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.     

Method for using complete and incomplete trios to identify genes related to a quantitative trait

A number of tests for linkage and association with qualitative traits have been developed, with the most well-known being the transmission/disequilibrium test (TDT). For quantitative traits, varying extensions of the TDT have been suggested. The quantitative trait approach we propose is based on extending the log-linear model for case-parent trio data (Weinberg et al. [1998] Am. J. Hum. Genet. 62:969-978). Like the log-linear approach for qualitative traits, our proposed polytomous logistic approach for quantitative traits allows for population admixture by conditioning on parental genotypes. Compared to other methods, simulations demonstrate good power and robustness of the proposed test under various scenarios of the genotype effect, distribution of the quantitative trait, and population stratification. In addition, missing parental genotype data can be accommodated through an expectation-maximization (EM) algorithm approach. The EM approach allows recovery of most of the lost power due to incomplete trios.     

Detection of parent-of-origin effects for quantitative traits in complete and incomplete nuclear families with multiple children

For a diallelic genetic marker locus, tests like the parental-asymmetry test (PAT) are simple and powerful for detecting parent-of-origin effects. However, these approaches are applicable only to qualitative traits and thus are currently not suitable for quantitative traits. In this paper, the authors propose a novel class of PAT-type parent-of-origin effects tests for quantitative traits in families with both parents and an arbitrary number of children, which is denoted by Q-PAT(c) for some constant c. The authors further develop Q-1-PAT(c) for detection of parent-of-origin effects when information is available on only 1 parent in each family. The authors suggest the Q-C-PAT(c) test for combining families with data on both parental genotypes and families with data on only 1 parental genotype. Simulation studies show that the proposed tests control the empirical type I error rates well under the null hypothesis of no parent-of-origin effects. Power comparison also demonstrates that the proposed methods are more powerful than the existing likelihood ratio test. Although normality is commonly assumed in methods for studying quantitative traits, the tests proposed in this paper do not make any assumption about the distribution of the quantitative trait.     

A more powerful robust sib-pair test of linkage for quantitative traits

A more powerful robust test for linkage is developed from the methodology of Haseman and Elston [Behav Genet 2(1):3-19, 1972]. This new robust test uses weighted least-squares (WLS) methods to detect linkage between a quantitative trait and a polymorphic marker. For comparison, the characteristics of a test for linakge that uses known trait genotypes for the parents are also studied. Sample sizes needed to detect linkage, calculated using asymptotic results, are compared for 1) the usual Haseman-Elston method, 2) the WLS method, and 3) the method that uses parental trait genotype data. The WLS method needs at most twice the number of sib pairs as does the method that uses information on the trait genotypes of the parents. The small sample properties of the Haseman-Elston (H-E) and WLS tests are investigated by simulation. The power calculations for the H-E method are found to be accurate. The power of the WLS method is overestimated when fewer than 300 sib pairs are studied, but the WLS method is nonetheless more powerful than the usual H-E method. In samples of fewer than 300 sib pairs, the WLS test tends to be anticonservative. Treating all sib pairs from sibships of size 3 or 5 as independent does not increase the significance of the tests.     

Family-based tests for associating haplotypes with general phenotype data: application to asthma genetics

We provide a general purpose family-based testing strategy for associating disease phenotypes with haplotypes when phase may be ambiguous and parental genotype data may be missing. These tests for linkage and association can be used in candidate gene studies with tightly linked markers. Our proposed weighted conditional approach extends the method described in Rabinowitz and Laird to multiple markers. It is attractive because it provides haplotype tests for family-based studies that are efficient and robust to population admixture, phenotype distribution specification, and ascertainment based on phenotypes. It can handle missing parental genotypes and/or missing phase in both offspring and parents. It yields either haplotype-specific (univariate) tests or multi-haplotype (global) tests. This extension has been implemented in the freely available software haplotype FBAT. We used the haplotype FBAT program to test for associations between asthma phenotypes and single nucleotide polymorphisms (SNPs) in the beta-2 adrenergic receptor gene. Whereas no single SNP showed significant association with asthma diagnosis or bronchodilator responsiveness (quantitative trait), a haplotype-based global test found a highly significant association with asthma diagnosis (P value <0.00005) and the measure of bronchodilator responsiveness (P value =0.016).     

Association and linkage analysis of ICD-10 diagnosis for alcoholism

We analyzed the GAW11 data on alcoholism provided by the Collaborative Study on the Genetics of Alcoholism (COGA) using an extension of a new test of linkage and association for quantitative traits developed by George et al. [1999]. This method determines linkage between marker loci and quantitative traits, when allelic association is present between the trait and marker loci, by regressing the disease trait on the parental transmission of the allele of interest. We found no strong evidence of linkage to any markers. However, we found several markers suggestive of possible linkage that may deserve further investigation.     

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.     

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.     

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.     

Robust methods for the detection of genetic linkage for quantitative data from pedigrees

The robust method for detecting linkage developed by Haseman and Elston [The investigation of linkage between a quantitative trait and a marker locus. Behav Genet 2:3-19, 1972] for data from sib pairs is extended to any type of noninbred relative pair. The regression of the squared relative-pair trait difference on the estimated proportion of genes identical by descent (i.b.d.) at a marker locus is shown to depend upon the recombination fraction between the two loci; the regression coefficient is negative if the trait and marker loci are linked. A test for linkage based on data from any informative type of relative pair can thus be obtained by testing that this regression coefficient is less than zero. Formulae for the asymptotic power of such tests for linkage based upon independent relative pairs are developed. Results are also given for the special case in which the proportion of genes shared i.b.d. for relative pairs is known. Finally, a general algorithm is described that will incorporate all available pedigree data to calculate an estimate of the proportion of genes that a relative pair shares i.b.d. at a marker locus.     

Power calculations for likelihood ratio tests for offspring genotype risks, maternal effects, and parent-of-origin (POO) effects in the presence of missing parental genotypes when unaffected siblings are available

Genotype-based likelihood-ratio tests (LRT) of association that examine maternal and parent-of-origin effects have been previously developed in the framework of log-linear and conditional logistic regression models. In the situation where parental genotypes are missing, the expectation-maximization (EM) algorithm has been incorporated in the log-linear approach to allow incomplete triads to contribute to the LRT. We present an extension to this model which we call the Combined_LRT that incorporates additional information from the genotypes of unaffected siblings to improve assignment of incompletely typed families to mating type categories, thereby improving inference of missing parental data. Using simulations involving a realistic array of family structures, we demonstrate the validity of the Combined_LRT under the null hypothesis of no association and provide power comparisons under varying levels of missing data and using sibling genotype data. We demonstrate the improved power of the Combined_LRT compared with the family-based association test (FBAT), another widely used association test. Lastly, we apply the Combined_LRT to a candidate gene analysis in Autism families, some of which have missing parental genotypes. We conclude that the proposed log-linear model will be an important tool for future candidate gene studies, for many complex diseases where unaffected siblings can often be ascertained and where epigenetic factors such as imprinting may play a role in disease etiology.     

X-LRT: a likelihood approach to estimate genetic risks and test association with X-linked markers using a case-parents design

Recently, there has been interest in family-based tests of association to identify X-chromosome genes. However, none of the approaches allow for estimation of genetic risks. We propose a likelihood approach to estimate disease-related marker relative risks and test genotype association using a case-parents design. The test uses nuclear families with a single affected proband and allows additional siblings and missing parental genotypes. Extension to a haplotype test is based on assumptions of random mating and multiplicative penetrance. We investigate power and type I error rate of the likelihood-based test, using simulated data and apply our method to marker data from the monoamine oxidase A&B genes in families with Parkinson disease. We show how efficiency with missing parental information can be improved with additional sibling genotype information. Our likelihood approach offers great flexibility for testing different penetrance relationships within and between sexes. In addition, estimation of disease-related marker relative risks provides a measure of the magnitude of X-linked genetic effects on complex disorders.     

Polytomous logistic regression analysis could be applied more often in diagnostic research

OBJECTIVE: Physicians commonly consider the presence of all differential diagnoses simultaneously. Polytomous logistic regression modeling allows for simultaneous estimation of the probability of multiple diagnoses. We discuss and (empirically) illustrate the value of this method for diagnostic research. STUDY DESIGN AND SETTING: We used data from a study on the diagnosis of residual retroperitoneal mass histology in patients presenting with nonseminomatous testicular germ cell tumor. The differential diagnoses include benign tissue, mature teratoma, and viable cancer. Probabilities of each diagnosis were estimated with a polytomous logistic regression model and compared with the probabilities estimated from two consecutive dichotomous logistic regression models. RESULTS: We provide interpretations of the odds ratios derived from the polytomous regression model and present a simple score chart to facilitate calculation of predicted probabilities from the polytomous model. For both modeling methods, we show the calibration plots and receiver operating characteristics curve (ROC) areas comparing each diagnostic outcome category with the other two. The ROC areas for benign tissue, mature teratoma, and viable cancer were similar for both modeling methods, 0.83 (95% confidence interval [CI]=0.80-0.85) vs. 0.83 (95% CI=0.80-0.85), 0.78 (95% CI=0.75-0.81) vs. 0.78 (95% CI=0.75-0.81), and 0.66 (95% CI=0.61-0.71) vs. 0.64 (95% CI=0.59-0.69), for polytomous and dichotomous regression models, respectively. CONCLUSION: Polytomous logistic regression is a useful technique to simultaneously model predicted probabilities of multiple diagnostic outcome categories. The performance of a polytomous prediction model can be assessed similarly to a dichotomous logistic regression model, and predictions by a polytomous model can be made with a user-friendly method. Because the simultaneous consideration of the presence of multiple (differential) conditions serves clinical practice better than consideration of the presence of only one target condition, polytomous logistic regression could be applied more often in diagnostic research.     

The impact of marker allele frequency misspecification in variance components quantitative trait locus analysis using sibship data

In cases where sibship data are collected for a quantitative trait locus (QTL) linkage study without access to parental genotypes, the proportion of genes shared identical by descent must be estimated using the marker allele frequencies. No systematic study has been conducted to date to evaluate the effect of misspecification of these frequencies on a test of quantitative trait linkage. Analysis of both simulated and actual data on quantitative traits was carried out under various sets of allele frequency estimates. While correctly specifying the allele frequency distribution led to a slightly more powerful test and higher lod scores, the differences were small and would not likely alter the conclusion of a study. These results suggest that, at least for QTL analysis, there is a great deal of tolerance for misspecifying marker allele frequencies with little, if any, appreciable effect on the linkage test. However, the observed variations may be sufficiently large to alter the priority on might give to a positive finding for follow up.     

A logistic regression extension of the transmission disequilibrium test for continuous traits: application to linkage disequilibrium between alcoholism and the candidate genes DRD2 and ADH3

The transmission disequilibrium test (TDT) recently has become a popular method of testing for linkage in the presence of association due to its simplicity and advantages over other within-family analytic methods. In this paper, we describe a logistic regression extension to the TDT that can be used to test for differences in linkage disequilibrium as a function of one or more continuous and/or categorical explanatory variables. We highlight important features of this method and demonstrate some of its possible uses. We applied these analyses to test for linkage disequilibrium between the dopamine receptor D2 (DRD2) and alcohol dehydrogenase 3 (ADH3) genes and both diagnostic and quantitative indices of alcoholism. Using data from the Collaborative Study on the Genetics of Alcoholism data set, we found evidence suggesting linkage disequilibrium between DRD2 and ADH3 and quantitative indices of alcoholism and correlated phenotypes corresponding to smoking and personality. None of the evidence for linkage disequilibrium varied by sex or age.     

Making the most of case-mother/control-mother studies

The prenatal environment plays an important role in many conditions, particularly those with onset early in life, such as childhood cancers and birth defects. Because both maternal and fetal genotypes can influence risk, investigators sometimes use a case-mother/control-mother design, with mother-offspring pairs as the unit of analysis, to study genetic factors. Risk models should account for both the maternal genotype and the correlated fetal genotype to avoid confounding. The usual logistic regression analysis, however, fails to fully exploit the fact that these are mothers and offspring. Consider an autosomal, diallelic locus, which could be related to disease susceptibility either directly or through linkage with a polymorphic causal locus. Three nested levels of assumptions are often natural and plausible. The first level simply assumes Mendelian inheritance. The second further assumes parental mating symmetry for the studied locus in the source population. The third additionally assumes parental allelic exchangeability. Those assumptions imply certain nonlinear constraints; the authors enforce those constraints by using Poisson regression together with the expectation-maximization algorithm. Calculations reveal that improvements in efficiency over the usual logistic analysis can be substantial, even if only the Mendelian assumption is honored. Benefits are even more marked if, as is typical, information on genotype is missing for some individuals.     

New approach to association testing in case-parent designs under informative parental missingness

The transmission/disequilibrium test (TDT) and related methods using genotype data on diseased probands and their both parents (triads) have been popular for testing linkage or association between a disease and a candidate gene. The usefulness of the TDT-type approaches lies mainly in their robustness, in the sense that they are valid under population stratification, arbitrary parental genotype distribution, and "informative" parental missingness where the parental missingness may depend on parental genotypes. Recently, a variety of extended TDTs were developed to accommodate parental missingness and to allow for using incomplete triads, including single-offspring-single-parent families (dyads) and single offspring with no parents (monads). However, these methods usually do not preserve the full robustness of the original TDT. In this paper, we propose a new TDT-type approach based on the conditional likelihood of the proband's genotype given the number and, if any, genotypes of the available parents, as well as the proband's phenotype. This new proposal keeps the full robust property of the original TDT. In addition, the new method is very easy to implement, without the need to specify models on parental mating-type probabilities and on parental missingness.     

Improved use of SNP information to detect the role of genes

A topical question in genetic association studies is the optimal use of the information provided by genotyped single-nucleotide polymorphisms (SNPs) in order to detect the role of a candidate gene in a multifactorial disease. We propose a strategy called "combination test" that tests the association between a quantitative trait and all possible phased combinations of various numbers of SNPs. We compare this strategy to two alternative strategies: the association test that considers each SNP separately, and a multilocus genotype-based test that considers the phased combination of all SNPs together. To compare these three tests, a quantitative trait was simulated under different models of correspondence between phenotype and genotype, including the extreme case when two SNPs interact with no marginal effects of each SNP. The genotypes were taken from a sample of 290 independent individuals genotyped for three genes with various number of SNPs (from 5-8 SNPs). The results show that the "combination test" is the only one able to detect the association when the two SNPs involved in disease susceptibility interact with no marginal effects. Interestingly, even in the case of a single etiological SNP, the "combination test" performed well. We apply the three tests to Genetic Analysis Workshop 12 (Almasy et al. [2001] Genet. Epidemiol. 21:332-338) simulated data, and show that although there was no interactions between the etiological SNPs, the "combination test" was preferable to the two other compared methods to detect the role of the candidate gene.     

Linkage between quantitative trait and marker loci: Methods using all relative pairs

Relative-pair methods for detection of linkage between a quantitative trait and a marker locus have been proposed by a number of authors [e.g., Haseman and Elston, Behav Genet 3–19, 1972; Amos and Elston, Genet Epidemiol 349–360, 1989]. However, development of tests of significance that combine information from different types of relative pairs has been hampered by the presence of correlations between relative pairs from the same pedigree. In this paper, the methodology of generalized estimating equations is used to provide an estimate of the robust covariance matrix of the estimates of the set of relative-pair-type-specific regression parameters. Using this matrix, an asymptotically most powerful test of linkage which optimally combines the information contained in the different types of relative pairs is constructed. This test requires optimal weights that depend on unknown values of heritability and recombination fraction to be chosen a priori. However, simulations show that, in the regions of recombination fraction and heritability of practical interest, the power of the test does not depend strongly on the assumptions made when chosing the optimal weights; as a result, weights that depend only on the number of each type of relative pair and the variability of the marker identity-by-descent probabilities work well in practice. In addition, an approximation to the regression model leads to a simple approach to testing linkage in which only a single regression parameter is estimated from data containing different types of relative pairs. The resulting test is slightly less powerful than the test described above, but its computational simplicity and lack of dependence on a priori weighting schemes suggest potential usefulness in large linkage studies. © 1993 Wiley-Liss. Inc.     

多分类有序反应变量logistic回归应用条件的检验

目的 对多分类有序反应变量logistic回归的应用条件寻求科学合理的检验方法。方法 使用卡方分布的理论，SAS软件及抽样调查方法。结果 设计出多分类有序反应变量logistic回归应用条件的卡方检验方法，推导出反应变量取各水平的概率计算公式及卡方检验中理论值、自由度的计算公式，并在作者主持的国家医师资格临床实践技能考试研究中取得了成功效果。结论 多分类有序反应变量logistic回归得到完善和补充，具有较大的理论和实际意义。