A method for identifying genes related to a quantitative trait, incorporating multiple siblings and missing parents

When studying either qualitative or quantitative traits, tests of association in the presence of linkage are necessary for fine-mapping. In a previous report, we suggested a polytomous logistic approach to testing linkage and association between a di-allelic marker and a quantitative trait locus, using genotyped triads, consisting of an individual whose quantitative trait has been measured and his or her two parents. Here we extend that approach to incorporate marker information from entire nuclear families. By computing a weighted score function instead of a maximum likelihood test, we allow for both an unspecified correlation structure between siblings and "informative" family size. Both this approach and our original approach allow for population admixture by conditioning on parental genotypes. The proposed method allows for missing parental genotype data through a multiple imputation procedure. We use simulations based on a population with admixture to compare our method to a popular non-parametric family-based association test (FBAT), testing the null of no association in the presence of linkage.     

Candidate gene association analysis for a quantitative trait, using parent-offspring trios

With the increasing availability of genetic data, many studies of quantitative traits focus on hypotheses related to candidate genes, and also gene-environment (G x E) and gene-gene (G x G) interactions. In a population-based sample, estimates and tests of candidate gene effects can be biased by ethnic confounding, also known as population stratification bias. This paper demonstrates that even a modest degree of ethnic confounding can lead to unacceptably high type I error rates for tests of genetic effects. The parent-offspring trio design is reviewed, and several forms of the quantitative transmission disequilibrium test (QTDT) are summarized. A variation of the QTDT (QTDTM) is described that is based on a linear regression model with multiple intercepts, one per parental mating type. This and other models are expanded to allow testing of G x E and G x G interactions. A method for computing required sample sizes using direct computations is described. Sample size requirements for tests of genetic main effects and G x E and G x G interactions are compared across various QTDT approaches to infer their efficiencies relative to one another. The QTDTM is found to meet or exceed the efficiency of other QTDT approaches. For example, the QTDTM is approximately 3% more efficient than the QTDT of Rabinowitz ([1997] Hum. Hered. 47:342-350) for testing a genetic main effect, but can be as much as twice as efficient for testing G x E interaction, and three times more efficient for testing G x G interaction.     

CAPL: a novel association test using case-control and family data and accounting for population stratification

The recent successes of GWAS based on large sample sizes motivate combining independent datasets to obtain larger sample sizes and thereby increase statistical power. Analysis methods that can accommodate different study designs, such as family-based and case-control designs, are of general interest. However, population stratification can cause spurious association for population-based association analyses. For family-based association analysis that infers missing parental genotypes based on the allele frequencies estimated in the entire sample, the parental mating-type probabilities may not be correctly estimated in the presence of population stratification. Therefore, any approach to combining family and case-control data should also properly account for population stratification. Although several methods have been proposed to accommodate family-based and case-control data, all have restrictions. Most of them require sampling a homogeneous population, which may not be a reasonable assumption for data from a large consortium. One of the methods, FamCC, can account for population stratification and uses nuclear families with arbitrary number of siblings but requires parental genotype data, which are often unavailable for late-onset diseases. We extended the family-based test, Association in the Presence of Linkage (APL), to combine family and case-control data (CAPL). CAPL can accommodate case-control data and families with multiple affected siblings and missing parents in the presence of population stratification. We used simulations to demonstrate that CAPL is a valid test either in a homogeneous population or in the presence of population stratification. We also showed that CAPL can have more power than other methods that combine family and case-control data.     

The TDT reveals linkage and linkage disequilibrium in a rare disease

We used the TDT as the basis for our analysis of data from Problem 1 of GAW9. Among the 360 marker loci on six chromosomes, we searched for any that might show both linkage and allelic association with the disease. We applied the TDT to each allele at every marker locus and found strong evidence for linkage in two regions: one on chromosome 1, another on chromosome 5. ©1995 Wiley-Liss, Inc.     

Issues concerning association studies for fine mapping a susceptibility gene for a complex disease

The usefulness of association studies for fine mapping loci with common susceptibility alleles for complex genetic diseases in outbred populations is unclear. We investigate this issue for a battery of tightly linked anonymous genetic markers spanning a candidate region centered around a disease locus, and study the joint behavior of chi-square statistics used to discover and to localize the disease locus. We used simulation methods based on a coalescent process with mutation, recombination, and genetic drift to examine the spatial distribution of markers with large noncentrality parameters in a case-control study design. Simulations with a disease allele at intermediate frequency, presumably representing an old mutation, tend to exhibit the largest noncentrality parameter values at markers near the disease locus. In contrast, simulations with a disease allele at low frequency, presumably representing a young mutation, often exhibit the largest noncentrality parameter values at markers scattered over the candidate region. In the former cases, sample sizes or marker densities sufficient to detect association are likely to lead to useful localization, whereas, in the latter case, localization of the disease locus within the candidate region is much less likely, regardless of the sample size or density of the map. The effects of increasing sample size or marker density are also investigated. Based upon a single marker analysis, we find that a simple strategy of choosing the marker with the smallest associated P value to begin a laboratory search for the disease locus performs adequately for a common disease allele. We also investigated a strategy of pooling nearby sites to form multiple allele markers. Using multiple degree of freedom chi-square tests for two or three nearby sites, we found no clear advantage of this form of pooling over a single marker analysis. Genet. Epidemiol. 20:432-457, 2001. Published by Wiley-Liss, 2001.     

Comparison of Novel and Existing Methods for Detection of Linkage Disequilibrium Using Parent‐Child Trios in the GAW12 Genetic Isolate Simulated Data

A novel method for joint detection of association caused by linkage disequilibrium (LD) and estimation of both recombination fraction and linkage disequilibrium parameters was compared to several existing implementations of the transmission/disequilibrium test (TDT) and modifications of the TDT in the simulated genetic isolate data from Genetic Analysis Workshop 12. The first completely genotyped trio of affected child and parents was selected from each family in each replicate so that the TDT tests are valid tests of linkage and association, rather than being only valid as tests for linkage. In general, power to detect LD using the genome‐wide scan markers was inadequate in the individual replicate samples, but the power was better when analyzing several SNP markers in candidate gene 1. © 2001 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.     

Investigation of the candidate genes ACTHR and Golf for bipolar illness by the transmission/disequilibrium test

Several versions of the transmission/disequilibrium test (TDT) were applied to the two candidate genes ACTHR and Golf for bipolar illness. Analyses were carried out separately for paternal and maternal transmission. Evidence for linkage and association was found for ACTHR for paternal transmission in support of a parent-of-origin effect. Possible evidence for segregation distortion was found for one of the two markers for Golf for maternal transmission. © 1997 Wiley-Liss, Inc.     

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.     

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.     

A general and accurate approach for computing the statistical power of the transmission disequilibrium test for complex disease genes.

Transmission disequilibrium test (TDT) is a nuclear family-based analysis that can test linkage in the presence of association. It has gained extensive attention in theoretical investigation and in practical application; in both cases, the accuracy and generality of the power computation of the TDT are crucial. Despite extensive investigations, previous approaches for computing the statistical power of the TDT are neither accurate nor general. In this paper, we develop a general and highly accurate approach to analytically compute the power of the TDT. We compare the results from our approach with those from several other recent papers, all against the results obtained from computer simulations. We show that the results computed from our approach are more accurate than or at least the same as those from other approaches. More importantly, our approach can handle various situations, which include (1) families that consist of one or more children and that have any configuration of affected and nonaffected sibs; (2) families ascertained through the affection status of parent(s); (3) any mixed sample with different types of families in (1) and (2); (4) the marker locus is not a disease susceptibility locus; and (5) existence of allelic heterogeneity. We implement this approach in a user-friendly computer program: TDT Power Calculator. Its applications are demonstrated. The approach and the program developed here should be significant for theoreticians to accurately investigate the statistical power of the TDT in various situations, and for empirical geneticists to plan efficient studies using the TDT.     

Parametric Linkage Analysis and Disequilibrium Methods to Identify Loci for Complex Disease

A two‐step process was used to find loci contributing to the qualitative disease phenotype in the Genetic Analysis Workshop (GAW) 12 simulated data. The first step used parametric linkage analysis with a limited number of dominant and recessive models to detect linkage to chromosomal regions. Subsequently, a subset of the simulated biallelic sequence polymorphisms was used for transmission/disequilibrium tests and to build haplotypes to fine map the disease‐predisposing polymorphism(s). A haplotype, strongly associated with the disease phenotype whose proximal end was within 39 base pairs of the functional allele for simulated major gene 6, was identified in the isolated population. © 2001 Wiley‐Liss, Inc.     

General score tests for associations of genetic markers with disease using cases and their parents

Association studies of genetic markers with disease play a critical role in the dissection of genetically complex traits because they are relatively easy to conduct and are useful for fine-scale mapping of genetic traits. The advantage of family-based controls has recently received much attention because spurious associations caused by population structure can be controlled for, and marker genotype information on diseased cases and their parents can be used to test the compound hypothesis of both linkage and linkage disequilibrium. However, debate still exists regarding the statistical methods of analysis. Herein are presented statistical methods to test for linkage (in the presence of linkage disequilibrium) between multiallelic genetic markers and disease when diseased subjects (cases) and their parents are sampled. Theoretical considerations for the development of general statistical tests are presented as well as asymptotic formulas to compute their power when planning a study. Furthermore, simulation results for nine specific statistics are used to contrast the power of these methods under different genetic mechanisms leading to disease (dominant vs. recessive, one vs. two high-risk alleles). These results demonstrate substantial gains in power for specific statistical tests designed to detect specified genetic mechanisms. However, without a priori knowledge of the likely genetic mechanism, it is desirable to rely on a fairly robust statistical method, robust so that power is not drastically lost when either dominant or recessive mechanisms are acting, and when either one or more than one marker alleles are associated with disease. Based on both theoretical and simulation results, a general score statistic, which generalizes the transmission/disequilibrium test, tends to offer sufficient power for a variety of genetic mechanisms, so that it is worth considering for broad use in studies which use genetic marker information from both diseased cases and their parents. © 1996 Wiley-Liss, Inc.     

The transmission disequilibrium test and imprinting effects test based on case-parent pairs

The transmission disequilibrium test (TDT) based on case-parents trios is a powerful tool in linkage analysis and association studies. When only one parent is available, the 1-TDT is applicable in the absence of imprinting. In the presence of imprinting, a statistic is proposed, based on case-mother pairs and case-father pairs to test for linkage when association is present as well as to test for association when linkage is present. The recombination fractions are allowed to be sex-specific in this test statistic. Meanwhile, a statistic based on case-parent pairs is proposed to test for imprinting. Both test statistics can be extended to include families with more than one affected offspring. A number of simulation studies are conducted to investigate the validity of the proposed tests. The effects of different ratios of the numbers of case-mother pairs and case-father pairs on the powers of the proposed tests are studied through simulation. The results show that the optimal ratio is 1:1. How to combine case-parents, case-mother pairs, and case-father pairs jointly in testing for linkage, association, and imprinting is addressed.     

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.     

A method for using incomplete triads to test maternally mediated genetic effects and parent-of-origin effects in relation to a quantitative trait

The authors recently developed a semiparametric family-based test for linkage and association between markers and quantitative traits. This quantitative polytomous logistic regression test allows for analysis of families with incomplete information on parental genotype. In addition, it is not necessary to assume normality of the quantitative trait. Previous simulations have shown that the new test is as powerful as the other widely used tests for linkage disequilibrium in relation to a quantitative trait. Here the authors propose an extension to quantitative polytomous logistic regression that allows testing for maternally mediated effects and parent-of-origin effects in the same framework. Missing data on parental genotype are accommodated through an expectation-maximization algorithm approach. Simulations show robustness of the new tests and good power for detecting effects in the presence or absence of offspring effects. Methods are illustrated with birth weight and gestational length, two quantitative outcomes for which data were collected in a Montreal, Canada, study of intrauterine growth restriction between May 1998 and June 2000.     

Genome scanning for complex disease genes using the transmission/disequilibrium test and haplotype-based haplotype relative risk

Two tests for allelic association were applied to a simulated complex disease for the Genetic Analysis Workshop 9. The transmission/disequilibrium test [Spielman et al., 1993] and the haplotype-based haplotype relative risk approach [Terwilliger and Ott, 1992] were used to detect disease-associated alleles in a set of 360 computer-simulated markers located on six chromosomes and genotyped in 200 nuclear families. This analysis emulates a genome-based search for linked markers. Computer simulations were also performed to clarify statistical properties of the TDT. ©1995 Wiley-Liss, Inc.     

Computational Methods for Single‐Point and Multipoint Analysis of Genetic Variants Associated with a Simulated Complex Disorder in a General Population

Several techniques for association analysis have been applied to simulated genetic data for a general population. We describe and compare the performance of three single‐point methods and two multipoint approaches rooted in machine learning and data mining. © 2001 Wiley‐Liss, Inc.     

Adjusting for population heterogeneity: a framework for characterizing statistical information and developing efficient test statistics

The focus of this work is the TDT-type and family-based test statistics used for adjusting for potential confounding due to population heterogeneity or misspecified allele frequencies. A variety of heuristics have been used to motivate and derive these statistics, and the statistics have been developed for a variety of analytic goals. There appears to be no general theoretical framework, however, that may be used to evaluate competing approaches. Furthermore, there is no framework to guide the development of efficient TDT-type and family-based methods for analytic goals for which methods have not yet been proposed. The purpose of this paper is to present a theoretical framework that serves both to identify the information which is available to methods that are immune to confounding due to population heterogeneity or misspecified allele frequencies, and to inform the construction of efficient unbiased tests in novel settings. The development relies on the existence of a characterization of the null hypothesis in terms of a completely specified conditional distribution of transmitted genotypes. An important observation is that, with such a characterization, when the conditioning event is unobserved or incomplete, there is statistical information that cannot be exploited by any exact conditional test. The main technical result of this work is an approach to computing test statistics for local alternatives that exploit all of the available statistical information.