Type I Error
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AbstractPleiotropy (i.e., genes with effects on multiple traits) leads to genetic correlations between traits and contributes to the development of many syndromes. Identifying variants with pleiotropic effects on multiple health-related traits can improve the biological understanding of gene action and disease etiology, and can help to advance disease-risk prediction. Sequential testing is a powerful approach for mapping genes with pleiotropic effects. However, the existing methods and the available software do not scale to analyses involving millions of SNPs and large datasets. This has limited the adoption of sequential testing for pleiotropy mapping at large scale. In this study, we present a sequential test and software that can be used to test pleiotropy in large systems of traits with biobank-sized data. Using simulations, we show that the methods implemented in the software are powerful and have adequate type-I error rate control. To demonstrate the use of the methods and software, we present a whole-genome scan in search of loci with pleiotropic effects on seven traits related to metabolic syndrome (MetS) using UK-Biobank data (n~300 K distantly related white European participants). We found abundant pleiotropy and report 170, 44, and 18 genomic regions harboring SNPs with pleiotropic effects in at least two, three, and four of the seven traits, respectively. We validate our results using previous studies documented in the GWAS-catalog and using data from GTEx. Our results confirm previously reported loci and lead to several novel discoveries that link MetS-related traits through plausible biological pathways.
Analysis of variance (ANOVA) is one of the most popular statistical methods employed for data analysis in psychology and other fields. Nevertheless, ANOVA is frequently used as an exploratory approach, even in confirmatory studies with explicit hypotheses. Such misapplication may invalidate ANOVA conventions, resulting in reduced statistical power, and even threatening the validity of conclusions. This paper evaluates the appropriateness of ANOVA conventions, discusses the potential motivations possibly misunderstood by researchers, and provides practical suggestions. Moreover, this paper proposes to control the Type I error rate with Hypothesis-based Type I Error Rate to consider both the number of tests and their logical relationships in rejecting the null hypothesis. Furthermore, this paper introduces the simple interaction analysis, which can employ the most straightforward interaction to test a hypothesis of interest. Finally, pre-registration is recommended to provide clarity for the selection of appropriate ANOVA tests in both confirmatory and exploratory studies.
Although the bias-corrected (BC) bootstrap is an often-recommended method for testing mediation due to its higher statistical power relative to other tests, it has also been found to have elevated Type I error rates with small sample sizes. Under limitations for participant recruitment, obtaining a larger sample size is not always feasible. Thus, this study examines whether using alternative corrections for bias in the BC bootstrap test of mediation for small sample sizes can achieve equal levels of statistical power without the associated increase in Type I error. A simulation study was conducted to compare Efron and Tibshirani’s original correction for bias, z 0, to six alternative corrections for bias: (a) mean, (b–e) Winsorized mean with 10%, 20%, 30%, and 40% trimming in each tail, and (f) medcouple (robust skewness measure). Most variation in Type I error (given a medium effect size of one regression slope and zero for the other slope) and power (small effect size in both regression slopes) was found with small sample sizes. Recommendations for applied researchers are made based on the results. An empirical example using data from the ATLAS drug prevention intervention study is presented to illustrate these results. Limitations and future directions are discussed.
Directional-sum test for nonparametric Behrens-Fisher problem with applications to the dietary intervention trial
For a nonparametric Behrens-Fisher problem, a directional-sum test is proposed based on division-combination strategy. A one-layer wild bootstrap procedure is given to calculate its statistical significance. We conduct simulation studies with data generated from lognormal, t and Laplace distributions to show that the proposed test can control the type I error rates properly and is more powerful than the existing rank-sum and maximum-type tests under most of the considered scenarios. Applications to the dietary intervention trial further show the performance of the proposed test.
MCGA: a multi-strategy conditional gene-based association framework integrating with isoform-level expression profiles reveals new susceptible and druggable candidate genes of schizophrenia
Linkage disequilibrium and disease-associated variants in non-coding regions make it difficult to distinguish truly associated genes from redundantly associated genes for complex diseases. In this study, we proposed a new conditional gene-based framework called MCGA that leveraged an improved effective chi-squared statistic to control the type I error rates and remove the redundant associations. MCGA initially integrated two conventional strategies to map genetic variants to genes, i.e., mapping a variant to its physically nearby gene and mapping a variant to a gene if the variant is a gene-level expression quantitative trait locus (eQTL) of the gene. We further performed a simulation study and demonstrated that the isoform-level eQTL was more powerful than the gene-level eQTL in the association analysis. Then the third strategy, i.e., mapping a variant to a gene if the variant is an isoform-level eQTL of the gene, was also integrated with MCGA. We applied MCGA to predict the potential susceptibility genes of schizophrenia and found that the potential susceptibility genes identified by MCGA were enriched with many neuronal or synaptic signaling-related terms in the Gene Ontology knowledgebase and antipsychotics-gene interaction terms in the drug-gene interaction database (DGIdb). More importantly, nine susceptibility genes were the target genes of multiple approved antipsychotics in DrugBank. Comparing the susceptibility genes identified by the above three strategies implied that strategy based on isoform-level eQTL could be an important supplement for the other two strategies and help predict more candidate susceptibility isoforms and genes for complex diseases in a multi-tissue context.
AbstractIn many meta-analyses, the variable of interest is frequently a count outcome reported in an intervention and a control group. Single- or double-zero studies are often observed in this type of data. Given this setting, the well-known Cochran’s Q statistic for testing homogeneity becomes undefined. In this paper, we propose two statistics for testing homogeneity of the risk ratio, particularly for application in the case of rare events in meta-analysis. The first one is a chi-square type statistic. It is constructed based on information of the conditional probability of the number of events in the treatment group given the total number of events. The second one is a likelihood ratio statistic, derived from the logistic regression models allowing fixed and random effects for the risk ratio. Both proposed statistics are well defined even in the situation of single-zero studies. In a simulation study, the proposed tests show a performance better than the traditional test in terms of type I error and power of the test under common and rare event situations. However, as the performance of the two newly proposed tests is still unsatisfactory in the very rare events setting, we suggest a bootstrap approach that does not rely on asymptotic distributional theory and it is shown that the bootstrap approach performs well in terms of type I error. Furthermore, a number of empirical meta-analyses are used to illustrate the methods.
AbstractBackground:Little is known about how symptom severity in the various neurologic domains commonly affected by MS vary by age, sex and race/ethnicity.Methods:This was a retrospective study of MS patients attending two tertiary centers in the NYC metropolitan area, who self-identified as White, African-American (AA), or Hispanic-American (HA). Disability was rated with Patient-determined Disability steps (PDDS) and symptom severity - with SymptoMScreen (SyMS), a validated battery for assessing symptoms in 12 domains. Analyses comparing race, sex, and age groups were carried out using ANOVA Models and Tukey’s HSD multiple comparison tests to control the overall Type I error. A multivariable model was constructed to predict good self-rated health (SRH) that included demographic variables, PDDS and SyMS domain scores.Results:Sample consisted of 2,622 MS patients (age 46.4 years; 73.6% female; 66.4% White, 21.7% AA, 11.9% HA). Men had higher adjusted PDDS than women (p=0.012), but similar total SyMS score. Women reported higher fatigue and anxiety scores (more botheration), while men had higher walking and dexterity scores. AA and HA had higher symptom domain scores than Whites in each of the 12 domains and worse SRH. In a multivariable logistic model, only pain, walking, depression, fatigue, and global disability (PDDS), but not sex or race/ethnicity predicted good SRH.Conclusions:AA and HA race/ethnicity was associated with higher overall disability, higher symptom severity in each of the 12 domains commonly affected by MS, and worse self-rated health relative to Whites. However, only symptom severity and disability, and not demographic variables, predicted good self-rated health.
The correlation coefficient is the most commonly used measure for summarizing the magnitude and direction of linear relationship between two response variables. Considerable literature has been devoted to the inference procedures for significance tests and confidence intervals of correlations. However, the essential problem of evaluating correlation equivalence has not been adequately examined. For the purpose of expanding the usefulness of correlational techniques, this article focuses on the Pearson product-moment correlation coefficient and the Fisher’s z transformation for developing equivalence procedures of correlation coefficients. Equivalence tests are proposed to assess whether a correlation coefficient is within a designated reference range for declaring equivalence decisions. The important aspects of Type I error rate, power calculation, and sample size determination are also considered. Special emphasis is given to clarify the nature and deficiency of the two one-sided tests for detecting a lack of association. The findings demonstrate the inappropriateness of existing methods for equivalence appraisal and validate the suggested techniques as reliable and primary tools in correlation analysis.
Genome-wide association studies (GWAS) are among the workhorses of statistical genetics, having detected thousands of variants associated with complex traits and diseases. A typical GWAS examines the association between genotypes and the phenotype of interest while adjusting for a set of covariates. While covariates potentially have non-linear effects on the phenotype in many real world settings, due to the challenge of specifying the model, GWAS seldom include non-linear terms. Here we introduce DeepNull, a method that models non-linear covariate effects on phenotypes using a deep neural network (DNN) and then includes the model prediction as a single extra term in the GWAS association. First, using simulated data, we show that DeepNull increases statistical power by up to 20% while maintaining tight control of the type I error in the presence of interactions or non-linear covariate effects. Second, DeepNull maintains similar results to a standard GWAS when covariates have only linear effects on the phenotype. Third, DeepNull detects larger numbers of significant hits and loci (7% additional loci averaged over 10 traits) than standard GWAS in ten phenotypes from the UK Biobank (n=370K). Many of the hits found only by DeepNull are biologically plausible or have previously been reported in the GWAS catalog. Finally, DeepNull improves phenotype prediction by 23% averaged over the same ten phenotypes, the highest improvement was observed in the case of Glaucoma referral probability where DeepNull improves the phenotype prediction by 83%.