the decision maker. Finally, we show that the Bayesian test of fuzzy hypotheses is an interesting approach from the theoretical point of view, in the sense that it combines two complementary areas of investigation, normally seen as competitive. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

Treadmill exercise testing of asymptomatic men and women without evidence of heart disease

The aim of this study was to test the hypothesis of differences in performance including differences in ST-T wave changes between healthy men and women submitted to an exercise stress test. Two hundred (45.4%) men and 241 (54.6%) women (mean age: 38.7 ± 11.0 years) were submitted to an exercise stress test. Physiologic and electrocardiographic variables were compared by the Student t-test and the chi-square test. To test the hypothesis of differences in ST-segment changes, data were ranked with functional models based on weighted least squares. To evaluate the influence of gender and age on the diagnosis of ST-segment abnormality, a logistic model was adjusted; P < 0.05 was considered to be significant. Rate-pressure product, duration of exercise and estimated functional capacity were higher in men (P < 0.05). Sixteen (6.7%) women and 9 (4.5%) men demonstrated ST-segment upslope ≥0.15 mV or downslope ≥0.10 mV; the difference was not statistically significant. Age increase of one year added 4% to the chance of upsloping of segment ST ≥0.15 mV or downsloping of segment ST ≥0.1 mV (P = 0.03; risk ratio = 1.040, 95% confidence interval (CI) = 1.002-1.080). Heart rate recovery was higher in women (P < 0.05). The chance of women showing an increase of systolic blood pressure ≤30 mmHg was 85% higher (P = 0.01; risk ratio = 1.85, 95%CI = 1.1-3.05). No significant difference in the frequency of ST-T wave changes was observed between men and women. Other differences may be related to different physical conditioning.

The full Bayesian significance test for mixture models: results in gene expression clustering

Gene clustering is a useful exploratory technique to group together genes with similar expression levels under distinct cell cycle phases or distinct conditions. It helps the biologist to identify potentially meaningful relationships between genes. In this study, we propose a clustering method based on multivariate normal mixture models, where the number of clusters is predicted via sequential hypothesis tests: at each step, the method considers a mixture model of m components (m = 2 in the first step) and tests if in fact it should be m - 1. If the hypothesis is rejected, m is increased and a new test is carried out. The method continues (increasing m) until the hypothesis is accepted. The theoretical core of the method is the full Bayesian significance test, an intuitive Bayesian approach, which needs no model complexity penalization nor positive probabilities for sharp hypotheses. Numerical experiments were based on a cDNA microarray dataset consisting of expression levels of 205 genes belonging to four functional categories, for 10 distinct strains of Saccharomyces cerevisiae. To analyze the method's sensitivity to data dimension, we performed principal components analysis on the original dataset and predicted the number of classes using 2 to 10 principal components. Compared to Mclust (model-based clustering), our method shows more consistent results.

Disequilibrium Coefficient: A Bayesian Perspective

Hardy-Weinberg Equilibrium (HWE) is an important genetic property that populations should have whenever they are not observing adverse situations as complete lack of panmixia, excess of mutations, excess of selection pressure, etc. HWE for decades has been evaluated; both frequentist and Bayesian methods are in use today. While historically the HWE formula was developed to examine the transmission of alleles in a population from one generation to the next, use of HWE concepts has expanded in human diseases studies to detect genotyping error and disease susceptibility (association); Ryckman and Williams (2008). Most analyses focus on trying to answer the question of whether a population is in HWE. They do not try to quantify how far from the equilibrium the population is. In this paper, we propose the use of a simple disequilibrium coefficient to a locus with two alleles. Based on the posterior density of this disequilibrium coefficient, we show how one can conduct a Bayesian analysis to verify how far from HWE a population is. There are other coefficients introduced in the literature and the advantage of the one introduced in this paper is the fact that, just like the standard correlation coefficients, its range is bounded and it is symmetric around zero (equilibrium) when comparing the positive and the negative values. To test the hypothesis of equilibrium, we use a simple Bayesian significance test, the Full Bayesian Significance Test (FBST); see Pereira, Stern andWechsler (2008) for a complete review. The disequilibrium coefficient proposed provides an easy and efficient way to make the analyses, especially if one uses Bayesian statistics. A routine in R programs (R Development Core Team, 2009) that implements the calculations is provided for the readers.

The impact of measurement errors in the identification of regulatory networks

Background: There are several studies in the literature depicting measurement error in gene expression data and also, several others about regulatory network models. However, only a little fraction describes a combination of measurement error in mathematical regulatory networks and shows how to identify these networks under different rates of noise. Results: This article investigates the effects of measurement error on the estimation of the parameters in regulatory networks. Simulation studies indicate that, in both time series (dependent) and non-time series (independent) data, the measurement error strongly affects the estimated parameters of the regulatory network models, biasing them as predicted by the theory. Moreover, when testing the parameters of the regulatory network models, p-values computed by ignoring the measurement error are not reliable, since the rate of false positives are not controlled under the null hypothesis. In order to overcome these problems, we present an improved version of the Ordinary Least Square estimator in independent (regression models) and dependent (autoregressive models) data when the variables are subject to noises. Moreover, measurement error estimation procedures for microarrays are also described. Simulation results also show that both corrected methods perform better than the standard ones (i.e., ignoring measurement error). The proposed methodologies are illustrated using microarray data from lung cancer patients and mouse liver time series data. Conclusions: Measurement error dangerously affects the identification of regulatory network models, thus, they must be reduced or taken into account in order to avoid erroneous conclusions. This could be one of the reasons for high biological false positive rates identified in actual regulatory network models.

Haplotype distribution of five nuclear genes based on network genealogies and Bayesian inference indicates that Trypanosoma cruzi hybrid strains are polyphyletic

Chagas disease is still a major public health problem in Latin America. Its causative agent, Trypanosoma cruzi, can be typed into three major groups, T. cruzi I, T. cruzi II and hybrids. These groups each have specific genetic characteristics and epidemiological distributions. Several highly virulent strains are found in the hybrid group; their origin is still a matter of debate. The null hypothesis is that the hybrids are of polyphyletic origin, evolving independently from various hybridization events. The alternative hypothesis is that all extant hybrid strains originated from a single hybridization event. We sequenced both alleles of genes encoding EF-1 alpha, actin and SSU rDNA of 26 T. cruzi strains and DHFR-TS and TR of 12 strains. This information was used for network genealogy analysis and Bayesian phylogenies. We found T. cruzi I and T. cruzi II to be monophyletic and that all hybrids had different combinations of T. cruzi I and T. cruzi II haplotypes plus hybrid-specific haplotypes. Bootstrap values (networks) and posterior probabilities (Bayesian phylogenies) of clades supporting the monophyly of hybrids were far below the 95% confidence interval, indicating that the hybrid group is polyphyletic. We hypothesize that T. cruzi I and T. cruzi II are two different species and that the hybrids are extant representatives of independent events of genome hybridization, which sporadically have sufficient fitness to impact on the epidemiology of Chagas disease.

Influence of the bonding substrate in dental composite polymerization stress testing

Our objective was to compare the polymerization stress (sigma(pol)) of a series of composites obtained using poly(methyl methacrylate) (PMMA) or glass as bonding substrates, and to compare the results with those from in vitro microleakage of composite restorations. The tested hypothesis was that stress values obtained in a less rigid testing system (i.e. using PMMA) would show a better relationship with microleakage data. Five dental composites were tested: Filtek Z250 (FZ), Z100 (Z1), Concept (CO), Durafill (DU) and Heliomolar (HM). sigma(pol) was determined in 1 mm high specimens inserted between two rods (empty set = 5 mm) of either PMMA or glass. The composite elastic modulus (E) was obtained by three-point bending. sigma(pol) and E data were submitted to a one-way analysis of variance/Tukey test (alpha = 0.05). For the microleakage test (MI), bovine incisors received cylindrical cavities (empty set = 5 mm, h = 2 mm), which were restored in bulk. After storage for 24 h in water, specimens were subjected to dye penetration using AgNO(3) as tracer. Specimens were sectioned twice, perpendicularly, and microleakage was measured (in millimeters) under 20x magnification. Data from MI were submitted to the Kruskal-Wallis test. Means (SD) of sigma(pol) (MPa) using glass/PMMA were FZ: 7.5(1.8)(A)/2.5(0.2)(bc); Z1: 7.3(0.5)(A)/2.8(0.3)(ab); CO: 6.8(1.1)(A)/3.2(0.5)(a); DU: 4.5(0.7)(B)/2.0(0.2)(bc); HM: 3.5(0.2)(B)/2.3(0.3)(c). sigma(pol) obtained using PMMA rods were 34-67% lower than with glass. Means (SD) for tooth average/tooth maximum microleakage were FZ: 0.92(0.19)(B)/1.53(0.30)(a); Z1: 1.19(0.21)(A)/1.75(0.20)(a); CO: 1.26(0.25)(A)/1.78(0.24)(a); DU: 0.83(0.30)(B)/1.68(0.46)(a): HM: 0.81(0.27)(B)/1.64(0.54)(a). The tested hypothesis was confirmed, as the composites showed the same ordering both in the polymerization stress test using PMMA rods and in the microleakage test. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The comparative field body temperature among Liolaemus lizards: Testing the static and the labile hypotheses

Two competing hypotheses have been suggested to explain thermal sensitivity of lizards to environmental conditions. These are the static and the labile hypotheses. The static hypothesis posits that thermal physiology is evolutionary conservative and consequently relatively insensitive to directional selection. Contrarily, the labile hypothesis states that thermal physiology does respond readily to directional selection in some lizard taxa. In this paper, we tested both hypotheses among species of Liolaemus lizards. The genus Liolaemus is diverse with about 200 species, being broadly distributed from central Peru to Tierra del Fuego at the southern end of South America. Data of field body temperature (T(b)) from Liolaemus species were collected from the literature. Based on the distributional range of the species we also collected data of mean annual ambient temperatures. We observed that both the traditional analysis and the phylogenetic approach indicate that in the genus Liolaemus T(b) of species varies in a manner that is consistent with ecological gradient of ambient temperature. The data suggest that the thermal physiology of Liolaemus lizards is evolutionarily flexible, and that this plasticity has been partially responsible for the colonization of a wide array of thermal environments. (C) 2009 Elsevier Ltd. All rights reserved.

Hypotheses Testing on a Multivariate Null Intercept Errors-in-Variables Model

Considering the Wald, score, and likelihood ratio asymptotic test statistics, we analyze a multivariate null intercept errors-in-variables regression model, where the explanatory and the response variables are subject to measurement errors, and a possible structure of dependency between the measurements taken within the same individual are incorporated, representing a longitudinal structure. This model was proposed by Aoki et al. (2003b) and analyzed under the bayesian approach. In this article, considering the classical approach, we analyze asymptotic test statistics and present a simulation study to compare the behavior of the three test statistics for different sample sizes, parameter values and nominal levels of the test. Also, closed form expressions for the score function and the Fisher information matrix are presented. We consider two real numerical illustrations, the odontological data set from Hadgu and Koch (1999), and a quality control data set.

Micromorphological and hardness analyses of human and bovine sclerotic dentin: a comparative study

The purpose of this study was to test the hypothesis that both human and bovine sclerotic dentin have similar hardness properties, in addition to similar micromorphological characteristics. Sixteen teeth (8 human and 8 bovine) exhibiting exposed dentin in the incisal edge and showing characteristics typical of sclerosis were used. Vickers surface microhardness testing was conducted. Three areas of the dentin surface of each specimen were selected. All teeth were processed for scanning electron microscopy in order to estimate the amount (in percentage) of solid dentin on the sclerotic dentin surface. The data were compared by Student's t test (α = 0.05). The micromorphological and microhardness data were compared by Pearson's linear correlation test (α = 0.05). The mean percentages of solid dentin of human and bovine sclerotic dentin were similar (human 90.71 ± 0.83 and bovine 89.08 ± 0.81, p = 0.18). The mean microhardness value (VHN) of human sclerotic dentin was significantly higher than that of bovine sclerotic dentin (human 45.26 ± 2.92 and bovine 29.93 ± 3.83, p = 0.006). No correlation was found between the microhardness values and the amount of solid dentin in the sclerotic dentin, irrespective of the species considered (human R² = 0.0240, p = 0.714; bovine R² = 0.0017, p = 0.923; and combined R² = 0.038, p = 0.46). We concluded that although both bovine and human sclerotic dentin present a similar amount of solid tissue, human sclerotic dentin presents higher microhardness than bovine sclerotic dentin.

Flexural and diametral tensile strength of composite resins

This study evaluated the flexural strength (sf) and the diametral tensile strength (st) of light-cured composite resins, testing the hypothesis that there is a positive relation between these properties. Twenty specimens were fabricated for each material (Filtek Z250- 3M-Espe; AM- Amelogen, Ultradent; VE- Vit-l-escence, Ultradent; EX- Esthet-X, Dentsply/Caulk), following ISO 4049 and ANSI/ADA 27 specifications and the manufacturers’ instructions. For the st test, cylindrical shaped (4 mm x 6 mm) specimens (n = 10) were placed with their long axes perpendicular to the applied compressive load at a crosshead speed of 1.0 mm/min. The sf was measured using the 3-point bending test, in which bar shaped specimens (n = 10) were tested at a crosshead speed of 0.5 mm/min. Both tests were performed in a universal testing machine (EMIC 2000) recording the fracture load (N). Strength values (MPa) were calculated and statistically analyzed by ANOVA and Tukey (a = 0.05). The mean and standard deviation values (MPa) were Z250-45.06 ± 5.7; AM-35.61 ± 5.4; VE-34.45 ± 7.8; and EX-42.87 ± 6.6 for st; and Z250-126.52 ± 3.3; AM-87.75 ± 3.8; VE-104.66 ± 4.4; and EX-119.48 ± 2.1 for sf. EX and Z250 showed higher st and sf values than the other materials evaluated (p < 0.05), which followed a decreasing trend of mean values. The results confirmed the study hypothesis, showing a positive relation between the material properties examined.