Complexity and power in case-control association studies

Power estimation of multiple SNP association test of case-control study and application

At the current stage, a large number of single nucleotide polymorphisms (SNPs) have been deployed in searching for genes underlying complex diseases. A powerful method is desirable for efficient analysis of SNP data. Recently, a novel method for multiple SNP association test using a combination of allelic association (AA) and Hardy-Weinberg disequilibrium (HWD) has been proposed. However, the power of this test has not been systematically examined. In this study, we conducted a simulation study to further evaluate the statistical power of the new procedure, as well as of the influence of the HWD on its performance. The simulation examined the scenarios of multiple disease SNPs among a candidate pool, assuming different parameters including allele frequencies and risk ratios, dominant, additive, and recessive genetic models, and the existence of gene-gene interactions and linkage disequilibrium (LD). We also evaluated the performance of this test in capturing real disease associated SNPs, when a significant global P value is detected. Our results suggest that this new procedure is more powerful than conventional single-point analyses with correction of multiple testing. However, inclusion of HWD reduces the power under most circumstances. We applied the novel association test procedure to a case-control study of preterm delivery (PTD), examining the effects of 96 candidate gene SNPs concurrently, and detected a global P value of 0.0250 by using Cochran-Armitage chi(2)s as "starting" statistics in the procedure. In the following single point analysis, SNPs on IL1RN, IL1R2, ESR1, Factor 5, and OPRM1 genes were identified as possible risk factors in PTD.

Re-screening serotonin receptors for genetic variants identifies population and molecular genetic complexity

We have re-screened the genes for the 5-HT1A, 5-HT2A, 5-HT2C, and 5-HT7 serotonin receptors for genetic variants in a large African-American and Caucasian-American population sample. We have identified eight novel variants in these genes including four that are predicted to cause amino acid substitutions. These variants are additional candidates for association studies of behavioral disorders such as depression and schizophrenia as well as quantitative personality traits. We have also detected some, but not all, previously identified variants in these genes suggesting that many previously identified variants are unique to specific populations. The results of this study, and previous screens of serotonin receptors, demonstrate that the genes for serotonin receptors display marked population and molecular genetic complexity. These levels of complexity may have a substantial effect on genetic association studies of human behavioral variability related to these genes. We discuss the implications of these findings and propose methods to address complexity in genetic association studies.

Sum statistics for the joint detection of multiple disease loci in case-control association studies with SNP markers

In complex traits, multiple disease loci presumably interact to produce the disease. For this reason, even with high-resolution single nucleotide polymorphism (SNP) marker maps, it has been difficult to map susceptibility loci by conventional locus-by-locus methods. Fine mapping strategies are needed that allow for the simultaneous detection of interacting disease loci while handling large numbers of densely spaced markers. For this purpose, sum statistics were recently proposed as a first-stage analysis method for case-control association studies with SNPs. Via sums of single-marker statistics, information over multiple disease-associated markers is combined and, with a global significance value alpha, a small set of "interesting" markers is selected for further analysis. Here, the statistical properties of such approaches are examined by computer simulation. It is shown that sum statistics can often be successfully applied when marker-by-marker approaches fail to detect association. Compared with Bonferroni or False Discovery Rate (FDR) procedures, sum statistics have greater power, and more disease loci can be detected. However, in studies with tightly linked markers, simple sum statistics can be suboptimal, since the intermarker correlation is ignored. A method is presented that takes the correlation structure among marker loci into account when marker statistics are combined.

[Human molecular genetics: from monogenic to polygenic or complex disorders]

Human molecular genetics has successfully identified the genes involved in several monogenic disorders. It now aims at pinpointing the genetic determinants of polygenic or complex traits with a strong genetic component. This constitutes a new challenge. We discuss the methodological and practical aspects of identifying such genes as well as the challenges facing physicians that will have to use efficiently these new diagnostic tools.

Improved use of SNP information to detect the role of genes

A topical question in genetic association studies is the optimal use of the information provided by genotyped single-nucleotide polymorphisms (SNPs) in order to detect the role of a candidate gene in a multifactorial disease. We propose a strategy called "combination test" that tests the association between a quantitative trait and all possible phased combinations of various numbers of SNPs. We compare this strategy to two alternative strategies: the association test that considers each SNP separately, and a multilocus genotype-based test that considers the phased combination of all SNPs together. To compare these three tests, a quantitative trait was simulated under different models of correspondence between phenotype and genotype, including the extreme case when two SNPs interact with no marginal effects of each SNP. The genotypes were taken from a sample of 290 independent individuals genotyped for three genes with various number of SNPs (from 5-8 SNPs). The results show that the "combination test" is the only one able to detect the association when the two SNPs involved in disease susceptibility interact with no marginal effects. Interestingly, even in the case of a single etiological SNP, the "combination test" performed well. We apply the three tests to Genetic Analysis Workshop 12 (Almasy et al. [2001] Genet. Epidemiol. 21:332-338) simulated data, and show that although there was no interactions between the etiological SNPs, the "combination test" was preferable to the two other compared methods to detect the role of the candidate gene.

Analysis of multilocus models of association

It is increasingly recognized that multiple genetic variants, within the same or different genes, combine to affect liability for many common diseases. Indeed, the variants may interact among themselves and with environmental factors. Thus realistic genetic/statistical models can include an extremely large number of parameters, and it is by no means obvious how to find the variants contributing to liability. For models of multiple candidate genes and their interactions, we prove that statistical inference can be based on controlling the false discovery rate (FDR), which is defined as the expected number of false rejections divided by the number of rejections. Controlling the FDR automatically controls the overall error rate in the special case that all the null hypotheses are true. So do more standard methods such as Bonferroni correction. However, when some null hypotheses are false, the goals of Bonferroni and FDR differ, and FDR will have better power. Model selection procedures, such as forward stepwise regression, are often used to choose important predictors for complex models. By analysis of simulations of such models, we compare a computationally efficient form of forward stepwise regression against the FDR methods. We show that model selection includes numerous genetic variants having no impact on the trait, whereas FDR maintains a false-positive rate very close to the nominal rate. With good control over false positives and better power than Bonferroni, the FDR-based methods we introduce present a viable means of evaluating complex, multivariate genetic models. Naturally, as for any method seeking to explore complex genetic models, the power of the methods is limited by sample size and model complexity.

Genetic variants of coagulation factor XIII, postmenopausal estrogen therapy, and risk of nonfatal myocardial infarction

We hypothesized that possession of either of 2 functional coagulation factor XIII polymorphisms, one within subunit A (Val34Leu) and one within subunit B (His95Arg), might modulate the prothrombotic effects of estrogen and help to explain the variation in incidence of arterial thrombotic events among postmenopausal women using hormone replacement therapy. In a population-based case-control study of 955 postmenopausal women, we assessed the associations of factor XIII genotypes and their interactions with estrogen therapy on risk of nonfatal myocardial infarction (MI). The presence of the factor XIIIA Leu34 allele was associated with a reduced risk of MI (odds ratio [OR] = 0.70, 95% confidence interval [95% CI] = 0.51-0.95). The presence of the factor XIIIB Arg95 allele had little association with MI risk. Neither factor XIII polymorphism alone significantly modified the association between the risk of MI and current estrogen use. In exploratory analyses, however, there was a significant factor XIII subunit gene-gene interaction. Compared to women homozygous for both common factor XIII alleles, the Arg95 variant was associated with a reduced risk of MI in the presence of the Leu34 variant (OR = 0.36, 95% CI = 0.17-0.75) but not in the absence of the Leu34 variant (OR = 1.11, 95% CI = 0.69-1.79). Moreover, among women who had at least 2 copies of the variant factor XIII alleles and were current estrogen users, the risk of MI was reduced by 70% relative to estrogen nonusers with fewer than 2 factor XIII variant alleles (P value for interaction =.03). If confirmed, these findings may permit a better assessment of the cardiovascular risks and benefits associated with postmenopausal estrogen therapy.

Beta-1-adrenergic receptor gene in major depression: influence on antidepressant treatment response

Noradrenergic dysfunction has been implicated in the development of affective disorders. beta-adrenergic receptors (betaARs) mediate the response to norephinephrine, are coupled to the cAMP signaling cascade, supposed to be altered in their density and/or sensitivity in depression, and down regulated in several brain regions after long term treatment with different but not all antidepressants. A recently identified functional polymorphism in the beta(1)-adrenergic receptor (G1165C) leading to the amino acid variation Gly389Arg was associated with an enhanced coupling to the stimulatory G(s)-protein and increased adenylyl cyclase activation, disturbances which are often observed in affective disorders. Therefore, we investigated whether this beta(1)AR polymorphism is associated with major depression or with the response to antidepressant treatment in a sample of 259 patients compared to 206 healthy controls. Although we could not detect an association between the beta(1)AR polymorphism and major depression we found a tendency for a relation between CC homozygosity and a better and even faster response to antidepressant treatment in those patients, which were treated with antidepressants affecting directly or indirectly the beta(1)AR system (tricyclic antidepressants, noradrenergic and serotonergic specific agents, selective noradrenaline reuptake inhibitors) determined by the HAMD and CGI score (P = 0.05). However, after correction for multiple testing (Bonferroni) these results did not remain significant. Nevertheless, these findings suggest that the presence of the C allele might be an indicator for antidepressant treatment response.

A multigene test for the risk of sporadic breast carcinoma

BACKGROUND

Although the identification of the BRCA1 and BRCA2 genes have been of great interest, these genes account for less than 5% of all breast carcinoma cases. The remaining cases are sporadic. Reanalysis of a large twin study suggested that genetic factors may play a significant role in sporadic breast and other carcinomas. Sporadic breast carcinoma is polygenically inherited. Multiple genes are likely to have an additive effect, each gene accounting for a fraction of the variance. One factor that may have an impact on the development of hormonally responsive breast tumors is the duration of exposure of the breast to estrogen. Therefore, one of the demographic risk factors for breast carcinoma is an early age of onset of menarche. The current study was based on the hypothesis that genes that play a role in demographic risk factors may be breast carcinoma risk genes in their own right. The authors hypothesized that six genes relevant to the timing of the onset of menarche and related risk factors might be candidate genes for breast carcinoma. These were the leptin gene (LEP), the leptin receptor gene (LEPR), the catechol-0-methyltransferase gene (COMT), the dopamine D(2) receptor gene (DRD2), the estrogen 1 receptor gene (ESR1), and the androgen receptor gene (AR).

METHODS

The authors examined 67 women with postmenopausal sporadic breast carcinoma and 145 gender and race-matched controls.

RESULTS

Five of these genes accounted for a significant percent of the variance (r(2)) of breast carcinoma. The following r(2) and P values were calculated: LEP: 0.073, P < or = 0.0001; LEPR: 0.064, P < or = 0.0002; COMT: 0.073, P < or = 0.0001; AR: 0.040, P < or = 0.0035; and DRD2: 0.018, P < or = 0.05. When evaluated in a multivariate regression analysis, they accounted collectively for 24% of the variance of breast carcinoma (P < or = 0.0001). These genes accounted for 40% of the variance (P < or = 0.00001) in a subset of age-matched cases. Individual gene scores were added to form a breast carcinoma risk score (BCRS) that ranged from 0 to 17. When the BCRS was evaluated in a receiver operator characteristic plot, the area under the curve was 0.80 for the full set and 0.869 for the age-matched set. The relative breast carcinoma risk for the different BCRS scores ranged from 0.10 to 11.9.

CONCLUSIONS

These results demonstrate a potentially powerful method of evaluating the additive effect of multiple breast carcinoma risk genes to form a potentially clinically useful assessment of women's risk for sporadic breast carcinoma.

Studying parents and grandparents to assess genetic contributions to early-onset disease

Suppose DNA is available from affected individuals, their parents, and their grandparents. Particularly for early-onset diseases, maternally mediated genetic effects can play a role, because the mother determines the prenatal environment. The proposed maximum-likelihood approach for the detection of apparent transmission distortion treats the triad consisting of the affected individual and his or her two parents as the outcome, conditioning on grandparental mating types. Under a null model in which the allele under study does not confer susceptibility, either through linkage or directly, and when there are no maternally mediated genetic effects, conditional probabilities for specific triads are easily derived. A log-linear model permits a likelihood-ratio test (LRT) and allows the estimation of relative penetrances. The proposed approach is robust against genetic population stratification. Missing-data methods permit the inclusion of incomplete families, even if the missing person is the affected grandchild, as is the case when an induced abortion has followed the detection of a malformation. When screening multiple markers, one can begin by genotyping only the grandparents and the affected grandchildren. LRTs based on conditioning on grandparental mating types (i.e., ignoring the parents) have asymptotic relative efficiencies that are typically >150% (per family), compared with tests based on parents. A test for asymmetry in the number of copies carried by maternal versus paternal grandparents yields an LRT specific to maternal effects. One can then genotype the parents for only the genes that passed the initial screen. Conditioning on both the grandparents' and the affected grandchild's genotypes, a third log-linear model captures the remaining information, in an independent LRT for maternal effects.

On the advantage of haplotype analysis in the presence of multiple disease susceptibility alleles

We investigated the effect of multiple susceptibility alleles at a single disease locus on the statistical power of a likelihood ratio test to detect association between alleles at a marker locus and a disease phenotype in a case-control design. Using simplifying assumptions to obtain the joint frequency distribution of marker and disease locus alleles, we present numerical results that illustrate the impact of historical variation of initial associations between marker alleles and susceptibility alleles on the power of a likelihood ratio test for association. Our results show that an increase in the number of susceptibility alleles produces a decrease in power of the likelihood ratio test. The decrease in power in the presence of multiple susceptibility alleles, however, is less for markers with multiple alleles than for markers with two alleles. We investigate the implications of this observation for tests of association based on haplotypes made up of tightly linked single-nucleotide polymorphisms (SNPs). Our results suggest that an analysis based on haplotypes can be advantageous over an analysis based on individual SNPs in the presence of multiple susceptibility alleles, particularly when linkage disequilibria between SNPs is weak. The results provide motivation for further development of statistical methods based on haplotypes for assessing the potential for association methods to identify and locate complex disease genes.

Association analysis of a polymorphism in the G-protein stimulatory alpha subunit in patients with major depression

Growing evidence suggests that G-proteins may be involved in pathogenesis and treatment of affective disorders. Several studies have reported altered levels and/or activities of stimulatory G-proteins in depression. The aim of this study was to investigate whether a polymorphism in the stimulatory alpha subunit of G-proteins (T/C point mutation in exon 5; ATT --> ATC at codon 131) is associated with major depression or response to antidepressant treatment. Therefore, we performed a case-control association study with 212 depressive patients and 137 healthy, unrelated controls. There was no evidence for an association between the investigated polymorphism in the G(alpha)(s) gene and major depression, as well as to treatment response. The results of our study are in concordance with recently published findings which do not support the hypothesis that the gene for the stimulatory alpha subunit of G-proteins is a major susceptibility factor in the pathophysiology of major depression.

Generalized T2 test for genome association studies

Recent progress in the development of single-nucleotide polymorphism (SNP) maps within genes and across the genome provides a valuable tool for fine-mapping and has led to the suggestion of genomewide association studies to search for susceptibility loci for complex traits. Test statistics for genome association studies that consider a single marker at a time, ignoring the linkage disequilibrium between markers, are inefficient. In this study, we present a generalized T2 statistic for association studies of complex traits, which can utilize multiple SNP markers simultaneously and considers the effects of multiple disease-susceptibility loci. This generalized T2 statistic is a corollary to that originally developed for multivariate analysis and has a close relationship to discriminant analysis and common measure of genetic distance. We evaluate the power of the generalized T2 statistic and show that power to be greater than or equal to those of the traditional chi2 test of association and a similar haplotype-test statistic. Finally, examples are given to evaluate the performance of the proposed T2 statistic for association studies using simulated and real data.

Analysis of polymorphisms in the olfactory G-protein Golf in major depression

It is well established that G-proteins represent essential regulatory components in transmembrane signaling. The alpha subunit of the olfactory G-protein Golf (GNAL) maps to a region on chromosome 18 where linkage to affective disorders has been reported, as well as a parent-of-origin effect in affective disorders with some markers near the locus for the alpha subunit of the Golf gene. We investigated whether two polymorphisms in the alpha subunit of the Golf gene (A-->G in intron 3, and T-->G in intron 10) are associated with major depression in 176 major depressive patients compared with 145 healthy control subjects, and additionally tested for a parent-of-origin effect in separated gender groups. In the control group, we found a significant increase in the G-allele frequency of the intron 3 polymorphism in females (P=0.0036, odds ratio=2.13, 95% confidence interval=1.29-3.54, Fisher's Exact Test). In patients, we found a similar tendency for higher G-allele frequencies in females. Concerning the intron 10 polymorphism, no differences in the genotype or allele frequencies were detectable for any of the separated gender groups. Also, the total patient and control groups showed no differences in allele or genotype frequencies for any of the investigated polymorphisms. The results of this study agree with the reported parent-of-origin effects on chromosome 18, but do not support the hypothesis that the Golf gene is a major susceptibility factor for major depression.

Genetic association mapping at the crossroads: which test and why? Overview and practical guidelines

Until about a decade ago, genetic association testing essentially meant case control association analysis using genetic markers. Concerns about population stratification propelled family-based tests of association into widespread use and challenged the classic case control design. The literature now contains a vast collection of different family-based methods, most of which are based on the transmission/disequilibrium test (TDT). Some methods extend the original TDT to accommodate multiallelic markers, variable pedigree constellations, multiple loci, etc. Other methods go beyond the original design of the TDT to detect genetic association via haplotype sharing. Most recently, we have witnessed a revival of case control methods that control for population stratification. The purpose of this review is to help orient readers to the rapidly developing methods of association testing and enhance their understanding of the basic principles of these approaches. We present an overview of the development of genetic association tests, with practical guidelines on which test might be the most suitable for a given study.

Association studies for quantitative traits in structured populations

Association between disease and genetic polymorphisms often contributes critical information in our search for the genetic components of common diseases. Devlin and Roeder [1999: Biometrics 55:997-1004] introduced genomic control, a statistical method that overcomes a drawback to the use of population-based samples for tests of association, namely spurious associations induced by population structure. In essence, genomic control (GC) uses markers throughout the genome to adjust for any inflation in test statistics due to substructure. To date, genomic control (GC) has been developed for binary traits and bi- or multiallelic markers. Tests of association using GC have been limited to single genes. In this report, we generalize GC to quantitative traits (QT) and multilocus models. Using statistical analysis and simulations, we show that GC controls spurious associations in reasonable settings of population substructure for QT models, including gene-gene interaction. Through simulations, we explore GC power for both random and selected samples, assuming the QT locus tested is causal and its specific heritability is 2.5-5%. We find that GC, combined with either random or selected samples, has good power in this setting, and that more complex models induce smaller GC corrections. The latter suggests greater power can be achieved by specifying more complex genetic models, but this observation only follows when such models are largely correct and specified a priori.

Haplotype tagging for the identification of common disease genes

Genome-wide linkage disequilibrium (LD) mapping of common disease genes could be more powerful than linkage analysis if the appropriate density of polymorphic markers were known and if the genotyping effort and cost of producing such an LD map could be reduced. Although different metrics that measure the extent of LD have been evaluated, even the most recent studies have not placed significant emphasis on the most informative and cost-effective method of LD mapping-that based on haplotypes. We have scanned 135 kb of DNA from nine genes, genotyped 122 single-nucleotide polymorphisms (SNPs; approximately 184,000 genotypes) and determined the common haplotypes in a minimum of 384 European individuals for each gene. Here we show how knowledge of the common haplotypes and the SNPs that tag them can be used to (i) explain the often complex patterns of LD between adjacent markers, (ii) reduce genotyping significantly (in this case from 122 to 34 SNPs), (iii) scan the common variation of a gene sensitively and comprehensively and (iv) provide key fine-mapping data within regions of strong LD. Our results also indicate that, at least for the genes studied here, the current version of dbSNP would have been of limited utility for LD mapping because many common haplotypes could not be defined. A directed re-sequencing effort of the approximately 10% of the genome in or near genes in the major ethnic groups would aid the systematic evaluation of the common variant model of common disease.