Gene-level association analysis of bivariate ordinal traits with functional regressions.

In genetic studies, many phenotypes have multiple naturally ordered discrete values. The phenotypes can be correlated with each other. If multiple correlated ordinal traits are analyzed simultaneously, the power of analysis may increase significantly while the false positives can be controlled well. In this study, we propose bivariate functional ordinal linear regression (BFOLR) models using latent regressions with cumulative logit link or probit link to perform a gene-based analysis for bivariate ordinal traits and sequencing data. In the proposed BFOLR models, genetic variant data are viewed as stochastic functions of physical positions, and the genetic effects are treated as a function of physical positions. The BFOLR models take the correlation of the two ordinal traits into account via latent variables. The BFOLR models are built upon functional data analysis which can be revised to analyze the bivariate ordinal traits and high-dimension genetic data. The methods are flexible and can analyze three types of genetic data: (1) rare variants only, (2) common variants only, and (3) a combination of rare and common variants. Extensive simulation studies show that the likelihood ratio tests of the BFOLR models control type I errors well and have good power performance. The BFOLR models are applied to analyze Age-Related Eye Disease Study data, in which two genes, CFH and ARMS2, are found to strongly associate with eye drusen size, drusen area, age-related macular degeneration (AMD) categories, and AMD severity scale.

Gene-level association analysis of ordinal traits with functional ordinal logistic regressions.

In this paper, we develop functional ordinal logistic regression (FOLR) models to perform gene-based analysis of ordinal traits. In the proposed FOLR models, genetic variant data are viewed as stochastic functions of physical positions and the genetic effects are treated as a function of physical positions. The FOLR models are built upon functional data analysis which can be revised to analyze the ordinal traits and high dimension genetic data. The proposed methods are capable of dealing with dense genotype data which is usually encountered in analyzing the next-generation sequencing data. The methods are flexible and can analyze three types of genetic data: (1) rare variants only, (2) common variants only, and (3) a combination of rare and common variants. Simulation studies show that the likelihood ratio test statistics of the FOLR models control type I errors well and have good power performance. The proposed methods achieve the goals of analyzing ordinal traits directly, reducing high dimensionality of dense genetic variants, being computationally manageable, facilitating model convergence, properly controlling type I errors, and maintaining high power levels. The FOLR models are applied to analyze Age-Related Eye Disease Study data, in which two genes are found to strongly associate with four ordinal traits.

Gene-based analysis of bi-variate survival traits via functional regressions with applications to eye diseases.

Genetic studies of two related survival outcomes of a pleiotropic gene are commonly encountered but statistical models to analyze them are rarely developed. To analyze sequencing data, we propose mixed effect Cox proportional hazard models by functional regressions to perform gene-based joint association analysis of two survival traits motivated by our ongoing real studies. These models extend fixed effect Cox models of univariate survival traits by incorporating variations and correlation of multivariate survival traits into the models. The associations between genetic variants and two survival traits are tested by likelihood ratio test statistics. Extensive simulation studies suggest that type I error rates are well controlled and power performances are stable. The proposed models are applied to analyze bivariate survival traits of left and right eyes in the age-related macular degeneration progression.

ComPaSS-GWAS: A method to reduce type I error in genome-wide association studies when replication data are not available.

Results from association studies are traditionally corroborated by replicating the findings in an independent data set. Although replication studies may be comparable for the main trait or phenotype of interest, it is unlikely that secondary phenotypes will be comparable across studies, making replication problematic. Alternatively, there may simply not be a replication sample available because of the nature or frequency of the phenotype. In these situations, an approach based on complementary pairs stability selection for genome-wide association study (ComPaSS-GWAS), is proposed as an ad-hoc alternative to replication. In this method, the sample is randomly split into two conditionally independent halves multiple times (resamples) and a GWAS is performed on each half in each resample. Similar in spirit to testing for association with independent discovery and replication samples, a marker is corroborated if its p-value is significant in both halves of the resample. Simulation experiments were performed for both nongenetic and genetic models. The type I error rate and power of ComPaSS-GWAS were determined and compared to the statistical properties of a traditional GWAS. Simulation results show that the type I error rate decreased as the number of resamples increased with only a small reduction in power and that these results were comparable with those from a traditional GWAS. Blood levels of vitamin pyridoxal 5'-phosphate from the Trinity Student Study (TSS) were used to validate this approach. The results from the validation study were compared to, and were consistent with, those obtained from previously published independent replication data and functional studies.

Gene-based association analysis of survival traits via functional regression-based mixed effect cox models for related samples.

The importance to integrate survival analysis into genetics and genomics is widely recognized, but only a small number of statisticians have produced relevant work toward this study direction. For unrelated population data, functional regression (FR) models have been developed to test for association between a quantitative/dichotomous/survival trait and genetic variants in a gene region. In major gene association analysis, these models have higher power than sequence kernel association tests. In this paper, we extend this approach to analyze censored traits for family data or related samples using FR based mixed effect Cox models (FamCoxME). The FamCoxME model effect of major gene as fixed mean via functional data analysis techniques, the local gene or polygene variations or both as random, and the correlation of pedigree members by kinship coefficients or genetic relationship matrix or both. The association between the censored trait and the major gene is tested by likelihood ratio tests (FamCoxME FR LRT). Simulation results indicate that the LRT control the type I error rates accurately/conservatively and have good power levels when both local gene or polygene variations are modeled. The proposed methods were applied to analyze a breast cancer data set from the Consortium of Investigators of Modifiers of BRCA1 and BRCA2 (CIMBA). The FamCoxME provides a new tool for gene-based analysis of family-based studies or related samples.

Linear mixed models for association analysis of quantitative traits with next-generation sequencing data.

We develop linear mixed models (LMMs) and functional linear mixed models (FLMMs) for gene-based tests of association between a quantitative trait and genetic variants on pedigrees. The effects of a major gene are modeled as a fixed effect, the contributions of polygenes are modeled as a random effect, and the correlations of pedigree members are modeled via inbreeding/kinship coefficients. F -statistics and χ 2 likelihood ratio test (LRT) statistics based on the LMMs and FLMMs are constructed to test for association. We show empirically that the F -distributed statistics provide a good control of the type I error rate. The F -test statistics of the LMMs have similar or higher power than the FLMMs, kernel-based famSKAT (family-based sequence kernel association test), and burden test famBT (family-based burden test). The F -statistics of the FLMMs perform well when analyzing a combination of rare and common variants. For small samples, the LRT statistics of the FLMMs control the type I error rate well at the nominal levels α = 0.01 and 0.05 . For moderate/large samples, the LRT statistics of the FLMMs control the type I error rates well. The LRT statistics of the LMMs can lead to inflated type I error rates. The proposed models are useful in whole genome and whole exome association studies of complex traits.

A genome-wide association study implicates the BMP7 locus as a risk factor for nonsyndromic metopic craniosynostosis.

Our previous genome-wide association study (GWAS) for sagittal nonsyndromic craniosynostosis (sNCS) provided important insights into the genetics of midline CS. In this study, we performed a GWAS for a second midline NCS, metopic NCS (mNCS), using 215 non-Hispanic white case-parent triads. We identified six variants with genome-wide significance (P ≤ 5 × 10-8): rs781716 (P = 4.71 × 10-9; odds ratio [OR] = 2.44) intronic to SPRY3; rs6127972 (P = 4.41 × 10-8; OR = 2.17) intronic to BMP7; rs62590971 (P = 6.22 × 10-9; OR = 0.34), located ~ 155 kb upstream from TGIF2LX; and rs2522623, rs2573826, and rs2754857, all intronic to PCDH11X (P = 1.76 × 10-8, OR = 0.45; P = 3.31 × 10-8, OR = 0.45; P = 1.09 × 10-8, OR = 0.44, respectively). We performed a replication study of these variants using an independent non-Hispanic white sample of 194 unrelated mNCS cases and 333 unaffected controls; only the association for rs6127972 (P = 0.004, OR = 1.45; meta-analysis P = 1.27 × 10-8, OR = 1.74) was replicated. Our meta-analysis examining single nucleotide polymorphisms common to both our mNCS and sNCS studies showed the strongest association for rs6127972 (P = 1.16 × 10-6). Our imputation analysis identified a linkage disequilibrium block encompassing rs6127972, which contained an enhancer overlapping a CTCF transcription factor binding site (chr20:55,798,821-55,798,917) that was significantly hypomethylated in mesenchymal stem cells derived from fused metopic compared to open sutures from the same probands. This study provides additional insights into genetic factors in midline CS.

Genetic associations with childhood brain growth, defined in two longitudinal cohorts.

Genome-wide association studies (GWASs) are unraveling the genetics of adult brain neuroanatomy as measured by cross-sectional anatomic magnetic resonance imaging (aMRI). However, the genetic mechanisms that shape childhood brain development are, as yet, largely unexplored. In this study we identify common genetic variants associated with childhood brain development as defined by longitudinal aMRI. Genome-wide single nucleotide polymorphism (SNP) data were determined in two cohorts: one enriched for attention-deficit/hyperactivity disorder (ADHD) (LONG cohort: 458 participants; 119 with ADHD) and the other from a population-based cohort (Generation R: 257 participants). The growth of the brain's major regions (cerebral cortex, white matter, basal ganglia, and cerebellum) and one region of interest (the right lateral prefrontal cortex) were defined on all individuals from two aMRIs, and a GWAS and a pathway analysis were performed. In addition, association between polygenic risk for ADHD and brain growth was determined for the LONG cohort. For white matter growth, GWAS meta-analysis identified a genome-wide significant intergenic SNP (rs12386571, P = 9.09 × 10-9 ), near AKR1B10. This gene is part of the aldo-keto reductase superfamily and shows neural expression. No enrichment of neural pathways was detected and polygenic risk for ADHD was not associated with the brain growth phenotypes in the LONG cohort that was enriched for the diagnosis of ADHD. The study illustrates the use of a novel brain growth phenotype defined in vivo for further study.

The FUT2 secretor variant p.Trp154Ter influences serum vitamin B12 concentration via holo-haptocorrin, but not holo-transcobalamin, and is associated with haptocorrin glycosylation.

Vitamin B12 deficiency is common in older individuals. Circulating vitamin B12 concentration can be used to diagnose deficiency, but this test has substantial false positive and false negative rates. We conducted genome-wide association studies (GWAS) in which we resolved total serum vitamin B12 into the fractions bound to transcobalamin and haptocorrin: two carrier proteins with very different biological properties. We replicated reported associations between total circulating vitamin B12 concentrations and a common null variant in FUT2. This allele determines the secretor phenotype in which blood group antigens are found in non-blood body fluids. Vitamin B12 bound to haptocorrin (holoHC) remained highly associated with FUT2 rs601338 (p.Trp154Ter). Transcobalamin bound vitamin B12 (holoTC) was not influenced by this variant. HoloTC is the bioactive the form of the vitamin and is taken up by all tissues. In contrast, holoHC is only taken up by the liver. Using holoHC from individuals with known FUT2 genotypes, we demonstrated that FUT2 rs601338 genotype influences the glycosylation of haptocorrin. We then developed an experimental model demonstrating that holoHC is transported into cultured hepatic cells (HepG2) via the asialoglycoprotein receptor (ASGR). Our data challenge current published hypotheses on the influence of genetic variation on this clinically important measure and are consistent with a model in which FUT2 rs601338 influences holoHC by altering haptocorrin glycosylation, whereas B12 bound to non-glycosylated transcobalamin (i.e. holoTC) is not affected. Our findings explain some of the observed disparity between use of total B12 or holoTC as first-line clinical tests of vitamin B12 status.

A Common Polymorphism in HIBCH Influences Methylmalonic Acid Concentrations in Blood Independently of Cobalamin.

Methylmalonic acid (MMA) is a by-product of propionic acid metabolism through the vitamin B12 (cobalamin)-dependent enzyme methylmalonyl CoA mutase. Elevated MMA concentrations are a hallmark of several inborn errors of metabolism and indicators of cobalamin deficiency in older persons. In a genome-wide analysis of 2,210 healthy young Irish adults (median age 22 years) we identified a strong association of plasma MMA with SNPs in 3-hydroxyisobutyryl-CoA hydrolase (HIBCH, p = 8.42 × 10(-89)) and acyl-CoA synthetase family member 3 (ACSF3, p = 3.48 × 10(-19)). These loci accounted for 12% of the variance in MMA concentration. The most strongly associated SNP (HIBCH rs291466; c:2T>C) causes a missense change of the initiator methionine codon (minor-allele frequency = 0.43) to threonine. Surprisingly, the resulting variant, p.Met1?, is associated with increased expression of HIBCH mRNA and encoded protein. These homozygotes had, on average, 46% higher MMA concentrations than methionine-encoding homozygotes in young adults with generally low MMA concentrations (0.17 [0.14-0.21] µmol/L; median [25(th)-75(th) quartile]). The association between MMA levels and HIBCH rs291466 was highly significant in a replication cohort of 1,481 older individuals (median age 79 years) with elevated plasma MMA concentrations (0.34 [0.24-0.51] µmol/L; p = 4.0 × 10(-26)). In a longitudinal study of 185 pregnant women and their newborns, the association of this SNP remained significant across the gestational trimesters and in newborns. HIBCH is unique to valine catabolism. Studies evaluating flux through the valine catabolic pathway in humans should account for these variants. Furthermore, this SNP could help resolve equivocal clinical tests where plasma MMA values have been used to diagnose cobalamin deficiency.

A comparison study of multivariate fixed models and Gene Association with Multiple Traits (GAMuT) for next-generation sequencing.

In this paper, extensive simulations are performed to compare two statistical methods to analyze multiple correlated quantitative phenotypes: (1) approximate F-distributed tests of multivariate functional linear models (MFLM) and additive models of multivariate analysis of variance (MANOVA), and (2) Gene Association with Multiple Traits (GAMuT) for association testing of high-dimensional genotype data. It is shown that approximate F-distributed tests of MFLM and MANOVA have higher power and are more appropriate for major gene association analysis (i.e., scenarios in which some genetic variants have relatively large effects on the phenotypes); GAMuT has higher power and is more appropriate for analyzing polygenic effects (i.e., effects from a large number of genetic variants each of which contributes a small amount to the phenotypes). MFLM and MANOVA are very flexible and can be used to perform association analysis for (i) rare variants, (ii) common variants, and (iii) a combination of rare and common variants. Although GAMuT was designed to analyze rare variants, it can be applied to analyze a combination of rare and common variants and it performs well when (1) the number of genetic variants is large and (2) each variant contributes a small amount to the phenotypes (i.e., polygenes). MFLM and MANOVA are fixed effect models that perform well for major gene association analysis. GAMuT can be viewed as an extension of sequence kernel association tests (SKAT). Both GAMuT and SKAT are more appropriate for analyzing polygenic effects and they perform well not only in the rare variant case, but also in the case of a combination of rare and common variants. Data analyses of European cohorts and the Trinity Students Study are presented to compare the performance of the two methods.

A Comparison Study of Fixed and Mixed Effect Models for Gene Level Association Studies of Complex Traits.

In association studies of complex traits, fixed-effect regression models are usually used to test for association between traits and major gene loci. In recent years, variance-component tests based on mixed models were developed for region-based genetic variant association tests. In the mixed models, the association is tested by a null hypothesis of zero variance via a sequence kernel association test (SKAT), its optimal unified test (SKAT-O), and a combined sum test of rare and common variant effect (SKAT-C). Although there are some comparison studies to evaluate the performance of mixed and fixed models, there is no systematic analysis to determine when the mixed models perform better and when the fixed models perform better. Here we evaluated, based on extensive simulations, the performance of the fixed and mixed model statistics, using genetic variants located in 3, 6, 9, 12, and 15 kb simulated regions. We compared the performance of three models: (i) mixed models that lead to SKAT, SKAT-O, and SKAT-C, (ii) traditional fixed-effect additive models, and (iii) fixed-effect functional regression models. To evaluate the type I error rates of the tests of fixed models, we generated genotype data by two methods: (i) using all variants, (ii) using only rare variants. We found that the fixed-effect tests accurately control or have low false positive rates. We performed simulation analyses to compare power for two scenarios: (i) all causal variants are rare, (ii) some causal variants are rare and some are common. Either one or both of the fixed-effect models performed better than or similar to the mixed models except when (1) the region sizes are 12 and 15 kb and (2) effect sizes are small. Therefore, the assumption of mixed models could be satisfied and SKAT/SKAT-O/SKAT-C could perform better if the number of causal variants is large and each causal variant contributes a small amount to the traits (i.e., polygenes). In major gene association studies, we argue that the fixed-effect models perform better or similarly to mixed models in most cases because some variants should affect the traits relatively large. In practice, it makes sense to perform analysis by both the fixed and mixed effect models and to make a comparison, and this can be readily done using our R codes and the SKAT packages.

A variant associated with sagittal nonsyndromic craniosynostosis alters the regulatory function of a non-coding element.

Craniosynostosis presents either as a nonsyndromic congenital anomaly or as a finding in nearly 200 genetic syndromes. Our previous genome-wide association study of sagittal nonsyndromic craniosynostosis identified associations with variants downstream from BMP2 and intronic in BBS9. Because no coding variants in BMP2 were identified, we hypothesized that conserved non-coding regulatory elements may alter BMP2 expression. In order to identify and characterize noncoding regulatory elements near BMP2, two conserved noncoding regions near the associated region on chromosome 20 were tested for regulatory activity with a Renilla luciferase assay. For a 711 base pair noncoding fragment encompassing the most strongly associated variant, rs1884302, the luciferase assay showed that the risk allele (C) of rs1884302 drives higher expression of the reporter than the common allele (T). When this same DNA fragment was tested in zebrafish transgenesis studies, a strikingly different expression pattern of the green fluorescent reporter was observed depending on whether the transgenic fish had the risk (C) or the common (T) allele at rs1884302. The in vitro results suggest that altered BMP2 regulatory function at rs1884302 may contribute to the etiology of sagittal nonsyndromic craniosynostosis. The in vivo results indicate that differences in regulatory activity depend on the presence of a C or T allele at rs1884302.

Genetic modifiers of neurofibromatosis type 1-associated café-au-lait macule count identified using multi-platform analysis.

Neurofibromatosis type 1 (NF1) is an autosomal dominant, monogenic disorder of dysregulated neurocutaneous tissue growth. Pleiotropy, variable expressivity and few NF1 genotype-phenotype correlates limit clinical prognostication in NF1. Phenotype complexity in NF1 is hypothesized to derive in part from genetic modifiers unlinked to the NF1 locus. In this study, we hypothesized that normal variation in germline gene expression confers risk for certain phenotypes in NF1. In a set of 79 individuals with NF1, we examined the association between gene expression in lymphoblastoid cell lines with NF1-associated phenotypes and sequenced select genes with significant phenotype/expression correlations. In a discovery cohort of 89 self-reported European-Americans with NF1 we examined the association between germline sequence variants of these genes with café-au-lait macule (CALM) count, a tractable, tumor-like phenotype in NF1. Two correlated, common SNPs (rs4660761 and rs7161) between DPH2 and ATP6V0B were significantly associated with the CALM count. Analysis with tiled regression also identified SNP rs4660761 as significantly associated with CALM count. SNP rs1800934 and 12 rare variants in the mismatch repair gene MSH6 were also associated with CALM count. Both SNPs rs7161 and rs4660761 (DPH2 and ATP6V0B) were highly significant in a mega-analysis in a combined cohort of 180 self-reported European-Americans; SNP rs1800934 (MSH6) was near-significant in a meta-analysis assuming dominant effect of the minor allele. SNP rs4660761 is predicted to regulate ATP6V0B, a gene associated with melanosome biology. Individuals with homozygous mutations in MSH6 can develop an NF1-like phenotype, including multiple CALMs. Through a multi-platform approach, we identified variants that influence NF1 CALM count.

Pleiotropy analysis of quantitative traits at gene level by multivariate functional linear models.

In genetics, pleiotropy describes the genetic effect of a single gene on multiple phenotypic traits. A common approach is to analyze the phenotypic traits separately using univariate analyses and combine the test results through multiple comparisons. This approach may lead to low power. Multivariate functional linear models are developed to connect genetic variant data to multiple quantitative traits adjusting for covariates for a unified analysis. Three types of approximate F-distribution tests based on Pillai-Bartlett trace, Hotelling-Lawley trace, and Wilks's Lambda are introduced to test for association between multiple quantitative traits and multiple genetic variants in one genetic region. The approximate F-distribution tests provide much more significant results than those of F-tests of univariate analysis and optimal sequence kernel association test (SKAT-O). Extensive simulations were performed to evaluate the false positive rates and power performance of the proposed models and tests. We show that the approximate F-distribution tests control the type I error rates very well. Overall, simultaneous analysis of multiple traits can increase power performance compared to an individual test of each trait. The proposed methods were applied to analyze (1) four lipid traits in eight European cohorts, and (2) three biochemical traits in the Trinity Students Study. The approximate F-distribution tests provide much more significant results than those of F-tests of univariate analysis and SKAT-O for the three biochemical traits. The approximate F-distribution tests of the proposed functional linear models are more sensitive than those of the traditional multivariate linear models that in turn are more sensitive than SKAT-O in the univariate case. The analysis of the four lipid traits and the three biochemical traits detects more association than SKAT-O in the univariate case.

Linkage analysis identifies a locus for plasma von Willebrand factor undetected by genome-wide association.

The plasma glycoprotein von Willebrand factor (VWF) exhibits fivefold antigen level variation across the normal human population determined by both genetic and environmental factors. Low levels of VWF are associated with bleeding and elevated levels with increased risk for thrombosis, myocardial infarction, and stroke. To identify additional genetic determinants of VWF antigen levels and to minimize the impact of age and illness-related environmental factors, we performed genome-wide association analysis in two young and healthy cohorts (n = 1,152 and n = 2,310) and identified signals at ABO (P < 7.9E-139) and VWF (P < 5.5E-16), consistent with previous reports. Additionally, linkage analysis based on sibling structure within the cohorts, identified significant signals at chromosome 2q12-2p13 (LOD score 5.3) and at the ABO locus on chromosome 9q34 (LOD score 2.9) that explained 19.2% and 24.5% of the variance in VWF levels, respectively. Given its strong effect, the linkage region on chromosome 2 could harbor a potentially important determinant of bleeding and thrombosis risk. The absence of a chromosome 2 association signal in this or previous association studies suggests a causative gene harboring many genetic variants that are individually rare, but in aggregate common. These results raise the possibility that similar loci could explain a significant portion of the "missing heritability" for other complex genetic traits.

Targeted resequencing implicates the familial Mediterranean fever gene MEFV and the toll-like receptor 4 gene TLR4 in Behçet disease.

Genome-wide association studies (GWAS) are a powerful means of identifying genes with disease-associated common variants, but they are not well-suited to detecting genes with disease-associated rare and low-frequency variants. In the current study of Behçet disease (BD), nonsynonymous variants (NSVs) identified by deep exonic resequencing of 10 genes found by GWAS (IL10, IL23R, CCR1, STAT4, KLRK1, KLRC1, KLRC2, KLRC3, KLRC4, and ERAP1) and 11 genes selected for their role in innate immunity (IL1B, IL1R1, IL1RN, NLRP3, MEFV, TNFRSF1A, PSTPIP1, CASP1, PYCARD, NOD2, and TLR4) were evaluated for BD association. A differential distribution of the rare and low-frequency NSVs of a gene in 2,461 BD cases compared with 2,458 controls indicated their collective association with disease. By stringent criteria requiring at least a single burden test with study-wide significance and a corroborating test with at least nominal significance, rare and low-frequency NSVs in one GWAS-identified gene, IL23R (P = 6.9 × 10(-5)), and one gene involved in innate immunity, TLR4 (P = 8.0 × 10(-4)), were associated with BD. In addition, damaging or rare damaging NOD2 variants were nominally significant across all three burden tests applied (P = 0.0063-0.045). Furthermore, carriage of the familial Mediterranean fever gene (MEFV) mutation Met694Val, which is known to cause recessively inherited familial Mediterranean fever, conferred BD risk in the Turkish population (OR, 2.65; P = 1.8 × 10(-12)). The disease-associated NSVs in MEFV and TLR4 implicate innate immune and bacterial sensing mechanisms in BD pathogenesis.

Generalized functional linear models for gene-based case-control association studies.

By using functional data analysis techniques, we developed generalized functional linear models for testing association between a dichotomous trait and multiple genetic variants in a genetic region while adjusting for covariates. Both fixed and mixed effect models are developed and compared. Extensive simulations show that Rao's efficient score tests of the fixed effect models are very conservative since they generate lower type I errors than nominal levels, and global tests of the mixed effect models generate accurate type I errors. Furthermore, we found that the Rao's efficient score test statistics of the fixed effect models have higher power than the sequence kernel association test (SKAT) and its optimal unified version (SKAT-O) in most cases when the causal variants are both rare and common. When the causal variants are all rare (i.e., minor allele frequencies less than 0.03), the Rao's efficient score test statistics and the global tests have similar or slightly lower power than SKAT and SKAT-O. In practice, it is not known whether rare variants or common variants in a gene region are disease related. All we can assume is that a combination of rare and common variants influences disease susceptibility. Thus, the improved performance of our models when the causal variants are both rare and common shows that the proposed models can be very useful in dissecting complex traits. We compare the performance of our methods with SKAT and SKAT-O on real neural tube defects and Hirschsprung's disease datasets. The Rao's efficient score test statistics and the global tests are more sensitive than SKAT and SKAT-O in the real data analysis. Our methods can be used in either gene-disease genome-wide/exome-wide association studies or candidate gene analyses.

Common Variants at Putative Regulatory Sites of the Tissue Nonspecific Alkaline Phosphatase Gene Influence Circulating Pyridoxal 5'-Phosphate Concentration in Healthy Adults.

BACKGROUND: Vitamin B-6 interconversion enzymes are important for supplying pyridoxal 5'-phosphate (PLP), the co-enzyme form, to tissues. Variants in the genes for these enzymes [tissue nonspecific alkaline phosphatase (ALPL), pyridoxamine 5'-phosphate oxidase, pyridoxal kinase, and pyridoxal phosphatase] could affect enzyme function and vitamin B-6 status. OBJECTIVES: We tested whether single-nucleotide polymorphisms (SNPs) in these genes influence vitamin B-6 status markers [plasma PLP, pyridoxal (PL), and 4-pyridoxic acid (PA)], and explored potential functional effects of the SNPs. METHODS: Study subjects were young, healthy adults from Ireland (n = 2345). We measured plasma PLP, PL, and PA with liquid chromatography-tandem mass spectrometry and genotyped 66 tag SNPs in the 4 genes. We tested for associations with single SNPs in candidate genes and also performed genome-wide association study (GWAS) and gene-based analyses. RESULTS: Seventeen SNPs in ALPL were associated with altered plasma PLP in candidate gene analyses (P < 1.89 × 10(-4)). In the GWAS, 5 additional ALPL SNPs were associated with altered plasma PLP (P < 5.0 × 10(-8)). Gene-based analyses that used the functional linear model ß-spline (P = 4.04 × 10(-15)) and Fourier spline (P = 5.87 × 10(-15)) methods also showed associations between ALPL and altered plasma PLP. No SNPs in other genes were associated with plasma PLP. The association of the minor CC genotype of 1 ALPL SNP, rs1256341, with reduced ALPL expression in the HapMap Northern European ancestry population is consistent with the positive association between the CC genotype and plasma PLP in our study (P = 0.008). No SNP was associated with altered plasma PL or PA. CONCLUSIONS: In healthy adults, common variants in ALPL influence plasma PLP concentration, the most frequently used biomarker for vitamin B-6 status. Whether these associations are indicative of functional changes in vitamin B-6 status requires more investigation.

Functional linear models for association analysis of quantitative traits.

Functional linear models are developed in this paper for testing associations between quantitative traits and genetic variants, which can be rare variants or common variants or the combination of the two. By treating multiple genetic variants of an individual in a human population as a realization of a stochastic process, the genome of an individual in a chromosome region is a continuum of sequence data rather than discrete observations. The genome of an individual is viewed as a stochastic function that contains both linkage and linkage disequilibrium (LD) information of the genetic markers. By using techniques of functional data analysis, both fixed and mixed effect functional linear models are built to test the association between quantitative traits and genetic variants adjusting for covariates. After extensive simulation analysis, it is shown that the F-distributed tests of the proposed fixed effect functional linear models have higher power than that of sequence kernel association test (SKAT) and its optimal unified test (SKAT-O) for three scenarios in most cases: (1) the causal variants are all rare, (2) the causal variants are both rare and common, and (3) the causal variants are common. The superior performance of the fixed effect functional linear models is most likely due to its optimal utilization of both genetic linkage and LD information of multiple genetic variants in a genome and similarity among different individuals, while SKAT and SKAT-O only model the similarities and pairwise LD but do not model linkage and higher order LD information sufficiently. In addition, the proposed fixed effect models generate accurate type I error rates in simulation studies. We also show that the functional kernel score tests of the proposed mixed effect functional linear models are preferable in candidate gene analysis and small sample problems. The methods are applied to analyze three biochemical traits in data from the Trinity Students Study.