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.     

Multipoint linkage analysis of quantitative traits on sex-chromosomes

Variance component models form a powerful and flexible tool for multipoint linkage analysis of quantitative traits. Estimates of genetic similarity are needed for the variance component model to detect linkage and to locate genes, and two methods are commonly used to calculate multipoint identity-by-descent (IBD) estimates for autosomes. Fulker et al. ([1995] Am. J. Hum. Genet. 56: 1229-1233) and Almasy and Blangero ([1998] Am. J. Hum. Genet. 62: 119-121) used multiple regression to estimate the IBD sharing along a chromosome, while the approach of Kruglyak and Lander ([1995] Am. J. Hum. Genet. 57: 439-454) is based on a hidden Markov model. In this paper, we modify the variance component model to accommodate sex-chromosomes, and we extend both multipoint IBD estimation methods to accommodate sex-linked loci. Simulation studies demonstrate the power and precision of the variance component model to detect QTLs located on the sex-chromosome. The two multipoint IBD estimation methods have the same accuracy to identify QTL position, but the hidden Markov model yields a larger average maximum LOD score to detect linkage than the regression model. The extension of the multipoint IBD estimation methods and the variance component model to the X chromosome shows that the variance component model is a powerful and flexible tool for linkage analysis of quantitative traits on both autosomes and sex-chromosomes.     

Combined haplotype relative risk (CHRR): a general and simple genetic association test that combines trios and unrelated case-controls

In some genetic association studies, samples contain both parental and unrelated controls. Under such scenarios, instead of analyzing only trios using family-based association tests or only unrelated subjects using a case-control study design, Nagelkerke et al. ([2004] Eur. J. Hum. Genet. 12:964-970) and Epstein et al. ([2005] Am. J. Hum. Genet. 76:592-608) proposed methods that implemented a likelihood ratio test to combine the two different types of data. In this article, we put forward a more powerful and simplified strategy to combine trios with unrelated subjects based on the haplotype relative risk (HRR) (Falk and Rubinstein [1987] Ann. Hum. Genet. 51:227-233). The HRR compares parental marker alleles transmitted to an affected offspring to those not transmitted as a test for association, a strategy that is similar to a case-control study that compares allele frequencies in diseased cases to those of unrelated controls. We prove that affected offspring can be pooled with diseased cases and that parental controls can be treated as unrelated controls when the trios and unrelated subjects are randomly sampled from the same population. Therefore, unrelated subjects can be incorporated into the HRR intuitively and effortlessly. For trios without complete parental genotypes, we adopted the strategy proposed by (Guo et al. [2005a] BMC Genet. 6:S90; [2005b] Hum. Hered. 59: 125-135), which is more feasible than the one proposed by Weinberg ([1999] Am. J. Hum. Genet. 64:1186-1193). In addition, simulation results suggest that the combined haplotype relative risk is more powerful than Epstein et al.'s method regardless of the disease prevalence in a homogeneous population.     

Testing association and linkage using affected-sib-parent study designs

We have developed a method for jointly testing linkage and association using data from affected sib pairs and their parents. We specify a conditional logistic regression model with two covariates, one that quantifies association (either direct association or indirect association via linkage disequilibrium), and a second that quantifies linkage. The latter covariate is computed based on expected identity-by-descend (ibd) sharing of marker alleles between siblings. In addition to a joint test of linkage and association, our general framework can be used to obtain a linkage test comparable to the mean test (Blackwelder and Elston [1985] Genet. Epidemiol. 2:85-97), and an association test comparable to the Family-Based Association Test (FBAT; Rabinowitz and Laird [2000] Hum. Hered. 50:211-223). We present simulation results demonstrating that our joint test can be more powerful than some standard tests of linkage or association. For example, with a relative risk of 2.7 per variant allele at a disease locus, the estimated power to detect a nearby marker with a modest level of LD was 58.1% by the mean test (linkage only), 69.8% by FBAT, and 82.5% by our joint test of linkage and association. Our model can also be used to obtain tests of linkage conditional on association and association conditional on linkage, which can be helpful in fine mapping.     

Family‐Based Association Tests for Qualitative and Quantitative Traits Using Single‐Nucleotide Polymorphism and Microsatellite Data

Using the Genetic Analysis Workshop 12 simulated data, we contrasted results for association tests in nuclear families and extended pedigrees using single‐nucleotide polymorphism (SNP) data, and we compared results for different trait definitions, for outbred and isolate populations, and for SNP and microsatellite data. SNPs in major genes 1 and 6 were analyzed using transmission disequilibrium testing (TDT) [Spielman et al., Am J Hum Genet 52:506–16, 1993], sibship disequilibrium testing (SDT) [Horvath and Laird, Am J Hum Genet 63:1886–97, 1998], family‐based association testing (FBAT) [Horvath et al., Eur J Hum Genet 9:301–6, 2001], and a chi‐square analysis of founders. TDT and SDT were applied in a sample of independent nuclear families, while FBAT was applied in extended pedigrees. SNPs and microsatellites were analyzed with dichotomous and quantitative trait definitions using FBAT in the isolate and outbred populations. The results of the TDT, SDT, and FBAT analyses are comparable using SNP data to identify the disease gene. However, these tests of association were not helpful in discriminating between functional and non‐functional SNPs in disequilibrium. SNP data were able to identify association with affection status in a gene that influences the liability directly (MG6), but did not perform as well when assessing association with affection status in a gene that influences the outcome only through a quantitative trait (MGI). Association with MGI was observed using the SNP data when the outcome was defined quantitatively. Microsatellite data were relatively unsuccessful in identifying association with the markers in the region of a major gene. The magnitude of the associations between SNPs and the dichotomous or quantitative trait definitions were similar in the outbred and isolated populations. © 2001 Wiley‐Liss, Inc.     

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.     

Impact of parental relationships in maximum lod score affected sib-pair method

Many studies are done in small isolated populations and populations where marriages between relatives are encouraged. In this paper, we point out some problems with applying the maximum lod score (MLS) method (Risch, [1990] Am. J. Hum. Genet. 46:242-253) in these populations where relationships exist between the two parents of the affected sib-pairs. Characterizing the parental relationships by the kinship coefficient between the parents (f), the maternal inbreeding coefficient (alpha(m), and the paternal inbreeding coefficient (alpha(p)), we explored the relationship between the identity by descent (IBD) vector expected under the null hypothesis of no linkage and these quantities. We find that the expected IBD vector is no longer (0.25, 0.5, 0.25) when f, alpha(m), and alpha(p) differ from zero. In addition, the expected IBD vector does not always follow the triangle constraints recommended by Holmans ([1993] Am. J. Hum. Genet. 52:362-374). So the classically used MLS statistic needs to be adapted to the presence of parental relationships. We modified the software GENEHUNTER (Kruglyak et al. [1996] Am. J. Hum. Genet. 58: 1347-1363) to do so. Indeed, the current version of the software does not compute the likelihood properly under the null hypothesis. We studied the adapted statistic by simulating data on three different family structures: (1) parents are double first cousins (f=0.125, alpha(m)=alpha(p)=0), (2) each parent is the offspring of first cousins (f=0, alpha(m)=alpha(p)=0.0625), and (3) parents are related as in the pedigree from Goddard et al. ([1996] Am. J. Hum. Genet. 58:1286-1302) (f=0.109, alpha(m)=alpha(p)=0.0625). The appropriate threshold needs to be derived for each case in order to get the correct type I error. And using the classical statistic in the presence of both parental kinship and parental inbreeding almost always leads to false conclusions.     

Gamma regression improves Haseman-Elston and variance components linkage analysis for sib-pairs

Existing standard methods of linkage analysis for quantitative phenotypes rest on the assumptions of either ordinary least squares (Haseman and Elston [1972] Behav. Genet. 2:3-19; Sham and Purcell [2001] Am. J. Hum. Genet. 68:1527-1532) or phenotypic normality (Almasy and Blangero [1998] Am. J. Hum. Genet. 68:1198-1199; Kruglyak and Lander [1995] Am. J. Hum. Genet. 57:439-454). The limitations of both these methods lie in the specification of the error distribution in the respective regression analyses. In ordinary least squares regression, the residual distribution is misspecified as being independent of the mean level. Using variance components and assuming phenotypic normality, the dependency on the mean level is correctly specified, but the remaining residual coefficient of variation is constrained a priori. Here it is shown that these limitations can be addressed (for a sample of unselected sib-pairs) using a generalized linear model based on the gamma distribution, which can be readily implemented in any standard statistical software package. The generalized linear model approach can emulate variance components when phenotypic multivariate normality is assumed (Almasy and Blangero [1998] Am. J. Hum Genet. 68: 1198-1211) and is therefore more powerful than ordinary least squares, but has the added advantage of being robust to deviations from multivariate normality and provides (often overlooked) model-fit diagnostics for linkage analysis.     

Analysis of multiple SNPs in a candidate gene or region

We consider the analysis of multiple single nucleotide polymorphisms (SNPs) within a gene or region. The simplest analysis of such data is based on a series of single SNP hypothesis tests, followed by correction for multiple testing, but it is intuitively plausible that a joint analysis of the SNPs will have higher power, particularly when the causal locus may not have been observed. However, standard tests, such as a likelihood ratio test based on an unrestricted alternative hypothesis, tend to have large numbers of degrees of freedom and hence low power. This has motivated a number of alternative test statistics. Here we compare several of the competing methods, including the multivariate score test (Hotelling's test) of Chapman et al. ([2003] Hum. Hered. 56:18-31), Fisher's method for combining P-values, the minimum P-value approach, a Fourier-transform-based approach recently suggested by Wang and Elston ([2007] Am. J. Human Genet. 80:353-360) and a Bayesian score statistic proposed for microarray data by Goeman et al. ([2005] J. R. Stat. Soc. B 68:477-493). Some relationships between these methods are pointed out, and simulation results given to show that the minimum P-value and the Goeman et al. ([2005] J. R. Stat. Soc. B 68:477-493) approaches work well over a range of scenarios. The Wang and Elston approach often performs poorly; we explain why, and show how its performance can be substantially improved.     

Perils and pitfalls of permutation tests for distinguishing the effects of neighbouring polymorphisms

In a small region several marker loci may be associated with a trait, either because they directly influence the trait or because they are in linkage disequilibrium (LD) with a causal variant. Having established a potentially causal effect at a primary variant, we may ask if any other variants in the region appear to further contribute to the trait, indicating that the additional variant is either causal or is in LD with another causal locus. Methods of approaching this problem using case-parent trio data include the stepwise conditional logistic regression approach described by Cordell and Clayton ([2002] Am. J. Hum. Genet. 70:124-141), and a constrained-permutation method recently proposed by Spijker et al. ([2005] Ann. Hum. Genet. 69:90-101). Through simulation we demonstrate that the procedure described by Spijker et al. [2005], as well as unconditional logistic regression with "affected family-based controls" (AFBACs), can lead to inflated type 1 errors in situations when haplotypes are not inferable for all trios, whereas the conditional logistic regression approach gives correct significance levels. We propose an alternative to the permutation method of Spijker et al. [2005], which does not rely on haplotyping, and results in correct type 1 errors and potentially high power when assumptions of random mating, Hardy-Weinberg Equilibrium, and multiplicative effects of disease alleles are satisfied.     

Strategy for mapping minor histocompatibility genes involved in graft-versus-host disease: A novel application of discordant sib pair methodology

We introduce a novel application for linkage analysis: using bone marrow donor-recipient sib pairs to search for genes influential in graft-versus-host disease (GVHD), a major cause of morbidity and mortality following allogeneic bone marrow transplantation. In particular, we show that transplant sib pairs in which the recipient developed severe GVHD can be used to map genes in the same way as traditional discordant (affected/unaffected) sib pairs (DSPs). For a plausible GVHD model, we demonstrate that the transplant/discordant sib pair analog of the “possible triangle test” [Holmans (1993) Am J Hum Genet 52:362–374] has similar power to that of the simpler “restricted test” proposed by Risch [(1990b) Am J Hum Genet 46:229–241; (1992) Am J Hum Genet 51:673–675]. Moreover, we show that the restricted test has superior power in much of the DSP possible triangle and significantly inferior power in only a small region. Thus, we conclude that the restricted test is preferable for localizing genes with transplant/discordant sib pairs. Finally, we examine the effects of heterogeneity on the power to detect GVHD loci and demonstrate the gain in efficiency by dividing the sample into genetically more homogeneous subgroups. Genet. Epidemiol. 15:595–607,1998. © 1998 Wiley-Liss, Inc.     

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.     

Association mapping by generalized linear regression with density-based haplotype clustering

Haplotypes of closely linked single-nucleotide polymorphisms (SNPs) potentially offer greater power than individual SNPs to detect association between genetic variants and disease. We present a novel approach for association mapping in which density-based clustering of haplotypes reduces the dimensionality of the general linear model (GLM)-based score test of association implemented in the HaploStats software (Schaid et al. [2002] Am. J. Hum. Genet. 70:425-434). A flexible haplotype similarity score, a generalization of previously used measures, forms the basis, for grouping haplotypes of probable recent common ancestry. All haplotypes within a cluster are assigned the same regression coefficient within the GLM, and evidence for association is assessed with a score statistic. The approach is applicable to both binary and continuous trait data, and does not require prior phase information. Results of simulation studies demonstrated that clustering enhanced the power of the score test to detect association, under a variety of conditions, while preserving valid Type-I error. Improvement in performance was most dramatic in the presence of extreme haplotype diversity, while a slight improvement was observed even at low diversity. Our method also offers, for binary traits, a slight advantage in power over a similar approach based on an evolutionary model (Tzeng et al. [2006] Am. J. Hum. Genet. 78:231-242).     

Robust ascertainment-adjusted parameter estimation

Nonrandom ascertainment is commonly used in genetic studies of rare diseases, since this design is often more convenient than the random-sampling design. When there is an underlying latent heterogeneity, Epstein et al. ([2002] Am. J. Hum. Genet. 70:886-895) showed that it is possible to get unbiased or consistent estimation of population parameters under ascertainment adjustment, but Glidden and Liang ([2002] Genet. Epidemiol. 23:201-208) showed in a simulation study that the resulting estimates are highly sensitive to misspecification of the latent components. To overcome this difficulty, we consider a heavy-tailed model for latent variables that allows a robust estimation of the parameters. We describe a hierarchical-likelihood approach that avoids the integration used in the standard marginal likelihood approach. We revisit and extend the previous simulation, and show that the resulting estimator is efficient and robust against misspecification of the distribution of latent variables.     

Informative-transmission disequilibrium test (i-TDT): combined linkage and association mapping that includes unaffected offspring as well as affected offspring

To date, there is no test valid for the composite null hypothesis of no linkage or no association that utilizes transmission information from heterozygous parents to their unaffected offspring as well as the affected offspring from ascertained nuclear families. Since the unaffected siblings also provide information about linkage and association, we introduce a new strategy called the informative-transmission disequilibrium test (i-TDT), which uses transmission information from heterozygous parents to all of the affected and unaffected offspring in ascertained nuclear families and provides a valid chi-square test for both linkage and association. The i-TDT can be used in various study designs and can accommodate all types of independent nuclear families with at least one affected offspring. We show that the transmission/disequilibrium test (TDT) (Spielman et al. [1993] Am. J. Hum. Genet. 52:506-516) is a special case of the i-TDT, if the study sample contains only case-parent trios. If the sample contains only affected and unaffected offspring without parental genotypes, the i-TDT is equivalent to the sibship disequilibrium test (SDT) (Horvath and Laird [1998] Am. J. Hum. Genet. 63:1886-1897. In addition, the test statistic of i-TDT is simple, explicit and can be implemented easily without intensive computing. Through computer simulations, we demonstrate that power of the i-TDT can be higher in many circumstances compared to a method that uses affected offspring only. Applying the i-TDT to the Framingham Heart Study data, we found that the apolipoprotein E (APOE) gene is significantly linked and associated with cross-sectional measures and longitudinal changes in total cholesterol.     

Quantitative trait linkage analysis by generalized estimating equations: unification of variance components and Haseman-Elston regression

Two of the major approaches for linkage analysis with quantitative traits in humans include variance components and Haseman-Elston regression. Previously, these were viewed as quite separate methods. We describe a general model, fit by use of generalized estimating equations (GEE), for which the variance components and Haseman-Elston methods (including many of the extensions to the original Haseman-Elston method) are special cases, corresponding to different choices for a working covariance matrix. We also show that the regression-based test of Sham et al. ([2002] Am. J. Hum. Genet. 71:238-253) is equivalent to a robust score statistic derived from our GEE approach. These results have several important implications. First, this work provides new insight regarding the connection between these methods. Second, asymptotic approximations for power and sample size allow clear comparisons regarding the relative efficiency of the different methods. Third, our general framework suggests important extensions to the Haseman-Elston approach which make more complete use of the data in extended pedigrees and allow a natural incorporation of environmental and other covariates.     

Equivalence of three score tests for association mapping of quantitative trait loci under selective genotyping

Huang and Lin ([2007] Am J Hum Genet 80:567–572) proposed a conditional‐likelihood approach for mapping quantitative trait loci (QTL) under selective genotyping, and demonstrated via simulation that their model tends to be more powerful than the prospective linear regression. However, we show that the three score tests based on the conditional, prospective and retrospective likelihoods are numerically identical in testing association between a quantitative trait and a candidate locus. Two approximations are derived for calculating power and sample size for the score test. Compared to the random sampling, a single‐tail selection generally reduces the power of the score test in mapping small effect QTLs. A two‐tail selection generally enhances the QTL heritability; however, in small samples, the power of the test may actually decrease if the sample sizes are highly unbalanced in the upper and lower tails of the trait distribution. Genet. Epidemiol. 34: 522–527, 2010. © 2010 Wiley‐Liss, Inc.     

Regressive threshold model for familial analysis of complex diseases with variable age of onset

Few models for segregation (or combined segregation-linkage) analysis have been developed to account for variable age of onset. The unified model (UM) can only take into account age at examination. In the logistic hazard model (LHM), Abel and Bonney ([1990] Genet. Epidemiol. 7:391-407) incorporated survival analysis concepts into the regressive logistic model of Bonney ([1986] Am. J. Med. Genet. 18:731-749), but interpretation of familial dependence parameters is difficult. In this article, we extended the regressive threshold model (RTM) proposed by Demenais ([1991] Am. J. Hum. Genet. 49:773-785) to account for a variable age of onset of complex diseases. This model assumes an underlying liability to disease and is more general than the original logistic formulation, since the phenotypes of each individual's antecedents can be adjusted for their own genotypes and covariate effects. The variation of risk with age can be expressed as a general step function, and variants of the model have been proposed by imposing different types of constraints among the time-dependent thresholds. The performances of the three models (UM, LHM, and RTM) were compared in the context of segregation analysis of family data generated with variable age of onset. All analysis models were robust with respect to false conclusion of a major gene, and the best results were obtained under RTM. The power to detect the major gene was higher under LHM than RTM, but the best fit of the estimated cumulative age-dependent penetrance with respect to the true value was obtained under RTM. This new model may thus prove helpful in contributing to identification of genes underlying complex diseases, since it can easily include linked marker loci and linkage disequilibrium.     

Test of Association for Quantitative Traits in General Pedigrees: The Quantitative Pedigree Disequilibrium Test

Many statistical methods have been proposed in recent years to test for genetic linkage and association between genetic markers and traits of interest through unrelated nuclear families. However, most of these methods are not valid tests of association in the presence of linkage when some of the nuclear families are related. As a result, related nuclear families in large pedigrees cannot be included in a single analysis to test for linkage disequilibrium. Recently, Martin et al. [Am J Hum Genet 67:146–54, 2000] proposed the pedigree disequilibrium test (PDT) to test for linkage and association in general pedigrees for qualitative traits. In this article, we develop a similar quantitative pedigree disequilibrium test (QPDT) to test for linkage and association in general pedigrees for quantitative traits. We apply both the PDT and the QPDT to analyze the sequence data from the seven candidate genes in the simulated data sets in the Genetic Analysis Workshop 12. © 2001 Wiley‐Liss, Inc.     

Power comparison of regression methods to test quantitative traits for association and linkage

George et al. [1999 Am J Hum Genet 65:236-245] proposed a regression-based TDT method for quantitative traits consisting of regressing the trait on the parental transmission of a marker allele. Zhu and Elston [2000] also developed a TDT method for quantitative traits by defining a linear transformation to condition out founder information. Both methods test the null hypothesis of no linkage or association and can be applied to general pedigree structures. In this paper, we compare the power of these two methods through simulation, sampling those nuclear families with at least one heterozygous parent. Overall, we find that a variant of Zhu and Elston's method with 2 d.f. is more powerful. However, if the mode of inheritance is known, then a most powerful test with 1 d.f. can be found. All these regression TDT tests require linkage to detect association, but a test that does not require linkage will be more powerful.