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.     

Power of non-parametric linkage analysis in mapping genes contributing to human longevity in long-lived sib-pairs

This report investigates the power issue in applying the non-parametric linkage analysis of affected sib-pairs (ASP) [Kruglyak and Lander, 1995: Am J Hum Genet 57:439-454] to localize genes that contribute to human longevity using long-lived sib-pairs. Data were simulated by introducing a recently developed statistical model for measuring marker-longevity associations [Yashin et al., 1999: Am J Hum Genet 65:1178-1193], enabling direct power comparison between linkage and association approaches. The non-parametric linkage (NPL) scores estimated in the region harboring the causal allele are evaluated to assess the statistical power for different genetic (allele frequency and risk) and heterogeneity parameters under various sampling schemes (age-cut and sample size). Based on the genotype-specific survival function, we derived a heritability calculation as an overall measurement for the effect of causal genes with different parameter settings so that the power can be compared for different modes (dominant, recessive) of inheritance. Our results show that the ASP approach is a powerful tool in mapping very strong effect genes, both dominant and recessive. To map a rare dominant genetic variation that reduces hazard of death by half, a large sample (above 600 pairs) with at least one extremely long-lived (over age 99) sib in each pair is needed. Again, with large sample size and high age cut-off, the method is able to localize recessive genes with relatively small effects, but the power is very limited in case of a dominant effect. Although the power issue may depend heavily on the true genetic nature in maintaining survival, our study suggests that results from small-scale sib-pair investigations should be referred with caution, given the complexity of human longevity.     

The “possible triangle” test for extreme discordant sib pairs

For the analysis of quantitative traits in nuclear families, extreme discordant sib pairs proved to be more powerful than unselected sib pairs. Here, we present a test that makes use of selected pairs and, in addition, restricts the parameters of the identical-by-descent distribution analogously to the “possible triangle” for affected sib pairs. In the Problem 2A data, extreme discordant sib pairs are selected. The analysis allowed the detection of most simulated major genes. © 1997 Wiley- Liss, Inc.     

Combined Multipoint Analysis of Multiple Asthma Data Sets Based on the Posterior Probability of Linkage

In the presence of multiple data sets, an important issue is how to best measure the overall evidence for linkage across data sets. Previously, we advocated the use of the posterior probability of linkage (PPL) for this purpose [Vieland, Am J Hum Genet 63:947–54, 1998; Wang et al., Ann Hum Genet 64:533–53, 2000; Vieland et al., Hum Hered 51:199–208, 2001]. In this paper, we propose a critical modification of our earlier two‐point PPL in order to handle multiple‐point calculations. The proposed modification is then applied to the genome‐screen data sets and the COAG chromosome 5 data sets provided by GAW 12. We find linkage signals at location (in the order of the strength of the signal) 45 cM on chromosome 6, 23 cM on chromosome 20, and 30 cM on chromosome 1. No linkage signal is found on chromosome 5. © 2001 Wiley‐Liss, Inc.     

A novel method to identify gene-gene effects in nuclear families: the MDR-PDT

It is now well recognized that gene-gene and gene-environment interactions are important in complex diseases, and statistical methods to detect interactions are becoming widespread. Traditional parametric approaches are limited in their ability to detect high-order interactions and handle sparse data, and standard stepwise procedures may miss interactions that occur in the absence of detectable main effects. To address these limitations, the multifactor dimensionality reduction (MDR) method [Ritchie et al., 2001: Am J Hum Genet 69:138-147] was developed. The MDR is well-suited for examining high-order interactions and detecting interactions without main effects. The MDR was originally designed to analyze balanced case-control data. The analysis can use family data, but requires a single matched pair be selected from each family. This may be a discordant sib pair, or may be constructed from triad data when parents are available. To take advantage of additional affected and unaffected siblings requires a test statistic that measures the association of genotype with disease in general nuclear families. We have developed a novel test, the MDR-PDT, by merging the MDR method with the genotype-Pedigree Disequilibrium Test (geno-PDT)[Martin et al., 2003: Genet Epidemiol 25:203-213]. MDR-PDT allows identification of single-locus effects or joint effects of multiple loci in families of diverse structure. We present simulations to demonstrate the validity of the test and evaluate its power. To examine its applicability to real data, we applied the MDR-PDT to data from candidate genes for Alzheimer disease (AD) in a large family dataset. These results show the utility of the MDR-PDT for understanding the genetics of complex diseases.     

Exploring causality via identification of SNPs or haplotypes responsible for a linkage signal

In a small chromosomal region, a number of polymorphisms may be both linked to and associated with a disease. Distinguishing the potential causal sites from those indirectly associated due to linkage disequilibrium (LD) with a causal site is an important problem. This problem may be approached by determining which of the associations can explain the observed linkage signal. Recently, several methods have been proposed to aid in the identification of disease associated polymorphisms that may explain an observed linkage signal, using genotype data from affected sib pairs (ASPs) [Li et al. [2005] Am. J. Hum. Genet. 76:934-949; Sun et al. [2002] Am. J. Hum. Genet. 70:399-411]. These methods can be used to test the null hypothesis that a candidate single nucleotide polymorphism (SNP) is the sole causal variant in the region, or is in complete LD with the sole causal variant in the region. We extend variations of these methods to test for complete LD between a disease locus and haplotypes composed of two or more tightly linked candidate SNPs. We study properties of the proposed methods by simulation and apply them to type 1 diabetes data for ASPs and their parents at candidate SNP and microsatellite marker loci in the Insulin (INS) gene region.     

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).     

Analysis of Single Nucleotide Polymorphisms in Candidate Genes Using the Pedigree Disequilibrium Test

The pedigree disequilibrium test (PDT) has been proposed recently as a test for association in general pedigrees [Martin et al., Am J Hum Genet 67:146–54, 2000]. The Genetic Analysis Workshop (GAW) 12 simulated data, with many extended pedigrees, is an example the type of data to which the PDT is ideally suited. In replicate 42 from the general population the PDT correctly identifies candidate genes 1, 2, and 6 as containing single nucleotide polymorphisms (SNPs) that arc significantly associated with the disease. We also applied the truncated product method (TPM) [Zaykin et al., Genet Epidemiol, in press] to combine p‐values in overlapping windows across the genes. Our results show that the TPM is helpful in identifying significant SNPs as well as removing spurious false positives. Our results indicate that, using the PDT, functional disease‐associated SNPs can be successfully identified with a dense map of moderately polymorphic SNPs. © 2001 Wiley‐Liss, Inc.     

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.     

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.     

Affected-sib-pair test for linkage based on constraints for identical-by-descent distributions corresponding to disease models with imprinting

Holmans' possible triangle test for affected sib pairs has proven to be a powerful tool for linkage analysis. This test is a likelihood-ratio test for which maximization is restricted to the set of possible sharing probabilities. Here, we extend the possible triangle test to take into account genomic imprinting, which is also known as parent-of-origin effect. While the classical test without imprinting looks at whether affected sib pairs share 0, 1, or 2 alleles identical-by-descent, the likelihood-ratio test allowing for imprinting further distinguishes whether the sharing of exactly one allele is through the father or mother. Thus, if the disease gene is indeed subject to imprinting, the extended test presented here can take into account that affecteds will have inherited the mutant allele preferentially from one particular parent. We calculate the sharing probabilities at a marker locus linked to a disease susceptibility locus. Using our formulation, the constraints on these probabilities given by Dudoit and Speed ([1999] Statistics in Genetics; New York: Springer) can easily be verified. Next, we derive the asymptotic distribution of the restricted likelihood-ratio test statistic under the null hypothesis of no linkage, and give LOD-score criteria for various test sizes. We show, for various disease models, that the test allowing for imprinting has significantly higher power to detect linkage if imprinting is indeed present, at the cost of only a small reduction in power in case of no imprinting. Altogether, unlike many methods currently available, our novel model-free sib-pair test adequately models the epigenetic parent-of-origin effect, and will hopefully prove to be a useful tool for the genetic mapping of complex traits.     

Empirical genomewide significance levels established by whole genome simulations

The advent of high-resolution genetic maps and semiautomated genotyping technology has opened the way for genome screening in genetically complex traits. Many such screens are now under way, or completed, most using multipoint nonparametric linkage analysis of affected sibling pairs. This type of linkage analysis uses all the available genotype information to calculate the maximum lod score (MLS) value at each point in the genome, and thereby generates MLS profiles along each chromosome. Any positive MLS values indicate potential linkage, but the peaks in these profiles, which may be referred to as “hits,” identify the most likely locations of disease susceptibility genes. However, such analysis presents serious problems of multiple testing, and the assessment of the statistical significance of hits has become a contentious issue [Lander and Kruglyak (1995) Nat Genet 11:241–247; Curtis (1996) Nat Genet 12:356–357; Witte et al. (1996) Nat Genet 12:355–356]. Having recently completed a genome screen in multiple sclerosis, we decided to investigate the statistical properties of our study by simulation. We report here in detail the results of this simulation study. Our main conclusion is that, for the particular set of families and markers used in our screen, an MLS of 3.2 carries a genome-wide significance of 5% (that is, there is a 5% probability of observing at least one false hit, above this threshold in a complete genome screen). This value is closer to the familiar limit of 3.0, originally suggested by Morton [1955; Am J Hum Genet 7:277–318] than to the more stringent limit of 4.0 recently proposed by Lander and Kruglyak [1995; Nat Genet 11:241–247]. This is somewhat reassuring, in view of the very large sample sizes that would be necessary to achieve adequate power to detect linkage at the more stringent threshold. Genet. Epidemiol. 14:223–229,1997. © 1997 Wiley-Liss, Inc.     

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.     

Combining Multiple Phenotypic Traits Optimally for Detecting Linkage with Sib‐Pair Observations

A number of investigators have proposed regression methods for testing linkage between a phenotypic trait and a genetic marker with sib‐pair observations. Xu et al. [Am J Hum Genet 67:1025–8, 2000] studied a unified method for testing linkage, which tends to be more powerful than existing procedures. Often there are multiple traits, which are linked to a common set of genetic markers. In this paper, we present a simple generalization of the unified test to combine information from multiple traits optimally. We use the simulated Genetic Analysis Workshop 12 data to illustrate this methodology and show the advantage of using the combined tests over the single‐trait tests. For the four quantitative traits (Q1,...,Q4) studied, our linkage results suggest that major loci affecting Q1 and Q2 localize at or near markers D02G172, D19G032, and D09G122, while loci affecting Q3 and Q4 localize at or near markers D09G122 and D17G051. © 2001 Wiley‐Liss, Inc.     

Asymptotic distributions of polylocus test statistics

Polylocus linkage analysis methods are modified two-point analyses which aim to approach the information gain of multilocus analysis. Terwilliger and Ott [(1992) Am J Hum Genet 51:A202, (1993) Genet Epidemiol 10:477–482] put forth two such methods. This paper presents asymptotic approximations to the null distribution of the likelihood ratio statistics for these two methods, correcting earlier reports [Terwilliger and Ott (1993) Genet Epidemiol 10:477–482; Schaid and Elston (1994) Genet Epidemiol 11:1–17]. The performance of the approximations is then assessed for finite samples of fully informative meioses. © 1995 Wiley-Liss, Inc.     

Sib-pair collection strategies for complex diseases

When planning an affected sib pair collection for use in a genomewide search for complex trait loci, researchers must ask: (a) Which family structures will yield the most informative pairs? And (b) should recruitment extend beyond the index sib pair? The optimal collection strategy will depend on the trait's genetic architecture, but this is rarely known for non-Mendelian diseases. In the present report, we study the consequences of collecting only those sib pairs arising from pedigrees with a precisely specified structure as opposed to a strategy that collects all affected sib pairs at random (i.e., blind to the affection status of first-degree relatives). The former approach turns out to be risky because the power of specific pedigree structures can vary dramatically even among models producing identical observable parameters (such as population prevalence and sibling recurrence rate). In contrast, the latter approach typically involves only a modest loss of power as compared with the optimal (but unknowable) design. Further, we compare the strategy of collecting all affected sib pairs at random with the alternative of imposing some modest limitations on family structure (e.g., presence of at least one unaffected sib or parent). The latter approach generally provides some increase in power but entails additional effort to contact and phenotype relatives: the overall merit of imposing such requirements needs to be evaluated in the context of the specific disease to be studied and of the clinical and analytical resources available. In addition, these findings suggest that a further explanation for failure to replicate positive complex trait linkages lies in differences in ascertainment strategy between data sets. Genet. Epidemiol. 15:317–340,1998. © 1998 Wiley-Liss, Inc.     

Model‐Free Linkage Analysis: Performance Under Real‐World Conditions

The simulated data of the Genetic Analysis Workshop 12 problem set affords an ideal environment for testing real‐world performance of model‐free linkage analysis methods. To this end, we applied three different methods of model‐free linkage analysis: mod scores [Hodge and Elston, Genet Epidemiol 11:329–42, 1994], maximized maximum lod score (MMLS) [Greenberg et al., Am J Hum Genet 63:870–9, 1998], and nonparametric linkage (NPL) scores [Whittemore and Halpern, Biometrics 50:118–27, 1994], as well as standard parametric linkage analysis to the detection of major gene 6 (MG6) using only the qualitative disease status data. Our results indicate that both mod scores and NPL scores perform well, even in the presence of an extremely complicated disease model. MMLS analysis did not perform well, except at the disease locus itself. © 2001 Wiley‐Liss, Inc.     

Triangle Test Statistic in Discordant Sib Pairs: Test of Genetic Heterogeneity of Asthma and Atopy in CSGA Families

The purpose of our study was to detect genetic heterogeneity (i.e., different genotype relative risks of genetic factor) between atopic and non‐atopic asthma and between atopy associated or independent of asthma. Genetic heterogeneity was tested in the Caucasian Collaborative Study on the Genetics of Asthma families using the TTS (triangle test statistic) and the predivided sample test. The ITS was proposed to detect both linkage and intra‐sib‐pair genetic heterogeneity; such heterogeneity may exist if the sibs differ for a factor on which the penetrances of the putative linked gene depend. The TTS has been applied to asthmatic pairs discordant for atopy and atopic sib pairs discordant for asthma. To confirm genetic heterogeneity detected by the ITS, the predivided sample test was also applied among concordant and discordant sib pairs. The analyses detected a genetic factor on chromosome 8p that could be involved in atopy with different genotype relative risks according to whether asthma is present. This would suggest a pleiotropic effect of this genetic factor in asthma and atopy. Two other regions located on chromosomes 8q and 20p were detected for genetic heterogeneity with asthma and atopy, respectively, but the factor of heterogeneity could be independent from the presence of atopy or asthma, respectively. It could be a characteristic of the disease such as the severity or the presence of an environmental factor. © 2001 Wiley‐Liss, Inc.     

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.     

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.