Genetic association mapping based on discordant sib pairs: the discordant-alleles test.

Family-based tests of association provide the opportunity to test for an association between a disease and a genetic marker. Such tests avoid false-positive results produced by population stratification, so that evidence for association may be interpreted as evidence for linkage or causation. Several methods that use family-based controls have been proposed, including the haplotype relative risk, the transmission-disequilibrium test, and affected family-based controls. However, because these methods require genotypes on affected individuals and their parents, they are not ideally suited to the study of late-onset diseases. In this paper, we develop several family-based tests of association that use discordant sib pairs (DSPs) in which one sib is affected with a disease and the other sib is not. These tests are based on statistics that compare counts of alleles or genotypes or that test for symmetry in tables of alleles or genotypes. We describe the use of a permutation framework to assess the significance of these statistics. These DSP-based tests provide the same general advantages as parent-offspring trio-based tests, while being applicable to essentially any disease; they may also be tailored to particular hypotheses regarding the genetic model. We compare the statistical properties of our DSP-based tests by computer simulation and illustrate their use with an application to Alzheimer disease and the apolipoprotein E polymorphism. Our results suggest that the discordant-alleles test, which compares the numbers of nonmatching alleles in DSPs, is the most powerful of the tests we considered, for a wide class of disease models and marker types. Finally, we discuss advantages and disadvantages of the DSP design for genetic association mapping.     

Mapping quantitative trait loci with extreme discordant sib pairs: sampling considerations.

Elsewhere we have proposed the use of extreme discordant sib pairs (EDSPs) for mapping quantitative trait loci in humans. Here we present sample sizes necessary to achieve a given level of power with this study design, as well as the number of sibs that need to be screened to obtain the required sample. Further, we present simple formulas for adjusting sample sizes to account for variable significance levels and power, as well as the density and informativeness of linkage markers in a multipoint sib-pair analysis. We conclude that with EDSPs, the most powerful study design, the smallest genetic effect detectable with a realistic sample size is approximately 10% of the variance of the trait.     

Linkage analysis of alcohol dependence using both affected and discordant sib pairs

The basic idea of affected-sib-pair (ASP) linkage analysis is to test whether the inheritance pattern of a marker deviates from Mendelian expectation in a sample of ASPs. The test depends on an assumed Mendelian control distribution of the number of marker alleles shared identical by descent (IBD), i.e., 1/4, 1/2, and 1/4 for 2, 1, and 0 allele(s) IBD, respectively. However, Mendelian transmission may not always hold, for example because of inbreeding or meiotic drive at the marker or a nearby locus. A more robust and valid approach is to incorporate discordant-sib-pairs (DSPs) as controls to avoid possible false-positive results. To be robust to deviation from Mendelian transmission, here we analyzed Collaborative Study on the Genetics of Alcoholism data by modifying the ASP LOD score method to contrast the estimated distribution of the number of allele(s) shared IBD by ASPs with that by DSPs, instead of with the expected distribution under the Mendelian assumption. This strategy assesses the difference in IBD sharing between ASPs and the IBD sharing between DSPs. Further, it works better than the conventional LOD score ASP linkage method in these data in the sense of avoiding false-positive linkage evidence.     

Exploiting excess sharing: a more powerful test of linkage for affected sib pairs than the transmission/disequilibrium test

The transmission/disequilibrium test (TDT) is a popular, simple, and powerful test of linkage, which can be used to analyze data consisting of transmissions to the affected members of families with any kind pedigree structure, including affected sib pairs (ASPs). Although it is based on the preferential transmission of a particular marker allele across families, it is not a valid test of association for ASPs. Martin et al. devised a similar statistic for ASPs, Tsp, which is also based on preferential transmission of a marker allele but which is a valid test of both linkage and association for ASPs. It is, however, less powerful than the TDT as a test of linkage for ASPs. What I show is that the differences between the TDT and Tsp are due to the fact that, although both statistics are based on preferential transmission of a marker allele, the TDT also exploits excess sharing in identity-by-descent transmissions to ASPs. Furthermore, I show that both of these statistics are members of a family of "TDT-like" statistics for ASPs. The statistics in this family are based on preferential transmission but also, to varying extents, exploit excess sharing. From this family of statistics, we see that, although the TDT exploits excess sharing to some extent, it is possible to do so to a greater extent-and thus produce a more powerful test of linkage, for ASPs, than is provided by the TDT. Power simulations conducted under a number of disease models are used to verify that the most powerful member of this family of TDT-like statistics is more powerful than the TDT for ASPs.     

Efficiency robust tests for mapping quantitative trait loci using extremely discordant sib pairs

In 1972, Haseman and Elston proposed a pioneering regression method for mapping quantitative trait loci using randomly selected sib pairs. Recently, the statistical power of their method was shown to be increased when extremely discordant sib pairs are ascertained. While the precise genetic model may not be known, prior information that constrains IBD probabilities is often available. We investigate properties of tests that are robust against model uncertainty and show that the power gain from further constraining IBD probabilities is marginal. The additional linkage information contained in the trait values can be incorporated by combining the Haseman-Elston regression method and a robust allele sharing test.     

Using discordant sib pairs to map loci for qualitative traits with high sibling recurrence risk.

A common approach for detecting genetic linkage using siblings is to collect affected sib pairs (ASPs) and to identify markers where allele sharing exceeds expectation. Alternatively, markers can be analyzed in discordant sib pairs (DSPs) for allele sharing below expectation. Relative to the ASP approach, according to Risch, the power of the DSP approach increases with sibling recurrence risk, the two approaches being equally effective at 50% recurrence risk. However, with many diseases associated with more moderate sibling recurrence risk, less emphasis has been placed on the use of DSPs and the development of the underlying theory. In this paper, we expand the work of Risch to provide a more general foundation for DSP studies, since power can be quite high under the appropriate conditions. For example, in some highly affected populations, such as the diabetes-prone Pima Indians, sibling recurrence risk can be very large and, thus, DSPs ideal. Similarly, as we show through simulation, DSPs are preferable for diabetic nephropathy due to a 70% recurrence rate among siblings with insulin-dependent diabetes mellitus. Following the diabetic nephropathy example, we consider more systematically the situations in which DSPs can provide an efficient alternative to ASPs.     

A sibship test for linkage in the presence of association: the sib transmission/disequilibrium test.

Linkage analysis with genetic markers has been successful in the localization of genes for many monogenic human diseases. In studies of complex diseases, however, tests that rely on linkage disequilibrium (the simultaneous presence of linkage and association) are often more powerful than those that rely on linkage alone. This advantage is illustrated by the transmission/disequilibrium test (TDT). The TDT requires data (marker genotypes) for affected individuals and their parents; for some diseases, however, data from parents may be difficult or impossible to obtain. In this article, we describe a method, called the "sib TDT" (or "S-TDT"), that overcomes this problem by use of marker data from unaffected sibs instead of from parents, thus allowing application of the principle of the TDT to sibships without parental data. In a single collection of families, there might be some that can be analyzed only by the TDT and others that are suitable for analysis by the S-TDT. We show how all the data may be used jointly in one overall TDT-type procedure that tests for linkage in the presence of association. These extensions of the TDT will be valuable for the study of diseases of late onset, such as non-insulin-dependent diabetes, cardiovascular diseases, and other diseases associated with aging.     

Performance of random forest when SNPs are in linkage disequilibrium

Background

Proteases of human pathogens are becoming increasingly important drug targets, hence it is necessary to understand their substrate specificity and to interpret this knowledge in practically useful ways. New methods are being developed that produce large amounts of cleavage information for individual proteases and some have been applied to extract cleavage rules from data. However, the hitherto proposed methods for extracting rules have been neither easy to understand nor very accurate. To be practically useful, cleavage rules should be accurate, compact, and expressed in an easily understandable way.

Results

A new method is presented for producing cleavage rules for viral proteases with seemingly complex cleavage profiles. The method is based on orthogonal search-based rule extraction (OSRE) combined with spectral clustering. It is demonstrated on substrate data sets for human immunodeficiency virus type 1 (HIV-1) protease and hepatitis C (HCV) NS3/4A protease, showing excellent prediction performance for both HIV-1 cleavage and HCV NS3/4A cleavage, agreeing with observed HCV genotype differences. New cleavage rules (consensus sequences) are suggested for HIV-1 and HCV NS3/4A cleavages. The practical usability of the method is also demonstrated by using it to predict the location of an internal cleavage site in the HCV NS3 protease and to correct the location of a previously reported internal cleavage site in the HCV NS3 protease. The method is fast to converge and yields accurate rules, on par with previous results for HIV-1 protease and better than previous state-of-the-art for HCV NS3/4A protease. Moreover, the rules are fewer and simpler than previously obtained with rule extraction methods.

Conclusion

A rule extraction methodology by searching for multivariate low-order predicates yields results that significantly outperform existing rule bases on out-of-sample data, but are more transparent to expert users. The approach yields rules that are easy to use and useful for interpreting experimental data.     

Performance of random forest when SNPs are in linkage disequilibrium

Background  

Single nucleotide polymorphisms (SNPs) may be correlated due to linkage disequilibrium (LD). Association studies look for both direct and indirect associations with disease loci. In a Random Forest (RF) analysis, correlation between a true risk SNP and SNPs in LD may lead to diminished variable importance for the true risk SNP. One approach to address this problem is to select SNPs in linkage equilibrium (LE) for analysis. Here, we explore alternative methods for dealing with SNPs in LD: change the tree-building algorithm by building each tree in an RF only with SNPs in LE, modify the importance measure (IM), and use haplotypes instead of SNPs to build a RF.     

A systematic genomewide linkage study in 353 sib pairs with schizophrenia

We undertook a genomewide linkage study in a total of 353 affected sib pairs (ASPs) with schizophrenia. Our sample consisted of 179 ASPs from the United Kingdom, 134 from Sweden, and 40 from the United States. We typed 372 microsatellite markers at approximately 10-cM intervals. Our strongest finding was a LOD score of 3.87 on chromosome 10q25.3-q26.3, with positive results being contributed by all three samples and a LOD-1 interval of 15 cM. This finding achieved genomewide significance (P<.05), on the basis of simulation studies. We also found two regions, 17p11.2-q25.1 (maximum LOD score [MLS] = 3.35) and 22q11 (MLS = 2.29), in which the evidence for linkage was highly suggestive. Linkage to all of these regions has been supported by other studies. Moreover, we found strong evidence for linkage (genomewide P<.02) to 17p11.2-q25.1 in a single pedigree with schizophrenia. In our view, the evidence is now sufficiently compelling to undertake detailed mapping studies of these three regions.     

Anxiety and depression in twin and sib pairs extremely discordant and concordant for neuroticism: prodromus to a linkage study.

Multivariate modelling of anxiety and depression data in twins has suggested that the two phenotypes are largely underpinned by one genetic factor, while other studies have indicated a relationship between these disorders and the neuroticism personality trait. As part of a study to identify quantitative trait loci for anxiety and depression, questionnaire responses and interviews of 15,027 Australian twins and 11,389 of their family members conducted during the past 20 years were reviewed to identify individuals with neuroticism, anxiety and depression scores in the upper or lower deciles of the population. This information was then used to identify extreme discordant and concordant (EDAC) sib pairs. 1373 high-scoring and 1571 low-scoring subjects (2357 sib pairs) were selected for participation, and extremely high participation rates were achieved, with over 90% of contactable prospective participants completing the interview phase, and over 90% of these providing blood or buccal samples. Participation bias arising from the nature of the selection variables was minimal, with only a small difference between rates of interview participation among prospective participants with high and low selection scores (89.4% vs 91.6%). The interview permitted the diagnosis of depression and several anxiety disorders (OCD, agoraphobia, panic disorder, generalised anxiety disorder) in this sample according to DSM-IV criteria. The methodology for selection of prospective subjects was demonstrated to be extremely successful, with highly significant differences in depression and anxiety disorder prevalence rates between individuals in the two selection groups. The success of this EDAC sampling scheme will enhance the power for QTL linkage and association analysis in this sample.     

Genetic copy number variants in sib pairs both affected with schizophrenia

Background  

Schizophrenia is a complex disorder with involvement of multiple genes.     

Analysis of affected sib pairs, with covariates--with and without constraints

Covariate models have previously been developed as an extension to affected-sib-pair methods in which the covariate effects are jointly estimated with the degree of excess allele sharing. These models can estimate the differences in sib-pair allele sharing that are associated with measurable environment or genes. When there are no covariates, the pattern of identical-by-descent allele sharing in affected sib pairs is expected to fall within a small triangular region of the potential parameter space, under most genetic models. By restriction of the estimated allele sharing to this triangle, improved power is obtained in tests for genetic linkage. When the affected-sib-pair model is generalized to allow for covariates that affect allele sharing, however, new constraints and new methods for the application of constraints are required. Three generalized constraint methods are proposed and evaluated by use of simulated data. The results compare the power of the different methods, with and without covariates, for a single-gene model with age-dependent onset and for quantitative and qualitative gene-environment and gene-gene interaction models. Covariates can improve the power to detect linkage and can be particularly valuable when there are qualitative gene-environment interactions. In most situations, the best strategy is to assume that there is no dominance variance and to obtain constrained estimates for covariate models under this assumption.     

Sib-parentage testing using molecular markers when parents are unknown

The formulae for computing the so-called Sib Index using codominant alleles for (1) full-sib and (2) half-sib parentage are given. Hypothesis testing is based on the distribution of conditional likelihood ratio or Bayes' factor. Thresholds for rejecting the null hypothesis and P-values were obtained in function of the number of alleles and their frequency distributions. Simulations showed that a relatively low number of marker systems (e.g. 20) are enough to accept the hypothesis of sib parentage with a reasonable power for usual significance levels, but that a higher number would be necessary if full-sib against half-sib parentage is the contrast to be carried out. The effect of sampling variation on the allele frequencies on power calculations is also analysed.     

Composite statistics for QTL mapping with moderately discordant sibling pairs

Extreme discordant sibling-pair (EDSP) designs have been shown in theory to be very powerful for mapping quantitative-trait loci (QTLs) in humans. However, their practical applicability has been somewhat limited by the need to phenotype very large populations to find enough pairs that are extremely discordant. In this paper, we demonstrate that there is also substantial power in pairs that are only moderately discordant, and that designs using moderately discordant pairs can yield a more practical balance between phenotyping and genotyping efforts. The power we demonstrate for moderately discordant pairs stems from a new statistical result. Statistical analysis in discordant-pair studies is generally done by testing for reduced identity by descent (IBD) sharing in the pairs. By contrast, the most commonly-used statistical methods for more standard QTL mapping are Haseman-Elston regression and variance-components analysis. Both of these use statistics that are functions of the trait values given IBD information for the pedigree. We show that IBD sharing statistics and "trait value given IBD" statistics contribute complementary rather than redundant information, and thus that statistics of the two types can be combined to form more powerful tests of linkage. We propose a simple composite statistic, and test it with simulation studies. The simulation results show that our composite statistic increases power only minimally for extremely discordant pairs. However, it boosts the power of moderately discordant pairs substantially and makes them a very practical alternative. Our composite statistic is straightforward to calculate with existing software; we give a practical example of its use by applying it to a Genetic Analysis Workshop (GAW) data set.     

Transmission/disequilibrium test based on haplotype sharing for tightly linked markers

Studies using haplotypes of multiple tightly linked markers are more informative than those using a single marker. However, studies based on multimarker haplotypes have some difficulties. First, if we consider each haplotype as an allele and use the conventional single-marker transmission/disequilibrium test (TDT), then the rapid increase in the degrees of freedom with an increasing number of markers means that the statistical power of the conventional tests will be low. Second, the parental haplotypes cannot always be unambiguously reconstructed. In the present article, we propose a haplotype-sharing TDT (HS-TDT) for linkage or association between a disease-susceptibility locus and a chromosome region in which several tightly linked markers have been typed. This method is applicable to both quantitative traits and qualitative traits. It is applicable to any size of nuclear family, with or without ambiguous phase information, and it is applicable to any number of alleles at each of the markers. The degrees of freedom (in a broad sense) of the test increase linearly as the number of markers considered increases but do not increase as the number of alleles at the markers increases. Our simulation results show that the HS-TDT has the correct type I error rate in structured populations and that, in most cases, the power of HS-TDT is higher than the power of the existing single-marker TDTs and haplotype-based TDTs.     

Insulin-gene sharing in sib pairs with insulin-dependent diabetes mellitus: no evidence for linkage

An association between insulin-dependent diabetes mellitus (IDDM) and an RFLP adjacent to the insulin gene has been consistently observed, but its etiological significance is unclear. We studied unrelated IDDM patients (N = 45) and controls (N = 65) to confirm the association--and assessed evidence for linkage in 22 families with at least two affected (IDDM) sibs--to determine whether the insulin-gene region actually contributes to susceptibility to IDDM. All individuals were typed for the RFLP in the 5'-flanking region of the insulin gene (5'FP) used in the previous studies, and the 12 families not fully informative for linkage with the 5'FP were typed for additional closely linked RFLPs. We found a higher frequency of class 1 alleles of the 5'FP in IDDM patients (.83) than in controls (.75), which is consistent with the reported association, but the difference was not statistically significant in our sample. Among the 33 affected sib pairs (ASPs) in 22 families, if maximum possible sharing is assumed when sharing is ambiguous, 10 pairs share both parental insulin genes, 17 pairs share one, and six share neither. This distribution is incompatible with close linkage. In contrast, for the HLA region, for which all 22 families are fully informative, 19 of the 33 ASPs share two haplotypes and the remaining 14 share one. There are no pairs that share neither HLA haplotype. Thus, although these data clearly illustrate the contribution of HLA-linked susceptibility to IDDM, they argue strongly against a contribution of similar magnitude by the insulin-gene region.