Further evidence for the increased power of LOD scores compared with nonparametric methods.

In genetic analysis of diseases in which the underlying model is unknown, "model free" methods-such as affected sib pair (ASP) tests-are often preferred over LOD-score methods, although LOD-score methods under the correct or even approximately correct model are more powerful than ASP tests. However, there might be circumstances in which nonparametric methods will outperform LOD-score methods. Recently, Dizier et al. reported that, in some complex two-locus (2L) models, LOD-score methods with segregation analysis-derived parameters had less power to detect linkage than ASP tests. We investigated whether these particular models, in fact, represent a situation that ASP tests are more powerful than LOD scores. We simulated data according to the parameters specified by Dizier et al. and analyzed the data by using a (a) single locus (SL) LOD-score analysis performed twice, under a simple dominant and a recessive mode of inheritance (MOI), (b) ASP methods, and (c) nonparametric linkage (NPL) analysis. We show that SL analysis performed twice and corrected for the type I-error increase due to multiple testing yields almost as much linkage information as does an analysis under the correct 2L model and is more powerful than either the ASP method or the NPL method. We demonstrate that, even for complex genetic models, the most important condition for linkage analysis is that the assumed MOI at the disease locus being tested is approximately correct, not that the inheritance of the disease per se is correctly specified. In the analysis by Dizier et al., segregation analysis led to estimates of dominance parameters that were grossly misspecified for the locus tested in those models in which ASP tests appeared to be more powerful than LOD-score analyses.     

A comparison of different linkage statistics in small to moderate sized pedigrees with complex diseases

ABSTRACT: BACKGROUND: In the last years GWA studies have successfully identified common SNPs associated with complex diseases. However, most of the variants found this way account for only a small portion of the trait variance. This fact leads researchers to focus on rare-variant mapping with large scale sequencing, which can be facilitated by using linkage information. The question arises why linkage analysis often fails to identify genes when analyzing complex diseases. Using simulations we have investigated the power of parametric and nonparametric linkage statistics (KC-LOD, NPL, LOD and MOD scores), to detect the effect of genes responsible for complex diseases using different pedigree structures. RESULTS: As expected, a small number of pedigrees with less than three affected individuals has low power to map disease genes with modest effect. Interestingly, the power decreases when unaffected individuals are included in the analysis, irrespective of the true mode of inheritance. Furthermore, we found that the best performing statistic depends not only on the type of pedigrees but also on the true mode of inheritance. CONCLUSIONS: When applied in a sensible way linkage is an appropriate and robust technique to map genes for complex disease. Unlike association analysis, linkage analysis is not hampered by allelic heterogeneity. So, why does linkage analysis often fail with complex diseases? Evidently, when using an insufficient number of small pedigrees, one might miss a true genetic linkage when actually a real effect exists. Furthermore, we show that the test statistic has an important effect on the power to detect linkage as well. Therefore, a linkage analysis might fail if an inadequate test statistic is employed. We provide recommendations regarding the most favorable test statistics, in terms of power, for a given mode of inheritance and type of pedigrees under study, in order to reduce the probability to miss a true linkage.     

Strategies for conditional two-locus nonparametric linkage analysis

In this article we deal with two-locus nonparametric linkage (NPL) analysis, mainly in the context of conditional analysis. This means that one incorporates single-locus analysis information through conditioning when performing a two-locus analysis. Here we describe different strategies for using this approach. Cox et al. [Nat Genet 1999;21:213-215] implemented this as follows: (i) Calculate the one-locus NPL process over the included genome region(s). (ii) Weight the individual pedigree NPL scores using a weighting function depending on the NPL scores for the corresponding pedigrees at speci fi c conditioning loci. We generalize this by conditioning with respect to the inheritance vector rather than the NPL score and by separating between the case of known (prede fi ned) and unknown (estimated) conditioning loci. In the latter case we choose conditioning locus, or loci, according to prede fi ned criteria. The most general approach results in a random number of selected loci, depending on the results from the previous one-locus analysis. Major topics in this article include discussions on optimal score functions with respect to the noncentrality parameter (NCP), and how to calculate adequate p values and perform power calculations. We also discuss issues related to multiple tests which arise from the two-step procedure with several conditioning loci as well as from the genome-wide tests.     

TLINKAGE-IMPRINT: a model-based approach to performing two-locus genetic imprinting analysis

OBJECTIVES: Imprinting refers to the expression of only one copy of a gene pair, which is determined by the parental origin of the copy. Imprinted genes play a role in the development of several complex diseases, including cancers and mental disorders. In certain situations, two-trait-loci models are shown to be more powerful than one-trait-locus models. However, no current methods use pedigree structure efficiently and perform two-locus imprinting analyses. In this paper, we apply the Elston-Stewart algorithm to the parametric two-trait-loci imprinting model used by Strauch et al. [2000] to obtain a method for qualitative trait linkage analyses that explicitly models imprinting and can be applied to large pedigrees. METHODS: We considered a parametric approach based on 4 x 4 penetrance matrix to account for imprinting and modified TLINKAGE software to implement this approach. We performed simulation studies using a small and a large pedigree under dominant and imprinted and dominant or imprinted scenarios. Furthermore, we developed a likelihood ratio-based test for imprinting that compares the logarithm of odds (LOD) score obtained using the two-locus imprinting model with that obtained using the standard two-locus model that does not allow for imprinting. RESULTS: In simulation studies of three scenarios where the true mode of inheritance included imprinting, accurate modeling through the proposed approach yielded higher LOD scores and better recombination fraction estimates than the traditional two-locus model that does not allow for imprinting. CONCLUSIONS: This imprinting model will be useful in identifying the genes responsible for several complex disorders that are potentially caused by a combination of imprinted and non-imprinted genes.     

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.     

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.     

Genomewide linkage scan for split-hand/foot malformation with long-bone deficiency in a large Arab family identifies two novel susceptibility loci on chromosomes 1q42.2-q43 and 6q14.1

Split-hand/foot malformation with long-bone deficiency (SHFLD) is a rare, severe limb deformity characterized by tibia aplasia with or without split-hand/split-foot deformity. Identification of genetic susceptibility loci for SHFLD has been unsuccessful because of its rare incidence, variable phenotypic expression and associated anomalies, and uncertain inheritance pattern. SHFLD is usually inherited as an autosomal dominant trait with reduced penetrance, although recessive inheritance has also been postulated. We conducted a genomewide linkage analysis, using a 10K SNP array in a large consanguineous family (UR078) from the United Arab Emirates (UAE) who had disease transmission consistent with an autosomal dominant inheritance pattern. The study identified two novel SHFLD susceptibility loci at 1q42.2-q43 (nonparametric linkage [NPL] 9.8, P=.000065) and 6q14.1 (NPL 7.12, P=.000897). These results were also supported by multipoint parametric linkage analysis. Maximum multipoint LOD scores of 3.20 and 3.78 were detected for genomic locations 1q42.2-43 and 6q14.1, respectively, with the use of an autosomal dominant mode of inheritance with reduced penetrance. Haplotype analysis with informative crossovers enabled mapping of the SHFLD loci to a region of approximately 18.38 cM (8.4 Mb) between single-nucleotide polymorphisms rs1124110 and rs535043 on 1q42.2-q43 and to a region of approximately 1.96 cM (4.1 Mb) between rs623155 and rs1547251 on 6q14.1. The study identified two novel loci for the SHFLD phenotype in this UAE family.     

Parametric and nonparametric linkage analysis: a unified multipoint approach.

In complex disease studies, it is crucial to perform multipoint linkage analysis with many markers and to use robust nonparametric methods that take account of all pedigree information. Currently available methods fall short in both regards. In this paper, we describe how to extract complete multipoint inheritance information from general pedigrees of moderate size. This information is captured in the multipoint inheritance distribution, which provides a framework for a unified approach to both parametric and nonparametric methods of linkage analysis. Specifically, the approach includes the following: (1) Rapid exact computation of multipoint LOD scores involving dozens of highly polymorphic markers, even in the presence of loops and missing data. (2) Non-parametric linkage (NPL) analysis, a powerful new approach to pedigree analysis. We show that NPL is robust to uncertainty about mode of inheritance, is much more powerful than commonly used nonparametric methods, and loses little power relative to parametric linkage analysis. NPL thus appears to be the method of choice for pedigree studies of complex traits. (3) Information-content mapping, which measures the fraction of the total inheritance information extracted by the available marker data and points out the regions in which typing additional markers is most useful. (4) Maximum-likelihood reconstruction of many-marker haplotypes, even in pedigrees with missing data. We have implemented NPL analysis, LOD-score computation, information-content mapping, and haplotype reconstruction in a new computer package, GENEHUNTER. The package allows efficient multipoint analysis of pedigree data to be performed rapidly in a single user-friendly environment.     

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)     

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.     

Two-locus linkage analysis of cutaneous malignant melanoma/dysplastic nevi.

Previous linkage analyses of 19 cutaneous malignant melanoma/dysplastic nevi (CMM/DN) kindreds showed significant evidence of linkage and heterogeneity to both chromosomes 1p and 9p. Five kindreds also showed evidence of linkage (Z>0.7) to both regions. To further examine these findings, we conducted two-trait-locus, two-marker-locus linkage analysis. We examined one homogeneity and one heterogeneity single-locus model (SL-Hom and SL-Het), and two-locus (2L) models: an epistatic model (Ep), in which CMM was treated as a genuine 2L disease, and a heterogeneity model (Het), in which CMM could result from disease alleles at either locus. Both loci were modeled as autosomal dominant. The LOD scores for CMM alone were highest using the SL-Het model (Z = 8.48, theta = .0). There was much stronger evidence of linkage to chromosome 9p than to 1p for CMM alone; the LOD scores were approximately two times greater on 9p than on 1p. The change in LOD scores from an evaluation of CMM alone to CMM/DN suggested that a chromosome 1p locus (or loci) contributed to both CMM and CMM/DN, whereas a 9p locus contributed more to CMM alone. For both 2L models, the LOD scores from 1p were greater for CMM/DN than for CMM alone (Ep: Z=4.63 vs. 3.83; Het: 4.94 vs. 3.80, respectively). In contrast, for 9p, the LOD scores were substantially lower with CMM/DN than with CMM alone (Ep: 4.64 vs. 7.06; Het: 5.38 vs. 7.99, respectively). After conditioning on linkage to the other locus, only the 9p locus consistently showed significant evidence for linkage to CMM alone. Thus, the application of 2L models may be useful to help unravel the complexities of familial melanoma.     

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.     

Autosomal dominant nonsyndromic cleft lip and palate: significant evidence of linkage at 18q21.1

Nonsyndromic cleft lip with or without cleft palate (NSCL/P) is one of the most common congenital facial defects, with an incidence of 1 in 700-1,000 live births among individuals of European descent. Several linkage and association studies of NSCL/P have suggested numerous candidate genes and genomic regions. A genomewide linkage analysis of a large multigenerational family (UR410) with NSCL/P was performed using a single-nucleotide-polymorphism array. Nonparametric linkage (NPL) analysis provided significant evidence of linkage for marker rs728683 on chromosome 18q21.1 (NPL=43.33 and P=.000061; nonparametric LOD=3.97 and P=.00001). Parametric linkage analysis with a dominant mode of inheritance and reduced penetrance resulted in a maximum LOD score of 3.61 at position 47.4 Mb on chromosome 18q21.1. Haplotype analysis with informative crossovers defined a 5.7-Mb genomic region spanned by proximal marker rs1824683 (42,403,918 bp) and distal marker rs768206 (48,132,862 bp). Thus, a novel genomic region on 18q21.1 was identified that most likely harbors a high-risk variant for NSCL/P in this family; we propose to name this locus "OFC11" (orofacial cleft 11).     

Interacting genetic loci on chromosomes 20 and 10 influence extreme human obesity

Obesity is a multigenic trait that has a substantial genetic component. Animal models confirm a role for gene-gene interactions, and human studies suggest that as much as one-third of the heritable variance may be due to nonadditive gene effects. To evaluate potential epistatic interactions among five regions, on chromosomes 7, 10, and 20, that have previously been linked to obesity phenotypes, we conducted pairwise correlation analyses based on alleles shared identical by descent (IBD) for independent obese affected sibling pairs (ASPs), and we determined family-specific nonparametric linkage (NPL) scores in 244 families. The correlation analyses were also conducted separately, by race, through use of race-specific allele frequencies. Conditional analyses for a qualitative trait (body mass index [BMI] >/=27) and hierarchical models for quantitative traits were used to further refine evidence of gene interaction. Both the ASP-specific IBD-sharing probability and the family-specific NPL score revealed that there were strong positive correlations between 10q (88-97 cM) and 20q (65-83 cM), through single-point and multipoint analyses with three obesity thresholds (BMI >/=27, >/=30, and >/=35) across African American and European American samples. Conditional analyses for BMI >/=27 found that the LOD score at 20q rises from 1.53 in the baseline analysis to 2.80 (empirical P=.012) when families were weighted by evidence for linkage at 10q (D10S1646) through use of zero-one weights (weight(0-1)) and to 3.32 (empirical P<.001) when proportional weights (weight(prop)) were used. For percentage fat mass, variance-component analysis based on a two-locus epistatic model yielded significant evidence for interaction between 20q (75 cM) and the chromosome 10 centromere (LOD = 1.74; P=.024), compared with a two-locus additive model (LOD = 0.90). The results from multiple methods and correlated phenotypes are consistent in suggesting that epistatic interactions between loci in these regions play a role in extreme human obesity.     

Reproducibility and complications in gene searches: linkage on chromosome 6, heterogeneity, association, and maternal inheritance in juvenile myoclonic epilepsy

Evidence for genetic influences in epilepsy is strong, but reports identifying specific chromosomal origins of those influences conflict. One early study reported that human leukocyte antigen (HLA) markers were genetically linked to juvenile myoclonic epilepsy (JME); this was confirmed in a later study. Other reports did not find linkage to HLA markers. One found evidence of linkage to markers on chromosome 15, another to markers on chromosome 6, centromeric to HLA. We identified families through a patient with JME and genotyped markers throughout chromosome 6. Linkage analysis assuming equal male-female recombination probabilities showed evidence for linkage (LOD score 2.5), but at a high recombination fraction (theta), suggesting heterogeneity. When linkage analysis was redone to allow independent male-female thetas, the LOD score was significantly higher (4.2) at a male-female theta of.5,.01. Although the overall pattern of LOD scores with respect to male-female theta could not be explained solely by heterogeneity, the presence of heterogeneity and predominantly maternal inheritance of JME might explain it. By analyzing loci between HLA-DP and HLA-DR and stratifying the families on the basis of evidence for or against linkage, we were able to show evidence of heterogeneity within JME and to propose a marker associated with the linked form. These data also suggest that JME may be predominantly maternally inherited and that the HLA-linked form is more likely to occur in families of European origin.     

Magnitude of type I error when single-locus linkage analysis is maximized over models: a simulation study.

It is well known that maximizing the maximum LOD score over multiple parameter values or models (i.e., the method of mod scores, or MMLS), will inflate type I error, compared with assuming only one parameter value/model in the linkage analysis. On the other hand, a mod score often has greater power to detect linkage than does a LOD score (Z) calculated under a wrong genetic model. Therefore, it is of interest to determine the actual magnitude of type I error in realistic genetic situations. Simulated data sets with no linkage were generated under three dominant and three recessive single-locus models, with reduced penetrance (f = .8, .5, and .2). Data sets were analyzed for linkage by (1) maximizing over penetrance only, (2) maximizing over "dominance model" (i.e., dominant versus recessive), and (3) maximizing over both penetrance and dominance model simultaneously. In (1), the resultant significance levels were approximately doubled, compared with baseline values if one had not maximized over penetrances (i.e., compared with a one-sided chi2(1)). In (2), significance levels were increased somewhat less, and, in (3), they were increased by approximately two to three times (but not more than four times) over those of the one-sided chi2(1). This means that, for a given size of test alpha, an investigator would need to increase the Z used as a test criterion, by approximately 0.30 LOD units for analyses as in (1) or (2) and by 0.60 Z units for analyses as in (3). These guidelines, which are valid up to approximately Z = 3.0, are conservative for (1) and are very conservative for (2) and (3). By quantifying the increase in significance level (or, correspondingly, the increase in Z), our findings will enable users to rationally assess the advantages versus the disadvantages of mod scores.     

Splitting schizophrenia: periodic catatonia-susceptibility locus on chromosome 15q15

The nature of subtypes in schizophrenia and the meaning of heterogeneity in schizophrenia have been considered a principal controversy in psychiatric research. We addressed these issues in periodic catatonia, a clinical entity derived from Leonhard's classification of schizophrenias, in a genomewide linkage scan. Periodic catatonia is characterized by qualitative psychomotor disturbances during acute psychotic outbursts and by long-term outcome. On the basis of our previous findings of a lifetime morbidity risk of 26.9% of periodic catatonia in first-degree relatives, we conducted a genome scan in 12 multiplex pedigrees with 135 individuals, using 356 markers with an average spacing of 11 cM. In nonparametric multipoint linkage analyses (by GENEHUNTER-PLUS), significant evidence for linkage was obtained on chromosome 15q15 (P = 2.6 x 10(-5); nonparametric LOD score [LOD*] 3.57). A further locus on chromosome 22q13 with suggestive evidence for linkage (P = 1.8 x 10(-3); LOD* 1.85) was detected, which indicated genetic heterogeneity. Parametric linkage analysis under an autosomal dominant model (affecteds-only analysis) provided independent confirmation of nonparametric linkage results, with maximum LOD scores 2.75 (recombination fraction [theta].04; two-point analysis) and 2.89 (theta =.029; four-point analysis), at the chromosome 15q candidate region. Splitting the complex group of schizophrenias on the basis of clinical observation and genetic analysis, we identified periodic catatonia as a valid nosological entity. Our findings provide evidence that periodic catatonia is associated with a major disease locus, which maps to chromosome 15q15.     

How to model a complex trait. 2. Analysis with two disease loci

Complex traits are often governed by more than one trait locus. The first step towards an adequate model for such diseases is a linkage analysis with two trait loci. Such an analysis can be expected to have higher power to detect linkage than a standard single-trait-locus linkage analysis. However, it is crucial to accurately specify the parameters of the two-locus model. Here, we recapitulate the general two-locus model with and without genomic imprinting. We relate heterogeneity, multiplicative, and additive two-locus models to biological or pathophysiological mechanisms, and give the corresponding averaged ("best-fitting") single-trait-locus models for each of the two loci. Furthermore, we derive the two-locus penetrances from the averaged single-locus models, under the assumption of one of the three model classes mentioned above. Using these formulae, if the best-fitting single-locus models are available, investigators may perform a two-trait-locus linkage analysis under a realistic model. This procedure will maximize the power to detect linkage for traits which are governed by two or more loci, and lead to more accurate estimates of the disease-locus positions.     

A high-density SNP genomewide linkage scan for chronic lymphocytic leukemia-susceptibility loci

Chronic lymphocytic leukemia (CLL) and other B-cell lymphoproliferative disorders (LPDs) show clear evidence of familial aggregation, but the inherited basis is largely unknown. To identify a susceptibility gene for CLL, we conducted a genomewide linkage analysis of 115 pedigrees, using a high-density single-nucleotide polymorphism (SNP) array containing 11,560 markers. Multipoint linkage analyses were undertaken using both nonparametric (model-free) and parametric (model-based) methods. Our results confirm that the presence of high linkage disequilibrium (LD) between SNP markers can lead to inflated nonparametric linkage (NPL) and LOD scores. After the removal of high-LD SNPs, we obtained a maximum NPL of 3.14 (P=.0008) on chromosome 11p11. The same genomic position also yielded the highest multipoint heterogeneity LOD (HLOD) score under both dominant (HLOD 1.95) and recessive (HLOD 2.78) models. In addition, four other chromosomal positions (5q22-23, 6p22, 10q25, and 14q32) displayed HLOD scores >1.15 (which corresponds to a nominal P value <.01). None of the regions coincided with areas of common chromosomal abnormalities frequently observed for CLL. These findings strengthen the argument for an inherited predisposition to CLL and related B-cell LPDs.     

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.