The cost of large numbers of hypothesis tests on power, effect size and sample size

Advances in high-throughput biology and computer science are driving an exponential increase in the number of hypothesis tests in genomics and other scientific disciplines. Studies using current genotyping platforms frequently include a million or more tests. In addition to the monetary cost, this increase imposes a statistical cost owing to the multiple testing corrections needed to avoid large numbers of false-positive results. To safeguard against the resulting loss of power, some have suggested sample sizes on the order of tens of thousands that can be impractical for many diseases or may lower the quality of phenotypic measurements. This study examines the relationship between the number of tests on the one hand and power, detectable effect size or required sample size on the other. We show that once the number of tests is large, power can be maintained at a constant level, with comparatively small increases in the effect size or sample size. For example at the 0.05 significance level, a 13% increase in sample size is needed to maintain 80% power for ten million tests compared with one million tests, whereas a 70% increase in sample size is needed for 10 tests compared with a single test. Relative costs are less when measured by increases in the detectable effect size. We provide an interactive Excel calculator to compute power, effect size or sample size when comparing study designs or genome platforms involving different numbers of hypothesis tests. The results are reassuring in an era of extreme multiple testing

Trend-TDT – a transmission/disequilibrium based association test on functional mini/microsatellites

<p>Abstract</p> <p>Background</p> <p>Minisatellites and microsatellites are associated with human disease, not only as markers of risk but also involved directly in disease pathogenesis. They may play significant roles in replication, repair and mutation of DNA, regulation of gene transcription and protein structure alteration. Phenotypes can thus be affected by mini/microsatellites in a manner proportional to the length of the allele. Here we propose a new method to assess the linear trend toward transmission of shorter or longer alleles from heterozygote parents to affected child.</p> <p>Results</p> <p>This test (trend-TDT) performs better than other TDT (Transmission/Disequilibrium Test) type tests, such as TDT_maxand TDT_L/S, under most marker-disease association models.</p> <p>Conclusion</p> <p>The trend-TDT test is a more powerful association test when there is a biological basis to suspect a relationship between allele length and disease risk.</p

Regional Variation in RBM20 Causes a Highly Penetrant Arrhythmogenic Cardiomyopathy

Background Variants in the cardiomyocyte-specific RNA splicing factor RBM20 have been linked to familial cardiomyopathy, but the causative genetic architecture and clinical consequences of this disease are incompletely defined. Methods and Results To define the genetic architecture of RBM20 cardiomyopathy, we first established a database of RBM20 variants associated with cardiomyopathy and compared these to variants observed in the general population with respect to their location in the RBM20 coding transcript. We identified 2 regions significantly enriched for cardiomyopathy-associated variants in exons 9 and 11. We then assembled a registry of 74 patients with RBM20 variants from 8 institutions across the world (44 index cases and 30 from cascade testing). This RBM20 patient registry revealed highly prevalent family history of sudden cardiac death (51%) and cardiomyopathy (72%) among index cases and a high prevalence of composite arrhythmias (including atrial fibrillation, nonsustained ventricular tachycardia, implantable cardiac defibrillator discharge, and sudden cardiac arrest, 43%). Patients harboring variants in cardiomyopathy-enriched regions identified by our variant database analysis were enriched for these findings. Further, these characteristics were more prevalent in the RBM20 registry than in large cohorts of patients with dilated cardiomyopathy and TTNtv cardiomyopathy and not significantly different from a cohort of patients with LMNA-associated cardiomyopathy. Conclusions Our data establish RBM20 cardiomyopathy as a highly penetrant and arrhythmogenic cardiomyopathy. These findings underline the importance of arrhythmia surveillance and family screening in this disease and represent the first step in defining the genetic architecture of RBM20 disease causality on a population level

Genome-wide association filtering using a highly locus-specific transmission/disequilibrium test

Multimarker transmission/disequilibrium tests (TDTs) are powerful association and linkage tests used to perform genome-wide filtering in the search for disease susceptibility loci. In contrast to case/control studies, they have a low rate of false positives for population stratification and admixture. However, the length of a region found in association with a disease is usually very large because of linkage disequilibrium (LD). Here, we define a multimarker proportional TDT (mTDTP) designed to improve locus specificity in complex diseases that has good power compared to the most powerful multimarker TDTs. The test is a simple generalization of a multimarker TDT in which haplotype frequencies are used to weight the effect that each haplotype has on the whole measure. Two concepts underlie the features of the metric: the ‘common disease, common variant’ hypothesis and the decrease in LD with chromosomal distance. Because of this decrease, the frequency of haplotypes in strong LD with common disease variants decreases with increasing distance from the disease susceptibility locus. Thus, our haplotype proportional test has higher locus specificity than common multimarker TDTs that assume a uniform distribution of haplotype probabilities. Because of the common variant hypothesis, risk haplotypes at a given locus are relatively frequent and a metric that weights partial results for each haplotype by its frequency will be as powerful as the most powerful multimarker TDTs. Simulations and real data sets demonstrate that the test has good power compared with the best tests but has remarkably higher locus specificity, so that the association rate decreases at a higher rate with distance from a disease susceptibility or disease protective locus

Genome-wide linkage analysis of inguinal hernia in pigs using affected sib pairs

BACKGROUND: Inguinal and scrotal hernias are of great concern to pig producers, and lead to poor animal welfare and severe economic loss. Selection against these conditions is highly preferable, but at this time no gene, Quantitative Trait Loci (QTL), or mode of inheritance has been identified in pigs or in any other species. Therefore, a complete genome scan was performed in order to identify genomic regions affecting inguinal and scrotal hernias in pigs. Records from seedstock breeding farms were collected. No clinical examinations were executed on the pigs and there was therefore no distinction between inguinal and scrotal hernias. The genome scan utilised affected sib pairs (ASP), and the data was analysed using both an ASP test based on Non-parametric Linkage (NPL) analysis, and a Transmission Disequilibrium Test (TDT). RESULTS: Significant QTLs (p < 0.01) were detected on 8 out of 19 porcine chromosomes. The most promising QTLs, however, were detected in SSC1, SSC2, SSC5, SSC6, SSC15, SSC17 and SSCX; all of these regions showed either statistical significance with both statistical methods, or convincing significance with one of the methods. Haplotypes from these suggestive QTL regions were constructed and analysed with TDT. Of these, six different haplotypes were found to be differently transmitted (p < 0.01) to healthy and affected pigs. The most interesting result was one haplotype on SSC5 that was found to be transmitted to hernia pigs with four times higher frequency than to healthy pigs (p < 0.00005). CONCLUSION: For the first time in any species, a genome scan has revealed suggestive QTLs for inguinal and scrotal hernias. While this study permitted the detection of chromosomal regions only, it is interesting to note that several promising candidate genes, including INSL3, MIS, and CGRP, are located within the highly significant QTL regions. Further studies are required in order to narrow down the suggestive QTL regions, investigate the candidate genes, and to confirm the suggestive QTLs in other populations. The haplotype associated with inguinal and scrotal hernias may help in achieving selection against the disorder

A P-value model for theoretical power analysis and its applications in multiple testing procedures

Background: Power analysis is a critical aspect of the design of experiments to detect an effect of a given size. When multiple hypotheses are tested simultaneously, multiplicity adjustments to p-values should be taken into account in power analysis. There are a limited number of studies on power analysis in multiple testing procedures. For some methods, the theoretical analysis is difficult and extensive numerical simulations are often needed, while other methods oversimplify the information under the alternative hypothesis. To this end, this paper aims to develop a new statistical model for power analysis in multiple testing procedures. Methods: We propose a step-function-based p-value model under the alternative hypothesis, which is simple enough to perform power analysis without simulations, but not too simple to lose the information from the alternative hypothesis. The first step is to transform distributions of different test statistics (e.g., t, chi-square or F) to distributions of corresponding p-values. We then use a step function to approximate each of the p-value’s distributions by matching the mean and variance. Lastly, the step-function-based p-value model can be used for theoretical power analysis. Results: The proposed model is applied to problems in multiple testing procedures. We first show how the most powerful critical constants can be chosen using the step-function-based p-value model. Our model is then applied to the field of multiple testing procedures to explain the assumption of monotonicity of the critical constants. Lastly, we apply our model to a behavioral weight loss and maintenance study to select the optimal critical constants. Conclusions: The proposed model is easy to implement and preserves the information from the alternative hypothesis

Updated measurements of exclusive J/ψ and ψ(2S) production cross-sections in pp collisions at √s = 7 TeV

The differential cross-section as a function of rapidity has been measured for the exclusive production of J/ψ and ψ(2S) mesons in proton–proton collisions at √s = 7 TeV, using data collected by the LHCb experiment, corresponding to an integrated luminosity of 930 pb−1. The cross-sections times branching fractions to two muons having pseudorapidities between 2.0 and 4.5 are measured to be where the first uncertainty is statistical and the second is systematic. The measurements agree with next-to-leading order QCD predictions as well as with models that include saturation effects

Studies of beauty baryon decays to D0ph− and Λ+ch− final states

Decays of beauty baryons to the D0ph− and Λ+ch− final states (where h indicates a pion or a kaon) are studied using a data sample of pp collisions, corresponding to an integrated luminosity of 1.0  fb−1, collected by the LHCb detector. The Cabibbo-suppressed decays Λ0b→D0pK− and Λ0b→Λ+cK− are observed, and their branching fractions are measured with respect to the decays Λ0b→D0pπ− and Λ0b→Λ+cπ−. In addition, the first observation is reported of the decay of the neutral beauty-strange baryon Ξ0b to the D0pK− final state, and a measurement of the Ξ0b mass is performed. Evidence of the Ξ0b→Λ+cK− decay is also reported