Title: Localization of linked genes for type I diabetes.
Abstract.
Methods that consider multiple susceptibility genes may increase the accuracy and precision of location estimates for disease genes involved in the predisposition to complex disorders, such as type I diabetes. When two genes contributing to one trait are located near one another on the same chromosome, effects of both genes must be taken into account when assessing linkage evidence for one of them. Conditional methods are designed to detect linkage to a second gene locus when the first gene locus has been specified (Farrall 1997 Genet Epidemiol 14:103-115; Cordell et al 2000 Am J Hum Genet 66:1273-1286), whereas simultaneous methods assess linkage for two linked gene loci when the location of both genes needs to be estimated from the data (Biernacka et al, 2003, Am J Hum Genet 75(5S):193). The latter method applies a generalized estimating equations approach to model IBD sharing data from multiple linked markers from ASPs. Confidence intervals for gene locations can be constructed based on large sample approximations, and test statistics calculated for evaluating evidence for two versus one disease genes in a single region (Biernacka and Bull, 2003). Here we present an application of our methods to data from a genome scan for type 1 diabetes (Nature Genetics 19: 297-300, 1998). We estimate the locations of two putative disease genes on chromosomes 6 estimated to be approximately 20 cM apart. We compare our results to conditional results from other studies of the same data. Specifically, we discuss differences between our method, which simultaneously estimates the locations of the two linked genes, to the conditional approach proposed by Farral (1997).
Title: A GEE approach for disease gene localization: Using IBD sharing proportions versus mean IBD.
Abstract.
Allele-sharing models for affected sib pairs (ASPs) can be based on identical-by-descent (IBD) sharing proportions, on mean IBD sharing, or on other parameters. Liang et al. (Hum Hered 51:64-78, 2001) introduced a generalized estimating equations (GEE) approach to estimate two parameters: the location of a trait gene and mean IBD sharing by ASPs at that locus. We recently extended this model to simultaneously localize two linked disease genes in a region (Biernacka et al., Am J Hum Genet 73(5S):193, 2003), and proposed test procedures to evaluate evidence for two versus one disease loci (Biernacka and Bull, Genet Epidemiol, 25(3):239, 2003). To compute empirical p-values of these test statistics, however, we need to specify the IBD proportions at the disease gene under the null one-locus model. Here we present a modification of the one-locus model of Liang et al. to estimate not only the two parameters estimated by their GEE procedure, but also the ASP IBD sharing proportions at a single disease gene. We studied the relative performance of the two methods by simulation and found that, in small samples, the procedure based on mean IBD sharing had better performance. In large samples, however, estimation of IBD sharing proportions at a disease gene yielded more efficient location estimates. Using a diabetes data example, we illustrate the application of the IBD sharing proportion estimates to empirical p-value computation.
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, general estimating equations can be used to estimate the putative disease gene locations and expected identical-by-descent allele sharing in affected sib pairs at these genes. We propose methods to evaluate the evidence for two versus one disease loci in a region in a quasi-likelihood framework. We formulated tests based on wald, modified quasi-score and approximate quasi-likelihood ratio test statistics. A number of issues arise in this testing problem that affect the null distributions of the test statistics, including an identifiability problem. Because of the difficulties in determining the asymptotic null distributions of these statistics and the small sample sizes generally available in genetic studies, we assess significance empirically by simulation. We evaluated the accuracy and efficiency of each of the tests by simulation, and found that the approximate quasi-likelihood ratio tests and our modified quasi-score test perform better than the wald test. Power to detect the presence of two linked disease genes increases with the number of affected sib pairs, greater IBD sharing at the two loci, and larger distance between the two loci.
Title: One gene or two? Methods for estimation and testing for two linked disease genes
Abstract.
Simultaneous consideration of multiple susceptibility genes may increase the power to detect genes involved in the predisposition to complex disorders, and improve their localization. We have developed a model for the simultaneous localization of two or more susceptibility genes in one region. We derived an expression for expected allele sharing in affected sib pairs across a chromosomal segment containing two or more susceptibility genes. With this expression for the mean allele sharing, the generalized estimating equation (GEE) approach can be used to estimate the locations of two disease genes simultaneously as was proposed by Liang et al. (Human Heredity 51, 2001, 64-78) for the case of a single disease gene in a region. We developed an algorithm that uses information on marker IBD sharing in affected sib pairs to estimate locations of two linked disease genes and the expected IBD sharing in affected sib pairs at these two disease loci. We studied properties of the estimates obtained by this new method through simulation for a variety of disease gene models. Here we propose several procedures which use estimates from one-locus and two-locus models to evaluate the evidence for two versus one disease loci in the region. We considered approximate testing procedures based on wald, quasi-likelihood, and quasi-score statistics. Simulation results show that standard deviations of parameter estimates obtained using robust variance estimates are biased downward, which has implications for properties of test statistics which rely on these estimates. We have applied the proposed estimation and testing methods to ASP data from a diabetes genome-scan (Nature Genetics 19: 297-300, 1998) and obtained suggestive evidence for two linked disease genes on chromosome 16. Our results suggest that the proposed method can improve disease gene localization when two disease genes are present in one chromosomal region. The power to identify two linked disease genes depends on the effect size of the two genes measured by excess allele sharing at the two loci, the distance between the two genes, and sample size.
Title: Joint localization of two linked disease genes: Derivation, evaluation, and application of a new method.
Abstract.
Methods that simultaneously consider multiple susceptibility genes may increase the power to detect genes involved in the predisposition to complex disorders. This belief has led to increased interest in procedures that test for the existence and/or interaction of secondary genes taking into account the presence of primary genes. Extending the work of Liang et al. (Human Heredity 51: 64-78, 2001), we have developed a model for the simultaneous localization of two susceptibility genes in one region. We derived an expression for expected allele sharing in affected sib pairs at each point across a chromosomal segment containing two susceptibility genes. With this expression for the mean allele sharing, generalized estimating equations (GEE) can be used to estimate the locations of both disease genes simultaneously. We developed an algorithm that uses information on marker IBD sharing in affected sib pairs to estimate the expected IBD sharing in affected sib pairs at two linked disease loci and the locations of the two genes. Furthermore, confidence regions for gene locations can be constructed based on large sample approximations using parameter estimates and a robust estimate of their covariance matrix. Via simulation studies we found that good estimates of disease gene locations can be obtained by this method. Properties of the estimates and confidence intervals, including bias, precision, and confidence interval coverage, have been studied for a range of genetic models. The ability of this method to localize disease genes improves with increased expected allele sharing at the disease genes, increased distance between the disease genes, and increased sample size. We applied the described methods to data from a genome scan for type 1 diabetes (n=263) (Nature Genetics 19: 297-300, 1998) and obtained estimates of two disease gene locations on chromosome 16, estimated to be approximately 50 cM apart. Our results suggest that the proposed method can improve disease gene localization and aid in separating large peaks when two disease genes are present in one chromosomal region.
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