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)     

Evidence for the localization of a malignant hyperthermia susceptibility locus (MHS2) to human chromosome 17q.

Malignant hyperthermia susceptibility is a lethal autosomal dominant disorder of skeletal muscle metabolism that is triggered by all potent inhalation anesthetic gases. Recent linkage studies suggest a genetic locus for this disorder on 19q13.1. We have previously reported three unrelated families diagnosed with MHS that are unlinked to markers surrounding this locus on 19q13.1. In this report we extend these observations and present linkage studies on 16 MHS families. Four families (25%) were found linked to the region 19q12-q13.2 (Zmax = 2.96 with the ryanodine receptor at theta = 0.0). Five families (31%) were found closely linked to the anonymous marker NME1 (previously designated NM23) on chromosome 17q11.2-q24 (Zmax = 3.26 at theta = 0.0). Two families (13%) were clearly unlinked to either of these chromosomal regions. In five additional families, data were insufficient to determine their linkage status (they were potentially linked to two or more sites). The results of our heterogeneity analyses are consistent with the hypothesis that MHS can be caused in humans by any one of at least three distinct genetic loci. Furthermore, we provide preliminary linkage data suggesting the localization of a gene in human MHS to 17q11.2-q24 (MHS2), with a gene frequency of this putative locus approximately equal to that of the MHS1 locus on 19q.     

Effect of genetic heterogeneity and assortative mating on linkage analysis: a simulation study.

Linkage studies of complex genetic traits raise questions about the effects of genetic heterogeneity and assortative mating on linkage analysis. To further understand these problems, I have simulated and analyzed family data for a complex genetic disease in which disease phenotype is determined by two unlinked disease loci. Two models were studied, a two-locus threshold model and a two-locus heterogeneity model. Information was generated for a marker locus linked to one of the disease-defining loci. Random-mating and assortative-mating samples were generated. Linkage analysis was then carried out by use of standard methods, under the assumptions of a single-locus disease trait and a random-mating population. Results were compared with those from analysis of a single-locus homogeneous trait in samples with the same levels of assortative mating as those considered for the two-locus traits. The results show that (1) introduction of assortative mating does not, in itself, markedly affect the estimate of the recombination fraction; (2) the power of the analysis, reflected in the LOD scores, is somewhat lower with assortative rather than random mating. Loss of power is greater with increasing levels of assortative mating; and (3) for a heterogeneous genetic disease, regardless of mating type, heterogeneity analysis permits more accurate estimate of the recombination fraction but may be of limited use in distinguishing which families belong to each homogeneous subset. These simulations also confirmed earlier observations that linkage to a disease "locus" can be detected even if the disease is incorrectly defined as a single-locus (homogeneous) trait, although the estimated recombination fraction will be significantly greater than the true recombination fraction between the linked disease-defining locus and the marker locus.     

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.     

A study of genetic linkage heterogeneity in 35 adult-onset polycystic kidney disease families

A genetic heterogeneity analysis of 35 kindreds with adult-onset polycystic kidney disease (ADPKD) was carried out using the D16S85, D16S84, D16S125 and D16S94 loci that are closely linked to the PKD1 locus on chromosome 16. The results show that the likelihood of two ADPKD loci is 2,514.9 times greater than for a single locus (P < 0.0001). The maximum likelihood lod score is 27.38 under heterogeneity with PKD1 lying 4.9 cM proximal to D16S85 (in males). At least 3% of kindreds are unlinked to PKD1, since the 95% confidence limits of alpha, the proportion of families linked to PKD1, are 0.54–0.97. Only 2 out of 35 kindreds (5.7%) show statistically significant evidence of non-linkage to PKD1, with conditional probabilities of 0.987 and 0.993 that the disease locus is unlinked. This confirms the existence of a small subgroup of ADPKD kindreds that are unlinked to PKD1 and provides a firm basis for genetic counselling of this population on the basis of DNA probes.     

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.     

An extension of the admixture test for the study of genetic heterogeneity in hereditary multiple exostoses

Hereditary multiple exostoses (EXT) is an autosomal dominant disorder characterized by the presence of multiple cartilage-capped exostoses in the juxta-epiphyseal regions of the long bones. EXT is heterogeneous with at least three different locations currently having been identified on chromosomes 8, 11 and 19. We have tested a series of 29 EXT families for possible linkage to the three disease loci and estimated the probability of linkage of the disease to each locus in our series, by using an extension of the admixture test, which makes modelling of heterogeneous monogenic disease feasible. The maximum likelihood was obtained for proportions of 44%, 28% and 28% of families being linked to chromosome 8, 11 and 19, respectively. The a posteriori probability of linkage of the disease to EXT1, EXT2 and EXT3 was greater than 80% for 8/29, 5/29 and 3/29 families, respectively, and did not give evidence of a fourth locus for the disease. The present approach can be generalized to the investigation of genetic heterogeneity in other monogenic diseases, as it simultaneously estimates the location of each disease gene and the proportion of families linked to each locus. Received: 28 May 1996 / Revised: 7 October 1996     

Genetic heterogeneity of polycystic kidney disease in Bulgaria

Linkage analysis was performed on 22 Bulgarian families with polycystic kidney disease (PKD) ascertained through the hemodialysis centers of two medical schools. A total of 128 affected and 59 unaffected individuals, and 54 spouses have been investigated using eight polymorphic markers linked to PKD1 and nine markers to PKD2. The results demonstrate locus heterogeneity with 0.67 as the maximum likelihood value of alpha, i.e., the proportion of families linked to PKD1. In five families, the results suggest linkage to PKD2, and observed recombinants place the gene between loci D4S1544 and D4S1542. In one family, two double recombinants for closely linked markers on chromosome 16 and on chromosome 4 give evidence for the lack of link-age to either PKD1 or PKD2, thus suggesting the involvement of a third locus. Analysis of clinical data in the PKD1 group versus the unlinked group shows no significant differences in the severity of the disease.     

Linkage of Wolfram syndrome to chromosome 4p16.1 and evidence for heterogeneity.

Wolfram syndrome (DIDMOAD syndrome; MIM 222300) is an autosomal recessive neurodegenerative disorder characterized by juvenile-onset diabetes mellitus and bilateral optic atrophy. Previous linkage analysis of multiply affected families indicated that the gene for Wolfram syndrome is on chromosome 4p, and it produced no evidence for locus heterogeneity. We have investigated 12 U.K. families with Wolfram syndrome, and we report confirmation of linkage to chromosome 4p, with a maximum two-point LOD score of 4.6 with DRD5, assuming homogeneity, and of 5.1, assuming heterogeneity. Overlapping multipoint analysis using six markers at a time produced definite evidence for locus heterogeneity: the maximum multipoint LOD score under homogeneity was <2, whereas when heterogeneity was allowed for an admixture a LOD of 6.2 was obtained in the interval between D4S432 and D4S431, with the peak close to the marker D4S3023. One family with an atypical phenotype was definitely unlinked to the region. Haplotype inspection of the remaining 11 families, which appear linked to chromosome 4p and had typical phenotypes, revealed crossover events during meiosis, which also placed the gene in the interval D4S432 and D4S431. In these families no recombinants were detected with the marker D4S3023, which maps within the same interval.     

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.     

Evidence for Locus Heterogeneity in Autosomal Dominant Limb-Girdle Muscular Dystrophy

Limb-girdle muscular dystrophy (LGMD) is a diagnostic classification encompassing a broad group of proximal myopathies. A gene for the dominant form of LGMD (LGMD1A) has recently been localized to a 7-cM region of chromosome 5q between D5S178 and IL9. We studied three additional dominant LGMD families for linkage to these two markers and excluded all from localization to this region, providing evidence for locus heterogeneity within the dominant form of LGMD. Although the patterns of muscle weakness were similar in all families studied, the majority of affected family members in the chromosome 5–linked pedigree have a dysarthric speech pattern, which is not present in any of the five unlinked families. The demonstration of heterogeneity within autosomal dominant LGMD is the first step in attempting to subclassify these families with similar clinical phenotypes on a molecular level.     

Detection of linkage for heterogeneous disorders by using multipoint linkage analysis.

We have compared the efficiency of the lod score test which assumes heterogeneity (lod2) to the standard lod score test which assumes homogeneity (lod1) when three-point linkage analysis is used in successive map intervals. If it is assumed that a gene located midway between two linked marker loci is responsible for a proportion of disease cases, then the lod1 test loses power relative to the lod2 test, as the proportion of linked families decreases, as the flanking markers are more closely linked, and as more map intervals are tested. Moreover, when multipoint analysis is used, linkage for a disease gene is more likely to be incorrectly excluded from a complete and dense linkage map if true genetic heterogeneity is ignored. We thus conclude that, in general, the lod2 linkage test is more efficient for detecting a true linkage when a complete genetic marker map is screened for a heterogeneous disorder.     

Analysis of alcohol dependence phenotype in the COGA families using covariates to detect linkage

Linkage analysis methods that incorporate etiological heterogeneity of complex diseases are likely to demonstrate greater power than traditional linkage analysis methods. Several such methods use covariates to discriminate between linked and unlinked pedigrees with respect to a certain disease locus. Here we apply several such methods including two mixture models, ordered subset analysis, and a conditional logistic model to genome scan data on the DSM-IV alcohol dependence phenotype on the Collaborative Studies on Genetics of Alcoholism families, and compare the results to traditional nonparametric linkage analysis. In general, there was little agreement among the various covariate-based linkage statistics. Linkage signals with empirical p-values less than 0.001 were detected on chromosomes 3, 4, 7, 10, and 12, with the highest peak occurring at the GABRB1 gene using the ecb21 covariate.     

<Emphasis Type="Italic">TDT-HET</Emphasis>: A new transmission disequilibrium test that incorporates locus heterogeneity into the analysis of family-based association data

Background  

Locus heterogeneity is one of the most documented phenomena in genetics. To date, relatively little work had been done on the development of methods to address locus heterogeneity in genetic association analysis. Motivated by Zhou and Pan's work, we present a mixture model of linked and unlinked trios and develop a statistical method to estimate the probability that a heterozygous parent transmits the disease allele at a di-allelic locus, and the probability that any trio is in the linked group. The purpose here is the development of a test that extends the classic transmission disequilibrium test (TDT) to one that accounts for locus heterogeneity.     

Combined analysis of hereditary prostate cancer linkage to 1q24-25: results from 772 hereditary prostate cancer families from the International Consortium for Prostate Cancer Genetics

A previous linkage study provided evidence for a prostate cancer-susceptibility locus at 1q24-25. Subsequent reports in additional collections of families have yielded conflicting results. In addition, evidence for locus heterogeneity has been provided by the identification of other putative hereditary prostate cancer loci on Xq27-28, 1q42-43, and 1p36. The present study describes a combined analysis for six markers in the 1q24-25 region in 772 families affected by hereditary prostate cancer and ascertained by the members of the International Consortium for Prostate Cancer Genetics (ICPCG) from North America, Australia, Finland, Norway, Sweden, and the United Kingdom. Overall, there was some evidence for linkage, with a peak parametric multipoint LOD score assuming heterogeneity (HLOD) of 1.40 (P=.01) at D1S212. The estimated proportion of families (alpha) linked to the locus was.06 (1-LOD support interval.01-.12). This evidence was not observed by a nonparametric approach, presumably because of the extensive heterogeneity. Further parametric analysis revealed a significant effect of the presence of male-to-male disease transmission within the families. In the subset of 491 such families, the peak HLOD was 2.56 (P=.0006) and alpha =.11 (1-LOD support interval.04-.19), compared with HLODs of 0 in the remaining 281 families. Within the families with male-to-male disease transmission, alpha increased with the early mean age at diagnosis (<65 years, alpha =.19, with 1-LOD support interval.06-.34) and the number of affected family members (five or more family members, alpha =.15, with 1-LOD support interval.04-.28). The highest value of alpha was observed for the 48 families that met all three criteria (peak HLOD = 2.25, P=.001, alpha=.29, with 1-LOD support interval.08-.53). These results support the finding of a prostate cancer-susceptibility gene linked to 1q24-25, albeit in a defined subset of prostate cancer families. Although HPC1 accounts for only a small proportion of all families affected by hereditary prostate cancer, it appears to play a more prominent role in the subset of families with several members affected at an early age and with male-to-male disease transmission.     

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.     

Huntington disease: no evidence for locus heterogeneity

A total of 63 families with Huntington disease (HD) were examined for linkage between HD and G8 (D4S10). The families included 57 Caucasian, four Black American, and two Japanese. The combined maximum lod score was 87.69 at theta = 0.04 (99% confidence interval 0.018-0.071). The maximum frequency of recombination was 0.03 in males and 0.05 in females. Fifty-seven families gave positive lod scores; five small families gave mildly negative lod scores. The maximum likelihood estimate of alpha, the proportion of linked loci, was 1.0 with a lower 99% confidence interval of 0.88. These data suggest that there is only one HD locus, although a second rare locus cannot be ruled out.     

Linkage variation at the sex-determining locus within Fraser strain Arctic charr Salvelinus alpinus

The association of genetic markers linked to the sex-determining locus (SEX) was investigated in five Arctic charr Salvelinus alpinus full sib families, all originating from the Fraser River strain, Labrador, Canada. Two distinct sex-linkage classes were identified: type I (two families), with previously reported markers on linkage group 4 (AC-4) linked with SEX; and type II (three families), with two unlinked segments of the AC-4 linkage group, but with markers in only one cluster associated with SEX. Large differences in recombination rates, pseudolinkage assembly or various chromosomal rearrangements may explain these findings.     

Heterogeneity analysis of breast cancer families by using age at onset as a covariate.

An extension of the usual mixture model of heterogeneity (two family types, one with and one without linkage) is proposed by introducing age at onset as a covariate. The extended model defines age-dependent penetrances where the exact parametrization of age-at-onset distributions depends on the given genotype and family type (linked or unlinked). This extension was applied to breast cancer families. We postulated that the mean age at onset in individuals affected by the linked gene was lower than the mean age at onset in all other affected individuals. Linkage heterogeneity for breast cancer families was detected at a significance level of .003.