Analytic power and sample size calculation for the genotypic transmission/disequilibrium test in case‐parent trio studies

Case‐parent trio studies considering genotype data from children affected by a disease and their parents are frequently used to detect single nucleotide polymorphisms (SNPs) associated with disease. The most popular statistical tests for this study design are transmission/disequilibrium tests (TDTs). Several types of these tests have been developed, for example, procedures based on alleles or genotypes. Therefore, it is of great interest to examine which of these tests have the highest statistical power to detect SNPs associated with disease. Comparisons of the allelic and the genotypic TDT for individual SNPs have so far been conducted based on simulation studies, since the test statistic of the genotypic TDT was determined numerically. Recently, however, it has been shown that this test statistic can be presented in closed form. In this article, we employ this analytic solution to derive equations for calculating the statistical power and the required sample size for different types of the genotypic TDT. The power of this test is then compared with the one of the corresponding score test assuming the same mode of inheritance as well as the allelic TDT based on a multiplicative mode of inheritance, which is equivalent to the score test assuming an additive mode of inheritance. This is, thus, the first time the power of these tests are compared based on equations, yielding instant results and omitting the need for time‐consuming simulation studies. This comparison reveals that these tests have almost the same power, with the score test being slightly more powerful.     

Evidence for recessive and against dominant inheritance at the HLA-"linked" locus in coeliac disease.

It has been proposed that gluten sensitive enteropathy (GSE) results from the interaction of two loci: one locus linked to HLA and associated with dominant inheritance, and the other, a non-HLA-linked GSE-associated B-cell alloantigen, exhibiting recessive inheritance. We have shown in previous analyses that a two-locus, dominant-recessive model is less compatible with the existing population prevalence and observed familial segregation data than is a recessive-recessive two-locus model. Here we present additional analyses of reported population and familial HLA data that support the recessive mode of inheritance for the HLA-linked disease locus. Reported data from HLA typing of affected sib pairs, the association of GSE with DR3 and DR7 in different populations, and the proportions of different HLA phenotypes and genotypes were compared with expected data derived by three different methods. The HLA data analyses consistently reject a dominant mode of inheritance for the presumed HLA-linked disease allele but do not reject a recessive model. The affected sib-pair data also support a recessive model. These analyses are consistent with our previous prediction that the HLA-"linked" disease allele in GSE is recessive inherited.     

Increasing the power and efficiency of disease-marker case-control association studies through use of allele-sharing information

Case-control disease-marker association studies are often used in the search for variants that predispose to complex diseases. One approach to increasing the power of these studies is to enrich the case sample for individuals likely to be affected because of genetic factors. In this article, we compare three case-selection strategies that use allele-sharing information with the standard strategy that selects a single individual from each family at random. In affected sibship samples, we show that, by carefully selecting sibships and/or individuals on the basis of allele sharing, we can increase the frequency of disease-associated alleles in the case sample. When these cases are compared with unrelated controls, the difference in the frequency of the disease-associated allele is therefore also increased. We find that, by choosing the affected sib who shows the most evidence for pairwise allele sharing with the other affected sibs in families, the test statistic is increased by >20%, on average, for additive models with modest genotype relative risks. In addition, we find that the per-genotype information associated with the allele sharing-based strategies is increased compared with that associated with random selection of a sib for genotyping. Even though we select sibs on the basis of a nonparametric statistic, the additional gain for selection based on the unknown underlying mode of inheritance is minimal. We show that these properties hold even when the power to detect linkage to a region in the entire sample is negligible. This approach can be extended to more-general pedigree structures and quantitative traits.     

Gene-environment interaction and affected sib pair linkage analysis

OBJECTIVES: Gene-environment (GxE) interaction influences risk for many complex disease traits. However, genome screens using affected sib pair linkage techniques are typically conducted without regard for GxE interaction. We propose a simple extension of the commonly used mean test and evaluate its power for several forms of GxE interaction. METHODS: We compute expected IBD sharing by sibling exposure profile, that is by whether two sibs are exposed (EE), unexposed (UU), or are discordant for exposure (EU). We describe a simple extension of the mean test, the "mean-interaction" test that utilizes heterogeneity in IBD sharing across EE, EU, and UU sib pairs in a test for linkage. RESULTS: The mean-interaction test provides greater power than the mean test for detecting linkage in the presence of moderate or strong GxE interaction, typically when the interaction relative risk (R(ge)) exceeds 3 or is less than 1/3. In the presence of strong interaction (R(ge) = 10), the required number of affected sib pairs to achieve 80% power for detecting linkage is approximately 30% higher when the environmental factor is ignored in the mean test, than when it is utilized in the mean-interaction test. CONCLUSION: Linkage methods that incorporate environmental data and allow for interaction can lead to increased power for localizing a disease gene involved in a GxE interaction.     

Power of sib-pair and sib-trio linkage analysis with assortative mating and multiple disease loci.

Sib-pair linkage analysis has been proposed for identifying genes that predispose to common diseases. We have shown that the presence of assortative mating and multiple disease-susceptibility loci (genetic heterogeneity) can increase the required sample size for affected-affected sib pairs several fold over the sample size required under random mating. We propose a new test statistic based on sib trios composed of either one unaffected and two affected siblings or one affected and two unaffected siblings. The sample-size requirements under assortative mating and multiple disease loci for these sib-trio statistics are much smaller, under most conditions, than the corresponding sample sizes for sib pairs. Study designs based on data from sib trios with one or two affected members are recommended whenever assortative mating and genetic heterogeneity are suspected.     

A novel framework for sib pair linkage analysis

Sib pair linkage analysis of a dichotomous trait is a popular method for narrowing the search for genes that influence complex diseases. Although the pedigree structures are uncomplicated and the underlying genetic principles straightforward, a surprising degree of complexity is involved in implementing a sib pair study and interpreting the results. Ascertainment may be based on affected, discordant, or unaffected sib pairs, as well as on pairs defined by threshold values for quantitative traits, such as extreme discordant sib pairs. To optimize power, various domain restrictions and null hypotheses have been proposed for each of these designs, yielding a wide array of choices for the analyst. To begin, we systematically classify the major sources of discretion in sib pair linkage analysis. Then, we extend the work of Kruglyak and Lander (1995), to bring the various forms into a unified framework and to facilitate a more general approach to the analysis. Finally, we describe a new, freely available computer program, Splat (Sib Pair Linkage Analysis Testing), that can perform any sib pair statistical test currently in use, as well as any user-defined test yet to be proposed. Splat uses the expectation maximization algorithm to calculate maximum-likelihood estimates of sharing (subject to user-specified conditions) and then plots LOD scores versus chromosomal position. It includes a novel grid-scanning capability that enables simultaneous visualization of multiple test statistics. This can lead to further insight into the genetic basis of the disease process under consideration. In addition, phenotype definitions can be modified without the recalculation of inheritance vectors, thereby providing considerable flexibility for exploratory analysis. The application of Splat will be illustrated with data from studies on the genetics of diabetic nephropathy.     

A note on power approximations for the transmission/disequilibrium test

The transmission/disequilibrium test (TDT) is a popular method for detection of the genetic basis of a disease. Investigators planning such studies require computation of sample size and power, allowing for a general genetic model. Here, a rigorous method is presented for obtaining the power approximations of the TDT for samples consisting of families with either a single affected child or affected sib pairs. Power calculations based on simulation show that these approximations are quite precise. By this method, it is also shown that a previously published power approximation of the TDT is erroneous.     

Weighting affected sib pairs by marker informativity

For the analysis of affected sib pairs (ASPs), a variety of test statistics is applied in genomewide scans with microsatellite markers. Even in multipoint analyses, these statistics might not fully exploit the power of a given sample, because they do not account for incomplete informativity of an ASP. For meta-analyses of linkage and association studies, it has been shown recently that weighting by informativity increases statistical power. With this idea in mind, the first aim of this article was to introduce a new class of tests for ASPs that are based on the mean test. To take into account how much informativity an ASP contributes, we weighted families inversely proportional to their marker informativity. The weighting scheme is obtained by use of the de Finetti representation of the distribution of identity-by-descent values. We derive the limiting distribution of the weighted mean test and demonstrate the validity of the proposed test. We show that it can be much more powerful than the classical mean test in the case of low marker informativity. In the second part of the article, we propose a Monte Carlo simulation approach for evaluating significance among ASPs. We demonstrate the validity of the simulation approach for both the classical and the weighted mean test. Finally, we illustrate the use of the weighted mean test by reanalyzing two published data sets. In both applications, the maximum LOD score of the weighted mean test is 0.6 higher than that of the classical mean test.     

The affected sib method. III. Selection and recombination.

The affected sib-pair method has been used to investigate the mode of inheritance, and to estimate the "disease" allele frequency, for a number of HLA-associated diseases. One of the assumptions of the original sib-pair method is that the disease confers no selective disadvantage on affected individuals. This is obviously not the situation for most diseases. We have determined the expected HLA haplotype-sharing distribution among affected sib-pairs when selection against individuals with the disease is taken into account. We have shown that if the mode of inheritance of the selectively disadvantageous disease is recessive or additive, the original affected sib-pair analysis, ignoring selection, still estimates the true mode of inheritance, but usually yields an underestimate of the "disease" allele frequency. For intermediate and dominant models of disease predisposition, both the estimates of the degree of penetrance of the "disease" genotypes, and the "disease" allele frequency, are altered if selection is ignored in the analysis. Similarly, allowing for recombination between the "disease" locus and the HLA region does not affect the determination of the mode of inheritance of the disease if it is recessive or additive; in other cases, however, the estimate of the mode of inheritance is affected. The "disease" allele frequency is overestimated when nonzero recombination is ignored for all the modes of inheritance that have been studied.     

A critical analysis of data presented in eight studies favouring X-linkage of bipolar illness with special emphasis on formal genetic aspects

High lod scores were obtained in several X-linkage studies of bipolar illness under the assumption that a subgroup of manic depression follows an X-linked dominant mode of inheritance. We have previously shown that the segregation patterns do not substantiate this assumption. We now statistically address the lack of evidence for X-linked inheritance by sex-dependently analyzing segregation ratios and clinical data presented in eight positive X-linkage studies. Accordingly, affected males have significantly fewer offspring, a lower mean age and a higher bipolar to unipolar ratio than affected females. There are two possible explanations for these findings: either the X-linked subgroup of bipolar illness has unique features that have not been accounted for clinically, or (more probably) the pedigree structures could also (and might be more likely to) result from ascertaining kindreds following autosomal or multifactorial inheritance only, with exclusion of kindreds encompassing male to male transmission.     

Consanguinity and the sib-pair method: an approach using identity by descent between and within individuals.

To test for linkage between a trait and a marker, one can consider identical marker alleles in related individuals, for instance, sibs. For recessive diseases, it has been shown that some information may be gained from the identity by descent (IBD) of the two alleles of an affected inbred individual at the marker locus. The aim of this paper is to extend the sib-pair method of linkage analysis to the situation of sib pairs sampled from consanguineous populations. This extension takes maximum advantage of the information provided by both the IBD pattern between sibs and allelic identity within each sib of the pair. This is possible through the use of the condensed identity coefficients. Here, we propose a new test of linkage based on a chi2. We compare the performance of this test with that of the classical chi2 test based on the distribution of sib pairs sharing 0, 1, or 2 alleles IBD. For sib pairs from first-cousin matings, the proposed test can better detect the role of a disease-susceptibility (DS) locus. Its power is shown to be greater than that of the classical test, especially for models where the DS allele may be common and incompletely penetrant; that is to say for situations that may be encountered in multifactorial diseases. A study of the impact of inbreeding on the expected proportions of sib pairs sharing 0, 1, or 2 alleles IBD is also performed here. Ignoring inbreeding, when in fact inbreeding exists, increases the rate of type I errors in tests of linkage.     

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.     

Multifactorial diseases: a nightmare for the geneticist

Common diseases are often familial, but they do not show in most families, a simple pattern of inheritance. In a few families these diseases may be caused by a mutation in a single gene. In most families these diseases are multifactorial, they result from a complex interaction between a genetic component which is often polygenic and many environmental factors. Two major, model free, methods are used to locate and identify susceptibility genes that predispose to multifactorial diseases. The first is a non parametric linkage analysis that relies on affected sib pairs, or an affected pedigree member, the second method is association studies which looks for increase frequency of particular alleles or genotypes in affected compared with unaffected individuals in the population. Most of the results have not been replicated, identifying susceptibility genes is proving much more difficult than most geneticists imagined 20 years ago. The main reason for this irreproducibility is genetic heterogeneity.     

The distributions of N and F: measures of HLA haplotype concordance

Nonrandom inheritance of the two HLA haplotypes of Chromosome 6, available from each parent among siblings affected by certain diseases, has afforded evidence of HLA-linked disease-susceptibility genes. Two algebraically equivalent measures of HLA haplotype concordance (that is, the excessive sharing of certain haplotypes among affected siblings) are used for family studies designed to test whether or not there is significant evidence of the existence of an HLA-linked disease-susceptibility gene or for inferring the mode of inheritance when this is already believed to apply. The distributions of these measures are derived under the null hypothesis of random inheritance of HLA haplotypes, and there is a short discussion of the case in which inheritance of a diseased gene causes a change, from the purely random case, in the distribution of haplotype concordance among affected siblings.     

Simple,robust linkage tests for affected sibs.

Parametric-linkage analysis applied to large pedigrees with many affected individuals has helped in the identification of highly penetrant genes; but, for diseases lacking a clear Mendelian inheritance pattern or caused by several genes of low to moderate penetrance, a more robust strategy is nonparametric analysis applied to small sets of affected relatives, such as affected sib pairs. Here we show that the robustness of affected-sib-pair tests is related to the shape of the constraint set for the sibs'' identity-by-descent (IBD) probabilities. We also derive a set of constraints for the IBD probabilities of affected sib triples and use common features of the shapes of the two constrain sets to introduce new nonparametric tests (called "minmax" tests) that are more robust than those in current use. Asymptotic-power computations support the robustness of the proposed minmax tests.     

Familial recurrence-pattern analysis of cleft lip with or without cleft palate.

Cleft lip with or without cleft palate (CL/P) is a common congenital malformation with an incidence in European white populations of about 1/1,000. The familial clustering of CL/P has been extensively characterized, and epidemiological studies have proposed monogenic models (with reduced penetrance), multifactorial/threshold models, and mixed major-gene/multifactorial models to explain its inheritance. The recognition of an association between two RFLPs at the transforming growth factor alpha (TGFA) locus and CL/P supports a major-gene component to the etiology of CL/P. Risch has shown that the recurrence risk ratio lambda R (risk to relatives, vs. population prevalence) is a useful pointer to the mode of inheritance. Here we further develop the use of lambda R to analyze recurrence-risk data for CL/P. Recurrence risks for first-, second-, and third-degree relatives equate well with oligogenic models with as few as four loci. A monogenic/additive model is strongly rejected. The limited available twin data are also consistent with this model. A "major gene" interacting epistatically with an oligogenic background is shown to be a plausible alternative. Power calculations for a linkage study to map the CL/P major-risk locus suggest that a sample of 50 affected sib pairs will be adequate, but linkage to minor-risk loci will require very much larger samples.     

A robust identity-by-descent procedure using affected sib pairs: multipoint mapping for complex diseases

Multipoint linkage analysis is a powerful tool to localize susceptibility genes for complex diseases. However, the conventional lod score method relies critically on the correct specification of mode of inheritance for accurate estimation of gene position. On the other hand, allele-sharing methods, as currently practiced, are designed to test the null hypothesis of no linkage rather than estimate the location of the susceptibility gene(s). In this paper, we propose an identity-by-descent (IBD)-based procedure to estimate the location of an unobserved susceptibility gene within a chromosomal region framed by multiple markers. Here we deal with the practical situation where some of the markers might not be fully informative. Rather the IBD statistic at an arbitrary within the region is imputed using the multipoint marker information. The method is robust in that no assumption about the genetic mechanism is required other than that the region contains no more than one susceptibility gene. In particular, this approach builds upon a simple representation for the expected IBD at any arbitrary locus within the region using data from affected sib pairs. With this representation, one can carry out a parametric inference procedure to locate an unobserved susceptibility gene. In addition, here we derive a sample size formula for the number of affected sib pairs needed to detect linkage with multiple markers. Throughout, the proposed method is illustrated through simulated data. We have implemented this method including exploratory and formal model-fitting procedures to locate susceptibility genes, plus sample size and power calculations in a program, GENEFINDER, which will be made available shortly.     

Gene-environment interactions and the affected-sib-pair designs

In genetic mapping of complex traits, the affected-sib-pair method (ASP) and the transmission disequilibrium test (TDT) are two methods of choice. The major appeal of both ASP and TDT is that they do not require the knowledge of mode of inheritance underlying the trait in question. The relative ease and economy for data collection also is the reason for their popularity. The basic idea of the ASP is to identify genes or chromosomal regions through identifying genetic similarity based on phenotypical similarity. TDT, on the other hand, detects susceptibility genes through detecting unusual transmission patterns in families. Since phenotypic similarity can also be caused by environmental similarity, we investigate how the presence of gene-environment interaction (GEI) affects the power of both methods. For a simple one-locus-one-risk-factor model, our results indicate that, in the presence of GEI, methods developed based on marginal penetrance functions (i.e. ignoring the risk factor) can give spurious results. The triangular restriction on allele-sharing probability may no longer be valid. If the environment effect is strong, using exposure-discordant affected sib pairs may have advantage over other designs. Above all, a genetic model involving both genetic and environmental factors behaves differently from a single-locus genetic model.     

The effect of linkage disequilibrium on linkage analysis of incomplete pedigrees

Dense SNP maps can be highly informative for linkage studies. But when parental genotypes are missing, multipoint linkage scores can be inflated in regions with substantial marker-marker linkage disequilibrium (LD). Such regions were observed in the Affymetrix SNP genotypes for the Genetic Analysis Workshop 14 (GAW14) Collaborative Study on the Genetics of Alcoholism (COGA) dataset, providing an opportunity to test a novel simulation strategy for studying this problem. First, an inheritance vector (with or without linkage present) is simulated for each replicate, i.e., locations of recombinations and transmission of parental chromosomes are determined for each meiosis. Then, two sets of founder haplotypes are superimposed onto the inheritance vector: one set that is inferred from the actual data and which contains the pattern of LD; and one set created by randomly selecting parental alleles based on the known allele frequencies, with no correlation (LD) between markers. Applying this strategy to a map of 176 SNPs (66 Mb of chromosome 7) for 100 replicates of 116 sibling pairs, significant inflation of multipoint linkage scores was observed in regions of high LD when parental genotypes were set to missing, with no linkage present. Similar inflation was observed in analyses of the COGA data for these affected sib pairs with parental genotypes set to missing, but not after reducing the marker map until r2 between any pair of markers was 相似文献   

Use of parents, sibs, and unrelated controls for detection of associations between genetic markers and disease.

Detecting the association between genetic markers and complex diseases can be a critical first step toward identification of the genetic basis of disease. Misleading associations can be avoided by choosing as controls the parents of diseased cases, but the availability of parents often limits this design to early-onset disease. Alternatively, sib controls offer a valid design. A general multivariate score statistic is presented, to detect the association between a multiallelic genetic marker locus and affection status; this general approach is applicable to designs that use parents as controls, sibs as controls, or even unrelated controls whose genotypes do not fit Hardy-Weinberg proportions or that pool any combination of these different designs. The benefit of this multivariate score statistic is that it will tend to be the most powerful method when multiple marker alleles are associated with affection status. To plan these types of studies, we present methods to compute sample size and power, allowing for varying sibship sizes, ascertainment criteria, and genetic models of risk. The results indicate that sib controls have less power than parental controls and that the power of sib controls can be increased by increasing either the number of affected sibs per sibship or the number of unaffected control sibs. The sample-size results indicate that the use of sib controls to test for associations, by use of either a single-marker locus or a genomewide screen, will be feasible for markers that have a dominant effect and for common alleles having a recessive effect. The results presented will be useful for investigators planning studies using sibs as controls.