A note on multiple testing procedures in linkage analysis.

Controversy over the impact of multiple testing procedures in linkage analysis is reexamined in this report. Despite some recent claims to the contrary, it is shown that testing multiple markers decreases the posterior false-positive rate among significant tests, rather than increasing it; this is true whether the trait of interest is simply monogenic or complex, or even if the genetic model is misspecified. However, if the true mode of inheritance is complex, or if the genetic model is misspecified, the power to obtain a significant result when linkage is present may be reduced, while the significance level is not, leading to an inflation of the posterior false-positive rate. Furthermore, the posterior false-positive rate increases with decreasing sample size and may be unacceptably high for very small samples. By contrast, testing multiple genetic models, by varying either mode-of-inheritance parameters or diagnostic categories, does lead to an inflation of the posterior false-positive rate. A conservative correction for this case is to subtract log10t from the obtained maximum lod score, where t different genetic and/or diagnostic models have been tested.     

Two-locus models of disease: comparison of likelihood and nonparametric linkage methods.

The power to detect linkage for likelihood and nonparametric (Haseman-Elston, affected-sib-pair, and affected-pedigree-member) methods is compared for the case of a common, dichotomous trait resulting from the segregation of two loci. Pedigree data for several two-locus epistatic and heterogeneity models have been simulated, with one of the loci linked to a marker locus. Replicate samples of 20 three-generation pedigrees (16 individuals/pedigree) were simulated and then ascertained for having at least 6 affected individuals. The power of linkage detection calculated under the correct two-locus model is only slightly higher than that under a single locus model with reduced penetrance. As expected, the nonparametric linkage methods have somewhat lower power than does the lod-score method, the difference depending on the mode of transmission of the linked locus. Thus, for many pedigree linkage studies, the lod-score method will have the best power. However, this conclusion depends on how many times the lod score will be calculated for a given marker. The Haseman-Elston method would likely be preferable to calculating lod scores under a large number of genetic models (i.e., varying both the mode of transmission and the penetrances), since such an analysis requires an increase in the critical value of the lod criterion. The power of the affected-pedigree-member method is lower than the other methods, which can be shown to be largely due to the fact that marker genotypes for unaffected individuals are not used.     

Joint linkage of multiple loci for a complex disorder.

Many investigators who have been searching for linkage to complex diseases have by now accumulated a drawer full of negative results. If disease is actually caused by genes at several loci, these data might contain multiple-locus system (MLS) information that the investigator does not realize. Trying to obtain this information formally, through the MLS likelihood, leads to severe computational and statistical difficulties. Therefore, we propose a scheme of inference based on single-locus (SL) statistics, considered jointly. By simulation, we find that the MLS lod score is closely approximated by the sum of SL lod scores. However, we also find that for moderately large systems, say three of four loci, both MLS and SL lod scores are likely to be inconclusive. Nonetheless, MLS can often be detected through the correlation of individual pedigree SL lod scores. Significant correlation is itself evidence of an MLS, because, in the absence of linkage, false-positive lod scores are necessarily random. Under epistasis SL lod scores tend to be positively correlated among pedigrees, while under independent action SL lod scores from high-density samples tend to be negatively correlated.     

A genome-wide search for genes predisposing to manic-depression, assuming autosomal dominant inheritance.

Manic-depressive illness (MDI), also known as "bipolar affective disorder," is a common and devastating neuropsychiatric illness. Although pivotal biochemical alterations underlying the disease are unknown, results of family, twin, and adoption studies consistently implicate genetic transmission in the pathogenesis of MDI. In order to carry out linkage analysis, we ascertained eight moderately sized pedigrees containing multiple cases of the disease. For a four-allele marker mapping 5 cM from the disease gene, the pedigree sample has > 97% power to detect a dominant allele under genetic homogeneity and has > 73% power under 20% heterogeneity. To date, the eight pedigrees have been genotyped with 328 polymorphic DNA loci throughout the genome. When autosomal dominant inheritance was assumed, 273 DNA markers gave lod scores < -2.0 at recombination fraction (theta) = .0, 174 DNA loci produced lod scores < -2.0 at theta = .05, and 4 DNA marker loci yielded lod scores > 1 (chromosome 5--D5S39, D5S43, and D5S62; chromosome 11--D11S85). Of the markers giving lod scores > 1, only D5S62 continued to show evidence for linkage when the affected-pedigree-member method was used. The D5S62 locus maps to distal 5q, a region containing neurotransmitter-receptor genes for dopamine, norepinephrine, glutamate, and gamma-aminobutyric acid. Although additional work in this region may be warranted, our linkage results should be interpreted as preliminary data, as 68 unaffected individuals are not past the age of risk.     

Distribution of lod scores under uncertain mode of inheritance.

We consider probability distributions of alternative lod statistics, differing in their treatment of segregation parameters when mode of inheritance is uncertain. A particular pedigree structure and a dominant genetic system displaying incomplete penetrance are analyzed. Lod scores calculated assuming an incorrect segregation model appear to conform quite well to the chi 2 distribution in the absence of linkage. In the presence of linkage, some power is lost. However, if lod scores are calculated under several different segregation models and the best one is accepted, opportunity for chance occurrence of high lod scores is enhanced. The distribution is still chi 2, but with extra degrees of freedom. These results hold over a wide range of sample sizes and segregation models, including small samples and low levels of penetrance.     

Does haplotype diversity predict power for association mapping of disease susceptibility?

Atopy is an IgE-mediated condition known to aggregate in families and is a major risk factor for asthma. As part of the Collaborative Study on the Genetics of Asthma (CSGA), a genome-wide scan for atopy, defined by skin sensitivity to one or more common environmental allergens, was conducted in 287 CSGA families (115 African American, 138 Caucasian and 34 Hispanic). Using a nonparametric genetic analysis approach, two regions were observed in the sample of all families that yielded multipoint lod scores >1.5 (chromosome 11q, lod=1.55 between D11S1986 and D11S1998; chromosome 20p between D20S473 and D20S604, lod=1.54). Modeling that included multiple genomic positions simultaneously indicated that four chromosomal regions accounted for the majority of evidence for linkage in the combined families. These four regions are on chromosomes 10p near D10S1412 (lod=0.94), 11q near D11S1986 (lod=1.76), 17q near D17S784 (lod=0.97) and 20p near D20S473 (lod=1.74). In the subset of pedigrees giving positive evidence for linkage on chromosome 11q, the evidence for linkage increased by lod scores greater than one in four other chromosomal regions: 5q (D5S1480, lod=1.65), 8p (D8S1113, lod=1.60), 12p (D12S372, lod=1.54) and 14q (D14S749, lod=1.70). These results suggest that several regions may harbor genes contributing to the risk for atopy and these may interact with one another in a complex manner.This work is published on behalf of the NHLBI Collaborative Study on the Genetics of Asthma     

Detecting linkage for genetically heterogeneous diseases and detecting heterogeneity with linkage data.

Interest in searching for genetic linkage between diseases and marker loci has been greatly increased by the recent introduction of DNA polymorphisms. However, even for the most well-behaved Mendelian disorders, those with clear-cut mode of inheritance, complete penetrance, and no phenocopies, genetic heterogeneity may exist; that is, in the population there may be more than one locus that can determine the disease, and these loci may not be linked. In such cases, two questions arise: (1) What sample size is necessary to detect linkage for a genetically heterogeneous disease? (2) What sample size is necessary to detect heterogeneity given linkage between a disease and a marker locus? We have answered these questions for the most important types of matings under specified conditions: linkage phase known or unknown, number of alleles involved in the cross at the marker locus, and different numbers of affected and unaffected children. In general, the presence of heterogeneity increases the recombination value at which lod scores peak, by an amount that increases with the degree of heterogeneity. There is a corresponding increase in the number of families necessary to establish linkage. For the specific case of backcrosses between disease and marker loci with two alleles, linkage can be detected at recombination fractions up to 20% with reasonable numbers of families, even if only half the families carry the disease locus linked to the marker. The task is easier if more than two informative children are available or if phase is known. For recessive diseases, highly polymorphic markers with four different alleles in the parents greatly reduce the number of families required.     

Linkage of prostate cancer susceptibility loci to chromosome 1

Three prostate cancer susceptibility genes have been reported to be linked to different regions on chromosome 1: HPC1 at 1q24-25, PCAP at 1q42-43, and CAPB at 1p36. Replication studies analyzing each of these regions have yielded inconsistent results. To evaluate linkage across this chromosome systematically, we performed multipoint linkage analyses with 50 microsatellite markers spanning chromosome 1 in 159 hereditary prostate cancer families (HPC), including 79 families analyzed in the original report describing HPC1 linkage. The highest lod scores for the complete dataset of 159 families were observed at 1q24-25 at which the parametric lod score assuming heterogeneity (hlod) was 2.54 (P=0.0006) with an allele sharing lod of 2.34 (P=0.001) at marker D1S413, although only weak evidence was observed in the 80 families not previously analyzed for this region (hlod=0.44, P=0.14, and allele sharing lod=0.67, P=0.08). In the complete data set, the evidence for linkage across this region was very broad, with allele sharing lod scores greater than 0.5 extending approximately 100 cM from 1p13 to 1q32, possibly indicating the presence of multiple susceptibility genes. Elsewhere on chromosome 1, some evidence of linkage was observed at 1q42-43, with a peak allele sharing lod of 0.56 (P=0.11) and hlod of 0.24 (P=0.25) at D1S235. For analysis of the CAPB locus at 1p36, we focused on six HPC families in our collection with a history of primary brain cancer; four of these families had positive linkage results at 1p36, with a peak allele sharing lod of 0.61 (P=0.09) and hlod of 0.39 (P=0.16) at D1S407 in all six families. These results are consistent with the heterogeneous nature of hereditary prostate cancer, and the existence of multiple loci on chromosome 1 for this disease.     

Linkage analysis of a complex disease through use of admixed populations

Linkage disequilibrium arising from the recent admixture of genetically distinct populations can be potentially useful in mapping genes for complex diseases. McKeigue has proposed a method that conditions on parental admixture to detect linkage. We show that this method tests for linkage only under specific assumptions, such as equal admixture in the parental generation and admixture that occurs in a single generation. In practice, these assumptions are unlikely to hold for natural populations, resulting in an inflation of the type I error rate when testing for linkage by this method. In this article, we generalize McKeigue's approach of testing for linkage to allow two different admixture models: (1) intermixture admixture and (2) continuous gene flow. We calculate the sample size required for a genomewide search by this method under different disease models: multiplicative, additive, recessive, and dominant. Our results show that the sample size required to obtain 90% power to detect a putative mutant allele at a genomewide significance level of 5% can usually be achieved in practice if informative markers are available at a density of 2 cM.     

Power to detect linkage based on multiple sets of data in the presence of locus heterogeneity: comparative evaluation of model-based linkage methods for affected sib pair data

The development of rigorous methods for evaluating the overall strength of evidence for genetic linkage based on multiple sets of data is becoming increasingly important in connection with genomic screens for complex disorders. We consider here what happens when we attempt to increase power to detect linkage by pooling multiple independently collected sets of families under conditions of variable levels of locus heterogeneity across samples. We show that power can be substantially reduced in pooled samples when compared to the most informative constituent subsamples considered alone, in spite of the increased sample size afforded by pooling. We demonstrate that for affected sib pair data, a simple adaptation of the lod score (which we call the compound lod), which allows for intersample admixture differences can afford appreciably higher power than the ordinary heterogeneity lod; and also, that a statistic we have proposed elsewhere, the posterior probability of linkage, performs at least as well as the compound lod while having considerable computational advantages. The companion paper (this issue, pp 217-225) shows further that in application to multiple data sets, familiar model-free methods are in some sense equivalent to ordinary lod scores based on data pooling, and that they therefore will also suffer dramatic losses in power for pooled data in the presence of locus heterogeneity and other complicating factors.     

The search for heterogeneity in insulin-dependent diabetes mellitus (IDDM): linkage studies, two-locus models, and genetic heterogeneity

One hundred families with insulin-dependent diabetes mellitus (IDDM) were analyzed for linkage with 27 genetic markers, including HLA, properdin factor B (BF), and glyoxalase 1(GLO) on chromosome 6, and Kidd blood group (Jk) on chromosome 2. The linkage analyses were performed under several different genetic models. An approximate correction for two-locus linkage analysis was developed and applied to four markers. Two different heterogeneity tests were implemented and applied to all the markers. One, the Predivided-Sample Test, utilizes various criteria thought to be relevant to genetic heterogeneity in IDDM. The other, the Admixture Test, looks for heterogeneity without specifying a prior how the sample should be divided. Results continued to support linkage of IDDM with three chromosome 6 markers: HLA, BF, and GLO. The total lod score for Kidd blood group, under the recessive model with 20% penetrance, is 1.63--down 1.2 from the 2.83 reported by us earlier. The only other marker whose lod score exceeded 1.0 under any model was pancreatic amylase (AMY2). The two-locus correction, which involved lowering the penetrance values used in the analysis, affected estimates of theta (recombination fraction) but did not markedly change the lod scores themselves. There was little evidence for heterogeneity within any of the lod scores, under either the Predivided-Sample Test or the Admixture Test.     

Combined linkage and association mapping of quantitative trait loci by multiple markers

Using multiple diallelic markers, variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL) based on nuclear families. The objective is to build a model that may fully use marker information for fine association mapping of QTL in the presence of prior linkage. The measures of linkage disequilibrium and the genetic effects are incorporated in the mean coefficients and are decomposed into orthogonal additive and dominance effects. The linkage information is modeled in variance-covariance matrices. Hence, the proposed methods model both association and linkage in a unified model. On the basis of marker information, a multipoint interval mapping method is provided to estimate the proportion of allele sharing identical by descent (IBD) and the probability of sharing two alleles IBD at a putative QTL for a sib-pair. To test the association between the trait locus and the markers, both likelihood-ratio tests and F-tests can be constructed on the basis of the proposed models. In addition, analytical formulas of noncentrality parameter approximations of the F-test statistics are provided. Type I error rates of the proposed test statistics are calculated to show their robustness. After comparing with the association between-family and association within-family (AbAw) approach by Abecasis and Fulker et al., it is found that the method proposed in this article is more powerful and advantageous based on simulation study and power calculation. By power and sample size comparison, it is shown that models that use more markers may have higher power than models that use fewer markers. The multiple-marker analysis can be more advantageous and has higher power in fine mapping QTL. As an application, the Genetic Analysis Workshop 12 German asthma data are analyzed using the proposed methods.     

Mapping by admixture linkage disequilibrium in human populations: limits and guidelines.

Certain human hereditary conditions, notably those with low penetrance and those which require an environmental event such as infectious disease exposure, are difficult to localize in pedigree analysis, because of uncertainty in the phenotype of an affected patient's relatives. An approach to locating these genes in human cohort studies would be to use association analysis, which depends on linkage disequilibrium of flanking polymorphic DNA markers. In theory, a high degree of linkage disequilibrium between genes separated by 10-20 cM will be generated and persist in populations that have a history of recent (3-20 generations ago) admixture between genetically differentiated racial groups, such as has occurred in African Americans and Hispanic populations. We have conducted analytic and computer simulations to quantify the effect of genetic, genomic, and population parameters that affect the amount and ascertainment of linkage disequilibrium in populations with a history of genetic admixture. Our goal is to thoroughly explore the ranges of all relevant parameters or factors (e.g., sample size and degree of genetic differentiation between populations) that may be involved in gene localization studies, in hopes of prescribing guidelines for an efficient mapping strategy. The results provide reasonable limits on sample size (200-300 patients), marker number (200-300 in 20-cM intervals), and allele differentiation (loci with allele frequency difference of > or = .3 between admixed parent populations) to produce an efficient approach (> 95% ascertainment) for locating genes not easily tracked in human pedigrees.     

Joint linkage and linkage disequilibrium mapping of quantitative trait loci in natural populations

Linkage analysis and allelic association (also referred to as linkage disequilibrium) studies are two major approaches for mapping genes that control simple or complex traits in plants, animals, and humans. But these two approaches have limited utility when used alone, because they use only part of the information that is available for a mapping population. More recently, a new mapping strategy has been designed to integrate the advantages of linkage analysis and linkage disequilibrium analysis for genome mapping in outcrossing populations. The new strategy makes use of a random sample from a panmictic population and the open-pollinated progeny of the sample. In this article, we extend the new strategy to map quantitative trait loci (QTL), using molecular markers within the EM-implemented maximum-likelihood framework. The most significant advantage of this extension is that both linkage and linkage disequilibrium between a marker and QTL can be estimated simultaneously, thus increasing the efficiency and effectiveness of genome mapping for recalcitrant outcrossing species. Simulation studies are performed to test the statistical properties of the MLEs of genetic and genomic parameters including QTL allele frequency, QTL effects, QTL position, and the linkage disequilibrium of the QTL and a marker. The potential utility of our mapping strategy is discussed.     

Linkage studies in a new X-linked myopathy, suggesting exclusion of DMD locus and tentative assignment to distal Xq.

We here report linkage studies in a family suffering from a recently described hereditary muscle disease named X-linked myopathy with excessive autophagy (XMEA). Significant lod scores excluding linkage to the Duchenne-Becker muscular dystrophy locus were found. Several other loci on the short and long arms of the X chromosome produced negative lod scores, whereas probe DX13-7 defining locus DXS15 showed no recombinants and a lod score of z = 0.903 at theta = .0. Further studies should be done to determine whether the gene for XMEA is (1) located at Xq and (2) caused by a mutation of the Emery-Dreifuss muscular dystrophy gene, which has been assigned to the same region.     

Evaluation of designs for reference families for livestock linkage mapping experiments

Abstract

The development of dense linkage maps consisting of highly polymorphic loci for livestock species is technically feasible. However, linkage mapping experiments are expensive as they involve many animals and marker typings per animal. To minimize costs of developing linkage maps for livestock species, optimizing designs for mapping studies is necessary. This study provides a general framework for evaluating the efficiency of designs for reference families consisting of two‐ or three‐ generation full‐sib or half‐sib families selected from a segregating population. The influence of number of families, number of offspring per family, family structure (either half‐sib or full‐sib) and marker polymorphism is determined. Evaluation is done for two markers with a recombination rate of .20 and for a marker and a dominant single gene with a recombination rate of .20. Two evaluation criteria are used: expected maximum lod score for detection of linkage and accuracy of an estimated recombination rate defined as probability that the true recombination rate is in an interval around the estimated recombination rate. First, for several designs the contribution of reference families to expected maximum lod score and accuracy is given. Second, the required number of families in a design to obtain a certain value for the evaluation criteria is calculated when number of offspring per family, family structure and marker polymorphism are specified. The required numbers increase when designs are optimized not only for expected maximum lod score but also for accuracy. The required number of animals to map a dominant single gene is very large. Therefore, a set of reference families should be designed for strictly mapping marker loci. Examples illustrate how tabulated results can be generalized to determine the values for a wide range of designs containing two‐ or three‐generation full‐sib or half‐sib families.     

Alström syndrome: further evidence for linkage to human chromosome 2p13

Alstr?m syndrome is a rare autosomal recessive disorder characterized by retinal degeneration, sensorineural hearing loss, early-onset obesity, and non-insulin-dependent diabetes mellitus. The gene for Alstr?m syndrome (ALMS1) has been previously localized to human chromosome 2p13 by homozygosity mapping in two distinct isolated populations - French Acadian and North African. Pair-wise analyses resulted in maximum lod (logarithm of the odds ratio) scores of 3.84 and 2.9, respectively. To confirm these findings, a large linkage study was performed in twelve additional families segregating for Alstr?m syndrome. A maximum two-point lod score of 7.13 (theta = 0.00) for marker D2S2110 and a maximum cumulative multipoint lod score of 9.16 for marker D2S2110 were observed, further supporting linkage to chromosome 2p13. No evidence of genetic heterogeneity was observed in these families. Meiotic recombination events have localized the critical region containing ALMS1 to a 6.1-cM interval flanked by markers D2S327 and D2S286. A fine resolution radiation hybrid map of 31 genes and markers has been constructed.     

A locus for Fanconi anemia on 16q determined by homozygosity mapping.

We report the results of a genomewide scan using homozygosity mapping to identify genes causing Fanconi anemia, a genetically heterogeneous recessive disorder. By studying 23 inbred families, we detected linkage to a locus causing Fanconi anemia near marker D16S520 (16q24.3). Although -65% of our families displayed clear linkage to D16S520, we found strong evidence (P = .0013) of genetic heterogeneity. This result independently confirms the recent mapping of the FAA gene to chromosome 16 by Pronk et al. Family ascertainment was biased against a previously identified FAC gene on chromosome 9, and no linkage was observed to this locus. Simultaneous search analysis suggested several additional chromosomal regions that could account for a small fraction of Fanconi anemia in our families, but the sample size is insufficient to provide statistical significance. We also demonstrate the strong effect of marker allele frequencies on LOD scores obtained in homozygosity mapping and discuss ways to avoid false positives arising from this effect.     

Evaluation of multi-locus models for genome-wide association studies: a case study in sugar beet

Association mapping has become a widely applied genomic approach to dissect the genetic architecture of complex traits. A major issue for association mapping is the need to control for the confounding effects of population structure, which is commonly done by mixed models incorporating kinship information. In this case study, we employed experimental data from a large sugar beet population to evaluate multi-locus models for association mapping. As in linkage mapping, markers are selected as cofactors to control for population structure and genetic background variation. We compared different biometric models with regard to important quantitative trait locus (QTL) mapping parameters like the false-positive rate, the QTL detection power and the predictive power for the proportion of explained genotypic variance. Employing different approaches we show that the multi-locus model, that is, incorporating cofactors, outperforms the other models, including the mixed model used as a reference model. Thus, multi-locus models are an attractive alternative for association mapping to efficiently detect QTL for knowledge-based breeding.     

Suggestive evidence for linkage of schizophrenia to markers on chromosome 13 in Caucasian but not Oriental populations

Previously we reported suggestive evidence for linkage of schizophrenia to markers on chromosome 13q14.1–q32. We have now studied an additional independent sample of 44 pedigrees consisting of 34 Taiwanese, 9 English and 1 Welsh family in an attempt to replicate this finding. Narrow and broad models based on Research Diagnostic Criteria or the Diagnostic and Statistical Manual of Mental Disorders, third edition, revised, were used to define the schizophrenia phenotype. Under a dominant genetic model, two-point lod scores obtained for most of the markers were negative except that marker D13S122 gave a total lod score of 1.06 (θ = 0.2, broad model). As combining pedigrees from different ethnic origins may be inappropriate, we combined this replication sample and our original sample, and then divided the total sample into Caucasian (English and Welsh pedigrees) and Oriental (Taiwanese and Japanese pedigrees) groups. The Caucasian pedigrees produced maximized admixture two-point lod scores (A-lod) of 1.41 for the marker D13S119 (θ = 0.2, α = 1.0) and 1.54 for D13S128 (θ = 0, α = 0.3) with nearby markers also producing positive A-lod scores. When five-point model-free linkage analysis was applied to the Caucasian sample, a maximum lod score of 2.58 was obtained around the markers D13S122 and D13S128, which are located on chromosome 13q32. The linkage results for the Oriental group were less positive than the Caucasian group. Our results again suggest that there is a potential susceptibility locus for schizophrenia on chromosome 13q14.1–q32, especially in the Caucasian population. Received: 13 September 1996