Empirical Significance Levels Research Articles

Constrained inference in scaled mixed effects models with applications to London Junior School Project data

Multiple outcomes arise frequently in many different settings. Mixed effect models are a useful tool for the analyses of such data. However, when outcomes are measured on different scales, analyses based on any one scale are misleading. Often parameters of the model are subject to known order restrictions. To incorporate heterogeneity across different outcomes, we propose a scaled linear mixed effect model. To estimate parameters, we propose a maximum likelihood estimation procedure based on a restricted version of the expectation-conditional maximization either algorithm. Constrained hypotheses testing procedures are developed using likelihood ratio tests. The empirical significance levels and powers are studied using simulations. This article shows that incorporating the restrictions improves the mean squared errors of the estimates and the power of the tests. The methodology is applied on the London Junior School Project data incorporating known restrictions of patterns of scores. Journal of Statistical Research 2023, Vol 57, No.1-2, pp.81-94

Digenic Analysis Finds Highly Interactive Genetic Variants Underlying Polygenic Traits.

We briefly review our recently published approach to mining digenic genotype patterns, which consist of two genotypes each originating in a different DNA variant. We do this for a genetic case-control study by evaluating all possible pairs of genotypes, distributing the workload over numerous CPUs (threads) in a high-performance computing environment and apply our methods to two known datasets, age-related macular degeneration (AMD) and Parkinson Disease (PD). Based on a list of (e.g., 100,000) genotype pairs with largest genotype pair frequency differences between cases and controls, we determine the number of unique variants occurring in this list. For each unique variant, we find the number of genotype pairs it participates in, which identifies a set of variants "connected" with the given unique variant. Among the total of variants "connected" with all unique variants, only a subset of variants is unique. The ratio of all connected variants divided by that subset of variants is a measure for the overall density or connectedness of variants interacting with each other. We find that variants for the AMD data are much more interconnected than those for PD, at least based on the 100,000 genotype pairs with largest chi-square we investigated. Further, for each of the unique variants, we use the number of variants connected with it as a test statistic, weighted by the inverse of the rank at which the unique variant first occurred in the original list of genotype patterns. This weighing scheme ties the number of connections to the genetics of the trait and allows us to obtain, for each of the unique variants, an empirical significance level by permuting ranks. We find 12 and 8 significant, highly connected variants for AMD and PD, respectively, some of which have previously been identified by other machine learning methods, thus providing credence to our approach. Among the 100,000 genotype pairs investigated for each of AMD and PD, significant variants showed connections with up to 7,093 and 3,777 other variants, respectively. Our approach has been implemented in a freely available piece of software, the Digenic Network Test. Thus, our statistical genetics method can provide important information on the genetic architecture of polygenic traits.

FOXA1 regulates alternative splicing in prostate cancer.

SummaryDysregulation of alternative splicing in prostate cancer is linked to transcriptional programs activated by AR, ERG, FOXA1, and MYC. Here, we show that FOXA1 functions as the primary orchestrator of alternative splicing dysregulation across 500 primary and metastatic prostate cancer transcriptomes. We demonstrate that FOXA1 binds to the regulatory regions of splicing-related genes, including HNRNPK and SRSF1. By controlling trans-acting factor expression, FOXA1 exploits an “exon definition” mechanism calibrating alternative splicing toward dominant isoform production. This regulation especially impacts splicing factors themselves and leads to a reduction of nonsense-mediated decay (NMD)-targeted isoforms. Inclusion of the NMD-determinant FLNA exon 30 by FOXA1-controlled oncogene SRSF1 promotes cell growth in vitro and predicts disease recurrence. Overall, we report a role for FOXA1 in rewiring the alternative splicing landscape in prostate cancer through a cascade of events from chromatin access, to splicing factor regulation, and, finally, to alternative splicing of exons influencing patient survival.

A generalized normal scores test that increases the power of a test of significance for a coefficient in a linear model

A generalization of the normal scores two-sample test is proposed. The empirical significance level of this test closely approximates the nominal level of significance and it is often more powerful than the traditional t test for a test of any single coefficient in a linear model. Based on an extensive simulation study we found that, for most applications, the generalized normal scores test maintains its level of significance and it has, for data sets having 50 or more observations, greater power than the t test if the distribution of the errors is long-tailed or skewed. But, we found that the empirical significance level slightly exceeds the nominal level for regression models having covariates that are skewed and highly correlated, and for those models the generalized normal scores test is not recommended. If a data set has fewer than 50 observations the generalized normal scores test is not recommended because for most error distributions it does not offer an increase in power over the t test. However, if the number of observations equals or exceeds 50 and the covariates are not highly correlated this generalized normal scores test can be used to increase the power of tests of significance.

Rationality is Service Receiver’s Trait

Purpose: The article constitutes the expansion of authorial research on rationality from a service provider point of view. This time, it is from a service receiver's standpoint. The research's main goal is to identify factors that positively affect a rational choice of healthcare or transport services and allow a consumer to evince a trait of rationality. Design/Methodology/Approach: Chi-square tests and empirical significance level tests in statistics were performed. It was verified whether there is a correlation between a social group and the proportion of answers. A cross-functional analysis was done in different social groups. Findings: A statistically significant test result indicated that particular social groups differed in terms of the frequency of pointing out a given answer. The research results that are presented cover the situations in which a consumer evinces rational behavior. The findings also highlight factors that influence a consumer's decision while buying a service. They clearly show that, in both service categories, high quality and efficiency are the factors that decide while making a final decision. Moreover, employed people and students stress the importance of an office in healthcare or the appearance of a service provider in transportation. Retired people appreciate the convenient location of a service facility in both categories. Practical implications: the analysis of the variable distribution showed that it was possible to create a list of service providers' recommendations. Thanks to recognizing factors that determine the choices of service receivers, the providers will be able to arrange a service offer better – adequately to market needs. Originality/Value: Rationality, from a service perspective, is a scarce subject. Raising it is original and makes the research unique, attested by the opinion comparison between three social groups – students, employed people, and pensioners. The analysis processes enabled the creation of action strategies for service receivers with regard to the future of selected service categories.

Testing global and local dependence of point patterns on covariates in parametric models

Testing for a covariate effect in a parametric point process model is usually done through the Wald test, which relies on an asymptotic null distribution of the test statistic. We propose a Monte Carlo version of the test that also allows local investigation of the covariate effect in the globally fitted model. Two different test statistics are suggested for this purpose: the first, a spatial statistic computed at every location of the observation window, resembles the classical F-statistic that is usually used in general linear models (GLMs) to express the distance between a model and its sub model. This statistic allows one to detect locations where the smoothed point process residuals are reduced by adding the interesting covariates into the model. The second spatial statistic tries to capture local improvements in the shape of the predicted intensity caused by an interesting, continuous covariate. A simulation scheme resembling the permutation inference for GLMs is used to obtain the null distribution of the statistics. Thereafter, a Monte Carlo test with graphical interpretation (a global envelope test) is applied to the empirical and simulated statistic fields to determine the global significance of the covariate and the spatially significant areas. We study the empirical significance level and power of the test in different scenarios and, by applying the test to simulated and real point pattern data, show that the proposed statistics can be valuable for model construction.

Testing the absence of random effects in the nested-error regression model using orthogonal transformations

Testing the absence of random effects in the nested error regression model is nonstandard because it requires the null value of the random effects variance to be on the boundary of its space. In this paper, we propose a test statistic that can be obtained by applying two successive orthogonal transformations to the response vector such that the components of the resulting new vector are uncorrelated variates having zero mean and a common variance. Consequently, two new tests are proposed. The first assumes the normality of the responses and is based on approximating the distribution of the test statistic as a weighted sum of chi-square variates. The second test is a distribution-free permutation test based on the same test statistic. Our simulation experiments indicate that both tests have empirical significance levels that are close to the chosen nominal level. The statistical power of the first test is studied analytically. Empirical power comparisons indicate that the first test outperforms recently developed tests. The second test also has a competitive performance among them. Using a real dataset, the use of the proposed tests is illustrated.

Point estimation and two new goodness of fit tests for the scale family based on general progressively Type-II censored samples

In this paper, we obtain an analytic and explicit estimator of the scale parameter using pivotal method and propose two new goodness of fit tests for the scale family based on general progressively Type-II censored samples. The properties about the test statistics are studied. Furthermore, we apply our methods to some specific life distributions for illustration. Moreover, we obtain critical values by simulations and compare the power of the two tests against various alternatives under many censoring schemes. We also obtain the empirical significance levels thorough Monte Carlo simulation. We do the comparison of the proposed estimator with the existing estimators given in the literature by means of a power study. The influence of the parameter in the alternative distribution to power is explored. The simulation results are presented using data visualization. We conclude that the estimator we derive and tests we propose perform well in many cases. Finally, a numerical example is presented.

Heterozygosity mapping for human dominant trait variants.

Homozygosity mapping is a well‐known technique to identify runs of homozygous variants that are likely to harbor genes responsible for autosomal recessive disease, but a comparable method for autosomal dominant traits has been lacking. We developed an approach to map dominant disease genes based on heterozygosity frequencies of sequence variants in the immediate vicinity of a dominant trait. We demonstrate through theoretical analysis that DNA variants surrounding an inherited dominant disease variant tend to have increased heterozygosity compared with variants elsewhere in the genome. We confirm existence of this phenomenon in sequence data with known dominant pathogenic variants obtained on family members and in unrelated population controls. A computer‐based approach to estimating empirical significance levels associated with our test statistics shows genome‐wide p‐values smaller than 0.05 for many but not all of the individuals carrying a pathogenic variant.

Small sample equivalence tests for exponentiality

ABSTRACTWe consider small sample equivalence tests for exponentialy. Statistical inference in this setting is particularly challenging since equivalence testing procedures typically require much larger sample sizes, in comparison with classical “difference tests,” to perform well. We make use of Butler's marginal likelihood for the shape parameter of a gamma distribution in our development of small sample equivalence tests for exponentiality. We consider two procedures using the principle of confidence interval inclusion, four Bayesian methods, and the uniformly most powerful unbiased (UMPU) test where a saddlepoint approximation to the intractable distribution of a canonical sufficient statistic is used. We perform small sample simulation studies to assess the bias of our various tests and show that all of the Bayes posteriors we consider are integrable. Our simulation studies show that the saddlepoint-approximated UMPU method performs remarkably well for small sample sizes and is the only method that consistently exhibits an empirical significance level close to the nominal 5% level.

A heteroskedasticity robust Breusch–Pagan test for Contemporaneous correlation in dynamic panel data models

This paper proposes a heteroskedasticity-robust Breusch–Pagan test of the null hypothesis of zero cross-section (or contemporaneous) correlation in linear panel data models, without necessarily assuming independence of the cross-sections. The procedure allows for either fixed, strictly exogenous and/or lagged dependent regressor variables, as well as quite general forms of both non-normality and heteroskedasticity in the error distribution. The asymptotic validity of the test procedure is predicated on the number of time series observations, T, being large relative to the number of cross-section units, N, in that: either (i) N is fixed as T→∞; or, (ii) N2/T→0 as both T and N diverge, jointly, to infinity. Given this, it is not expected that asymptotic theory would necessarily provide an adequate guide to finite sample performance when T/N is “small”. Because of this we also propose, and establish asymptotic validity of, a number of wild bootstrap schemes designed to provide improved inference when T/N is small. Across a variety of experimental designs, a Monte Carlo study suggests that the predictions from asymptotic theory do, in fact, provide a good guide to the finite sample behaviour of the test when T is large relative to N. However, when T and N are of similar orders of magnitude, discrepancies between the nominal and empirical significance levels occur as predicted by the first-order asymptotic analysis. On the other hand, for all the experimental designs, the proposed wild bootstrap approximations do improve agreement between nominal and empirical significance levels, when T/N is small, with a recursive-design wild bootstrap scheme performing best, in general, and providing quite close agreement between the nominal and empirical significance levels of the test even when T and N are of similar size. Moreover, in comparison with the wild bootstrap “version” of the original Breusch–Pagan test (Godfrey and Yamagata, 2011) our experiments indicate that the corresponding version of the heteroskedasticity-robust Breusch–Pagan test appears reliable. As an illustration, the proposed tests are applied to a dynamic growth model for a panel of 20 OECD countries.

A simulation study of the Bennett test and Miller test for coefficients of variation

ABSTRACTIn the article, properties of the Bennett test and Miller test are analyzed. Assuming that the sample size is the same for each sample and considering the null hypothesis that the coefficients of variation for k populations are equal against the hypothesis that k − 1 coefficients of variation are the same but differ from the coefficient of variation for the kth population, the empirical significance level and the power of the test are studied. Moreover, the dependence of the test statistic and the power of the test on the ratio of coefficients of variation are considered. The analyses are performed on simulated data.

Simulation Study on Improved Shapiro–Wilk Tests for Normality

The article concerns tests for normality based on the Shapiro–Wilk W statistic. The constants in the test statistic are recalculated as those given in Shapiro and Wilk are incorrect. The empirical significance levels and power of improved tests have been evaluated in simulation study and compared to original ones. The improved tests were also applied to the multivariate case. In this case, we consider two implementations of the W statistic, the first one proposed by Srivastava and Hui and the other by Hanusz and Tarasinska. Empirical size of tests and their power have been compared to the Henze–Zirkler test.

Implementation of Competency-Based Curriculum in Medical Education: Perspective of Different Roles

This cross-sectional case study investigates the curriculum implementation at the School of Medicine at the Universidade Federal de São Carlos (UFSCar), comparing the perspectives of the different participant types involved in this training (i.e., students, lecturers, and preceptors) and the programme goals. The sample included 22 lecturers, 55 students, and 16 preceptors. The researchers created a structured questionnaire based on study indicators extracted from the following aspects of the educational programme: teaching and learning process, integration of competency areas, teaching and learning scenarios, integration of theory and practice, and assessment. A Likert scale with four response options was used to score the respondents' choices. The participants answered the questionnaire online, and the responses were entered into a MySQL database. Using this database, an analysis was conducted based on the subjects' responses and the indicators. Comparative analysis was performed using the bootstrap method for responses and analysis feasibility with a 5% empirical significance level. The teaching and learning process, integration of theory and practice, and assessment indicators were in agreement with the educational programme, while integration of competency areas and teaching and learning scenarios require greater attention to establish consistency with the educational programme and training qualifications.

Improving the J Test in the SARAR Model by Likelihood-based Estimation

It has been demonstrated recently that in small-to-medium samples the empirical significance levels of the asymptotic J-type tests for the SARAR model introduced by Kelejian (2008) can be controlled in many cases by the use of a bootstrap to construct a reference distribution. A feature of the popular GMM estimator in this context that deserves to receive more attention is that in small samples it will often deliver spatial parameter estimates that lie outside the invertibility region of the model. Using such illegitimate estimates to construct bootstrap samples is then problematic; the present paper finds that this practical obstacle may be removed by the use of quasi-maximum likelihood estimates that guarantee invertibility. The effects of different spatial weight patterns and sample size on the empirical significance levels and power of the tests are illustrated, and the paper demonstrates that estimation using QMLE, allied to a simple bootstrap, yields tests with reliable significance levels and reasonable power, in a majority of cases. RÉSUMÉ dans des échantillons petits à moyens, il est possible, dans de nombreux cas, de contrôler les niveaux à signification empirique des tests asymptotiques introduits par Kelejian (2008) à l'aide d'un ‘bootstrap’. Dans ce contexte, une caractéristique de l'estimateur GMM, très répandu, est qu'il fournit, dans de petits échantillons, des estimations de paramètres spatiaux situés hors de la région d'inversibilité du modèle. L'emploi de telles estimations illégitimes pour la réalisation d’échantillons ‘bootstrap’ devient alors problématique; la présente communication indique que l'on peut supprimer cet obstacle pratique en utilisant le QMLE garantissant l'inversibilité. Les effets des tendances du poids spatial et la taille des échantillons sur les niveaux d'importance et la puissance sont illustrés, et la communication démontre que le QMLE, allié à un simple ‘bootstrap’, permet de réaliser des tests offrant, dans la plupart des vas, des niveaux d'importance fiables et une puissance raisonnable. EXTRACTO En muestras entre pequeñas y medianas, los niveles de significancia empírica de las pruebas asintóticas de tipo J para el modelo SARAR introducidas por Kelejian (2008) pueden controlarse en muchos casos mediante el uso de un bootstrap. Una característica del popular estimador GMM dentro de este contexto es que en las muestras pequeñas, a menudo producirá estimaciones de parámetros espaciales que están fuera de la región de reversibilidad del modelo. No obstante, el empleo de este tipo de estimaciones ilegítimas para construir muestras bootstrap es problemático; el estudio actual muestra que este obstáculo práctico puede eliminarse mediante el uso del QMLE que garantiza la reversibilidad. Se ilustran los efectos de las pautas de peso espacial y del tamaño de la muestra sobre el poder y los niveles de significancia, y el estudio demuestra que el QMLE, aliado a un bootstrap simple, dota a las pruebas de niveles de significancia fiables y de un poder razonable, en la mayoría de los casos.

Multilocus association analysis under polygenic models

For each variant in a genome-wide association study, the risk allele is the one with an odds ratio greater than 1. For a given set of variants, the number of risk alleles in cases minus that in controls is evaluated and a p-value is obtained for this difference. Successive sums of these differences over the best 2, 3, etc. variants and associated p-values are obtained. The smallest such p-value is our genome-wide test statistic, for which an empirical significance level is obtained by permutation analysis. Applied to disease datasets, our approach furnishes significant results even with little single-locus effects.

Constrained inference in mixed-effects models for longitudinal data with application to hearing loss

In medical studies, endpoints are often measured for each patient longitudinally. The mixed-effects model has been a useful tool for the analysis of such data. There are situations in which the parameters of the model are subject to some restrictions or constraints. For example, in hearing loss studies, we expect hearing to deteriorate with time. This means that hearing thresholds which reflect hearing acuity will, on average, increase over time. Therefore, the regression coefficients associated with the mean effect of time on hearing ability will be constrained. Such constraints should be accounted for in the analysis. We propose maximum likelihood estimation procedures, based on the expectation-conditional maximization either algorithm, to estimate the parameters of the model while accounting for the constraints on them. The proposed methods improve, in terms of mean square error, on the unconstrained estimators. In some settings, the improvement may be substantial. Hypotheses testing procedures that incorporate the constraints are developed. Specifically, likelihood ratio, Wald, and score tests are proposed and investigated. Their empirical significance levels and power are studied using simulations. It is shown that incorporating the constraints improves the mean squared error of the estimates and the power of the tests. These improvements may be substantial. The methodology is used to analyze a hearing loss study.

Sex-Specific Association of Depression and a Haplotype in Leukotriene A4 Hydrolase Gene

To assess whether genetic variants involved in inflammation play a role in the sex difference in depression. Depression is, in part, genetically determined and inflammation has been implicated. Women are twice as likely to develop depression as men. We examined the association, separately in men and women, between seven single nucleotide polymorphisms (SNPs) in the arachidonate 5-lipoxygenase-activating protein (ALOX5AP) gene and 12 SNPs in the leukotriene A4 hydrolase (LTA4H) gene and depression in 1368 white subjects (30.4% female) referred for cardiovascular evaluation. Depression was defined as a score of >or=10 in the Patient Health Questionnaire 9. Single marker analysis was assessed by the chi(2) test. Haplotype-specific associations were performed, using likelihood ratio tests. Empirical significance levels were determined by permutation tests. Depressed individuals, comprising 14.5% of the total, were more likely to be female, current smokers, have a history of diabetes and myocardial infarction. None of the SNPs in the ALOX5AP gene, either singly or in combination, was associated with depression. The 12 SNPs in the LTA4H gene were not individually associated with depression. However, a six-SNP haplotype in LTA4H gene, named HapE, showed a significant protective effect on depression in women, but not in men, after correcting for cardiovascular effects. The interaction between HapE and sex on depression was statistically significant. This study provides the first evidence for a sex-specific association of a novel haplotype in the LTA4H gene on depression. Although replication is needed, our study suggests that genetic variations may underlie sex differences in depression.

Genomewide linkage scans for ocular refraction and meta-analysis of four populations in the Myopia Family Study.

Genomewide linkage scans were performed in Caucasian (CAUC) and Old Order Amish (OOA) families to identify genomic regions containing genes responsible for refractive error control. We also performed a meta-analysis by combining these results with our previous linkage results from Ashkenazi Jewish (ASHK) and African American (AFRAM) families. Two hundred seventy-one CAUC and 411 OOA participants (36 and 61 families, respectively) were recruited to participate in the Myopia Family Study. Recruitment criteria were designed to enrich the sample for multiplex myopic families. Genomewide, model-free, multipoint linkage analyses were performed separately for each population by using >370 microsatellite markers. Empirical significance levels were determined via gene-dropping simulations. A meta-analysis was performed by combining linkage results from the CAUC, OOA, AFRAM, and ASHK samples, and results were compared to previously reported loci for myopia and refraction. Suggestive evidence of linkage was found at 12q24 (LOD = 4.583, P = 0.00037) and 4q21 (LOD = 2.72, P = 0.0028) in the CAUC sample and at 5qter (LOD = 3.271, P = 0.0014) in the OOA. Meta-analysis linkage results were largely driven by population-specific signals from ASHK and AFRAM families. The meta-analysis showed suggestive evidence of linkage to 4q21-22 (meta-P = 0.00214) adjacent to the previously reported MYP9 and MYP11 loci. The results showed suggestive evidence of linkage of ocular refraction to 12q24 and 4q21 in CAUC and to 5qter in OOA families. The meta-analysis supports the view that several genes play a role in refractive development across populations. In MFS families, four broad genomic regions (on 1p, 4q, 7p, and 12q) most likely contain genes that influence ocular refraction.

Genomewide scan of ocular refraction in African‐American families shows significant linkage to chromosome 7p15

Refractive development is influenced by environmental and genetic factors. Genetic studies have identified several regions of linkage to ocular refraction, but none have been carried out in African-derived populations. We performed quantitative trait locus linkage analyses in African-American (AA) families to identify genomic regions responsible for refraction. We recruited 493 AA individuals in 96 families to participate in the Myopia Family Study. Genotyping of 387 microsatellite markers was performed on 398 participants. The mean refraction among genotyped individuals was -2.87 D (SD=3.58) and myopia of at least 1 D was present in 267 (68%) participants. Multipoint, regression-based, linkage analyses were carried out on a logarithmic transformation of ocular refraction using the statistical package MERLIN-REGRESS. Empirical significance levels were determined via 4,898 whole-genome gene-dropping simulations. Linkage analyses were repeated after clustering families into two subgroups based on admixture proportions as determined by the software package STRUCTURE. Genomewide significant linkage was seen at 47 cM on chromosome 7 (logarithm of the odds ratio (LOD)=5.87, P=0.00005). In addition, three regions on chromosomes 2p, 3p and 10p showed suggestive evidence of linkage (LOD>2, P<0.005) for ocular refraction. We mapped the first quantitative trait locus for ocular refraction in an AA population to chr.7p15. Two previous studies in European-derived families reported some evidence of linkage to a nearby region, suggesting that this region may contain polymorphisms that mediate refraction across populations. The genomic region under our linkage peak spans approximately 17 Mb and contains approximately 170 genes. Further refinement of this region will be pursued in future studies.