Quantifying posterior effect size distribution of susceptibility loci by common summary statistics.

Testing millions of single nucleotide polymorphisms (SNPs) in genetic association studies has become a standard routine for disease gene discovery. In light of recent re-evaluation of statistical practice, it has been suggested that p-values are unfit as summaries of statistical evidence. Despite this criticism, p-values contain information that can be utilized to address the concerns about their flaws. We present a new method for utilizing evidence summarized by p-values for estimating odds ratio (OR) based on its approximate posterior distribution. In our method, only p-values, sample size, and standard deviation for ln(OR) are needed as summaries of data, accompanied by a suitable prior distribution for ln(OR) that can assume any shape. The parameter of interest, ln(OR), is the only parameter with a specified prior distribution, hence our model is a mix of classical and Bayesian approaches. We show that our method retains the main advantages of the Bayesian approach: it yields direct probability statements about hypotheses for OR and is resistant to biases caused by selection of top-scoring SNPs. Our method enjoys greater flexibility than similarly inspired methods in the assumed distribution for the summary statistic and in the form of the prior for the parameter of interest. We illustrate our method by presenting interval estimates of effect size for reported genetic associations with lung cancer. Although we focus on OR, the method is not limited to this particular measure of effect size and can be used broadly for assessing reliability of findings in studies testing multiple predictors.

DOT: Gene-set analysis by combining decorrelated association statistics.

Historically, the majority of statistical association methods have been designed assuming availability of SNP-level information. However, modern genetic and sequencing data present new challenges to access and sharing of genotype-phenotype datasets, including cost of management, difficulties in consolidation of records across research groups, etc. These issues make methods based on SNP-level summary statistics particularly appealing. The most common form of combining statistics is a sum of SNP-level squared scores, possibly weighted, as in burden tests for rare variants. The overall significance of the resulting statistic is evaluated using its distribution under the null hypothesis. Here, we demonstrate that this basic approach can be substantially improved by decorrelating scores prior to their addition, resulting in remarkable power gains in situations that are most commonly encountered in practice; namely, under heterogeneity of effect sizes and diversity between pairwise LD. In these situations, the power of the traditional test, based on the added squared scores, quickly reaches a ceiling, as the number of variants increases. Thus, the traditional approach does not benefit from information potentially contained in any additional SNPs, while our decorrelation by orthogonal transformation (DOT) method yields steady gain in power. We present theoretical and computational analyses of both approaches, and reveal causes behind sometimes dramatic difference in their respective powers. We showcase DOT by analyzing breast cancer and cleft lip data, in which our method strengthened levels of previously reported associations and implied the possibility of multiple new alleles that jointly confer disease risk.

The more you test, the more you find: The smallest P-values become increasingly enriched with real findings as more tests are conducted.

The increasing accessibility of data to researchers makes it possible to conduct massive amounts of statistical testing. Rather than follow specific scientific hypotheses with statistical analysis, researchers can now test many possible relationships and let statistics generate hypotheses for them. The field of genetic epidemiology is an illustrative case, where testing of candidate genetic variants for association with an outcome has been replaced by agnostic screening of the entire genome. Poor replication rates of candidate gene studies have improved dramatically with the increase in genomic coverage, due to factors such as adoption of better statistical practices and availability of larger sample sizes. Here, we suggest that another important factor behind the improved replicability of genome-wide scans is an increase in the amount of statistical testing itself. We show that an increase in the number of tested hypotheses increases the proportion of true associations among the variants with the smallest P-values. We develop statistical theory to quantify how the expected proportion of genuine signals (EPGS) among top hits depends on the number of tests. This enrichment of top hits by real findings holds regardless of whether genome-wide statistical significance has been reached in a study. Moreover, if we consider only those "failed" studies that produce no statistically significant results, the same enrichment phenomenon takes place: the proportion of true associations among top hits grows with the number of tests. The enrichment occurs even if the true signals are encountered at the logarithmically decreasing rate with the additional testing.

Uncovering Local Trends in Genetic Effects of Multiple Phenotypes via Functional Linear Models.

Recent technological advances equipped researchers with capabilities that go beyond traditional genotyping of loci known to be polymorphic in a general population. Genetic sequences of study participants can now be assessed directly. This capability removed technology-driven bias toward scoring predominantly common polymorphisms and let researchers reveal a wealth of rare and sample-specific variants. Although the relative contributions of rare and common polymorphisms to trait variation are being debated, researchers are faced with the need for new statistical tools for simultaneous evaluation of all variants within a region. Several research groups demonstrated flexibility and good statistical power of the functional linear model approach. In this work we extend previous developments to allow inclusion of multiple traits and adjustment for additional covariates. Our functional approach is unique in that it provides a nuanced depiction of effects and interactions for the variables in the model by representing them as curves varying over a genetic region. We demonstrate flexibility and competitive power of our approach by contrasting its performance with commonly used statistical tools and illustrate its potential for discovery and characterization of genetic architecture of complex traits using sequencing data from the Dallas Heart Study.

Previous GWAS hits in relation to young-onset breast cancer.

PURPOSE: Genome-wide association studies (GWAS) have identified dozens of single-nucleotide polymorphisms (SNPs) associated with breast cancer. Few studies focused on young-onset breast cancer, which exhibits etiologic and tumor-type differences from older-onset disease. Possible confounding by prenatal effects of the maternal genome has also not been considered. METHODS: Using a family-based design for breast cancer before age 50, we assessed the relationship between breast cancer and 77 GWAS-identified breast cancer risk SNPs. We estimated relative risks (RR) for inherited and maternally mediated genetic effects. We also used published RR estimates to calculate genetic risk scores and model joint effects. RESULTS: Seventeen of the candidate SNPs were nominally associated with young-onset breast cancer in our 1296 non-Hispanic white affected families (uncorrected p value <0.05). Top-ranked SNPs included rs3803662-A (TOX3, RR = 1.39; p = 7.0 × 10-6), rs12662670-G (ESR1, RR = 1.56; p = 5.7 × 10-4), rs2981579-A (FGFR2, RR = 1.24; p = 0.002), and rs999737-G (RAD51B, RR = 1.37; p = 0.003). No maternally mediated effects were found. A risk score based on all 77 SNPs indicated that their overall relationship to young-onset breast cancer risk was more than additive (additive-fit p = 2.2 × 10-7) and consistent with a multiplicative joint effect (multiplicative-fit p = 0.27). With the multiplicative formulation, the case sister's genetic risk score exceeded that of her unaffected sister in 59% of families. CONCLUSIONS: The results of this family-based study indicate that no effects of previously identified risk SNPs were explained by prenatal effects of maternal variants. Many of the known breast cancer risk variants were associated with young-onset breast cancer, with evidence that TOX3, ESR1, FGFR2, and RAD51B are important for young-onset disease.

Integrative framework for identification of key cell identity genes uncovers determinants of ES cell identity and homeostasis.

Identification of genes associated with specific biological phenotypes is a fundamental step toward understanding the molecular basis underlying development and pathogenesis. Although RNAi-based high-throughput screens are routinely used for this task, false discovery and sensitivity remain a challenge. Here we describe a computational framework for systematic integration of published gene expression data to identify genes defining a phenotype of interest. We applied our approach to rank-order all genes based on their likelihood of determining ES cell (ESC) identity. RNAi-mediated loss-of-function experiments on top-ranked genes unearthed many novel determinants of ESC identity, thus validating the derived gene ranks to serve as a rich and valuable resource for those working to uncover novel ESC regulators. Underscoring the value of our gene ranks, functional studies of our top-hit Nucleolin (Ncl), abundant in stem and cancer cells, revealed Ncl's essential role in the maintenance of ESC homeostasis by shielding against differentiation-inducing redox imbalance-induced oxidative stress. Notably, we report a conceptually novel mechanism involving a Nucleolin-dependent Nanog-p53 bistable switch regulating the homeostatic balance between self-renewal and differentiation in ESCs. Our findings connect the dots on a previously unknown regulatory circuitry involving genes associated with traits in both ESCs and cancer and might have profound implications for understanding cell fate decisions in cancer stem cells. The proposed computational framework, by helping to prioritize and preselect candidate genes for tests using complex and expensive genetic screens, provides a powerful yet inexpensive means for identification of key cell identity genes.

Large candidate gene association study reveals genetic risk factors and therapeutic targets for fibromyalgia.

OBJECTIVE: Fibromyalgia (FM) represents a complex disorder that is characterized by widespread pain and tenderness and is frequently accompanied by additional somatic and cognitive/affective symptoms. Genetic risk factors are known to contribute to the etiology of the syndrome. The aim of this study was to examine >350 genes for association with FM, using a large-scale candidate gene approach. METHODS: The study group comprised 496 patients with FM (cases) and 348 individuals with no chronic pain (controls). Genotyping was performed using a dedicated gene array chip, the Pain Research Panel, which assays variants characterizing >350 genes known to be involved in the biologic pathways relevant to nociception, inflammation, and mood. Association testing was performed using logistic regression. RESULTS: Significant differences in allele frequencies between cases and controls were observed for 3 genes: GABRB3 (rs4906902; P = 3.65 × 10(-6)), TAAR1 (rs8192619; P = 1.11 × 10(-5)), and GBP1 (rs7911; P = 1.06 × 10(-4)). These 3 genes and 7 other genes with suggestive evidence for association were examined in a second, independent cohort of patients with FM and control subjects who were genotyped using the Perlegen 600K platform. Evidence of association in the replication cohort was observed for TAAR1, RGS4, CNR1, and GRIA4. CONCLUSION: Variation in these 4 replicated genes may serve as a basis for development of new diagnostic approaches, and the products of these genes may contribute to the pathophysiology of FM and represent potential targets for therapeutic action.

DOMINE: a comprehensive collection of known and predicted domain-domain interactions.

DOMINE is a comprehensive collection of known and predicted domain-domain interactions (DDIs) compiled from 15 different sources. The updated DOMINE includes 2285 new domain-domain interactions (DDIs) inferred from experimentally characterized high-resolution three-dimensional structures, and about 3500 novel predictions by five computational approaches published over the last 3 years. These additions bring the total number of unique DDIs in the updated version to 26,219 among 5140 unique Pfam domains, a 23% increase compared to 20,513 unique DDIs among 4346 unique domains in the previous version. The updated version now contains 6634 known DDIs, and features a new classification scheme to assign confidence levels to predicted DDIs. DOMINE will serve as a valuable resource to those studying protein and domain interactions. Most importantly, DOMINE will not only serve as an excellent reference to bench scientists testing for new interactions but also to bioinformaticans seeking to predict novel protein-protein interactions based on the DDIs. The contents of the DOMINE are available at http://domine.utdallas.edu.

Pain perception is altered by a nucleotide polymorphism in SCN9A.

The gene SCN9A is responsible for three human pain disorders. Nonsense mutations cause a complete absence of pain, whereas activating mutations cause severe episodic pain in paroxysmal extreme pain disorder and primary erythermalgia. This led us to investigate whether single nucleotide polymorphisms (SNPs) in SCN9A were associated with differing pain perception in the general population. We first genotyped 27 SCN9A SNPs in 578 individuals with a radiographic diagnosis of osteoarthritis and a pain score assessment. A significant association was found between pain score and SNP rs6746030; the rarer A allele was associated with increased pain scores compared to the commoner G allele (P = 0.016). This SNP was then further genotyped in 195 pain-assessed people with sciatica, 100 amputees with phantom pain, 179 individuals after lumbar discectomy, and 205 individuals with pancreatitis. The combined P value for increased A allele pain was 0.0001 in the five cohorts tested (1277 people in total). The two alleles of the SNP rs6746030 alter the coding sequence of the sodium channel Nav1.7. Each was separately transfected into HEK293 cells and electrophysiologically assessed by patch-clamping. The two alleles showed a difference in the voltage-dependent slow inactivation (P = 0.042) where the A allele would be predicted to increase Nav1.7 activity. Finally, we genotyped 186 healthy females characterized by their responses to a diverse set of noxious stimuli. The A allele of rs6746030 was associated with an altered pain threshold and the effect mediated through C-fiber activation. We conclude that individuals experience differing amounts of pain, per nociceptive stimulus, on the basis of their SCN9A rs6746030 genotype.

P-value based analysis for shared controls design in genome-wide association studies.

An appealing genome-wide association study design compares one large control group against several disease samples. A pioneering study by the Wellcome Trust Case Control Consortium that employed such a design has identified multiple susceptibility regions, many of which have been independently replicated. While reusing a control sample provides effective utilization of data, it also creates correlation between association statistics across diseases. An observation of a large association statistic for one of the diseases may greatly increase chances of observing a spuriously large association for a different disease. Accounting for the correlation is also particularly important when screening for SNPs that might be involved in a set of diseases with overlapping etiology. We describe methods that correct association statistics for dependency due to shared controls, and we describe ways to obtain a measure of overall evidence and to combine association signals across multiple diseases. The methods we describe require no access to individual subject data, instead, they efficiently utilize information contained in P-values for association reported for individual diseases. P-value based combined tests for association are flexible and essentially as powerful as the approach based on aggregating the individual subject data.

Using imputed genotypes for relative risk estimation in case-parent studies.

Meta-analyses of genome-wide association studies are often based on imputed single nucleotide polymorphism (SNP) data, because component studies were genotyped using different platforms. One would like to include case-parent triad studies along with case-control studies in such meta-analyses. However, there are no published methods for estimating relative risks from imputed data for case-parent triad studies. The authors propose a method for estimating the relative risk for a variant SNP allele based on a log-additive model. Their simulations first confirm that the proposed method performs well with genotyped SNP data. As an empirical test of the method's behavior with imputed SNPs, the authors then apply it to chromosome 22 data from the Mexico City Childhood Asthma Study (1998-2003). For chromosome 22, the authors had data on 7,293 SNPs that were both genotyped and imputed using the software MACH, which relies on linkage disequilibrium with nearby SNPs. Correlation between estimated relative risks based on the actual genotypes and those based on the imputed genotypes was remarkably high (r(2) = 0.95), validating this method of relative risk estimation for the case-parent study design. This method should be useful to investigators who wish to conduct meta-analyses using imputed SNP data from both case-parent triad and case-control studies.

Expansion of the human mu-opioid receptor gene architecture: novel functional variants.

The mu-opioid receptor (OPRM1) is the principal receptor target for both endogenous and exogenous opioid analgesics. There are substantial individual differences in human responses to painful stimuli and to opiate drugs that are attributed to genetic variations in OPRM1. In searching for new functional variants, we employed comparative genome analysis and obtained evidence for the existence of an expanded human OPRM1 gene locus with new promoters, alternative exons and regulatory elements. Examination of polymorphisms within the human OPRM1 gene locus identified strong association between single nucleotide polymorphism (SNP) rs563649 and individual variations in pain perception. SNP rs563649 is located within a structurally conserved internal ribosome entry site (IRES) in the 5'-UTR of a novel exon 13-containing OPRM1 isoforms (MOR-1K) and affects both mRNA levels and translation efficiency of these variants. Furthermore, rs563649 exhibits very strong linkage disequilibrium throughout the entire OPRM1 gene locus and thus affects the functional contribution of the corresponding haplotype that includes other functional OPRM1 SNPs. Our results provide evidence for an essential role for MOR-1K isoforms in nociceptive signaling and suggest that genetic variations in alternative OPRM1 isoforms may contribute to individual differences in opiate responses.

Multiple chronic pain states are associated with a common amino acid-changing allele in KCNS1.

Not all patients with nerve injury develop neuropathic pain. The extent of nerve damage and age at the time of injury are two of the few risk factors identified to date. In addition, preclinical studies show that neuropathic pain variance is heritable. To define such factors further, we performed a large-scale gene profiling experiment which plotted global expression changes in the rat dorsal root ganglion in three peripheral neuropathic pain models. This resulted in the discovery that the potassium channel alpha subunit KCNS1, involved in neuronal excitability, is constitutively expressed in sensory neurons and markedly downregulated following nerve injury. KCNS1 was then characterized by an unbiased network analysis as a putative pain gene, a result confirmed by single nucleotide polymorphism association studies in humans. A common amino acid changing allele, the 'valine risk allele', was significantly associated with higher pain scores in five of six independent patient cohorts assayed (total of 1359 subjects). Risk allele prevalence is high, with 18-22% of the population homozygous, and an additional 50% heterozygous. At lower levels of nerve damage (lumbar back pain with disc herniation) association with greater pain outcome in homozygote patients is P = 0.003, increasing to P = 0.0001 for higher levels of nerve injury (limb amputation). The combined P-value for pain association in all six cohorts tested is 1.14 E-08. The risk profile of this marker is additive: two copies confer the most, one intermediate and none the least risk. Relative degrees of enhanced risk vary between cohorts, but for patients with lumbar back pain, they range between 2- and 3-fold. Although work still remains to define the potential role of this protein in the pathogenic process, here we present the KCNS1 allele rs734784 as one of the first prognostic indicators of chronic pain risk. Screening for this allele could help define those individuals prone to a transition to persistent pain, and thus requiring therapeutic strategies or lifestyle changes that minimize nerve injury.

Multi-ethnic GWAS and meta-analysis of sleep quality identify MPP6 as a novel gene that functions in sleep center neurons.

Poor sleep quality can have harmful health consequences. Although many aspects of sleep are heritable, the understandings of genetic factors involved in its physiology remain limited. Here, we performed a genome-wide association study (GWAS) using the Pittsburgh Sleep Quality Index (PSQI) in a multi-ethnic discovery cohort (n = 2868) and found two novel genome-wide loci on chromosomes 2 and 7 associated with global sleep quality. A meta-analysis in 12 independent cohorts (100 000 individuals) replicated the association on chromosome 7 between NPY and MPP6. While NPY is an important sleep gene, we tested for an independent functional role of MPP6. Expression data showed an association of this locus with both NPY and MPP6 mRNA levels in brain tissues. Moreover, knockdown of an orthologue of MPP6 in Drosophila melanogaster sleep center neurons resulted in decreased sleep duration. With convergent evidence, we describe a new locus impacting human variability in sleep quality through known NPY and novel MPP6 sleep genes.

A functional polymorphism in the ATP-Binding Cassette B1 transporter predicts pharmacologic response to combination of nortriptyline and morphine in neuropathic pain patients.

Many genetic markers have been associated with variations in treatment response to analgesics, but none have been assessed in the context of combination therapies. In this study, the treatment effects of nortriptyline and morphine were tested for an association with genetic markers relevant to pain pathways. Treatment effects were determined for single and combination therapies. A total of 24 functional single nucleotide polymorphisms were tested within the gene loci of mu-opioid receptor (OPRM1) gene locus, ATP-Binding Cassette B1 Transporter (ABCB1), Cytochrome P450 gene family (CYP2C19 and CYP2D6), catecholamine inactivator Catechol-O-Methyl Transferase (COMT), and serotonin receptor 2A (HTR2A). Genotyping was performed in a population of neuropathic pain patients who previously participated in a clinical trial. For monotherapy, neither nortriptyline nor morphine responses were associated with single nucleotide polymorphisms. However, for nortriptyline + morphine combination therapy, the single nucleotide polymorphism rs1045642 within the drug efflux pump ABCB1 transporter significantly predicted analgesic response. The presence of the C allele accounted for 51% of pain variance in this subgroup in response to combination treatment. The T-allele homozygotes demonstrated only 20% improvement in pain scores, whereas the C-allele homozygotes 88%. There was no significant contribution of rs1045642 to the medication side effects under all treatment conditions. The UK Biobank data set was then used to validate this genetic association. Here, patients receiving similar combination therapy (opioid + tricyclic antidepressant) carrying the C allele of rs1045642 displayed 33% fewer body pain sites than patients without that allele, suggesting better pain control. In all, our results show a robust effect of the rs1045642 polymorphism in response to chronic pain treatment with a nortriptyline + morphine combination.

Correlation-based inference for linkage disequilibrium with multiple alleles.

The correlation between alleles at a pair of genetic loci is a measure of linkage disequilibrium. The square of the sample correlation multiplied by sample size provides the usual test statistic for the hypothesis of no disequilibrium for loci with two alleles and this relation has proved useful for study design and marker selection. Nevertheless, this relation holds only in a diallelic case, and an extension to multiple alleles has not been made. Here we introduce a similar statistic, R2, which leads to a correlation-based test for loci with multiple alleles: for a pair of loci with k and m alleles, and a sample of n individuals, the approximate distribution of n(k - 1)(m - 1)/(km)R2 under independence between loci is chi2(k-1(m-1). One advantage of this statistic is that it can be interpreted as the total correlation between a pair of loci. When the phase of two-locus genotypes is known, the approach is equivalent to a test for the overall correlation between rows and columns in a contingency table. In the phase-known case, R2 is the sum of the squared sample correlations for all km 2 x 2 subtables formed by collapsing to one allele vs. the rest at each locus. We examine the approximate distribution under the null of independence for R2 and report its close agreement with the exact distribution obtained by permutation. The test for independence using R2 is a strong competitor to approaches such as Pearson's chi square, Fisher's exact test, and a test based on Cressie and Read's power divergence statistic. We combine this approach with our previous composite-disequilibrium measures to address the case when the genotypic phase is unknown. Calculation of the new multiallele test statistic and its P-value is very simple and utilizes the approximate distribution of R2. We provide a computer program that evaluates approximate as well as "exact" permutational P-values.

Detecting Weak Signals by Combining Small P-Values in Genetic Association Studies.

We approach the problem of combining top-ranking association statistics or P-values from a new perspective which leads to a remarkably simple and powerful method. Statistical methods, such as the rank truncated product (RTP), have been developed for combining top-ranking associations, and this general strategy proved to be useful in applications for detecting combined effects of multiple disease components. To increase power, these methods aggregate signals across top ranking single nucleotide polymorphisms (SNPs), while adjusting for their total number assessed in a study. Analytic expressions for combined top statistics or P-values tend to be unwieldy, which complicates interpretation and practical implementation and hinders further developments. Here, we propose the augmented rank truncation (ART) method that retains main characteristics of the RTP but is substantially simpler to implement. ART leads to an efficient form of the adaptive algorithm, an approach where the number of top ranking SNPs is varied to optimize power. We illustrate our methods by strengthening previously reported associations of µ-opioid receptor variants with sensitivity to pain.

Genome-wide association reveals contribution of MRAS to painful temporomandibular disorder in males.

Painful temporomandibular disorders (TMDs) are the leading cause of chronic orofacial pain, but its underlying molecular mechanisms remain obscure. Although many environmental factors have been associated with higher risk of developing painful TMD, family and twin studies support a heritable genetic component as well. We performed a genome-wide association study assuming an additive genetic model of TMD in a discovery cohort of 999 cases and 2031 TMD-free controls from the Orofacial Pain: Prospective Evaluation and Risk Assessment (OPPERA) study. Using logistic models adjusted for sex, age, enrollment site, and race, we identified 3 distinct loci that were significant in combined or sex-segregated analyses. A single-nucleotide polymorphism on chromosome 3 (rs13078961) was significantly associated with TMD in males only (odds ratio = 2.9, 95% confidence interval: 2.02-4.27, P = 2.2 × 10). This association was nominally replicated in a meta-analysis of 7 independent orofacial pain cohorts including 160,194 participants (odds ratio = 1.16, 95% confidence interval: 1.0-1.35, P = 2.3 × 10). Functional analysis in human dorsal root ganglia and blood indicated this variant is an expression quantitative trait locus, with the minor allele associated with decreased expression of the nearby muscle RAS oncogene homolog (MRAS) gene (beta = -0.51, P = 2.43 × 10). Male mice, but not female mice, with a null mutation of Mras displayed persistent mechanical allodynia in a model of inflammatory pain. Genetic and behavioral evidence support a novel mechanism by which genetically determined MRAS expression moderates the resiliency to chronic pain. This effect is male-specific and may contribute to the lower rates of painful TMD in men.

Bayesian prediction intervals for assessing P-value variability in prospective replication studies.

Increased availability of data and accessibility of computational tools in recent years have created an unprecedented upsurge of scientific studies driven by statistical analysis. Limitations inherent to statistics impose constraints on the reliability of conclusions drawn from data, so misuse of statistical methods is a growing concern. Hypothesis and significance testing, and the accompanying P-values are being scrutinized as representing the most widely applied and abused practices. One line of critique is that P-values are inherently unfit to fulfill their ostensible role as measures of credibility for scientific hypotheses. It has also been suggested that while P-values may have their role as summary measures of effect, researchers underappreciate the degree of randomness in the P-value. High variability of P-values would suggest that having obtained a small P-value in one study, one is, ne vertheless, still likely to obtain a much larger P-value in a similarly powered replication study. Thus, "replicability of P-value" is in itself questionable. To characterize P-value variability, one can use prediction intervals whose endpoints reflect the likely spread of P-values that could have been obtained by a replication study. Unfortunately, the intervals currently in use, the frequentist P-intervals, are based on unrealistic implicit assumptions. Namely, P-intervals are constructed with the assumptions that imply substantial chances of encountering large values of effect size in an observational study, which leads to bias. The long-run frequentist probability provided by P-intervals is similar in interpretation to that of the classical confidence intervals, but the endpoints of any particular interval lack interpretation as probabilistic bounds for the possible spread of future P-values that may have been obtained in replication studies. Along with classical frequentist intervals, there exists a Bayesian viewpoint toward interval construction in which the endpoints of an interval have a meaningful probabilistic interpretation. We propose Bayesian intervals for prediction of P-value variability in prospective replication studies. Contingent upon approximate prior knowledge of the effect size distribution, our proposed Bayesian intervals have endpoints that are directly interpretable as probabilistic bounds for replication P-values, and they are resistant to selection bias. We showcase our approach by its application to P-values reported for five psychiatric disorders by the Psychiatric Genomics Consortium group.

Genome-Wide Association Analysis of the Sense of Smell in U.S. Older Adults: Identification of Novel Risk Loci in African-Americans and European-Americans.

The human sense of smell decreases with age, and a poor sense of smell are among the most important prodromal symptoms of several neurodegenerative diseases. Recent evidence further suggests a racial difference in the sense of smell among U.S. older adults. However, no genome-wide association study (GWAS) on the sense of smell has been conducted in African-Americans (AAs). We performed the first genome-wide meta-analysis of the sense of smell among 1979 AAs and 6582 European-Americans (EAs) from three U.S. aging cohorts. In the AA population, we identified nine novel regions (KLF4-ACTL7B, RAPGEF2-FSTL5, TCF4-LOC100505474, PCDH10, KIAA1751, MYO5B, MIR320B1-CD2, NR5A2-LINC00862, SALL1-C16orf97) that were associated with the sense of smell (P < 5 × 10-8). Many of these regions have been previously linked to neuropsychiatric (schizophrenia or epilepsy) or neurodegenerative (Parkinson's or Alzheimer's disease) diseases associated with a decreased sense of smell. In the EA population, we identified two novel loci in or near RASGRP1 and ANXA2P3 associated with sense of smell. In conclusion, this study identified several ancestry-specific loci that are associated with the sense of smell in older adults. While these findings need independent confirmation, they may lead to novel insights into the biology of the sense of smell in older adults and its relationships to neuropsychological and neurodegenerative diseases.