Increase in power of transmission-disequilibrium tests for quantitative traits

Allison ([1997] Am. J. Hum. Genet. 60:676-690) proposed four versions of the transmission-disequilibrium test (TDT) for quantitative traits when there is extreme-threshold sampling, i.e., the trios having an offspring trait value between a priori defined thresholds are excluded from the analysis. Keeping intact the ideology and construction of these tests, we propose here an extreme-offspring design for the trios: for each parent pair of which at least one is heterozygous at a marker locus, the offspring having the most extreme trait value is selected for the trio. Our simulation studies show that the effect of the extreme-offspring design can be quite substantial (up to 30% increase in test power), and that the increase is greater for smaller values of the association parameter and for traits with smaller heritability: just those cases where the increase in power is especially desirable.     

Interpretation of simultaneous linkage and family-based association tests in genome screens

Linkage and association analyses have played important roles in identifying susceptibility genes for complex diseases. Linkage tests and family-based tests of association are often applied in the same data to help fine-map disease loci or validate results. This paradigm increases efficiency by making maximal use of family data sets. However, it is not intuitively clear under what conditions association and linkage tests performed in the same data set may be correlated. Understanding this relationship is important for interpreting the combined results of both tests. We used computer simulations and theoretical statements to estimate the correlation between linkage statistics (affected sib pair maximum LOD scores) and family-based association statistics (pedigree disequilibrium test (PDT) and association in the pressure of linkage (APL)) under various hypotheses. Different types of pedigrees were studied: nuclear families with affected sib pairs, extended pedigrees and incomplete pedigrees. Both simulation and theoretical results showed that when there is no linkage or no association, the linkage and association tests are not correlated. When there is linkage and association in the data, the two tests have a positive correlation. We concluded that when linkage and association tests are applied in the same data, the type I error rate of neither test will be affected and that power can be increased by applying tests conditionally.     

Removing phenotypic distribution assumptions from tests of linkage disequilibrium for quantitative traits

The transmission disequilibrium test (TDT) has become a family-based method of reference to search for linkage disequilibrium (LD). Although it was first developed for dichotomous traits, numerous approaches have extended the TDT to quantitative phenotypes that either rely on regression or variance component techniques. Both of these approaches are based on some phenotypic distribution assumptions, the violation of which can lead to inflation of type I error rates, and derive information from phenotypic variability, so that their power is very low under some selection schemes (e.g., one-tailed selection). We propose a new family-based test of association for quantitative traits, denoted maximum-likelihood-binomial (MLB)-QTDT, which addresses the two previous issues by incorporating a latent binary variable that captures the LD information between the marker allele and the quantitative phenotype. The method can be understood as a classical TDT for binary traits that would include pure affected and pure unaffected children, and the probability for a child to be affected or unaffected depends on his/her quantitative phenotypic value. Simulation studies under the null hypothesis show that the MLB-QTDT provides very consistent type I errors even in small and/or selected samples. Under the alternative hypothesis, the MLB-QTDT has good power to analyze one-tailed selected samples, and performs as well as a classical approach in other designs. The MLB-QTDT is a flexible distribution-free method to test for LD with quantitative phenotypes in nuclear families, and can easily incorporate previous extensions developed in the context of family-based association studies with binary traits.     

Association and linkage with quantitative traits

This paper examines two approaches for the analysis of quantitative traits: (1) association studies and (2) linkage studies. The trait studied was Q1 from simulated Problem 2 data set in Genetic Analysis Workshop 9. Our purpose was to evaluate associations present in the data, to identify nongenetic and genetic predictors of the trait, and to explore the simulated genome for linkage. Through the association study, we found evidence for the primary major gene associated with this trait. The linkage study found evidence of residual genetic effect acting through other traits. Adjustments of Q1 for Q2 and Q3 led to a failure to find significant effects of MG2 and MG3. This supports the suggestion that adjustment for genetically influenced traits for effects of other genetic traits can reduce the power to detect major gene effects. In summary, we detected the major gene directly associated with the trait of interest through association studies. Linkage analysis detected evidence for two other genes associated to a lesser degree with the trait. © 1995 Wiley-Liss, Inc.     

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.     

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.     

Sequential sib-pair and association studies to detect genes in quantitative traits

We applied sib-pair and association methods to a GAW data set of nuclear families with quantitative traits. Our approaches included 1) preliminary statistical studies including correlations and linear regressions, 2) sib-pair methods, and 3) association studies. We used a single data set to screen for linkage and association and, subsequently, additional data sets to confirm the preliminary results. Using this sequential approach, sib-pair analysis provided evidence for the genes influencing Q1, Q2, and Q4. We correctly predicted MG1 for Q1, MG2 for Q2, and MG4 for Q4. We did not find any false positives using this approach. Association studies identified chromosomes 8 and 9 to be associated with Q4; however these are assumed to be false positives as no associations were modeled into the data. © 1997 Wiley-Liss, Inc.     

Bivariate combined linkage and association mapping of quantitative trait loci

In this paper, bivariate/multivariate variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL), based on combinations of pedigree and population data. Suppose that a quantitative trait locus is located in a chromosome region that exerts pleiotropic effects on multiple quantitative traits. In the region, multiple markers such as single nucleotide polymorphisms are typed. Two regression models, "genotype effect model" and "additive effect model", are proposed to model the association between the markers and the trait locus. The linkage information, i.e., recombination fractions between the QTL and the markers, is modeled in the variance and covariance matrix. By analytical formulae, we show that the "genotype effect model" can be used to model the additive and dominant effects simultaneously; the "additive effect model" only takes care of additive effect. Based on the two models, F-test statistics are proposed to test association between the QTL and markers. By analytical power analysis, we show that bivariate models can be more powerful than univariate models. For moderate-sized samples, the proposed models lead to correct type I error rates; and so the models are reasonably robust. As a practical example, the method is applied to analyze the genetic inheritance of rheumatoid arthritis for the data of The North American Rheumatoid Arthritis Consortium, Problem 2, Genetic Analysis Workshop 15, which confirms the advantage of the proposed bivariate models.     

Genotype-based association test for general pedigrees: the genotype-PDT

Many family-based tests of linkage disequilibrium (LD) are based on counts of alleles rather than genotypes. However, allele-based tests may not detect interactions among alleles at a single locus that are apparent when examining associations with genotypes. Family-based tests of LD based on genotypes have been developed, but they are typically valid as tests of association only in families with a single affected individual. To take advantage of families with multiple affected individuals, we propose the genotype-pedigree disequilibrium test (geno-PDT) to test for LD between marker locus genotypes and disease. Unlike previous tests for genotypic association, the geno-PDT is valid in general pedigrees. Simulations to compare the power of the allele-based PDT and geno-PDT reveal that under an additive model, the allele-based PDT is more powerful, but that the geno-PDT can have greater power when the genetic model is recessive or dominant. Perhaps the most important property of the geno-PDT is the ability to test for association with particular genotypes, which can reveal underlying patterns of association at the genotypic level. These genotype-specific tests can be used to suggest possible underlying genetic models that are consistent with the pattern of genotypic association. This is illustrated through an application to a candidate gene analysis of the MLLT3 gene in families with Alzheimer disease. The geno-PDT approach for testing genotypes in general family data provides a useful tool for identifying genes in complex disease, and partitioning individual genotype contributions will help to dissect the influence of genotype on risk.     

Improving the power of association tests for quantitative traits in family studies

Association mapping based on family studies can identify genes that influence complex human traits while providing protection against population stratification. Because no gene is likely to have a very large effect on a complex trait, most family studies have limited power. Among the commonly used family-based tests of association for quantitative traits, the quantitative transmission-disequilibrium tests (QTDT) based on the variance-components model is the most flexible and most powerful. This method assumes that the trait values are normally distributed. Departures from normality can inflate the type I error and reduce the power. Although the family-based association tests (FBAT) and pedigree disequilibrium tests (PDT) do not require normal traits, nonnormality can also result in loss of power. In many cases, approximate normality can be achieved by transforming the trait values. However, the true transformation is unknown, and incorrect transformations may compromise the type I error and power. We propose a novel class of association tests for arbitrarily distributed quantitative traits by allowing the true transformation function to be completely unspecified and empirically estimated from the data. Extensive simulation studies showed that the new methods provide accurate control of the type I error and can be substantially more powerful than the existing methods. We applied the new methods to the Collaborative Study on the Genetics of Alcoholism and discovered significant association of single nucleotide polymorphisms (SNP) tsc0022400 on chromosome 7 with the quantitative electrophysiological phenotype TTTH1, which was not detected by any existing methods. We have implemented the new methods in a freely available computer program.     

Score test for detecting linkage to quantitative traits

The two most popular methods to detect linkage of a quantitative trait to a marker are the Haseman-Elston regression method and the variance components likelihood-ratio test. In the literature, these methods are frequently compared and the relative advantages and disadvantages of each method are well known. In this article, we derive a score test for the variance component attributable to a specific quantitative trait locus and show that for sib-pairs it is mathematically equivalent to a recently proposed version of the Haseman-Elston method that optimally combines the sum squared and the difference squared of the centered phenotype values of the sibs. Because score tests and likelihood-ratio tetsts are equivalent for large sample sizes, the variance components likelihood-ratio test is also asymptotically equivalent to this optimal Haseman-Elston test. This fact gives a theoretical explanation of the empirical observation from simulation studies reporting similar power of the variance components likelihood-ratio test and the optimal Haseman-Elston method. Perhaps more importantly for practical purposes, the score test can also be extended in a natural way to support the simultaneous analysis of more than two subjects and multivariate phenotypes.     

A general class of association tests for family-based data using weight functions

Based on the symmetry of transmitted/nontransmitted alleles from heterozygous parents under the null hypothesis of no association, the work proposed here establishes a general statistical framework for constructing association tests with data from nuclear families with multiple affected children. A class of association tests is proposed for both diallelic and multiallelic markers. The proposed test statistics reduce to the transmission disequilibrium test for trios, to T(su) by Martin et al. ([1997] Am. J. Hum. Genet. 61:439-448) for affected sib pairs, and to the pedigree disequilibrium test by Martin et al. ([2000] Am. J. Hum. Genet. 67:146-154); [2001] Am. J. Hum. Genet. 68:1065-1067) when using affected sibships only. The association test used in simulation and for real data (sitosterolemia) is the one which has the best overall power in detecting association. This association test is generally more powerful than the association tests proposed by Martin et al. ([2000] Am. J. Hum. Genet. 67:146-154); [2001] Am. J. Hum. Genet. 68:1065-1067) when using only affected sibships. For the sitosterolemia data set, the association test has its most significant result (P-value=0.0012) for the marker locus on the same bacterial artificial chromosome as the disease locus.     

Using extreme phenotype sampling to identify the rare causal variants of quantitative traits in association studies

Variants identified in recent genome-wide association studies based on the common-disease common-variant hypothesis are far from fully explaining the hereditability of complex traits. Rare variants may, in part, explain some of the missing hereditability. Here, we explored the advantage of the extreme phenotype sampling in rare-variant analysis and refined this design framework for future large-scale association studies on quantitative traits. We first proposed a power calculation approach for a likelihood-based analysis method. We then used this approach to demonstrate the potential advantages of extreme phenotype sampling for rare variants. Next, we discussed how this design can influence future sequencing-based association studies from a cost-efficiency (with the phenotyping cost included) perspective. Moreover, we discussed the potential of a two-stage design with the extreme sample as the first stage and the remaining nonextreme subjects as the second stage. We demonstrated that this two-stage design is a cost-efficient alternative to the one-stage cross-sectional design or traditional two-stage design. We then discussed the analysis strategies for this extreme two-stage design and proposed a corresponding design optimization procedure. To address many practical concerns, for example measurement error or phenotypic heterogeneity at the very extremes, we examined an approach in which individuals with very extreme phenotypes are discarded. We demonstrated that even with a substantial proportion of these extreme individuals discarded, an extreme-based sampling can still be more efficient. Finally, we expanded the current analysis and design framework to accommodate the CMC approach where multiple rare-variants in the same gene region are analyzed jointly.     

Unified sampling approach for multipoint linkage disequilibrium mapping of qualitative and quantitative traits

Rapid development in biotechnology has enhanced the opportunity to deal with multipoint gene mapping for complex diseases, and association studies using quantitative traits have recently generated much attention. Unlike the conventional hypothesis-testing approach for fine mapping, we propose a unified multipoint method to localize a gene controlling a quantitative trait. We first calculate the sample size needed to detect linkage and linkage disequilibrium (LD) for a quantitative trait, categorized by decile, under three different modes of inheritance. Our results show that sampling trios of offspring and their parents from either extremely low (EL) or extremely high (EH) probands provides greater statistical power than sampling in the intermediate range. We next propose a unified sampling approach for multipoint LD mapping, where the goal is to estimate the map position (tau) of a trait locus and to calculate a confidence interval along with its sampling uncertainty. Our method builds upon a model for an expected preferential transmission statistic at an arbitrary locus conditional on the sampling scheme, such as sampling from EL and EH probands. This approach is valid regardless of the underlying genetic model. The one major assumption for this model is that no more than one quantitative trait locus (QTL) is linked to the region being mapped. Finally we illustrate the proposed method using family data on total serum IgE levels collected in multiplex asthmatic families from Barbados. An unobserved QTL appears to be located at tau; = 41.93 cM with 95% confidence interval of (40.84, 43.02) through the 20-cM region framed by markers D12S1052 and D12S1064 on chromosome 12. The test statistic shows strong evidence of linkage and LD (chi-square statistic = 18.39 with 2 df, P-value = 0.0001).     

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.     

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.     

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.     

A rare variant association test in family‐based designs and non‐normal quantitative traits

Rare variant studies are now being used to characterize the genetic diversity between individuals and may help to identify substantial amounts of the genetic variation of complex diseases and quantitative phenotypes. Family data have been shown to be powerful to interrogate rare variants. Consequently, several rare variants association tests have been recently developed for family‐based designs, but typically, these assume the normality of the quantitative phenotypes. In this paper, we present a family‐based test for rare‐variants association in the presence of non‐normal quantitative phenotypes. The proposed model relaxes the normality assumption and does not specify any parametric distribution for the marginal distribution of the phenotype. The dependence between relatives is modeled via a Gaussian copula. A score‐type test is derived, and several strategies to approximate its distribution under the null hypothesis are derived and investigated. The performance of the proposed test is assessed and compared with existing methods by simulations. The methodology is illustrated with an association study involving the adiponectin trait from the UK10K project. Copyright © 2015 John Wiley & Sons, Ltd.     

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 with age at onset

Many diseases or traits exhibit a varying age at onset. Recent data examples of prostate cancer and childhood diabetes show that compared to simply treating the disease outcome as affected vs. unaffected, incorporation of age-at-onset information into the transmission/disequilibrium type of test (TDT) does not appear to change the results much. In this paper, we evaluate the power of TDT as a function of age at onset, and show that age-at-onset information is most useful when the disease is common, or the relative risk associated with the high-risk genotype varies with age. Moreover, an extremely old unaffected subject can contribute substantially to the power of the TDT, sometimes as much as old-onset subjects. We propose a modified test statistic for testing no association between the marker at the candidate locus and age at onset. The simulation study was conducted to evaluate the finite sample properties of proposed and the TDT test statistics under various sampling schemes for trios of parents and offspring, as well as for sibling clusters where unaffected siblings were used as controls.