ASP – a simulation-based power calculator for genetic linkage studies of qualitative traits, using sib-pairs

An easy-to-use, simulation-based power calculator (ASP) for linkage analysis using sib-pair designs (concordant or discordant) has been developed and made publicly available via the Internet. The program employs a diallelic model for the trait locus, at which parental/offspring genotypes are simulated, assuming Hardy-Weinberg equilibrium in the parental generation. Genotypes at a linked multiallelic marker locus are simulated conditional upon the inheritance pattern at the trait locus, allowing for recombination. Marker genotypes are tested for non-Mendelian identity-by-descent sharing, using both an unrestricted and a restricted likelihood ratio test, the latter representing an extension of the "mean test" from fully to partially informative families. The power of user-defined datasets is estimated by the number of simulations giving significant results at varying type I error levels.     

Evaluating pedigree data. II. Identifying the cause of error in families with inconsistencies

Pedigree data can be evaluated, and subsequently corrected, by analysis of the distribution of genetic markers, taking account of the possibility of mistyping . Using a model of pedigree error developed previously, we obtained the maximum likelihood estimates of error parameters in pedigree data from Tokelau. Posterior probabilities for the possible true relationships in each family are conditional on the putative relationships and the marker data are calculated using the parameter estimates. These probabilities are used as a basis for discriminating between pedigree error and genetic marker errors in families where inconsistencies have been observed. When applied to the Tokelau data and compared with the results of retyping inconsistent families, these statistical procedures are able to discriminate between pedigree and marker error, with approximately 90% accuracy, for families with two or more offspring. The large proportion of inconsistencies inferred to be due to marker error (61%) indicates the importance of discriminating between error sources when judging the reliability of putative relationship data. Application of our model of pedigree error has proved to be an efficient way of determining and subsequently correcting sources of error in extensive pedigree data collected in large surveys.     

Segregation of HLA A,B haplotypes and the distribution of antigen mismatches between mother and offspring in Hutterite families

Segregation of HLA haplotypes and offspring genotype distributions were analyzed in families from an inbred Caucasoid population, the Dariusleut Hutterite Brethren. Both parents and from one to 12 offspring were typed for HLA-A and -B antigens in 108 families. Segregation of paternal haplotypes was analyzed conditional on sibship size in 95 sibships (a total of 547 offspring), and segregation of maternal haplotypes, in 90 sibships (a total of 515 offspring). The distribution of the number of different genotypes among the offspring was analyzed conditional on sibship size in 90 families (515 offspring) where four equiprobable genotypes were expected. The distribution of the number of antigenic differences or mismatches for broad specificities between mother and offspring was analyzed in pooled family data consisting of a total of 377 offspring comprising 68 families. Compared with the multinomial distribution of segregation classes of haplotypes, there was no significant departure (probability .05 or less) from the expected segregation ratio for either paternal or maternal haplotypes. Compared with the multinomial distribution of the number of genotypes among the offspring, only two of the 11 sibship sizes had configurations that exceeded the 5% level of significance. Given the number of statistical tests performed, it is likely that these results could be explained by chance variation. Finally, there was no relative deficiency of offspring who were less mismatched with their mother for HLA-A and -B broad specificities. Therefore, if HLA-A,B region variation does have a major effect on the differential survival of fetuses in some families, it is an uncommon factor among fertile couples from this inbred population.     

Genetic variability in the tumor necrosis factor-lymphotoxin region influences susceptibility to rheumatoid arthritis.

The major histocompatibility complex class III tumor necrosis factor-lymphotoxin (TNF-LT) region (6p21.3) was investigated as a possible susceptibility locus for rheumatoid arthritis (RA). Inheritance of five TNF microsatellite markers was determined in 50 multiplex families. Overall, 47 different haplotypes were observed. One of these, the TNF a6, b5, c1, d3, e3 (H1) haplotype, was present in 35.3% of affected, but in only 20.5% of unaffected, individuals (P < .005). This haplotype accounted for 21.5% of the parental haplotypes transmitted to affected offspring and only 7.3% not transmitted to affected offspring (P = .0003). The TNF a6 and TNF c1 alleles were individually associated with RA (P = .0005 and .0008, respectively), as were the HLA-DRB1 "shared epitope" (SE) (P = .0001) and HLA-DRB1*0401 (P = .0018). Both univariate and bivariate conditional logistic regression analysis showed significant effects of TNF c1 and SE in increasing risk to RA (P < .001). Stratification by the presence of SE indicated an independent effect of the TNFc1 allele (P = .0003) and the HLA A1, B8, DR3 extended haplotype (always TNFa2, b3, c1, d1, e3) (P = .0027) in SE heterozygotes, while the H1 haplotype was associated with RA in SE homozygotes (P = .0018). The TNF-LT region appears to influence susceptibility to RA, distinct from HLA-DR.     

A Unified Stepwise Regression Procedure for Evaluating the Relative Effects of Polymorphisms within a Gene Using Case/Control or Family Data: Application to HLA in Type 1 Diabetes

A stepwise logistic-regression procedure is proposed for evaluation of the relative importance of variants at different sites within a small genetic region. By fitting statistical models with main effects, rather than modeling the full haplotype effects, we generate tests, with few degrees of freedom, that are likely to be powerful for detecting primary etiological determinants. The approach is applicable to either case/control or nuclear-family data, with case/control data modeled via unconditional and family data via conditional logistic regression. Four different conditioning strategies are proposed for evaluation of effects at multiple, closely linked loci when family data are used. The first strategy results in a likelihood that is equivalent to analysis of a matched case/control study with each affected offspring matched to three pseudocontrols, whereas the second strategy is equivalent to matching each affected offspring with between one and three pseudocontrols. Both of these strategies require you be able to infer parental phase (i.e., those haplotypes present in the parents). Families in which phase cannot be determined must be discarded, which can considerably reduce the effective size of a data set, particularly when large numbers of loci that are not very polymorphic are being considered. Therefore, a third strategy is proposed in which knowledge of parental phase is not required, which allows those families with ambiguous phase to be included in the analysis. The fourth and final strategy is to use conditioning method 2 when parental phase can be inferred and to use conditioning method 3 otherwise. The methods are illustrated using nuclear-family data to evaluate the contribution of loci in the HLA region to the development of type 1 diabetes.     

Association tests in nuclear families

We present a conditional likelihood approach for testing linkage disequilibrium in nuclear families having multiple affected offspring. The likelihood, conditioned on the identity-by-descent (IBD) structure of the sibling genotypes, is unaffected by familial correlation in disease status that arises from linkage between a marker locus and the unobserved trait locus. Two such conditional likelihoods are compared: one that conditions on IBD and phase of the transmitted alleles and a second which conditions only on IBD of the transmitted alleles. Under the log-additive model, the first likelihood is equivalent to the allele-counting methods proposed in the literature. The second likelihood is valid under the added assumption of equal male and female recombination fractions. In a simulation study, we demonstrated that in sibships having two or three affected siblings the score test from each likelihood had the correct test size for testing disequilibrium. They also led to equivalent power to detect linkage disequilibrium at the 5% significance level.     

Family-size distribution and Ewens'' equivalence theorem.

Segregation analysis of a data set containing nuclear families of more than one sibship size is considered, and two different formulations of the likelihood are examined. One is the "separate-multinomials" formulation, which treats each family size as representing a separate multinomial distribution; the other is the "grand-multinomial" formulation, which treats the entire data set as representing one distribution. It is shown that these two formulations are equivalent, if and only if the population distribution of family sizes is completely unknown. However, if anything is known about the family-size distribution, the grand-multinomial formulation, although more cumbersome, makes more complete use of the data; moreover, it enables the use of one-child families in a segregation analysis. The relationship of this work to Ewens' equivalence theorem concerning "unconditional" and "conditional" likelihoods is discussed. The findings are illustrated with a simple example, and their practical relevance to real-life segregation analysis is discussed.     

The structure of genetic linkage data: from LIPED to 1M SNPs

There are three assumptions of independence or conditional independence that underlie linkage likelihood computations on sets of related individuals. The first is the independence of meioses, which gives rise to the conditional independence of haplotypes carried by offspring, given those of their parents. The second derives from the assumption of absence of genetic interference, which gives rise to the conditional independence of inheritance vectors, given the inheritance vector at an intermediate location. The third is the assumption of independence of allelic types, at the population level, both among haplotypes of unrelated individuals and also over the loci along a given haplotype. These three assumptions have been integral to likelihood computations since the first lod scores were computed, and remain key components in analysis of modern genetic data. In this paper we trace the role of these assumptions through the history of linkage likelihood computation, through to a new framework of genetic linkage analysis in the era of dense genomic marker data.     

Segregation Analysis of Body Mass Index in an Unselected French-Canadian Sample: The Québec Family Study

Interest in a single gene etiology for obesity, as assessed by the body mass index (BMI), has been spurred recently by reports of a putative recessive major gene for extreme values, which accounts for as much as 40% of the variance. The major gene hypothesis was evaluated here in the Québec Family Study, a random sample of 375 French-Canadian volunteer families. This report represents one component in a more complete investigation of obesity in these families. In contrast to the recent studies, a major gene hypothesis for BMI was not verified here. Although there was a major effect, it did not conform to a Mendelian pattern of transmission. A multifactorial component (i.e., polygenic and/or common environmental factors) accounted for 42% of the phenotypic variance. In addition, evidence of heterogeneity between the generations was found. The heterogeneity was traced to the major non-Mendelian component (which accounted for 0.01% of the variance in parents and over 40% in offspring) rather than to the multifactorial one. These results would suggest that a simple recessive gene mixed model may not be sufficient to explain the familial distribution of the BMI. Several factors which may have contributed to these results include temporal trends and surrogate effects such as those related to variation in body composition and energy balance components. (OBESITY RESEARCH 1993; 1:288–294)     

Segregation and linkage analyses in families of patients with bipolar,unipolar, and schizoaffective mood disorders.

Hypotheses of single major locus transmission (autosomal and X chromosome) of major affective disorder (i.e., bipolar, unipolar, and schizoaffective) are tested using the Elston-Stewart likelihood method of pedigree segregation analysis. The sample consists of families of varying size ascertained through patients treated at the National Institute of Mental Health in Bethesda, Maryland. We test hypotheses on subsamples of families according to: (1) diagnosis of proband (75 bipolar I, 22 bipolar II, 18 unipolar, and six schizoaffective); (2) extreme value of a biological trait in the proband ("low" monoamine oxidase, "low" cerebrospinal fluid serotonin metabolite 5-HIAA); and (3) positive response to lithium in the proband. We cannot find evidence for single major locus transmission of major affective disorder from segregation analysis in any subsample of family even when the diagnostic classification of ill phenotypes is widened to include possible affective "spectrum" diagnoses. In addition, linkage studies of 21 autosomal markers do not provide evidence for single major locus transmission of illness. The maximum lod score, found for 30 families at the MNS locus, was 1.39 at 20% recombination.     

Genetics of nonsyndromic cleft lip with or without cleft palate: is there a Mendelian sub-entity?

The mode of inheritance of nonsyndromic cleft lip with or without cleft palate (NSCLP) is still a matter of dispute. We performed segregation analysis on three data sets of families ascertained through an affected child with NSCLP. The first two data sets were selected in France and were pooled for a global analysis. No major gene effect could be evidenced in spite of a very large number of families (666 pedigrees including 719 nuclear families). The third data set was British and consisted of three-generation families including the offspring of probands. A major gene effect, as well as a strong residual multifactorial component, were highly significant and we could show that this evidence almost entirely came from the information on probands' offspring. We conclude that a mixture of monogenic and of multifactorial cases is probably the best explanation for the observations made in this study. Analyses performed in pedigrees with multiple cases closely related might allow reducing heterogeneity and help identifying those Mendelian sub-entities.     

Generalized case-control sampling under generalized linear models

A generalized case-control (GCC) study, like the standard case-control study, leverages outcome-dependent sampling (ODS) to extend to nonbinary responses. We develop a novel, unifying approach for analyzing GCC study data using the recently developed semiparametric extension of the generalized linear model (GLM), which is substantially more robust to model misspecification than existing approaches based on parametric GLMs. For valid estimation and inference, we use a conditional likelihood to account for the biased sampling design. We describe analysis procedures for estimation and inference for the semiparametric GLM under a conditional likelihood, and we discuss problems with estimation and inference under a conditional likelihood when the response distribution is misspecified. We demonstrate the flexibility of our approach over existing ones through extensive simulation studies, and we apply the methodology to an analysis of the Asset and Health Dynamics Among the Oldest Old study, which motives our research. The proposed approach yields a simple yet versatile solution for handling ODS in a wide variety of possible response distributions and sampling schemes encountered in practice.     

Evidence of linkage of familial hypoalphalipoproteinemia to a novel locus on chromosome 11q23

Coronary heart disease (CHD) accounts for half of the 1 million deaths annually ascribed to cardiovascular disease and for almost all of the 1.5 million acute myocardial infarctions. Within families affected by early and apparently heritable CHD, dyslipidemias have a much higher prevalence than in the general population; 20%-30% of early familial CHD has been ascribed to primary hypoalphalipoproteinemia (low HDL-C). This study assesses the evidence for linkage of low HDL-C to chromosomal region 11q23 in 105 large Utah pedigrees ascertained with closely related clusters of early CHD and expanded on the basis of dyslipidemia. Linkage analysis was performed by use of 22 STRP markers in a 55-cM region of chromosome 11. Two-point analysis based on a general, dominant-phenotype model yielded LODs of 2.9 for full pedigrees and 3.5 for 167 four-generation split pedigrees. To define a localization region, model optimization was performed using the heterogeneity, multipoint LOD score (mpHLOD). This linkage defines a region on 11q23.3 that is approximately 10 cM distal to-and apparently distinct from-the ApoAI/CIII/AIV gene cluster and thus represents a putative novel localization for the low HDL-C phenotype.     

Several interacting genes influence the malignant hyperthermia phenotype

Malignant hyperthermia (MH), a potentially lethal disorder of skeletal muscle calcium homeostasis, manifests only on exposure to certain anaesthetic drugs. The mode of inheritance appears to be autosomal dominant with both locus and allelic heterogeneity having been reported. Association analysis of eight MH candidate loci in UK families has indicated that several genes influence susceptibility in individual families, rather than MH simply being a major gene defect. In support of this hypothesis, we present data on a replica analysis of an independent sample of European MH families.     

Further analysis of familial transmission of congenital glaucoma.

A re-analysis of familial transmission of congenital glaucoma is performed here using the unified model and considering, respectively, joint and conditional likelihoods. Whereas the familial aggregation of this malformation is consistent with the segregation of a recessive major gene and a high proportion of sporadic cases using conditional likelihood, this is rejected using joint likelihood. The difference in the results obtained using each of these two strategies is discussed.     

The IBD2 locus shows linkage heterogeneity between ulcerative colitis and Crohn disease

The IBD2 locus on chromosome 12 has been linked to both Crohn disease (CD) and ulcerative colitis (UC) but has not been detected in some CD-dominated data sets. In the present study, we genotyped 581 relative pairs with inflammatory bowel disease (252 from CD-only families, 138 from UC-only families, and 191 from mixed families containing cases of both CD and UC), using 12 markers spanning the IBD2 locus. A GENEHUNTER-PLUS multipoint LOD score of 3.91 was detected for pairs from UC-only families, compared with 1.66 for CD-only and 1.29 for mixed families. The difference between the LOD scores for UC and CD was significant in two different tests for heterogeneity (P=.0057 for one test and P=.0375 for the other). IBD2 thus appears to make a major contribution to UC susceptibility but to have only a relatively minor effect with regard to CD, for which there may be substantially more locus heterogeneity.     

Resolution of genetic and cultural inheritance in twin families by path analysis: application to HDL-cholesterol.

A path model and associated statistical method for the analysis of data on twin families are introduced and applied to high density lipoprotein cholesterol (HDL-c) observations in the Swedish Twin Family Study. The proposed path model incorporates both genetic and environmental sources of familial resemblance, maternal environmental effects, intergenerational differences in heritabilities, marital resemblance due to either primary or secondary phenotypic homogamy, and twin residual environmental correlations. Application of the model to HDL-c levels resulted in parameter estimates consistent with those reported in earlier reviews and in the analysis of nuclear family and twin data. Genetic heritability was estimated as h2 = .363 +/- .243, cultural heritability as c2 = .187 +/- .082, and the proportion of phenotypic variance due to residual environmental effects as r2 = .450 +/- .207. Although the parameter estimates were comparable, the statistical tests of hypotheses were, relative to other designs, of low statistical power. It appears that environmental indices are necessary for powerful tests of hypotheses.     

Parental origin-dependent, male offspring-specific transmission-ratio distortion at loci on the human X chromosome.

We have analyzed the transmission of maternal alleles at loci spanning the length of the X chromosome in 47 normal, genetic disease-free families. We found a significant deviation from the expected Mendelian 1:1 ratio of grandpaternal:grandmaternal alleles at loci in Xp11.4-p21.1. The distortion in inheritance ratio was found only among male offspring and was manifested as a strong bias in favor of the inheritance of the alleles of the maternal grandfather. We found no evidence for significant heterogeneity among the families, which implies that the major determinant involved in the generation of the non-Mendelian ratio is epigenetic. Our analysis of recombinant chromosomes inherited by male offspring indicates that an 11.6-cM interval on the short arm of the X chromosome, bounded by DXS538 and DXS7, contains an imprinted gene that affects the survival of male embryos.     

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

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

Model-free linkage analysis with covariates confirms linkage of prostate cancer to chromosomes 1 and 4

As with many complex genetic diseases, genome scans for prostate cancer have given conflicting results, often failing to provide replication of previous findings. One factor contributing to the lack of consistency across studies is locus heterogeneity, which can weaken or even eliminate evidence for linkage that is present only in a subset of families. Currently, most analyses either fail to account for locus heterogeneity or attempt to account for it only by partitioning data sets into smaller and smaller portions. In the present study, we model locus heterogeneity among affected sib pairs with prostate cancer by including covariates in the linkage analysis that serve as surrogate measures of between-family linkage differences. The model is a modification of the Olson conditional logistic model for affected relative pairs. By including Gleason score, age at onset, male-to-male transmission, and/or number of affected first-degree family members as covariates, we detected linkage near three locations that were previously identified by linkage (1q24-25 [HPC1; LOD score 3.25, P=.00012], 1q42.2-43 [PCAP; LOD score 2.84, P=.0030], and 4q [LOD score 2.80, P=.00038]), near the androgen-receptor locus on Xq12-13 (AR; LOD score 3.06, P=.00053), and at five new locations (LOD score > 2.5). Without covariates, only a few weak-to-moderate linkage signals were found, none of which replicate findings of previous genome scans. We conclude that covariate-based linkage analysis greatly improves the likelihood that linked regions will be found by incorporation of information about heterogeneity within the sample.