Inter- and intrafamilial heterogeneity: effective sampling strategies and comparison of analysis methods.

Heterogeneity, both inter- and intrafamilial, represents a serious problem in linkage studies of common complex diseases. In this study we simulated different scenarios with families who phenotypically have identical diseases but who genotypically have two different forms of the disease (both forms genetic). We examined the proportion of families displaying intrafamilial heterogeneity, as a function of mode of inheritance, gene frequency, penetrance, and sampling strategies. Furthermore, we compared two different ways of analyzing linkage in these data sets: a two-locus (2L) analysis versus a one-locus (SL) analysis combined with an admixture test. Data were simulated with tight linkage between one disease locus and a marker locus; the other disease locus was not linked to a marker. Our findings are as follows: (1) In contrast to what has been proposed elsewhere to minimize heterogeneity, sampling only "high-density" pedigrees will increase the proportion of families with intrafamilial heterogeneity, especially when the two forms are relatively close in frequency. (2) When one form is dominant and one is recessive, this sampling strategy will greatly decrease the proportions of families with a recessive form and may therefore make it more difficult to detect linkage to the recessive form. (3) An SL analysis combined with an admixture test achieves about the same lod scores and estimate of the recombination fraction as does a 2L analysis. Also, a 2L analysis of a sample of families with intrafamilial heterogeneity does not perform significantly better than an SL analysis. (4) Bilineal pedigrees have little effect on the mean maximum lod score and mean maximum recombination fraction, and therefore there is little danger that including these families will lead to a false exclusion of linkage.     

Using lod-score differences to determine mode of inheritance: a simple, robust method even in the presence of heterogeneity and reduced penetrance.

Determining the mode of inheritance is often difficult under the best of circumstances, but when segregation analysis is used, the problems of ambiguous ascertainment procedures, reduced penetrance, heterogeneity, and misdiagnosis make mode-of-inheritance determinations even more unreliable. The mode of inheritance can also be determined using a linkage-based method (maximized maximum lod score or mod score) and association-based methods, which can overcome many of these problems. In this work, we determined how much information is necessary to reliably determine the mode of inheritance from linkage data when heterogeneity and reduced penetrance are present in the data set. We generated data sets under both dominant and recessive inheritance with reduced penetrance and with varying fractions of linked and unlinked families. We then analyzed those data sets, assuming reduced penetrance, both dominant and recessive inheritance, and no heterogeneity. We investigated the reliability of two methods for determining the mode of inheritance from the linkage data. The first method examined the difference (delta) between the maximum lod scores calculated under the two mode-of-inheritance assumptions. We found that if delta was > 1.5, then the higher of the two maximum lod scores reflected the correct mode of inheritance with high reliability and that a delta of 2.5 appeared to practically guarantee a correct mode-of-inheritance inference. Furthermore, this reliability appeared to be virtually independent of alpha, the fraction of linked families in the data set, although the reliability decreased slightly as alpha fell below .50.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Direct power comparisons between simple LOD scores and NPL scores for linkage analysis in complex diseases.

Several methods have been proposed for linkage analysis of complex traits with unknown mode of inheritance. These methods include the LOD score maximized over disease models (MMLS) and the "nonparametric" linkage (NPL) statistic. In previous work, we evaluated the increase of type I error when maximizing over two or more genetic models, and we compared the power of MMLS to detect linkage, in a number of complex modes of inheritance, with analysis assuming the true model. In the present study, we compare MMLS and NPL directly. We simulated 100 data sets with 20 families each, using 26 generating models: (1) 4 intermediate models (penetrance of heterozygote between that of the two homozygotes); (2) 6 two-locus additive models; and (3) 16 two-locus heterogeneity models (admixture alpha = 1.0,.7,.5, and.3; alpha = 1.0 replicates simple Mendelian models). For LOD scores, we assumed dominant and recessive inheritance with 50% penetrance. We took the higher of the two maximum LOD scores and subtracted 0.3 to correct for multiple tests (MMLS-C). We compared expected maximum LOD scores and power, using MMLS-C and NPL as well as the true model. Since NPL uses only the affected family members, we also performed an affecteds-only analysis using MMLS-C. The MMLS-C was both uniformly more powerful than NPL for most cases we examined, except when linkage information was low, and close to the results for the true model under locus heterogeneity. We still found better power for the MMLS-C compared with NPL in affecteds-only analysis. The results show that use of two simple modes of inheritance at a fixed penetrance can have more power than NPL when the trait mode of inheritance is complex and when there is heterogeneity in the data set.     

Linkage analysis of juvenile myoclonic epilepsy and microsatellite loci spanning 61 cM of human chromosome 6p in 19 nuclear pedigrees provides no evidence for a susceptibility locus in this region.

Linkage analysis in separately ascertained families of probands with juvenile myoclonic epilepsy (JME) has previously provided evidence both for and against the existence of a locus (designated "EJM1"), on chromosome 6p, predisposing to a trait defined as either clinical JME, its associated electroencephalographic abnormality, or idiopathic generalized epilepsy. Linkage analysis was performed in 19 families in which a proband and at least one first- or two second-degree relatives have clinical JME. Family members were typed for seven highly polymorphic microsatellite markers on chromosome 6p: D6S260, D6S276, D6S291, D6S271, D6S465, D6S257, and D6S254. Pairwise and multipoint linkage analysis was carried out under the assumptions of autosomal dominant inheritance at 70% and 50% penetrance and autosomal recessive inheritance at 70% and 50% penetrance. No significant evidence in favor of linkage to the clinical trait of JME was obtained for any locus. The region formally excluded (LOD score < -2) by using multipoint analysis varies depending on the assumptions made concerning inheritance parameters and the proportion of linked families, alpha-that is, the degree of locus heterogeneity. Further analysis either classifying all unaffected individuals as unknown or excluding a subset of four families in which pyknoleptic absence seizures were present in one or more individuals did not alter these conclusions.     

Evaluating genetic heterogeneity in complex disorders

OBJECTIVES: The Admixture test is routinely used in linkage analysis to take account of genetic heterogeneity, and yields an estimate of the proportion of families (alpha) segregating the linked disease gene. In complex disorders, the assumptions of the Admixture test are violated. We therefore explore how the estimate of alpha relates to the true proportion of linked families with a complex disorder in a population or dataset. METHODS: We simulated a two-locus heterogeneity model and varied genetic parameters, ascertainment scheme and phenocopy frequency. RESULTS: In this model, alpha is almost always overestimated, by as little as 5% to as much as 60%. The bias is largely attributable to (1). intrafamilial heterogeneity arising from ascertainment of families with many affected members or from analysis of dense pedigrees; (2). low informativeness, which occurs in the presence of reduced penetrance; and (3). differences in the evidence for linkage in linked and unlinked families. This bias is also affected by the analysis phenocopy frequency, but only if the linked locus is dominant and the unlinked locus is recessive. CONCLUSIONS: We conclude that, in complex diseases, the Admixture test has greater value in detecting linkage than in estimating the proportion of linked families in a dataset.     

Dominant cataract and recessive specific locus mutations in offspring of X-irradiated male mice

Male mice were X-irradiated with 3.0 + 3.0 Gy or 5.1 + 5.1 Gy (fractionation interval 24 h). The offspring were screened for dominant cataract and recessive specific locus mutations. In the 3.0 + 3.0-Gy spermatogonial treatment group, 3 dominant cataract mutations were confirmed in 15 551 offspring examined and 29 specific locus mutations were recovered in 18 139 offspring. In the post-spermatogonial treatment group, 1 dominant cataract mutation was obtained in 1120 offspring and 1 recessive specific locus mutation was recovered in 1127 offspring. The induced mutation rate per locus, per gamete, per Gy calculated for recessive specific locus mutations is 2.0 X 10(-5) in post-spermatogonial stages and 3.7 X 10(-5) in spermatogonia. For dominant cataract mutations, assuming 30 loci, the induced mutation rate is 5.0 X 10(-6) in the post-spermatogonial stages and 1.1 X 10(-6) in spermatogonia. In the 5.1 + 5.1-Gy spermatogonial treatment group, 3 dominant cataract mutations were obtained in 11 205 offspring, whereas in 13 201 offspring 27 recessive specific locus mutations were detected in the spermatogonial group. In the post-spermatogonial treatment group no dominant cataract mutation was observed in 425 offspring and 2 recessive specific locus mutations were detected in 445 offspring. The induced mutation rate per locus, gamete and Gy in spermatogonia for recessive specific locus mutations is 2.8 X 10(-5) and for dominant cataract mutations 0.9 X 10(-6). In post-spermatogonial stages, the mutation rate for recessive specific locus alleles is 6.2 X 10(-5). In the concurrent untreated control group, in 11 036 offspring no dominant cataract mutation and in 23 518 offspring no recessive specific locus mutation was observed. Litter size and the number of carriers at weaning have been determined in the confirmation crosses of the obtained dominant cataract mutants as indicators of viability and penetrance effects. Two mutants had a statistically significantly reduced litter size and one mutant had a statistically significantly reduced penetrance.     

Complex segregation analysis of Parkinson's disease in the Finnish population

The risk of Parkinson's disease (PD) is higher among relatives of affected individuals than among other members of the population, and most family studies have suggested autosomal dominant inheritance, although both autosomal dominant and recessive susceptibility genes have recently been identified. We carried out a complex segregation analysis with POINTER to assess the mode of inheritance of PD in the population of northern Finland. Nuclear families (n=265) were identified through a proband with idiopathic PD. The analysis was first carried out for the total data set, and then the heterogeneity between early-onset (proband under 55 years at onset) and late-onset families was examined. Finally, families with more than one affected individual were analyzed separately. The sporadic model was rejected (P<0.0001). Significant heterogeneity was found between the early-onset and late-onset families, suggesting that major genes have a greater role in early-onset PD than in late-onset PD and that the etiology of idiopathic PD is heterogeneous, even in the Finnish population, which has evolved from a small group of founders. The analysis of familial PD supported the hypothesis that a major locus was present in this subset, but it was not possible to distinguish between a recessive model with a high penetrance and a dominant model with lower penetrance.     

Segregation and linkage analyses of 72 leprosy pedigrees

Data on 72 families with multiple cases of leprosy were analyzed for a susceptibility gene linked to the HLA loci. We conducted segregation analysis with the program POINTER and identity of HLA types by descent analysis to determine the most likely mode of inheritance. We then conducted linkage analysis with the program LINKAS, first assuming linkage equilibrium and then allowing for linkage disequilibrium and etiological heterogeneity. Segregation results suggest a recessive mode of inheritance, especially for the tuberculoid forms of leprosy. The linkage results, limited to tuberculoid forms and assuming a recessive model, suggest a hypothesis of loose linkage with no unlinked locus. When an additive model is assumed, the best fit is obtained with a hypothesis of complete linkage (theta = 0.0) with heterogeneity. We currently favor the additive model as the more plausible one.     

Progress in the search for genetic linkage with Tourette syndrome: An exclusion map covering more than 50% of the autosomal genome

Gilles de la Tourette syndrome is a neuropsychiatric disorder with an autosomal dominant mode of inheritance and reduced penetrance at a single genetic locus. Several research groups have genetic linkage studies underway to detect the chromosomal location of the gene that predisposes for this disorder. Strong and clear evidence of linkage has not yet been produced for Tourette syndrome. This paper presents an overview of the methods and progress of the groups centered at Yale University and Erasmus University in excluding linkage from a large portion of the genome. Our labs have screened 228 genetic marker loci for linkage with a gene for this disorder in a series of affected families in the United States, Canada, The Netherlands, and Norway. More than 50% (and perhaps as much as 66%) of the autosomal genome has now been excluded on the assumption that genetic heterogeneity is not an important factor in the Tourette syndrome pedigrees pooled for this summary.     

A robust method for the detection of linkage in familial disease.

A nonparametric method for the detection of critical genes associated with familial disease was presented. The method involves the detection of deviations from expected identity by descent distributions at polymorphic marker loci for affected sib pairs. The method thus avoids the difficulties arising from incomplete penetrance, variable age of onset and other complications present in other forms of linkage analysis. The theoretical properties of method were worked out in detail for two important cases -- that of an incompletely penetrant recessive or incompletely penetrant dominant critical autosomal gene linked to a codominant marker locus. An easily implementable decision rule for the detection of linkage was proposed, and its operating characteristics for a variety of alternative hypothesis were obtained.     

Linkage analysis of idiopathic generalized epilepsy (IGE) and marker loci on chromosome 6p in families of patients with juvenile myoclonic epilepsy: no evidence for an epilepsy locus in the HLA region.

Evidence for a locus (EJM1) in the HLA region of chromosome 6p predisposing to idiopathic generalized epilepsy (IGE) in the families of patients with juvenile myoclonic epilepsy (JME) has been obtained in two previous studies of separately ascertained groups of kindreds. Linkage analysis has been undertaken in a third set of 25 families including a patient with JME and at least one first-degree relative with IGE. Family members were typed for eight polymorphic loci on chromosome 6p: F13A, D6S89, D6S109, D6S105, D6S10, C4B, DQA1/A2, and TCTE1. Pairwise and multipoint linkage analysis was carried out assuming autosomal dominant and autosomal recessive inheritance and age-dependent high or low penetrance. No significant evidence in favor of linkage was obtained at any locus. Multipoint linkage analysis generated significant exclusion data (lod score < -2.0) at HLA and for a region 10-30 cM telomeric to HLA, the extent of which varied with the level of penetrance assumed. These observations indicate that genetic heterogeneity exists within this epilepsy phenotype.     

Utility and efficiency of linked marker genes for genetic counseling. II. Identification of linkage phase by offspring phenotypes

For a linked marker locus to be useful for genetic counseling, the counselee must be heterozygous for both disease and marker loci and his or her linkage phase must be known. It is shown that when the phenotypes of the counselee's previous children for the disease and marker loci are known, the linkage phase can often be inferred with a high probability, and thus it is possible to conduct genetic counseling. To evaluate the utility of linked marker genes for genetic counseling, the accuracy of prediction of the risk for a prospective child with a given marker gene to develop the genetic disease and the proportion of families in which a particular marker locus can be used for genetic counseling are studied for X-linked recessive, autosomal dominant, and autosomal recessive diseases. In the case of X-linked genetic diseases, information from children is very useful for determining the linkage phase of the counselee and predicting the genetic disease. In the case of autosomal dominant diseases, not all children are informative, but if the number of children is large, the phenotypes of children are often more informative than the information from grandparents. In the case of autosomal recessive diseases, information from grandparents is usually useless, since they show a normal phenotype for the disease locus. If we use information on the phenotypes of children, however, the linkage phase of the counselee and the risk of a prospective child can be inferred with a high probability. The proportion of informative families depends on the dominance relationship and frequencies of marker alleles, and the number of children. In general, codominant markers are more useful than are dominant markers, and a locus with high heterozygosity is more useful than is a locus with low heterozygosity.     

Utility and efficiency of linked marker genes for genetic counseling. III. Proportion of informative families under linkage disequilibrium.

A marker locus closely linked to a disease locus is often useful for genetic counseling provided that a counselee is heterozygous at both disease and marker loci. Furthermore, the linkage phase of these genes in the counselee must be known. When the linkage between the disease and marker loci is very close, one often finds linkage disequilibrium between the loci. To evaluate the effect of such nonrandom associations on the utility of linked marker genes for genetic counseling, the proportion of informative families is studied for X-linked recessive and autosomal dominant diseases. This proportion is higher for X-linked genes than for autosomal genes, if other factors are the same. In general, codominant markers are more useful than dominant markers. Also, under appropriate conditions, the proportion of informative families is higher when linkage disequilibrium is present. The results obtained in this paper are useful for evaluating the utility of polymorphic restriction endonuclease cleavage sites as markers in genetic counseling.     

Selective intestinal malabsorption of vitamin B12 displays recessive mendelian inheritance: assignment of a locus to chromosome 10 by linkage.

Juvenile megaloblastic anemia caused by selective intestinal malabsorption of vitamin B12 has been considered a distinct condition displaying autosomal recessive inheritance. It appears to have a worldwide distribution, and comparatively high incidences were reported 30 years ago in Finland and Norway. More recently, the Mendelian inheritance of the condition has been questioned because almost no new cases have occurred in these populations. Here we report linkage studies assigning a recessive-gene locus for the disease to chromosome 10 in previously diagnosed multiplex families from Finland and Norway, proving the Mendelian mode of inheritance. The locus is tentatively assigned to the 6-cM interval between markers D10S548 and D10S466, with a multipoint maximum lod score (Zmax) of 5.36 near marker D10S1477. By haplotype analysis, the healthy sibs in these families did not appear to constitute any examples of nonpenetrance. We hypothesize that the paucity of new cases in these populations is due either to a dietary effect on the gene penetrance that has changed with time, or to a drop in the birth rate in subpopulations showing enrichment of the mutation, or to both of these causes.     

Additional glomangioma families link to chromosome 1p: no evidence for genetic heterogeneity

Venous malformations are a common abnormality of the vasculature that may occur sporadically or, more rarely, as an autosomal dominant trait. One familial form of venous malformations has previously been linked to chromosome 9p. Mutations in the gene encoding Tie2, an endothelial specific receptor tyrosine kinase, have been identified in four different families. Glomangiomas are a subtype of venous malformations with glomus cell involvement. These cutaneous lesions can be inherited as an autosomal dominant disease with reduced penetrance and variable expressivity. We present evidence of linkage to chromosome 1p21-1p22 using four new glomangioma families, with a combined maximum two-point lod score of 7.32 at marker D1S2804. Markers D1S2129 and D1S2881 define the 24-cM linkage interval determined by recombination within affected individuals. A recent report also showed linkage of the glomangioma locus to chromosome 1p. A total of 9 families now map to this region, suggesting a decreased likelihood of locus heterogenity in familial glomangiomas. Investigation of candidate genes within the interval should provide new insights into lesion formation in inherited venous malformations.     

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.     

Familial juvenile hyperuricemic nephropathy: localization of the gene on chromosome 16p11.2-and evidence for genetic heterogeneity

Familial juvenile hyperuricemic nephropathy (FJHN), is an autosomal dominant renal disease characterized by juvenile onset of hyperuricemia, gouty arthritis, and progressive renal failure at an early age. Using a genomewide linkage analysis in three Czech affected families, we have identified, on chromosome 16p11.2, a locus for FJHN and have found evidence for genetic heterogeneity and reduced penetrance of the disease. The maximum two-point LOD score calculated with allowance for heterogeneity (HLOD) was 4.70, obtained at recombination fraction 0, with marker D16S3036; multipoint linkage analysis yielded a maximum HLOD score of 4.76 at the same location. Haplotype analysis defined a 10-cM candidate region between flanking markers D16S501 and D16S3113, exhibiting crossover events with the disease locus. The candidate interval contains several genes expressed in the kidney, two of which-uromodulin and NADP-regulated thyroid-hormone-binding protein-represent promising candidates for further analysis.     

Genetic linkage analysis in familial breast and ovarian cancer: results from 214 families. The Breast Cancer Linkage Consortium.

Breast cancer is known to have an inherited component, consistent in some families with autosomal dominant inheritance; in such families the disease often occurs in association with ovarian cancer. Previous genetic linkage studies have established that in some such families disease occurrence is linked to markers on chromosome 17q. This paper reports the results of a collaborative linkage study involving 214 breast cancer families, including 57 breast-ovarian cancer families; this represents almost all the known families with 17q linkage data. Six markers on 17q, spanning approximately 30 cM, were typed in the families. The aims of the study were to define more precisely the localization of the disease gene, the extent of genetic heterogeneity and the characteristics of linked families and to estimate the penetrance of the 17q gene. Under the assumption of no genetic heterogeneity, the strongest linkage evidence was obtained with D17S588 (maximum LOD score [Zmax] = 21.68 at female recombination fraction [theta f] = .13) and D17S579 (Zmax = 13.02 at theta f = .16). Multipoint linkage analysis allowing for genetic heterogeneity provided evidence that the predisposing gene lies between the markers D17S588 and D17S250, an interval whose genetic length is estimated to be 8.3 cM in males and 18.0 cM in females. This position was supported over other intervals by odds of 66:1. The location of the gene with respect to D17S579 could not be determined unequivocally. Under the genetic model used in the analysis, the best estimate of the proportion of linked breast-ovarian cancer families was 1.0 (lower LOD-1 limit 0.79). In contrast, there was significant evidence of genetic heterogeneity among the families without ovarian cancer, with an estimated 45% being linked. These results suggest that a gene(s) on chromosome 17q accounts for the majority of families in which both early-onset breast cancer and ovarian cancer occur but that other genes predisposing to breast cancer exist. By examining the fit of the linkage data to different penetrance functions, the cumulative risk associated with the 17q gene was estimated to be 59% by age 50 years and 82% by age 70 years. The corresponding estimates for the breast-ovary families were 67% and 76%, and those for the families without ovarian cancer were 49% and 90%; these penetrance functions did not differ significantly from one another.