Ordered-subset analysis (OSA) for family-based association mapping of complex traits

Association analysis provides a powerful tool for complex disease gene mapping. However, in the presence of genetic heterogeneity, the power for association analysis can be low since only a fraction of the collected families may carry a specific disease susceptibility allele. Ordered-subset analysis (OSA) is a linkage test that can be powerful in the presence of genetic heterogeneity. OSA uses trait-related covariates to identify a subset of families that provide the most evidence for linkage. A similar strategy applied to genetic association analysis would likely result in increased power to detect association. Association in the presence of linkage (APL) is a family-based association test (FBAT) for nuclear families with multiple affected siblings that properly infers missing parental genotypes when linkage is present. We propose here APL-OSA, which applies the OSA method to the APL statistic to identify a subset of families that provide the most evidence for association. A permutation procedure is used to approximate the distribution of the APL-OSA statistic under the null hypothesis that there is no relationship between the family-specific covariate and the family-specific evidence for allelic association. We performed a comprehensive simulation study to verify that APL-OSA has the correct type I error rate under the null hypothesis. This simulation study also showed that APL-OSA can increase power relative to other commonly used association tests (APL, FBAT and FBAT with covariate adjustment) in the presence of genetic heterogeneity. Finally, we applied APL-OSA to a family study of age-related macular degeneration, where cigarette smoking was used as a covariate.     

An efficient family-based association test using multiple markers

In genetic association studies, multiple markers are usually employed to cover a genomic region of interest for localizing a trait locus. In this report, we propose a novel multi-marker family-based association test (T(LC)) that linearly combines the single-marker test statistics using data-driven weights. We examine the type-I error rate in a numerical study and compare its power to identify a common trait locus using tag single nucleotide polymorphisms (SNPs) within the same haplotype block that the trait locus resides with three competing tests including a global haplotype test (T(H)), a multi-marker test similar to the Hotelling-T(2) test for the population-based data (T(MM)), and a single-marker test with Bonferroni's correction for multiple testing (T(B)). The type-I error rate of T(LC) is well maintained in our numeric study. In all the scenarios we examined, T(LC) is the most powerful, followed by T(B). T(MM) and T(H) are the poorest. T(H) and T(MM) have essentially the same power when parents are available. However, when both parents are missing, T(MM) is substantially more powerful than T(H). We also apply this new test on a data set from a previous association study on nicotine dependence.     

Perspectives on genome-wide multi-stage family-based association studies

With the establishment of large consortiums of researchers, genome-wide association (GWA) studies have become increasingly popular and feasible. Although most of these association studies focus on unrelated individuals, a lot of advantages can be exploited by including families in the analysis as well. To overcome the additional genotyping cost, multi-stage designs are particularly useful. In this article, I offer a perspective view on genome-wide family-based association analyses, both within a model-based and model-free paradigm. I highlight how multi-stage designs and analysis techniques, which are quite popular in clinical epidemiology, can enter GWA settings. I furthermore discuss how they have proven successful in reducing analysis complexity, and in overcoming one of the most cumbersome statistical hurdles in the genome-wide context, namely controlling increased false positives due to multiple testing.     

New joint covariance- and marginal-based tests for association and linkage for quantitative traits for random and non-random sampling

We develop novel statistical tests for transmission disequilibrium testing (tests of linkage in the presence of association) for quantitative traits using parents and offspring. These joint tests utilize information in both the covariance (or more generally, dependency) between genotype and phenotype and the marginal distribution of genotype. Using computer simulation we test the validity (Type I error rate control) and power of the proposed methods, for additive, dominant, and recessive modes of inheritance, locus-specific heritability of the trait 0.05, 0.1, 0.2 with allele frequencies of P=0.2 and 0.4, and sample sizes of 500, 200, and 100 trios. Both random sampling and extreme sampling schemes were investigated. A multinomial logistic joint test provides the highest overall power irrespective of sample size, allele frequency, heritability, and modes of inheritance.     

Simple association analysis combining data from trios/sibships and unrelated controls

We consider genetic association analysis that combines data from case-parent trios/sibships and unrelated controls. A general and simple methodology is proposed, using a weighted least-squares approach to combine separate information from the case-parent/case-sibling analysis and the case-unrelated control analysis. The new proposal improves over the existing methods in that it requires no assumptions and estimation on the mating-type distribution. Simulation results show that the new method competes well with the likelihood-based method when the latter is applicable, and achieves substantial power gains over separate analyses in general. Therefore, the proposed combined association analysis can enjoy wide applications, including the multiallele/locus, haplotype, and genome-wide association studies.     

Asymptotic tests of association with multiple SNPs in linkage disequilibrium

We consider detecting associations between a trait and multiple single nucleotide polymorphisms (SNPs) in linkage disequilibrium (LD). To maximize the use of information contained in multiple SNPs while minimizing the cost of large degrees of freedom (DF) in testing multiple parameters, we first theoretically explore the sum test derived under a working assumption of a common association strength between the trait and each SNP, testing on the corresponding parameter with only one DF. Under the scenarios that the association strengths between the trait and the SNPs are close to each other (and in the same direction), as considered by Wang and Elston [Am. J. Hum. Genet. [2007] 80:353–360], we show with simulated data that the sum test was powerful as compared to several existing tests; otherwise, the sum test might have much reduced power. To overcome the limitation of the sum test, based on our theoretical analysis of the sum test, we propose five new tests that are closely related to each other and are shown to consistently perform similarly well across a wide range of scenarios. We point out the close connection of the proposed tests to the Goeman test. Furthermore, we derive the asymptotic distributions of the proposed tests so that P‐values can be easily calculated, in contrast to the use of computationally demanding permutations or simulations for the Goeman test. A distinguishing feature of the five new tests is their use of a diagonal working covariance matrix, rather than a full covariance matrix as used in the usual Wald or score test. We recommend the routine use of two of the new tests, along with several other tests, to detect disease associations with multiple linked SNPs. Genet. Epidemiol. 33:497–507, 2009. © 2009 Wiley‐Liss, Inc.     

Sample size calculations for population- and family-based case-control association studies on marker genotypes

Most previous sample size calculations for case-control studies to detect genetic associations with disease assumed that the disease gene locus is known, whereas, in fact, markers are used. We calculated sample sizes for unmatched case-control and sibling case-control studies to detect an association between a biallelic marker and a disease governed by a putative biallelic disease locus. Required sample sizes increase with increasing discrepancy between the marker and disease allele frequencies, and with less-than-maximal linkage disequilibrium between the marker and disease alleles. Qualitatively similar results were found for studies of parent offspring triads based on the transmission disequilibrium test (Abel and Müller-Myhsok, 1998, Am. J. Hum. Genet. 63:664-667; Tu and Whittemore, 1999, Am. J. Hum. Genet. 64:641-649). We also studied other factors affecting required sample size, including attributable risk for the disease allele, inheritance mechanism, disease prevalence, and for sibling case-control designs, extragenetic familial aggregation of disease and recombination. The large sample-size requirements represent a formidable challenge to studies of this type.     

On the analysis of copy-number variations in genome-wide association studies: a translation of the family-based association test

Though there is an increasing support for an important contribution of copy number variation (CNV) to the genetic architecture of complex disease, few methods have been developed for the analysis of such variation in the context of genetic association studies. In this paper, we propose a generalization of family-based association tests (FBATs) to allow for the analysis of CNVs at a genome-wide level. We translate the popular FBAT approach so that, instead of genotypes, raw intensity values that reflect copy number are used directly in the test statistic, thereby bypassing the need for a CNV genotyping algorithm. Moreover, both inherited and de novo CNVs can be analyzed without any prior knowledge about the type of CNV, making it easily applicable to large-scale association studies. All robustness properties of the genotype FBAT approach are maintained and all previously developed FBAT extensions, including FBATs for time-to-onset, multivariate FBATs, and FBAT-testing strategies, can be directly transferred to the analysis of CNVs. Using simulation studies, we evaluate the power and the robustness of the new approach. Furthermore, for those CNVs that can be genotyped, we compare FBATs based on genotype calls with FBATs that are directly based on the intensity data. An application to one of the first CNV genome-wide-association studies of asthma identifies a very plausible candidate gene. A software implementation of the approach is freely available at http://www.hsph.harvard.edu/research/iuliana-ionita/software. The approach has also been completely integrated in the PBAT software package.     

A general method for linkage disequilibrium correction for multipoint linkage and association

Lately, many different methods of linkage, association or joint analysis for family data have been invented and refined. Common to most of those is that they require a map of markers that are in linkage equilibrium. However, at the present day, high-density single nucleotide polymorphisms (SNPs) maps are both more inexpensive to create and they have lower genotyping error. When marker data is incomplete, the crucial and computationally most demanding moment in the analysis is to calculate the inheritance distribution at a certain position on the chromosome. Recently, different ways of adjusting traditional methods of linkage analysis to denser maps of SNPs in linkage disequilibrium (LD) have been proposed. We describe a hidden Markov model which generalizes the Lander-Green algorithm. It combines Markov chain for inheritance vectors with a Markov chain modelling founder haplotypes and in this way takes account for LD between SNPs. It can be applied to association, linkage or combined association and linkage analysis, general phenotypes and arbitrary score functions. We also define a joint likelihood for linkage and association that extends an idea of Kong and Cox (1997 Am. J. Hum. Genet. 61: 1179-1188) for pure linkage analysis.     

Genetic Analysis Workshop II: combined segregation, linkage, and association analysis

A combined segregation, linkage, and association analysis using the program COMBIN was performed on the simulated pedigree data prepared for the Second Genetic Analysis Workshop. The model used in COMBIN is described and the presented results illustrate its effectiveness in the analysis of such data. Linkage analysis was performed and maps for each linkage group are presented.     

VALID: visualization of association study results and linkage disequilibrium

Promising findings from genetic association studies are commonly presented with two distinct figures: one gives the association study results and the other indicates linkage disequilibrium (LD) between genetic markers in the region(s) of interest. Fully interpreting the results of such studies requires synthesizing the information in these figures, which is generally done in a subjective and unsystematic manner. Here we present a method to formally combine association results and LD and display them in the same figure; we have developed a freely available web‐based application that can be used to generate figures to display the combined data. To demonstrate this approach we apply it to fine mapping data from the prostate cancer 8q24 loci. Combining these two sources of information in a single figure allows one to more clearly assess patterns of association, facilitating the interpretation of genome‐wide and fine mapping data and improving our ability to localize causal variants. Genet. Epidemiol. 33:599–603, 2009. © 2009 Wiley‐Liss, Inc.     

Genetic association tests for family data with missing parental genotypes: a comparison

We consider three tests for genetic association in data from nuclear families (the Family-Based Association Test (FBAT) test proposed by Rabinowitz and Laird ([2000] Hum. Hered. 50:211-223), a second test proposed by Rabinowitz ([2002] J. Am. Stat. Assoc. 97:742-758), and the Family Genotype Analysis Program (FGAP) nonfounder or partial score test proposed by Clayton ([1999] Am. J. Hum. Genet. 65:1170-1177) and Whittemore and Tu ([2000] Am. J. Hum. Genet. 66:1329-1340)). We show that each test statistic arises from the efficient score of the family data as the solution to a set of constraints on its null expectation. Moreover, the FBAT and Rabinowitz tests (but not the FGAP test) are locally the most powerful among all tests satisfying their constraints. We used simulations to examine how the three tests perform in situations when their assumptions are violated and the number of families is not huge. We found that the FBAT test tended to have less power than the other two tests, particularly when applied to families in whom all offspring were affected. The Rabinowitz and FGAP tests performed similarly, although the latter tended to extract more information from families containing one typed parent. While none of the tests showed good power to detect rare, recessively acting genes, the Rabinowitz test with a sample variance estimate performed particularly poorly in this case. However, the Rabinowitz test with a model-based variance had power comparable to that of the FGAP test, and more accurate type I error rates. We conclude that for the situations we considered, the Rabinowitz test with model-based variance has good power without forfeiting robustness against misspecification of parental genotype probabilities. However, its utility is limited by the lack of a simple algorithm to apply it to families with varying structures and phenotypes.     

Genetic association tests based on ranks (GATOR) for quantitative traits with and without censoring

Linkage disequilibrium mapping of quantitative traits is a powerful method for dissecting the genetic etiology of complex phenotypes. Quantitative traits, however, often exhibit characteristics that make their use problematic. For example, the distribution of the trait may be censored, highly skewed, or contaminated with outlying values. We propose here a rank-based framework for deriving tests of gene and trait association that explicitly take censoring into account and are insensitive to skewness and outlying values. Standard methods for mapping quantitative traits do not take these characteristics into account, which leads to the discarding of valuable information or their improper application. We show how this framework can be applied in nuclear families and discuss its implementation in general pedigrees. The power and efficacy of the approach is illustrated through a series of simulation experiments in which the approach is compared to existing methods.     

Validity, efficiency, and robustness of a family-based test of association

We propose a new test of linkage in the presence of allelic association that uses all available information in a sample of nuclear families, including parental phenotypes, genotypes from both affected and unaffected siblings, and families with homozygous parents. The test is based on the conditional framework developed by Rabinowitz and Laird [2000: Hum Hered 50:211-223] and is thus immune to population stratification and can be applied to families with any pattern of missing information. The test statistic is a conditional likelihood ratio based on a standard two-point linkage model with allelic association, where parameters are estimated from the sample. Through a simulation study, we determined that the proposed test has near optimal power for a wide range of scenarios, outperforming FBAT both when data were complete and when parental genotypes were missing, although differences between the two tests diminish as the genetic effect is reduced. To assess robustness, we also evaluated the performance of the tests under scenarios with population stratification and found that although there is a loss of efficiency, our proposed test remains a strong competitor to FBAT.     

Pedigree disequilibrium tests for multilocus haplotypes

Association tests of multilocus haplotypes are of interest both in linkage disequilibrium mapping and in candidate gene studies. For case-parent trios, I discuss the extension of existing multilocus methods to include ambiguous haplotypes in tests of models which distinguish between the cis and trans phase. A likelihood-ratio test is proposed, using the expectation-maximization (E-M) algorithm to account for haplotype ambiguities. Assumptions about the population structure are required, but realistic situations, including population stratification, which violate the assumptions lead to conservative tests. I describe a permutation procedure for the null hypothesis of interest, which controls for violation of the assumptions. For general pedigrees, I describe extensions of the pedigree disequilibrium test to include uncertain haplotypes. The summary statistics are replaced by their expected values over prior distributions of haplotype frequencies. If prior distributions are not available, a valid test is possible by using the E-M algorithm to estimate the null distribution of haplotype frequencies. Similar methods are available for quantitative traits. Exact permutation tests are difficult to construct in small samples, but an approximate procedure is appropriate in large samples, and can be used to account for dependencies between tests of multiple haplotypes and loci.     

Identification of susceptibility loci contributing to a complex disease using conventional segregation,linkage, and association methods

We set out to apply conventional analytic methods to a GAW data set of nuclear families with an oligogenic disease that has a population prevalence of 0.023. We chose methods generally applied to disorders with at least one major gene. Our approaches included: (1) complex segregation analysis under two models of ascertainment, (2) linkage analysis assuming either a single-locus trait with possible genetic heterogeneity or a two-locus trait, and (3) allelic association studies using both a case/control approach and the haplotype relative risk (HRR) test. The association study was the only analysis of the three that provided evidence for genes playing a role in the etiology of this disorder. ©1995 Wiley-Liss, Inc.     

Testing association in the presence of linkage using the GRE and multiple markers

It has recently been shown that testing for association in the presence of linkage using a score test based on a gamma random effects (GRE) model is substantially more powerful than using the Family-Based Association Test. A reason for the increased power lies in better specification of the within family correlation structure, induced by linkage. The GRE, as presented in (Jonasdottir et al. 2007 Genet Epidemiol. 31:528-540), only considers one marker at a time and does not readily handle missing parental information. Here we extend the GRE to incorporate information from more than one marker. This extension leads to a haplotype GRE test and also to efficient handling of missing data on parental genotypes. We show that the haplotype GRE, the H-GRE, is substantially more powerful than the haplotype FBAT, the Haplotype-Based-Association Test. We demonstrate the usefulness of the extended GRE, by reanalyzing the collaborative study on the genetics of alcoholism data, allowing for missing parental information.     

Gene‐environment interaction tests for dichotomous traits in trios and sibships

When testing for genetic effects, failure to account for a gene‐environment interaction can mask the true association effects of a genetic marker with disease. Family‐based association tests are popular because they are completely robust to population substructure and model misspecification. However, when testing for an interaction, failure to model the main genetic effect correctly can lead to spurious results. Here we propose a family‐based test for interaction that is robust to model misspecification, but still sensitive to an interaction effect, and can handle continuous covariates and missing parents. We extend the FBAT‐I gene‐environment interaction test for dichotomous traits to using both trios and sibships. We then compare this extension to joint tests of gene and gene‐environment interaction, and compare the joint test additionally to the main effects test of the gene. Lastly, we apply these three tests to a group of nuclear families ascertained according to affection with Bipolar Disorder. Genet. Epidemiol. 33:691–699, 2009. © 2009 Wiley‐Liss, Inc.     

Haplotype sharing transmission/disequilibrium tests that allow for genotyping errors

The present study introduces new Haplotype Sharing Transmission/Disequilibrium Tests (HS-TDTs) that allow for random genotyping errors. We evaluate the type I error rate and power of the new proposed tests under a variety of scenarios and perform a power comparison among the proposed tests, the HS-TDT and the single-marker TDT. The results indicate that the HS-TDT shows a significant increase in type I error when applied to data in which either Mendelian inconsistent trios are removed or Mendelian inconsistent markers are treated as missing genotypes, and the magnitude of the type I error increases both with an increase in sample size and with an increase in genotyping error rate. The results also show that a simple strategy, that is, merging each rare haplotype to a most similar common haplotype, can control the type I error inflation for a wide range of genotyping error rates, and after merging rare haplotypes, the power of the test is very similar to that without merging the rare haplotypes. Therefore, we conclude that a simple strategy may make the HS-TDT robust to genotyping errors. Our simulation results also show that this strategy may also be applicable to other haplotype-based TDTs.     

X chromosome association testing in genome wide association studies

Genome wide association studies (GWAS) have revealed many fascinating insights into complex diseases even from simple, single-marker statistical tests. Most of these tests are designed for testing of associations between a phenotype and an autosomal genotype and are therefore not applicable to X chromosome data. Testing for association on the X chromosome raises unique challenges that have motivated the development of X-specific statistical tests in the literature. However, to date there has been no study of these methods under a wide range of realistic study designs, allele frequencies and disease models to assess the size and power of each test. To address this, we have performed an extensive simulation study to investigate the effects of the sex ratios in the case and control cohorts, as well as the allele frequencies, on the size and power of eight test statistics under three different disease models that each account for X-inactivation. We show that existing, but under-used, methods that make use of both male and female data are uniformly more powerful than popular methods that make use of only female data. In particular, we show that Clayton's one degree of freedom statistic [Clayton, 2008] is robust and powerful across a wide range of realistic simulation parameters. Our results provide guidance on selecting the most appropriate test statistic to analyse X chromosome data from GWAS and show that much power can be gained by a more careful analysis of X chromosome GWAS data.