Allelic penetrance approach as a tool to model two-locus interaction in complex binary traits

Many binary phenotypes do not follow a classical Mendelian inheritance pattern. Interaction between genetic and environmental factors is thought to contribute to the incomplete penetrance phenomena often observed in these complex binary traits. Several two-locus models for penetrance have been proposed to aid the genetic dissection of binary traits. Such models assume linear genetic effects of both loci in different mathematical scales of penetrance, resembling the analytical framework of quantitative traits. However, changes in phenotypic scale are difficult to envisage in binary traits and limited genetic interpretation is extractable from current modeling of penetrance. To overcome this limitation, we derived an allelic penetrance approach that attributes incomplete penetrance to the stochastic expression of the alleles controlling the phenotype, the genetic background and environmental factors. We applied this approach to formulate dominance and recessiveness in a single diallelic locus and to model different genetic mechanisms for the joint action of two diallelic loci. We fit the models to data on the genetic susceptibility of mice following infections with Listeria monocytogenes and Plasmodium berghei. These models gain in genetic interpretation, because they specify the alleles that are responsible for the genetic (inter)action and their genetic nature (dominant or recessive), and predict genotypic combinations determining the phenotype. Further, we show via computer simulations that the proposed models produce penetrance patterns not captured by traditional two-locus models. This approach provides a new analysis framework for dissecting mechanisms of interlocus joint action in binary traits using genetic crosses.     

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.     

Evidence for recessive and against dominant inheritance at the HLA-"linked" locus in coeliac disease.

It has been proposed that gluten sensitive enteropathy (GSE) results from the interaction of two loci: one locus linked to HLA and associated with dominant inheritance, and the other, a non-HLA-linked GSE-associated B-cell alloantigen, exhibiting recessive inheritance. We have shown in previous analyses that a two-locus, dominant-recessive model is less compatible with the existing population prevalence and observed familial segregation data than is a recessive-recessive two-locus model. Here we present additional analyses of reported population and familial HLA data that support the recessive mode of inheritance for the HLA-linked disease locus. Reported data from HLA typing of affected sib pairs, the association of GSE with DR3 and DR7 in different populations, and the proportions of different HLA phenotypes and genotypes were compared with expected data derived by three different methods. The HLA data analyses consistently reject a dominant mode of inheritance for the presumed HLA-linked disease allele but do not reject a recessive model. The affected sib-pair data also support a recessive model. These analyses are consistent with our previous prediction that the HLA-"linked" disease allele in GSE is recessive inherited.     

The affected sib method. III. Selection and recombination.

The affected sib-pair method has been used to investigate the mode of inheritance, and to estimate the "disease" allele frequency, for a number of HLA-associated diseases. One of the assumptions of the original sib-pair method is that the disease confers no selective disadvantage on affected individuals. This is obviously not the situation for most diseases. We have determined the expected HLA haplotype-sharing distribution among affected sib-pairs when selection against individuals with the disease is taken into account. We have shown that if the mode of inheritance of the selectively disadvantageous disease is recessive or additive, the original affected sib-pair analysis, ignoring selection, still estimates the true mode of inheritance, but usually yields an underestimate of the "disease" allele frequency. For intermediate and dominant models of disease predisposition, both the estimates of the degree of penetrance of the "disease" genotypes, and the "disease" allele frequency, are altered if selection is ignored in the analysis. Similarly, allowing for recombination between the "disease" locus and the HLA region does not affect the determination of the mode of inheritance of the disease if it is recessive or additive; in other cases, however, the estimate of the mode of inheritance is affected. The "disease" allele frequency is overestimated when nonzero recombination is ignored for all the modes of inheritance that have been studied.     

Selection, Hitchhiking and Disequilibrium Analysis at Three Linked Loci with Application to Hla Data

The HLA system has been extensively studied from an evolutionary perspective. Although it is clear that selection has acted on the genes in the HLA complex, the nature of this selection has yet to be fully clarified. A study of constrained disequilibrium values is presented that is applicable to HLA and other less polymorphic systems with three or more linked loci, with the purpose of identifying selection events. The method uses the fact that three locus systems impose additional constraints on the range of possible disequilibrium values for any pair of loci. We have thus examined the behavior of the normalized pairwise disequilibrium measures using two locus (D'), and also three locus (D"), constraints on pairwise disequilibria in a three locus system when one of the three loci is under positive selection. The difference between these measures, delta = magnitude of D' - magnitude of D", has a distribution for the two unselected loci differing from that for the selected locus with either of the unselected loci (the hallmark is a high positive value of delta for the two unselected loci). An examination of genetic drift indicates that positive delta values are unlikely to be found in human populations in the absence of selection when recombination is greater than about 0.1%. This measure can thus provide insight into which allele of several linked loci might have been subject to selection. Application of this method to HLA haplotypes from a large French population study (Provinces Francaise) identifies selected alleles on particular haplotypes. Application of a complementary method, disequilibrium pattern analysis also confirms the action of selection on these haplotypes.     

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.     

Detecting two-locus gene-gene effects using monotonisation of the penetrance matrix

As more genetic loci are genotyped simultaneously and as the interest in effects of combinations of loci increases, the need for more powerful analysis methods is increased. In the present paper we present a method aimed at increasing the power of likelihood ratio tests for case-control studies investigating possible two-locus effects. The method is based on the notion that the expected effect pattern of one locus, as well as the expected pattern of a penetrance matrix representing the effect of two loci, is a monotone one. By using an algorithm for making the estimated penetrance matrix monotone, the alternative hypothesis is restricted to monotone penetrance matrices only. The evaluation of the likelihood ratio tests for several underlying monotone models shows that the power is substantially increased by using a monotone alternative as compared to when an unrestricted alternative is used.     

Definition and Properties of Disequilibria within Nuclear-Mitochondrial-Chloroplast and Other Nuclear-Dicytoplasmic Systems

We define and determine the interrelationships among five sets of disequilibrium parameters that measure two- and three-locus nonrandom associations in nuclear-dicytoplasmic systems. These assume a diploid nuclear locus and two haploid cytoplasmic loci, with special reference to nuclear-mitochondrial-chloroplast systems. Three sets of two-locus disequilibria measure the association between haplotypes at the two cytoplasmic loci (DMC) and associations between each cytoplasmic locus and nuclear alleles or genotypes (DM, D1M, D2M, D3M; DC, D1C, D2C, D3C). In addition, we present two classes of higher-order disequilibria that measure nonrandom allelic or genotypic associations involving all three loci. The first class quantifies associations between the nuclear locus and the two cytoplasmic loci taken jointly (DA/MC, DAA/MC, DAa/MC, Daa/MC, etc.), whereas the second measures only those associations remaining after all two-locus associations have been taken into account (DA/M/C, DAA/M/C, DAa/M/C, Daa/M/C). Based on combinations of these five sets of measures, we suggest a variety of parameterizations of three-locus, nuclear-dicytoplasmic systems. The dynamics of these disequilibria are then investigated under models of random and mixed mating, either with both cytoplasmic genomes inherited through the same parent or through opposite parents. Except for associations between the cytoplasmic haplotypes, which are constant when the two cytoplasmic genomes are inherited through the same parent, all disequilibria ultimately decay to zero. These randomizations do not necessarily occur monotonically, however, and in some cases are preceded by an initial increase in magnitude or sign change. For both inheritance patterns, the asymptotic decay rates are steadily retarded by increasing levels of self-fertilization. This behavior contrasts with that in the extreme case of complete selfing, for which only the heterozygote disequilibria always decay to zero. For all models considered, the dynamics of the two-locus cytonuclear subsystems are solely a function of the mating system, whereas the dynamical behavior and sign patterns of the cytoplasmic and three-locus disequilibria also depend strongly on the mode of cytoplasmic inheritance.     

The relationship between the sibling recurrence-risk ratio and genotype relative risk

The recurrence-risk ratio of disease in siblings, lambdaS, is a standard parameter used in genetic analysis to estimate the statistical power for detection of a disease locus. However, the relationship between the underlying risk conferred by a disease-susceptibility allele and lambdaS has not been well described. The former is generally quantified as a genotype relative risk, gamma, and measures the ratio of disease risks between those with and those without the susceptibility genotype(s). We demonstrate that lambdaS varies significantly more with respect to gamma and the disease-allele frequency for two-locus multiplicative models than for other two-locus and for single-locus models. For the single- and two-locus dominant-inheritance models that we studied, when a disease-susceptibility allele had a frequency >/=.2, lambdaS had an upper limit of <10. In general, lambdaS values >10 are possible only under recessive inheritance, dominant inheritance with relatively rare (<5%) disease-susceptibility alleles, or when two or more disease loci have alleles acting either epistatically or multiplicatively. We introduce the idea of a restricted sib recurrence-risk ratio (lambda*S) estimated by restriction of sibships to those ascertained through a proband who already has a putative high-risk allele. A lambda*S larger than the lambdaS value estimated from randomly selected probands can serve as an indirect way of testing whether the posited susceptibility allele increases disease risk. Our results demonstrate that a lambdaS of 2-3 may portend successful mapping for a variety of genetic models but that, for some two-locus models, a lambdaS as high as 10 does not guarantee underlying genes easily mapped by linkage.     

Inheritance mode of multiple sclerosis: the effect of <Emphasis Type="Italic">HLA</Emphasis> class II alleles is stronger than additive

We previously identified on chromosome 6 an interval of 51 kb as the most likely interval in the HLA region for a disease-susceptibility locus for multiple sclerosis (MS). The interval was located between markers G511525 and D6S1666 and identified by the haplotype sharing statistic (HSS). The study comprised 124 patients with ancestry within the northeastern part of the Netherlands. Haplotype clustering indicated that two different ancestral haplotypes likely include a polymorphism involved in susceptibility to MS. To investigate the dominance characteristics of the MS susceptibility locus in the HLA class II region, we reanalyzed our data, performing genotype association analyses for both marker loci separately and for the two-locus haplotype. The two-locus genotype association analysis showed that in individuals who carry only one of the risk haplotypes the risk for MS is moderately increased (odds ratio (OR) 2.82; 95% confidence interval (CI) 1.50–5.31). However, in individuals carrying two risk haplotypes the risk for MS is highly increased compared with individuals who carry no risk haplotypes (OR 37.00; 95% CI 8.31–164.74). This susceptibility locus for MS seems to follow an intermediate mode of inheritance. Fitting additive, multiplicative and third power risk models to the data, the effect appears to be significantly stronger than additive.     

A combined segregation and linkage analysis of insulin-dependent diabetes mellitus.

In an effort to clarify the mode of inheritance of insulin-dependent diabetes mellitus (IDDM), a total of 230 nuclear families with pointers were analyzed using the computer program COMBIN. Each family was ascertained without deliberate selection for multiplex families, and most families were completely typed for HLA-B, HLA-DR, and properdin factor B (Bf). There were 186 families with normal parents, 44 families with one affected parent, and no families with two affected parents. The computer program COMBIN evaluates evidence for a major locus of disease susceptibility, linkage of the major locus to a known genetic marker locus, linkage disequilibrium between the marker haplotypes and disease susceptibility, pleiotropic effects, and presence of an unlinked modifier. The parameters of COMBIN are T, Q, and D, representing the displacement, gene frequency of the IDDM allele, and dominance, respectively, of the major locus--and TM, QM, and DM being the analogous parameters of the modifier. In addition, the recombination fraction, theta, between the IDDM locus and HLA as well as the coupling frequencies are estimated. Finally, COMBIN simultaneously performs segregation and linkage analysis, with the optimal model being adjusted by the fit to the haplotype sharing distribution of IDDM. The results of these analyses indicated that the best-fitting genetic model of diabetic susceptibility appears to be a single major locus with near recessivity on a scale of standardized genetic liability, with gene frequency of the IDDM susceptibility allele of approximately 14%. In addition, the recombination fraction between the major locus and HLA is zero in all models; that is, for the B-BF-DR haplotype, the IDDM locus is tightly linked, probably (according to data from previous studies) to HLA-DR. Information determined by magnitude of coupling frequencies indicated that there is significant positive linkage disequilibrium with the haplotypes B8-BfS-DR4 and B15-BfS-DR4, significant negative linkage disequilibrium with B7-BfS-DR2, and intermediate disequilibrium for B8-BfS-DR3, B18-BfF1-DR3, and B40-BfS-DR4. Significant evidence in favor of an unlinked (to HLA) modifier (either single major locus or polygenes) could not be demonstrated. In conclusion, genetic susceptibility to IDDM appears to be most consistent with a single major locus with near recessivity that is tightly linked to HLA.     

A simple method for testing two-locus models of inheritance

A graphic method for testing simple two-locus models of inheritance is developed. The model assumes two alleles at each locus where both loci exhibit dominant, both exhibit recessive, or one locus exhibits dominant and one locus exhibits recessive inheritance. Examples of applying the graphs using published data on three diseases are given.     

The distributions of N and F: measures of HLA haplotype concordance

Nonrandom inheritance of the two HLA haplotypes of Chromosome 6, available from each parent among siblings affected by certain diseases, has afforded evidence of HLA-linked disease-susceptibility genes. Two algebraically equivalent measures of HLA haplotype concordance (that is, the excessive sharing of certain haplotypes among affected siblings) are used for family studies designed to test whether or not there is significant evidence of the existence of an HLA-linked disease-susceptibility gene or for inferring the mode of inheritance when this is already believed to apply. The distributions of these measures are derived under the null hypothesis of random inheritance of HLA haplotypes, and there is a short discussion of the case in which inheritance of a diseased gene causes a change, from the purely random case, in the distribution of haplotype concordance among affected siblings.     

Estimating the power of a proposed linkage study for a complex genetic trait.

Many genetic traits have complex modes of inheritance; they may exhibit incomplete or age-dependent penetrance or fail to show any clear Mendelian inheritance pattern. As primary linkage maps for the human genome near completion, it is becoming increasingly possible to map these traits. Prior to undertaking a linkage study, it is important to consider whether the pedigrees available for the proposed study are likely to provide sufficient information to demonstrate linkage, assuming a linked marker is tested. In the current paper, we describe a computer simulation method to estimate the power of a proposed study to detect linkage for a complex genetic trait, given a hypothesized genetic model for the trait. Our method simulates trait locus genotypes consistent with observed trait phenotypes, in such a way that the probability to detect linkage can be estimated by sample statistics of the maximum lod score distribution. The method uses terms available when calculating the likelihood of the trait phenotypes for the pedigree and is applicable to any trait determined by one or a few genetic loci; individual-specific environmental effects can also be dealt with. Our method provides an objective answer to the question, Will these pedigrees provide sufficient information to map this complex genetic trait?     

Maternal-Fetal Interactions and the Maintenance of Hla Polymorphism

There is some empirical evidence that a fetus with an HLA antigen not present in its mother has a higher survival than a fetus sharing antigens with its mother. We have developed both single locus and two-locus theoretical models to examine this mode of selection. First, this immunologically based model appears to have the potential to maintain many alleles at a single locus and to result in an excess of heterozygotes when selection is strong. Second, substantial gametic disequilibrium is maintained between alleles at two loci for this selection mode when recombination is that observed between HLA loci A, B, and DR. Overall, it appears that this mode of selection has the potential to strongly affect genetic variation in the HLA region.     

Segregation analysis incorporating linkage markers. I. Single-locus models with an application to type I diabetes.

A method is described for segregation analysis that incorporates linkage markers. The model allows for segregation (penetrance), linkage (recombination fraction), and association (linkage disequilibrium) parameters. A single-locus-multiple-allele model underlying the trait phenotype is assumed. When families have been ascertained in a systematic fashion, a joint (markers, phenotypes) likelihood with ascertainment is advocated. When ascertainment correction is not feasible, a conditional (markers given phenotypes) approach is recommended, which is also valid in the presence of reduced fertility and assortative mating. This approach, oriented toward determining mode of inheritance, differs from conventional linkage analysis, which is oriented toward detection of linkage. Therefore, it is more appropriately considered an extension of the affected sib-pair method to arbitrary pedigrees, including association information and allowing for multiple alleles. Incorporation of coupling parameters allows for discrimination between pleiotropy and linkage disequilibrium. The method is demonstrated through a reanalysis of four recently published family studies on type 1 diabetes and HLA. Recessive inheritance is rejected in all four data sets. For three of them, dominant inheritance is not rejected, while in the fourth, all two-allele models are rejected in favor of three alleles. Although association with the DR3 and DR4 alleles is quite strong, pleiotropy with regard to these alleles is unlikely. The results also suggest an additional familial factor(s) (e.g., locus).     

Allele polymorphism and haplotype diversity of HLA-A, -B and -DRB1 loci in sequence-based typing for Chinese Uyghur ethnic group

Background

Previous studies indicate that the frequency distributions of HLA alleles and haplotypes vary from one ethnic group to another or between the members of the same ethnic group living in different geographic areas. It is necessary and meaningful to study the high-resolution allelic and haplotypic distributions of HLA loci in different groups.

Methodology/Principal Findings

High-resolution HLA typing for the Uyghur ethnic minority group using polymerase chain reaction-sequence-based-typing method was first reported. HLA-A, -B and -DRB1 allelic distributions were determined in 104 unrelated healthy Uyghur individuals and haplotypic frequencies and linkage disequilibrium parameters for HLA loci were estimated using the maximum-likelihood method. A total of 35 HLA-A, 51 HLA-B and 33 HLA-DRB1 alleles were identified at the four-digit level in the population. High frequency alleles were HLA-A*1101 (13.46%), A*0201 (12.50%), A*0301 (10.10%); HLA-B*5101(8.17%), B*3501(6.73%), B*5001 (6.25%); HLA-DRB1*0701 (16.35%), DRB1*1501 (8.65%) and DRB1*0301 (7.69%). The two-locus haplotypes at the highest frequency were HLA-A*3001-B*1302 (2.88%), A*2402-B*5101 (2.86%); HLA-B*5001-DRB1*0701 (4.14%) and B*0702-DRB1*1501 (3.37%). The three-locus haplotype at the highest frequency was HLA-A*3001-B*1302-DRB1*0701(2.40%). Significantly high linkage disequilibrium was observed in six two-locus haplotypes, with their corresponding relative linkage disequilibrium parameters equal to 1. Neighbor-joining phylogenetic tree between the Uyghur group and other previously reported populations was constructed on the basis of standard genetic distances among the populations calculated using the four-digit sequence-level allelic frequencies at HLA-A, HLA-B and HLA-DRB1 loci. The phylogenetic analyses reveal that the Uyghur group belongs to the northwestern Chinese populations and is most closely related to the Xibe group, and then to Kirgiz, Hui, Mongolian and Northern Han.

Conclusions/Significance

The present findings could be useful to elucidate the genetic background of the population and to provide valuable data for HLA matching in clinical bone marrow transplantation, HLA-linked disease-association studies, population genetics, human identification and paternity tests in forensic sciences.     

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.     

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

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

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.