The detection of linkage and heterogeneity in nuclear families for complex disorders: one versus two marker loci.

Using exact expected likelihoods, we have computed the average number of phase-unknown nuclear families needed to detect linkage and heterogeneity. We have examined the case of both dominant and recessive inheritance with reduced penetrance and phenocopies. Most of our calculations have been carried out under the assumption that 50% of families are linked to a marker locus. We have varied both the number of offspring per family and the sampling scheme. We have also investigated the increased power when the disease locus is midway between two marker loci 10 cM apart. For recessive inheritance, both linkage and heterogeneity can be detected in clinically feasible sample sizes. For dominant inheritance, linkage can be detected but heterogeneity cannot be detected unless larger sibships (four offspring) are sampled or two linked markers are available. As expected, if penetrance is reduced, sampling families with all sibs affected is most efficient. Our results provide a basis for estimating the amount of resources needed to find genes for complex disorders under conditions of heterogeneity.     

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.     

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.     

Genetics of Type I diabetes mellitus: a single, recessive predisposition gene mapping between HLA-B and GLO. With an appendix on the estimation of selection bias.

Three different published sets of HLA-typed families of juvenile diabetes mellitus (JDM) patients have been analyzed. There was no significant genetic heterogeneity between them according to the criterion of Morton, and the total material was analyzed on the assumption of a single recessive (JDM-P) gene with incomplete penetrance. The analysis, carried out with the NYLIP program modified to account for penetrance less than 1 and for selection bias, yields highly significant lod scores for linkage between HLA and JDM-P, with a maximum value of 7.40 at theta = .05 +/- .03. The segregation of HLA and GLO in five affected sib pairs, in which one of the sibs carries an HLA/GLO recombinant, places JDM-P closer to HLA than the GLO locus: four of these five pairs are HLA-identical and GLO-different, in agreement with the conclusions of the formal linkage analysis. The data from these three independent sets of families are therefore consistent with our earlier claim that JDM is inherited as a recessive trait closely linked to HLA with reduced penetrance, and its analysis does not require more complicated genetic models.     

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.     

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.     

Genetic analysis of multiply-affected families of insulin-dependent diabetes mellitus (IDDM) probands

The present study combines segregation and linkage information on 30 families ascertained through a proband and a first degree relative affected with insulin-dependent diabetes mellitus (IDDM). An autosomal dominant model with incomplete penetrance was much more likely to fit the family data than a recessive model, whether or not linkage to HLA was assumed. The lod scores for linkage to HLA were 2.46 at theta M = theta F = 0.00 for dominant and 1.45 at theta M = theta F = 0.22 for a recessive model. The results are discussed in light of heterogeneity in likelihood and lod scores when the families are grouped by familial types, which indicate that the increase in likelihood of a dominant hypothesis can be attributed to the parent-child families and not the sib-sib families.     

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.     

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.     

HLA and the inheritance of multiple sclerosis: linkage analysis of 72 pedigrees.

Linkage analysis of 72 pedigrees by the maximum-likelihood method provides evidence of linkage between HLA and the hypothesized multiple sclerosis susceptibility gene (MSSG) for both the dominant and recessive models of inheritance and for penetrance values ranging from 5%--65% (or higher). This MSSG, if it exists, is most likely located at 15%--20% recombination units from the HLA complex, probably on the B-D side. The analysis also shows that there is no heterogeneity in the estimates of linkage, and lod scores are not artifically inflated because of the association of multiple sclerosis (MS) with HLA-B7.     

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.     

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.     

Possible heterogeneity in the phosphoglycolate phosphatase (PGP)-haptoglobin alpha (HPA) linkage.

Previous investigators have reported loose linkage in both sexes for phosphoglycolate phosphatase (PGP) and haptoglobin alpha (HPA). We present results of linkage studies between PGP and HPA in two data sets, one from Houston and the other an update of an earlier report from Los Angeles. Using quadratic interpolation to estimate the male (theta m) and female (theta f) recombination values from bivariate lod tables, we found for the Houston data that theta m = 0.43 and theta f = 0.03 at the maximum lod score of z = 2.23. For the Los Angeles series, we found that theta m = 0.31, theta f = 0.48, and z = 0.27. We invoke heterogeneity in the recombination value in different families as an explanation of our findings. We also recommend that bivariate lod tables should always be generated, even though not reported. This is because the usual assumption of theta m = theta f (and, rarely, theta f = 1.8 theta f) under which lod scores are computed may be invalid in many cases.     

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.     

HLODs, trait models, and ascertainment: implications of admixture for parameter estimation and linkage detection

Maximizing the homogeneity lod is known to be an appropriate procedure for estimating parameters of the trait model in an approximately 'ascertainment assumption free' (AAF) manner. We have investigated whether this same property also holds for the heterogeneity lod (HLOD). We show that, when the genetic models at linked and unlinked loci differ, HLODs are not AAF, and maximizing the HLOD yields parameter estimates that are for all practical purposes meaningless; indeed, the admixture parameter alpha does not even measure the proportion of linked families within the sample, as is commonly supposed. In spite of this, our results confirm a large body of evidence supporting the use of HLODs as robust tools for linkage detection, and suggest further that maximizing the HLOD over both alpha and parameters of the trait model can improve accuracy in estimation of the recombination fraction theta;. These findings have important implications for the optimal handling of nuisance parameters in linkage analysis, particularly when evaluating the evidence for or against linkage based on multiple independent heterogeneous sets of data.     

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.     

Genetic linkage of systemic lupus erythematosus to 13q32 in African American families with affected male members

Systemic lupus erythematosus (SLE) is a complex autoimmune disorder involving genetic and environmental factors. Previously, our group showed that SLE females with affected male relatives have higher prevalence of renal disease than SLE females with no affected male relatives in a sample of 372 individuals from 159 families. By adding 392 individuals from 181 new families, we replicated this finding in the largest collection of families with affected males, confirming our hypothesis that multiplex SLE families with at least one affected male member (“male families”) comprise a distinct subpopulation of SLE multiplex families. We studied 64 male families by a genome-wide scan for SLE and found the largest signal (lod=3.08) at 13q32 in 18 African American male families using an affected-relative-pair model-free linkage method. Closer examination of IBD sharing at this region suggested a dominant mode of inheritance. Multipoint model-based linkage analysis generated a lod score of 3.13 in the same chromosomal region with a low-disease allele frequency of 0.0004 and a disease penetrance of 0.5 for the 18 African American male families. We performed fine mapping in these and three additional African American male families and the SLE predisposing locus was localized to a region tightly linked to the marker D13S892. We have therefore confirmed the linkage of SLE to 13q32, which was reported previously, and suggested that an SLE susceptibility gene in this region is specific to predisposition of African Americans to a specific form of SLE, with males at high risk.     

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.     

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.     

Linkage to D3S47 (C17) in one large autosomal dominant retinitis pigmentosa family and exclusion in another: confirmation of genetic heterogeneity.

Recently Dryja and his co-workers observed a mutation in the 23d codon of the rhodopsin gene in a proportion of autosomal dominant retinitis pigmentosa (ADRP) patients. Linkage analysis with a rhodopsin-linked probe C17 (D3S47) was carried out in two large British ADRP families, one with diffuse-type (D-type) RP and the other with regional-type (R-type) RP. Significantly positive lod scores (lod score maximum [Zmax] = +5.58 at recombination fraction [theta] = .0) were obtained between C17 and our D-type ADRP family showing complete penetrance. Sequence and oligonucleotide analysis has, however, shown that no point mutation at the 23d codon exists in affected individuals in our complete-penetrance pedigree, indicating that another rhodopsin mutation is probably responsible for ADRP in this family. Significantly negative lod scores (Z less than -2 at theta = .045) were, however, obtained between C17 and our R-type family which showed incomplete penetrance. Previous results presented by this laboratory also showed no linkage between C17 and another large British R-type ADRP family with incomplete penetrance. This confirms genetic heterogeneity. Some types of ADRP are being caused by different mutations in the rhodopsin locus (3q21-24) or another tightly linked gene in this region, while other types of ADRP are the result of mutations elsewhere in the genome.