Incongruence between test statistics and P values in medical papers

Given an observed test statistic and its degrees of freedom, one may compute the observed P value with most statistical packages. It is unknown to what extent test statistics and P values are congruent in published medical papers. Methods: We checked the congruence of statistical results reported in all the papers of volumes 409–412 of Nature (2001) and a random sample of 63 results from volumes 322–323 of BMJ (2001). We also tested whether the frequencies of the last digit of a sample of 610 test statistics deviated from a uniform distribution (i.e., equally probable digits).Results: 11.6% (21 of 181) and 11.1% (7 of 63) of the statistical results published in Nature and BMJ respectively during 2001 were incongruent, probably mostly due to rounding, transcription, or type-setting errors. At least one such error appeared in 38% and 25% of the papers of Nature and BMJ, respectively. In 12% of the cases, the significance level might change one or more orders of magnitude. The frequencies of the last digit of statistics deviated from the uniform distribution and suggested digit preference in rounding and reporting.Conclusions: this incongruence of test statistics and P values is another example that statistical practice is generally poor, even in the most renowned scientific journals, and that quality of papers should be more controlled and valued

Bayes Factors Based on Test Statistics

Traditionally, the use of Bayes factors has required the specification of proper prior distributions on model parameters implicit to both null and alternative hypotheses. In this paper, I describe an approach to defining Bayes factors based on modeling test statistics. Because the distributions of test statistics do not depend on unknown model parameters, this approach eliminates the subjectivity normally associated with the definition of Bayes factors. For standard test statistics, including the _2, F, t and z statistics, the values of Bayes factors that result from this approach can be simply expressed in closed form.

MODIFIED TEST STATISTICS BY INTER-VOXEL VARIANCE SHRINKAGE WITH AN APPLICATION TO fMRI

Functional Magnetic Resonance Imaging (fMRI) is a non-invasive technique which is commonly used to quantify changes in blood oxygenation and flow coupled to neuronal activation. One of the primary goals of fMRI studies is to identify localized brain regions where neuronal activation levels vary between groups. Single voxel t-tests have been commonly used to determine whether activation related to the protocol differs across groups. Due to the generally limited number of subjects within each study, accurate estimation of variance at each voxel is difficult. Thus, combining information across voxels in the statistical analysis of fMRI data is desirable in order to improve efficiency. Here we construct a hierarchical model and apply an Empirical Bayes framework on the analysis of group fMRI data, employing techniques used in high throughput genomic studies. The key idea is to shrink residual variances by combining information across voxels, and subsequently to construct an improved test statistic in lieu of the classical t-statistic. This hierarchical model results in a shrinkage of voxel-wise residual sample variances towards a common value. The shrunken estimator for voxelspecific variance components on the group analyses outperforms the classical residual error estimator in terms of mean squared error. Moreover, the shrunken test-statistic decreases false positive rate when testing differences in brain contrast maps across a wide range of simulation studies. This methodology was also applied to experimental data regarding a cognitive activation task.

Contributions dans l'analyse des modèles vectoriels de séries chronologiques saisonnières et périodiques

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

A versatile gene-based test for genome-wide association studies

We have derived a versatile gene-based test for genome-wide association studies (GWAS). Our approach, called VEGAS (versatile gene-based association study), is applicable to all GWAS designs, including family-based GWAS, meta-analyses of GWAS on the basis of summary data, and DNA-pooling-based GWAS, where existing approaches based on permutation are not possible, as well as singleton data, where they are. The test incorporates information from a full set of markers (or a defined subset) within a gene and accounts for linkage disequilibrium between markers by using simulations from the multivariate normal distribution. We show that for an association study using singletons, our approach produces results equivalent to those obtained via permutation in a fraction of the computation time. We demonstrate proof-of-principle by using the gene-based test to replicate several genes known to be associated on the basis of results from a family-based GWAS for height in 11,536 individuals and a DNA-pooling-based GWAS for melanoma in approximately 1300 cases and controls. Our method has the potential to identify novel associated genes; provide a basis for selecting SNPs for replication; and be directly used in network (pathway) approaches that require per-gene association test statistics. We have implemented the approach in both an easy-to-use web interface, which only requires the uploading of markers with their association p-values, and a separate downloadable application.

Les tests de causalité en variance entre deux séries chronologiques multivariées

Les modèles de séries chronologiques avec variances conditionnellement hétéroscédastiques sont devenus quasi incontournables afin de modéliser les séries chronologiques dans le contexte des données financières. Dans beaucoup d'applications, vérifier l'existence d'une relation entre deux séries chronologiques représente un enjeu important. Dans ce mémoire, nous généralisons dans plusieurs directions et dans un cadre multivarié, la procédure dévéloppée par Cheung et Ng (1996) conçue pour examiner la causalité en variance dans le cas de deux séries univariées. Reposant sur le travail de El Himdi et Roy (1997) et Duchesne (2004), nous proposons un test basé sur les matrices de corrélation croisée des résidus standardisés carrés et des produits croisés de ces résidus. Sous l'hypothèse nulle de l'absence de causalité en variance, nous établissons que les statistiques de test convergent en distribution vers des variables aléatoires khi-carrées. Dans une deuxième approche, nous définissons comme dans Ling et Li (1997) une transformation des résidus pour chaque série résiduelle vectorielle. Les statistiques de test sont construites à partir des corrélations croisées de ces résidus transformés. Dans les deux approches, des statistiques de test pour les délais individuels sont proposées ainsi que des tests de type portemanteau. Cette méthodologie est également utilisée pour déterminer la direction de la causalité en variance. Les résultats de simulation montrent que les tests proposés offrent des propriétés empiriques satisfaisantes. Une application avec des données réelles est également présentée afin d'illustrer les méthodes

Sur la validation des modèles de séries chronologiques spatio-temporelles multivariées

Dans ce mémoire, nous avons utilisé le logiciel R pour la programmation.

A score test for binary data with patient non-compliance

A score test is developed for binary clinical trial data, which incorporates patient non-compliance while respecting randomization. It is assumed in this paper that compliance is all-or-nothing, in the sense that a patient either accepts all of the treatment assigned as specified in the protocol, or none of it. Direct analytic comparisons of the adjusted test statistic for both the score test and the likelihood ratio test are made with the corresponding test statistics that adhere to the intention-to-treat principle. It is shown that no gain in power is possible over the intention-to-treat analysis, by adjusting for patient non-compliance. Sample size formulae are derived and simulation studies are used to demonstrate that the sample size approximation holds. Copyright © 2003 John Wiley & Sons, Ltd.

Testing for Seasonal Unit Roots when Residuals Contain Serial Correlations under HEGY Test Framework

This paper introduces a corrected test statistic for testing seasonal unit roots when residuals contain serial correlations, based on the HEGY test proposed by Hylleberg,Engle, Granger and Yoo (1990). The serial correlations in the residuals of test regressionare accommodated by making corrections to the commonly used HEGY t statistics. Theasymptotic distributions of the corrected t statistics are free from nuisance parameters.The size and power properties of the corrected statistics for quarterly and montly data are investigated. Based on our simulations, the corrected statistics for monthly data havemore power compared with the commonly used HEGY test statistics, but they also have size distortions when there are strong negative seasonal correlations in the residuals.

Rank test of location optimal for hyperbolic secant distribution

There are at least two reasons for a symmetric, unimodal, diffuse tailed hyperbolic secant distribution to be interesting in real-life applications. It displays one of the common types of non normality in natural data and is closely related to the logistic and Cauchy distributions that often arise in practice. To test the difference in location between two hyperbolic secant distributions, we develop a simple linear rank test with trigonometric scores. We investigate the small-sample and asymptotic properties of the test statistic and provide tables of the exact null distribution for small sample sizes. We compare the test to the Wilcoxon two-sample test and show that, although the asymptotic powers of the tests are comparable, the present test has certain practical advantages over the Wilcoxon test.

Comparative phylogeographic summary statistics for testing simultaneous vicariance

Testing for simultaneous vicariance across comparative phylogeographic data sets is a notoriously difficult problem hindered by mutational variance, the coalescent variance, and variability across pairs of sister taxa in parameters that affect genetic divergence. We simulate vicariance to characterize the behaviour of several commonly used summary statistics across a range of divergence times, and to characterize this behaviour in comparative phylogeographic datasets having multiple taxon-pairs. We found Tajima's D to be relatively uncorrelated with other summary statistics across divergence times, and using simple hypothesis testing of simultaneous vicariance given variable population sizes, we counter-intuitively found that the variance across taxon pairs in Nei and Li's net nucleotide divergence (pi(net)), a common measure of population divergence, is often inferior to using the variance in Tajima's D across taxon pairs as a test statistic to distinguish ancient simultaneous vicariance from variable vicariance histories. The opposite and more intuitive pattern is found for testing more recent simultaneous vicariance, and overall we found that depending on the timing of vicariance, one of these two test statistics can achieve high statistical power for rejecting simultaneous vicariance, given a reasonable number of intron loci (> 5 loci, 400 bp) and a range of conditions. These results suggest that components of these two composite summary statistics should be used in future simulation-based methods which can simultaneously use a pool of summary statistics to test comparative the phylogeographic hypotheses we consider here.

Modified CADF and CIPS panel unit root statistics with standard chi-squared and normal limiting distributions

In an influential paper Pesaran ('A simple panel unit root test in presence of cross-section dependence', Journal of Applied Econometrics, Vol. 22, pp. 265-312, 2007) proposes two unit root tests for panels with a common factor structure. These are the CADF and CIPS test statistics, which are amongst the most popular test statistics in the literature. One feature of these statistics is that their limiting distributions are highly non-standard, making for relatively complicated implementation. In this paper, we take this feature as our starting point to develop modified CADF and CIPS test statistics that support standard chi-squared and normal inference.

Modeling multivariate autoregressive conditional heteroskedasticity with the double smooth transition conditional correlation GARCH Model

In this paper, we propose a multivariate GARCH model with a time-varying conditional correlation structure. The new double smooth transition conditional correlation (DSTCC) GARCH model extends the smooth transition conditional correlation (STCC) GARCH model of Silvennoinen and Teräsvirta (2005) by including another variable according to which the correlations change smoothly between states of constant correlations. A Lagrange multiplier test is derived to test the constancy of correlations against the DSTCC-GARCH model, and another one to test for another transition in the STCC-GARCH framework. In addition, other specification tests, with the aim of aiding the model building procedure, are considered. Analytical expressions for the test statistics and the required derivatives are provided. Applying the model to the stock and bond futures data, we discover that the correlation pattern between them has dramatically changed around the turn of the century. The model is also applied to a selection of world stock indices, and we find evidence for an increasing degree of integration in the capital markets.