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.     

Evidence for heterogeneity in facioscapulohumeral muscular dystrophy (FSHD)

Facioscapulohumeral muscular dystrophy (FSHD) is a slowly progressive primary disease of muscle which is usually inherited as an autosomal dominant disorder. FSHD has been localized to the long arm of chromosome 4, specifically to the 4q3.5-qter region. Initially published linkage studies showed no evidence for heterogeneity in FSHD. In the present study we have examined individuals in seven FSHD families. Two-point lod scores show significant evidence for linkage for D4S163 (lod score 3.04 at recombination fraction .21) and D4S139 (lod score 3.84 at recombination fraction .20). D4S171 also gave a positive score (lod score 2.56 at recombination fraction .24). Significant evidence for heterogeneity was found for each of the three markers. Multipoint linkage analysis in this region resulted in a peak multipoint lod score of 6.47. The multipoint analysis supported the two-point studies with odds of 20:1 showing linkage and heterogeneity over linkage and homogeneity. Five of the seven families gave a posterior probability of >95% of being of the linked type, while two families appeared unlinked to this region of 4q (P < .01%). Individuals in the two unlinked families met the clinical criteria for the diagnosis of FSHD, including facial weakness, clavicular flattening, scapula winging, proximal muscle weakness, and myopathic changes on muscle biopsies without inflammatory or mitochondrial pathology. This study demonstrates genetic heterogeneity in FSHD and has important implications for both genetic counseling and the elucidation of the etiology of FSHD.     

Autosomal dominant polycystic kidney disease: evidence for the existence of a third locus in a Portuguese family

Autosomal dominant polycystic kidney disease is characterized by clinical and genetic heterogeneity. Two loci implicated in the disease have previously been mapped (PKD1 on chromosome 16 and PKD2 on chromosome 4). By two point and multipoint linkage analysis, negative lod scores have been found for both chromosome 16 and chromosome 4 markers in a large Portuguese family, indicating that a third PKD locus is involved in the development of the disease.     

Genetic heterogeneity in X-linked amelogenesis imperfecta.

The AMELX gene located at Xp22.1-p22.3 encodes for the enamel protein amelogenin and has been implicated as the gene responsible for the inherited dental abnormality X-linked amelogenesis imperfecta (XAI). Three families with XAI have been investigated using polymorphic DNA markers flanking the position of AMELX. Using two-point linkage analysis, linkage was established between XAI and several of these markers in two families, with a combined lod score of 6.05 for DXS16 at theta = 0.04. This supports the involvement of AMELX, located close to DXS16, in the XAI disease process (AIH1) in those families. Using multipoint linkage analysis, the combined maximum lod score for these two families was 7.30 for a location of AIH1 at 2 cM distal to DXS16. The support interval around this location extended about 8 cM proximal to DXS92, and the AIH1 location could not be precisely defined by multipoint mapping. Study of recombination events indicated that AIH1 lies in the interval between DXS143 and DXS85. There was significant evidence against linkage to this region in the third family, indicating locus heterogeneity in XAI. Further analysis with markers on the long arm of the X chromosome showed evidence of linkage to DXS144E and F9 with no recombination with either of these markers. Two-point analysis gave a peak lod score at DXS144E with a maximum lod score of 2.83 at theta = 0, with a peak lod score in multipoint linkage analysis of 2.84 at theta = 0. The support interval extended 9 cM proximal to DXS144E and 14 cM distal to F9.(ABSTRACT TRUNCATED AT 250 WORDS)     

Calculation of multipoint likelihoods using flanking marker data: a simulation study

The calculation of multipoint likelihoods is computationally challenging, with the exact calculation of multipoint probabilities only possible on small pedigrees with many markers or large pedigrees with few markers. This paper explores the utility of calculating multipoint likelihoods using data on markers flanking a hypothesized position of the trait locus. The calculation of such likelihoods is often feasible, even on large pedigrees with missing data and complex structures. Performance characteristics of the flanking marker procedure are assessed through the calculation of multipoint heterogeneity LOD scores on data simulated for Genetic Analysis Workshop 14 (GAW14). Analysis is restricted to data on the Aipotu population on chromosomes 1, 3, and 4, where chromosomes 1 and 3 are known to contain disease loci. The flanking marker procedure performs well, even when missing data and genotyping errors are introduced.     

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.     

Linkage disequilibrium inflates type I error rates in multipoint linkage analysis when parental genotypes are missing

OBJECTIVES: Describe the inflation in nonparametric multipoint LOD scores due to inter-marker linkage disequilibrium (LD) across many markers with varied allele frequencies. METHOD: Using simulated two-generation families with and without parents, we conducted nonparametric multipoint linkage analysis with 2 to 10 markers with minor allele frequencies (MAF) of 0.5 and 0.1. RESULTS: Misspecification of population haplotype frequencies by assuming linkage equilibrium caused inflated multipoint LOD scores due to inter-marker LD when parental genotypes were not included. Inflation increased as more markers in LD were included and decreased as markers in equilibrium were added. When marker allele frequencies were unequal, the r2 measure of LD was a better predictor of inflation than D'. CONCLUSION: This observation strongly supports the evaluation of LD in multipoint linkage analyses, and further suggests that unaccounted for LD may be suspected when two-point and multipoint linkage analyses show a marked disparity in regions with elevated r2 measures of LD. Given the increasing popularity of high-density genome-wide SNP screens, inter-marker LD should be a concern in future linkage studies.     

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.     

Multipoint linkage analysis and heterogeneity testing in 20 X-linked retinitis pigmentosa families

Using multipoint linkage analysis in 20 families segregating for X-linked retinitis pigmentosa (XLRP), the lod scores on a map of eight RFLP loci were obtained. Our results indicate that under the hypothesis of homogeneity the maximal multipoint lod score supports one disease locus located slightly distal to OTC at Xp21.1. Heterogeneity testing for two XLRP loci suggested that a second XLRP locus may be located 8.5 cM proximal to DXS28 at Xp21.3. Further heterogeneity testing for three disease loci failed to detect a third XLRP locus proximal to DXS7 in any of our 20 XLRP families.     

Exclusion of linkage to the pericentromeric region of chromosome 21 in the Canadian pedigree with familial Alzheimer disease

Summary Alzheimer disease (AD) is a devastating neurodegenerative disease leading to global dementia. The familial form (FAD) has been linked to markers on chromosome 21 in some families, most tightly to the loci D21S16 and D21S13 located close to the centromere of the long arm. In other families the FAD mutation has been excluded from the more telomeric D21S1/S11 region, but not from the centromeric region of chromosome 21. We identified two new restriction fragment length polymorphisms (RFLPs) for the locus D21S13 and have used these RFLPs for the analysis of one of the largest known early-onset FAD pedigrees. We calculated pairwise and multipoint lod scores for the loci D21S13, D21S110, and D21S11. Linkage to this region of chromosome 21 was excluded with maximum negative lod scores of -6.4 at D21S13 and D21S110. Thus, it is unlikely that the FAD mutation in this family is located in the region that has shown linkage in other FAD pedigrees. This result provides evidence for genetic heterogeneity of early-onset FAD or a location of FAD centromeric to D21S13.     

Mapping of a gene determining tuberous sclerosis to human chromosome 11q14-11q23

Tuberous sclerosis (TSC) is a dominantly inherited disorder characterized by hamartomas and hamartias in one or more organs, most often in skin, brain, and kidneys. Analysis of the basic genetic defect in tuberous sclerosis would be greatly expedited by definitive determination of the chromosomal location of the TSC gene or genes. We have carried out genetic linkage studies in 15 TSC families, using 34 polymorphic markers including protein markers and DNA markers. Pairwise lod scores were calculated using LIPED, and multipoint analyses were carried out using MENDEL. In the pairwise linkage analysis, using a penetrance value of 90%, a significant positive lod score was obtained with MCT128.1 (D11S144), 11q22-11q23, Zmax 3.26 at theta = 0.08. The tyrosinase probe TYR (11q14-11q22) gave a maximum lod score of 2.88 at theta = 0. In the multipoint analyses the most likely order is (TYR,TSC)-MCT128.1-HHH172. Homogeneity analysis was carried out using the USERM9 subprogram of MENDEL, which conducts the admixture test of C. Smith (1963, Ann. Hum. Genet. 27: 175-182). This test provided no evidence for genetic heterogeneity (that is, non-11-linked families) in this data set.     

Linkage of a gene causing familial focal segmental glomerulosclerosis to chromosome 11 and further evidence of genetic heterogeneity.

Focal segmental glomerulosclerosis (FSGS) is a pathological entity characterized by proteinuria, nephrotic syndrome, and the progressive loss of renal function. It is a common cause of end-stage renal disease (ESRD). Recently, familial forms of FSGS have been identified. Two families with autosomal dominant FSGS were evaluated for linkage using 351 genomic microsatellite markers. Linkage, multipoint analysis, and tests for heterogeneity were performed on the subsequent results. In addition, three small families were used for haplotype analysis. Evidence for linkage was found on chromosome 11q21-q22 for the largest family, with a maximum lod score of 9.89. The gene is currently localized to an 18-cM area between flanking markers D11S2002 and D11S1986. The disease in a second family was not linked to this locus or to a previously described locus on chromosome 19q13. There were no shared haplotypes among affected individuals in the three smaller families. Our findings demonstrate that genetic heterogeneity is prevalent in FSGS in that at least three genes cause the FSGS phenotype. Identification of the genes that cause familial FSGS will provide valuable insights into the molecular basis and pathophysiology of FSGS.     

Using Linkage Analysis to Detect Gene-Gene Interaction by Stratifying Family Data on Known Disease,or Disease-Associated,Alleles

Detecting gene-gene interaction in complex diseases is a major challenge for common disease genetics. Most interaction detection approaches use disease-marker associations and such methods have low power and unknown reliability in real data. We developed and tested a powerful linkage-analysis-based gene-gene interaction detection strategy based on conditioning the family data on a known disease-causing allele or disease-associated marker allele. We computer-generated multipoint linkage data for a disease caused by two epistatically interacting loci (A and B). We examined several two-locus epistatic inheritance models: dominant-dominant, dominant-recessive, recessive-dominant, recessive-recessive. At one of the loci (A), there was a known disease-related allele. We stratified the family data on the presence of this allele, eliminating family members who were without it. This elimination step has the effect of raising the “penetrance” at the second locus (B). We then calculated the lod score at the second locus (B) and compared the pre- and post-stratification lod scores at B. A positive difference indicated interaction. We also examined if it was possible to detect interaction with locus B based on a disease-marker association (instead of an identified disease allele) at locus A. We also tested whether the presence of genetic heterogeneity would generate false positive evidence of interaction. The power to detect interaction for a known disease allele was 60–90%. The probability of false positives, based on heterogeneity, was low. Decreasing linkage disequilibrium between the disease and marker at locus A decreased the likelihood of detecting interaction. The allele frequency of the associated marker made little difference to the power.     

Handling marker-marker linkage disequilibrium: pedigree analysis with clustered markers

Single-nucleotide polymorphisms (SNPs) are rapidly replacing microsatellites as the markers of choice for genetic linkage studies and many other studies of human pedigrees. Here, we describe an efficient approach for modeling linkage disequilibrium (LD) between markers during multipoint analysis of human pedigrees. Using a gene-counting algorithm suitable for pedigree data, our approach enables rapid estimation of allele and haplotype frequencies within clusters of tightly linked markers. In addition, with the use of a hidden Markov model, our approach allows for multipoint pedigree analysis with large numbers of SNP markers organized into clusters of markers in LD. Simulation results show that our approach resolves previously described biases in multipoint linkage analysis with SNPs that are in LD. An updated version of the freely available Merlin software package uses the approach described here to perform many common pedigree analyses, including haplotyping and haplotype frequency estimation, parametric and nonparametric multipoint linkage analysis of discrete traits, variance-components and regression-based analysis of quantitative traits, calculation of identity-by-descent or kinship coefficients, and case selection for follow-up association studies. To illustrate the possibilities, we examine a data set that provides evidence of linkage of psoriasis to chromosome 17.     

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.     

On computation of p-values in parametric linkage analysis

Parametric linkage analysis is usually used to find chromosomal regions linked to a disease (phenotype) that is described with a specific genetic model. This is done by investigating the relations between the disease and genetic markers, that is, well-characterized loci of known position with a clear Mendelian mode of inheritance. Assume we have found an interesting region on a chromosome that we suspect is linked to the disease. Then we want to test the hypothesis of no linkage versus the alternative one of linkage. As a measure we use the maximal lod score Z(max). It is well known that the maximal lod score has asymptotically a (2 ln 10)(-1) x (1/2 chi2(0) + 1/2 chi2(1)) distribution under the null hypothesis of no linkage when only one point (one marker) on the chromosome is studied. In this paper, we show, both by simulations and theoretical arguments, that the null hypothesis distribution of Zmax has no simple form when more than one marker is used (multipoint analysis). In fact, the distribution of Zmax depends on the number of families, their structure, the assumed genetic model, marker denseness, and marker informativity. This means that a constant critical limit of Zmax leads to tests associated with different significance levels. Because of the above-mentioned problems, from the statistical point of view the maximal lod score should be supplemented by a p-value when results are reported.     

Using Linkage Analysis to Detect Gene-Gene Interactions. 2. Improved Reliability and Extension to More-Complex Models

Detecting gene-gene interaction in complex diseases has become an important priority for common disease genetics, but most current approaches to detecting interaction start with disease-marker associations. These approaches are based on population allele frequency correlations, not genetic inheritance, and therefore cannot exploit the rich information about inheritance contained within families. They are also hampered by issues of rigorous phenotype definition, multiple test correction, and allelic and locus heterogeneity. We recently developed, tested, and published a powerful gene-gene interaction detection strategy based on conditioning family data on a known disease-causing allele or a disease-associated marker allele⁴. We successfully applied the method to disease data and used computer simulation to exhaustively test the method for some epistatic models. We knew that the statistic we developed to indicate interaction was less reliable when applied to more-complex interaction models. Here, we improve the statistic and expand the testing procedure. We computer-simulated multipoint linkage data for a disease caused by two interacting loci. We examined epistatic as well as additive models and compared them with heterogeneity models. In all our models, the at-risk genotypes are “major” in the sense that among affected individuals, a substantial proportion has a disease-related genotype. One of the loci (A) has a known disease-related allele (as would have been determined from a previous analysis). We removed (pruned) family members who did not carry this allele; the resultant dataset is referred to as “stratified.” This elimination step has the effect of raising the “penetrance” and detectability at the second locus (B). We used the lod scores for the stratified and unstratified data sets to calculate a statistic that either indicated the presence of interaction or indicated that no interaction was detectable. We show that the new method is robust and reliable for a wide range of parameters. Our statistic performs well both with the epistatic models (false negative rates, i.e., failing to detect interaction, ranging from 0 to 2.5%) and with the heterogeneity models (false positive rates, i.e., falsely detecting interaction, ≤1%). It works well with the additive model except when allele frequencies at the two loci differ widely. We explore those features of the additive model that make detecting interaction more difficult. All testing of this method suggests that it provides a reliable approach to detecting gene-gene interaction.     

Linkage of the gene for an X-linked mental retardation disorder to a hypervariable (AGAT)n repeat motif within the human hypoxanthine phosphoribosyltransferase (HPRT) locus (Xq26).

We recently reported a new X-linked mental retardation (XLMR) disorder in a four-generation family of Dutch descent. Features included Dandy-Walker malformation, basal ganglia disease, and seizures. Twenty-six family members, including two living affected males and two obligate carriers, were available for study. No evidence of linkage was observed between the disease locus and RFLPs from several X-chromosome regions, including Xp21-p22 (13 markers), proximal Xq (four markers), and Xq28 (three markers). However, a new hypervariable short tandem repeat (STR) within the HPRT gene at Xq26 showed positive linkage to the disease locus, with a maximum lod score of 2.19 at a recombination fraction of 0. A second hypervariable marker in Xq26, the dinucleotide repeat XL90A3 (DXS425), showed a lod score of .84 at a recombination fraction of .11. Both the HPRT and DXS425 markers were typed in 40 CEPH families, and subsequent multipoint linkage analysis showed the following order: Xcen-DXS425-(HPRT,XLMR)-F9-qter. HPRT and these flanking markers are therefore useful for carrier detection and prenatal diagnosis in this family. This study illustrates that hypervariable STRs will be powerful tools for linkage analysis and genetic diagnosis, particularly when relatively small families are involved.     

A Locus in 2p13–p14 (OFC2), in Addition to That Mapped in 6p23, Is Involved in Nonsyndromic Familial Orofacial Cleft Malformation

An allelic association between the transforming growth factor α gene (TGFA) situated in the chromosome 2p13 region and nonsyndromic cleft lip with or without cleft palate, also named orofacial cleft (OFC), was found in several population studies. However, no linkage between gene and malformation has shown up until now, probably due to the presence of genetic heterogeneity and the small sample size analyzed. Previously, we employed a collection of 38 OFC families to demonstrate linkage to the 6p23 chromosome region with the presence of genetic heterogeneity. In the present study we tested whether, in the same sample, linkage between OFC and markers on 2p13 could be determined. Evidence for genetic heterogeneity in our family set was apparent, by both pairwise and multipoint linkage analyses. Moreover, lod scores >3 were found for marker D2S378 when families linked to the 6p23 markers were analyzed. Taken together these results indicate a role for the TGFA, or for another gene physically close to it, and suggest an interaction between two different genes, OFC1 and OFC2, mapped in 6p23 and 2p13, respectively, in the development of the cleft.     

Model-free linkage analysis using likelihoods.

Misspecification of transmission model parameters can produce artifactually negative lod scores at small recombination fractions and in multipoint analysis. To avoid this problem, we have tried to devise a test that aims to detect a genetic effect at a particular locus, rather than attempting to estimate the map position of a locus with specified effect. Maximizing likelihoods over transmission model parameters, as well as linkage parameters, can produce seriously biased parameter estimates and so yield tests that lack power for the detection of linkage. However, constraining the transmission model parameters to produce the correct population prevalence largely avoids this problem. For computational convenience, we recommend that the likelihoods under linkage and non-linkage are independently maximized over a limited set of transmission models, ranging from Mendelian dominant to null effect and from null effect to Mendelian recessive. In order to test for a genetic effect at a given map position, the likelihood under linkage is maximized over admixture, the proportion of families linked. Application to simulated data for a wide range of transmission models in both affected sib pairs and pedigrees demonstrates that the new method is well behaved under the null hypothesis and provides a powerful test for linkage when it is present. This test requires no specification of transmission model parameters, apart from an approximate estimate of the population prevalence. It can be applied equally to sib pairs and pedigrees, and, since it does not diminish the lod score at test positions very close to a marker, it is suitable for application to multipoint data.