Optimal Selection of Sib Pairs from Random Samples for Linkage Analysis of a QTL Using the EDAC Test

Percentages of extremely concordant and extremely discordant sib pairs are calculated that maximize the power to detect a quantitative trait locus (QTL) under a variety of circumstances using the EDAC test. We assume a large fixed number of randomly sampled sib pairs, such as one would hope to find in the large twin registries, and limited resources to genotype a certain number of selected sib pairs. Our aim is to investigate whether optimal selection can be achieved when prior knowledge concerning the QTL gene action, QTL allele frequency, QTL effect size, and background (residual) sib correlation is limited or absent. To this end we calculate the best selection percentages for a large number of models, which differ in QTL gene action allele frequency, background correlation, and QTL effect size. By averaging these percentages over gene action, over allele frequency, over gene action, and over allele frequencies, we arrive at general recommendations concerning selection percentages. The soundness of these recommendations is subsequently in a number of test cases.     

Recurrence risk for major congenital heart defects in Sweden: A registry study

During the period 1981–1986, 1605 infants presenting a major congenital heart defect (CHD) were identified in Sweden. Using the personal identification numbers of the mothers, 1507 of them could be linked to the Medical Birth Registry and two controls were selected for each infant. For this total of 4521 infants, 2686 postoccurrence sibs born during the period 1981–1989 were identified from the Medical Birth Registry. The tendency to have one or more sibs was higher among cases than among controls and was correlated to the life status of the proband. This tendency did not vary according to the type of CHD when controlling for life status. The prevalence at birth of CHD was almost four times higher among sibs of CHD infants than among sibs of normal infants. The tendency to have a sib with an extracardiac malformation did not differ between CHD probands and normal probands. The importance of only including births occurring after the proband when evaluating recurrence risks is stressed. © 1994 Wiley-Liss, Inc.     

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.     

Tests for the presence of two linked disease susceptibility genes

For diseases with complex genetic etiology, more than one susceptibility gene may exist in a single chromosomal region. Under explicit assumptions about the number of disease genes in a region, generalized estimating equations (GEE) can be used to estimate the putative disease gene location(s) and expected identical-by-descent allele sharing in affected sib pairs at these gene(s). Extending the work of Liang et al. developed a method for simultaneous localization of two susceptibility genes in one region using marker identical-by-descent (IBD) sharing in affected sib pairs. Here we propose methods to evaluate the evidence for two versus one disease loci in a region in a quasi-likelihood/GEE framework. We describe tests based on approximate quasi-likelihood ratio and generalized score test statistics. Because of difficulties in determining the asymptotic null distributions of these statistics and the small sample sizes that can be available in genetic studies, we recommend that significance be evaluated empirically. Application of the described methods to data from a genome scan for type 1 diabetes yielded some evidence for two linked disease genes on chromosome 6, approximately 20 cM apart (p value for an approximate quasi-likelihood ratio test=0.049). In simulation studies, we found that both tests performed quite well for a range of scenarios. Power to detect the presence of two linked disease genes increased with the number of affected sib pairs, greater IBD sharing at the two loci, and larger distance between the two loci.     

Simultaneous localization of two linked disease susceptibility genes

For diseases with complex genetic etiology, more than one susceptibility gene may exist in a single chromosomal region. Extending the work of Liang et al. ([2001] Hum. Hered. 51:64-78), we developed a method for simultaneous localization of two susceptibility genes in one region. We derived an expression for expected allele sharing of an affected sib pair (ASP) at each point across a chromosomal segment containing two susceptibility genes. Using generalized estimating equations (GEE), we developed an algorithm that uses marker identical-by-descent (IBD) sharing in affected sib pairs to simultaneously estimate the locations of the two genes and the mean IBD sharing in ASPs at these two disease loci. Confidence intervals for gene locations can be constructed based on large sample approximations. Application of the described methods to data from a genome scan for type 1 diabetes (Mein et al. [1998] Nat. Genet. 19:297-300) yielded estimates of two putative disease gene locations on chromosome 6, approximately 20 cM apart. Properties of the estimators, including bias, precision, and confidence interval coverage, were studied by simulation for a range of genetic models. The simulations demonstrated that the proposed method can improve disease gene localization and aid in resolving large peaks when two disease genes are present in one chromosomal region. Joint localization of two disease genes improves with increased excess allele sharing at the disease gene loci, increased distance between the disease genes, and increased number of affected sib pairs in the sample.     

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.     

Multipoint analysis using affected sib pairs: incorporating linkage evidence from unlinked regions

In this paper, we proposed a multipoint method to assess evidence of linkage to one region by incorporating linkage evidence from another region. This approach uses affected sib pairs in which the number of alleles shared identical by descent (IBD) is the primary statistic. This generalized estimating equation (GEE) approach is robust in that no assumption about the mode of inheritance is required, other than assuming the two regions being considered are unlinked and that there is no more than one susceptibility gene in each region. The method proposed here uses data from all available families to simultaneously test the hypothesis of statistical interaction between regions and to estimate the location of the susceptibility gene in the target region. As an illustration, we have applied this GEE method to an asthma sib pair study (Wjst et al. [1999] Genomics 58:1-8), which earlier reported evidence of linkage to chromosome 6 but showed no evidence for chromosome 20. Our results yield strong evidence to chromosome 20 (P value = 0.0001) after incorporating linkage information from chromosome 6. Furthermore, it estimates with 95% certainty that the map location of the susceptibility gene is flanked by markers D20S186 and D20S101, which are approximately 16.3 cM apart.     

Homozygous parent affected sib pair method for detecting disease predisposing variants: Application to insulin dependent diabetes mellitus

For complex genetic diseases involving incomplete penetrance, genetic heterogeneity, and multiple disease genes, it is often difficult to determine the molecular variant (s) responsible for the disease pathogenesis. Linkage and association studies may help identify genetic regions and molecular variants suspected of being directly responsible for disease predisposition or protection, but, especially for complex diseases, they are less useful for determining when a predisposing molecular variant has been identified. In this paper, we expand upon the simple concept that if a genetic factor predisposing to disease has been fully identified, then a parent homozygous for this factor should transmit either of his/her copies at random to any affected children. Closely linked markers are used to determine identity by descent values in affected sib pairs from a parent homozygous for a putative disease predisposing factor. The expected deviation of haplotype sharing from 50%, when not all haplotypes carrying this factor are in fact equally predisposing, has been algebraically determined for a single locus general disease model. Equations to determine expected sharing for multiple disease alleles or multiple disease locus models have been formulated. The recessive case is in practice limiting and therefore can be used to estimate the maximum proportion of putative susceptibility haplotypes which are in fact predisposing to disease when the mode of inheritance of a disease is unknown. This method has been applied to 27 DR3/DR3 parents and 50 DR4/DR4 parents who have at least 2 children affected with insulin dependent diabetes mellitus (IDDM). The transmission of both DR3 and DR4 haplotypes is statistically different from 50% (P < 0.05 and P < 0.001, respectively). An upper estimate for the proportion of DR3 haplotypes associated with a high IDDM susceptibility is 49%, and for DR4 haplotypes 38%. Our results show that the joint presence of non-Asp at DQP position 57 and Arg at DQa position 52, which has been proposed as a strong IDDM predisposing factor, is insufficient to explain the HLA component of IDDM predisposition. © 1993 Wiley-Liss, Inc.     

Sib-based detection of QTLs

Association and transmission/nontransmission analyses were used in a split sample design to identify disease susceptibility alleles at two loci. Sib-pair analysis on various subsets of the data identified an additional four regions that yielded signals of disease predisposing quantitative trait loci (QTLs). Three of these four regions represented Type I errors. A new simulation indicates that a multiplex sampling strategy would substantially improve QTL detection for this oligogenic transmission model. © 1995 Wiley-Liss, Inc.     

系统性红斑狼疮的传递/不平衡分析

目的　应用传递 /不平衡方法 ,分析HLA -D区系统性红斑狼疮 (SLE)等位基因的家系相关性。方法　对 42个SLE家系提取DNA ,PCR并进行杂交 ,根据DQA1、DQB1、DRB1位点的关联分析结果 ,对这 3个位点关联显著的等位基因进行传递 /不平衡分析。结果　DQA1 0 10 2在家系中经TDT传递不平衡检验 ,χ2 =5 .80 ,Pc<0 .0 5 ;DQA1 0 5 0 1,χ2 =3.2 4,P >0 .0 5 ;DQB1、DRB1位点等位基因经TDT与sTDT的联合检验 ,未发现显著相关性 ,z值均小于 1.96 ,P >0 .0 5。结论　传递 /不平衡检验结果发现 ,DQA1 0 10 2等位基因与SLE相关 ,提示该等位基因可能是中国南方汉族人群中与SLE有关的一个易感等位基因。