Multipoint linkage disequilibrium mapping using case-control designs

Case-control study has been and continues to be one of the most popular designs in epidemiology. More recently, this design has been adopted to test for candidate genes when searching for disease genetic etiology. In this report, we present a multipoint linkage disequilibrium (LD) mapping approach with the focus on estimating the location of the target trait locus. It builds upon a representation, which shows that the difference between a case and a control in probabilities of carrying the target allele of a marker is proportional to that of the trait locus and that the proportionality factor is simply a measure of LD between the trait locus and the marker. Our method has the desired properties that (1) there is no need to specify phases of genotypic data with multiple markers, (2) it provides an estimate of location of the disease locus along with sampling uncertainty to help investigators to narrow chromosomal regions, and (3) a single test statistic is provided to test for LD in the framed region rather than testing the hypothesis one marker at a time. Our simulation work suggests that the proposed method performs well in terms of bias and coverage probability. Extension of the proposed method to account for confounding and genetic heterogeneity is discussed. We apply the proposed method to a published case-control data set for cystic fibrosis.     

Testing association and linkage using affected-sib-parent study designs

We have developed a method for jointly testing linkage and association using data from affected sib pairs and their parents. We specify a conditional logistic regression model with two covariates, one that quantifies association (either direct association or indirect association via linkage disequilibrium), and a second that quantifies linkage. The latter covariate is computed based on expected identity-by-descend (ibd) sharing of marker alleles between siblings. In addition to a joint test of linkage and association, our general framework can be used to obtain a linkage test comparable to the mean test (Blackwelder and Elston [1985] Genet. Epidemiol. 2:85-97), and an association test comparable to the Family-Based Association Test (FBAT; Rabinowitz and Laird [2000] Hum. Hered. 50:211-223). We present simulation results demonstrating that our joint test can be more powerful than some standard tests of linkage or association. For example, with a relative risk of 2.7 per variant allele at a disease locus, the estimated power to detect a nearby marker with a modest level of LD was 58.1% by the mean test (linkage only), 69.8% by FBAT, and 82.5% by our joint test of linkage and association. Our model can also be used to obtain tests of linkage conditional on association and association conditional on linkage, which can be helpful in fine mapping.     

Screening for linkage and association in nuclear families

We applied linkage analysis with a sib-pair method, which also takes into account information on unaffected siblings, and family-based methods of association analysis to determine the disease affecting loci in Problem 1. Whereas the first two disease loci were correctly identified by association analysis, the sib-pair linkage method failed to detect the disease loci 3 and 4. We therefore determined the data structure and sample size necessary for demonstrating linkage to these loci. ©1995 Wiley-Liss, Inc.     

Incorporation of covariates into multipoint linkage disequilibrium mapping in case-control studies

Case-control designs are commonly adopted in genetic epidemiological studies because they are cost effective and offer powerful tests for genetic and environmental risk factors, as well as their interactions. Previously, we proposed an association mapping approach to estimate the position of an unobserved disease locus as well as measuring its genetic effect on risk. The method provides a confidence interval for the estimated map position to help narrow the chromosomal region potentially harboring a disease locus. However, concerns often rise about case-control designs including possible false positives or bias due to confounders, heterogeneity or interactions among genes and between genes and environments. In the present work, we extended the multipoint linkage disequilibrium mapping approach for case-control studies to incorporate information about factors influencing the effect of causal genes to improve precision and efficiency of the estimated location. The efficiency, bias and coverage probability of this extended approach for locating a disease locus using case-control data with and without additional information on a covariate were compared through simulation. An example of a case-control study for type 2 diabetes was used to illustrate this extended method. In this study, a strong association between diabetes and a candidate gene, SCL2A10, was detected among nonobese subjects, whereas no evidence of association was found for either obese subjects or the whole sample when obesity was ignored. Simulation studies and these diabetes data both demonstrate how the efficiency of the estimated location of a disease gene can be improved substantially by incorporating information on covariates.     

Informativeness of twin-nuclear family and nuclear family designs for segregation analysis.

This brief note examines the precision of segregation parameter estimates from both twin-nuclear family and conventional nuclear family designs. The program MENDEL was used to derive expected frequencies of different family patterns of affectation (with fixed sibship size) under various single gene models, and then to estimate the standard errors (and information) associated with gene frequency and penetrance values at given sample sizes. As might be expected, a 2- to 5-fold increase in relative efficiency was found for the same family size if families included an MZ twin pair among their offspring. The methods used allow convenient calculation of expected informativeness of a given study design.     

Bivariate combined linkage and association mapping of quantitative trait loci

In this paper, bivariate/multivariate variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL), based on combinations of pedigree and population data. Suppose that a quantitative trait locus is located in a chromosome region that exerts pleiotropic effects on multiple quantitative traits. In the region, multiple markers such as single nucleotide polymorphisms are typed. Two regression models, "genotype effect model" and "additive effect model", are proposed to model the association between the markers and the trait locus. The linkage information, i.e., recombination fractions between the QTL and the markers, is modeled in the variance and covariance matrix. By analytical formulae, we show that the "genotype effect model" can be used to model the additive and dominant effects simultaneously; the "additive effect model" only takes care of additive effect. Based on the two models, F-test statistics are proposed to test association between the QTL and markers. By analytical power analysis, we show that bivariate models can be more powerful than univariate models. For moderate-sized samples, the proposed models lead to correct type I error rates; and so the models are reasonably robust. As a practical example, the method is applied to analyze the genetic inheritance of rheumatoid arthritis for the data of The North American Rheumatoid Arthritis Consortium, Problem 2, Genetic Analysis Workshop 15, which confirms the advantage of the proposed bivariate models.     

Allocation designs in cohort and case-control studies

Four unequal allocation designs for cohort and case-control studies that incorporate cost and power are considered and compared with the equal allocation design, with the aim of providing researchers some flexibility in planning their studies. It is found that the type of design to be adopted depends on available resources and projected needs. In the case of tight expenditure, the minimized cost design is the optimal, whereas the maximized power design may be sought if the researcher intends to ensure a high chance of detecting any clinically significant relative risk of disease.     

Strategies for genetic association analyses combining unrelated case-control individuals and family trios

In genetic association studies, analyses integrating data or estimates from unrelated case-control individuals and case trios (case offspring and their parents) can increase statistical power to identify disease susceptibility loci. Data on control trios may also be available, but how and when their use is advantageous is less familiar and is described here. In addition, the authors examine assumptions and properties of hybrid analyses combining association estimates from unrelated case-control individuals together with case and control family trios, focusing on low-prevalence disease. One such assumption is absence of population stratification bias (PSB), a potential source of confounding in case-control analyses. For detection of PSB, the authors discuss 4 possible tests that assess equality between individual-level and family-based estimates. Furthermore, a weighted framework is presented, in which estimates from analyses combining unrelated individuals and families (most powerful but subject to PSB) and family-based analyses (robust to PSB) are weighted according to the observed PSB test P value. In contrast to existing hybrid designs that combine individuals and families only if no significant PSB is detected, the weighted framework does not require specification of an arbitrary PSB testing level to establish significance. The statistical methods are evaluated using simulations and applied to a candidate gene study of childhood leukemia (Quebec Childhood Leukemia Study, 1980-2000).     

Asymptotic bias and efficiency in case-control studies of candidate genes and gene-environment interactions: basic family designs

Case-control designs that use population controls are compared with those that use controls selected from their relatives (i.e., siblings, cousins, or "pseudosibs" based on parental alleles) for estimating the effect of candidate genes and gene-environment interactions. The authors first evaluate the asymptotic bias in relative risk estimates resulting from using population controls when there is confounding due to population stratification. Using siblings or pseudosibs as controls completely addresses this issue, whereas cousins provide only partial protection from population stratification. Next, they show that the conventional conditional likelihood for matched case-control studies can give asymptotically biased effect estimates when applied to the pseudosib approach; the asymptotic bias is toward the null and disappears with disease rarity. They show how to reparameterize the pseudosib likelihood so this approach gives consistent effect estimates. They then show that the designs using population or pseudosib controls are generally the most efficient for estimating the main effect of a candidate gene, followed in efficiency by the design using cousins. Finally, they show that the design using sibling controls can be quite efficient when studying gene-environment interactions. In addition to asymptotic bias and efficiency issues, family-based designs might benefit from a higher motivation to participate among cases' relatives, but these designs have the disadvantage that many potential cases will be excluded from study by having no available controls.     

Issues in association mapping with high-density SNP data and diverse family structures

Genetic association studies have the potential to identify causative genetic variants with small effects in complex diseases, but it is not at all clear which study designs best balance power with sample size, especially when taking into account the difficulty of obtaining a sample of the necessary structure. The 14 contributions from the Genetic Analysis Workshop 15 group 3 used data sets with rheumatoid arthritis as primary phenotype from problem 2 (real data) and Problem 3 (simulated data) to investigate design and analysis problems that arise in candidate-gene, candidate-region, and genome-wide association studies. We identified three major themes that were addressed by multiple groups: (1) comparing family-based and case-control study designs with each other and with hybrid designs incorporating both related and unrelated individuals; (2) exploring and comparing techniques of combining information from multiple, correlated single-nucleotide polymorphisms; and (3) comparing analyses that select the model(s) of best fit with the ultimate aim of detecting the joint effects of several unlinked single-nucleotide polymorphisms. These contributions achieved some success in improving upon existing methods. For example, tests using related cases and unrelated controls can achieve higher power than the tests using unrelated cases and unrelated controls. Aside from these successes, the group 3 contributions highlight some interesting areas for future research.     

Combined linkage and linkage disequilibrium mapping for genome screens

Linkage analysis and association studies, two major approaches for genetic studies of human diseases, are useful for mapping genes that are highly penetrant, but both use only part of the information that is available for mapping disease genes. Therefore, they provide limited utility when used alone. In this report, we present combined linkage and linkage disequilibrium mapping that simultaneously utilizes linkage and linkage disequilibrium information for mapping human disease genes. Compared with the existing linkage analysis and association study methods, this method has several advantages: 1) it has high statistical power by a joint analysis of linkage and linkage disequilibrium for localizing disease susceptibility loci: 2) it unifies the theory of linkage analysis and linkage disequilibrium mapping, 3) it retains the general framework for linkage analysis and, hence, can be easily incorporated into the existing software for the linkage analysis. The proposed LLDM is applied to familial hemophagocytic lymphohistiocytosis (FHL) disease.     

Sib-pair linkage analyses of nuclear family data: Quantitative versus dichotomous disease classification

Model-free sib-pair linkage analysis was used to screen 367 highly polymorphic markers for evidence of linkage to a disease, defined either quantitatively (Q1) or dichotomously (AF). Five individual replicates, plus a case family data set containing all families in these replicates with at least one individual with AF, were analyzed. Sib-pair linkage results for Q1 and AF varied considerably among the five replicates and did not consistently detect any of the three underlying major loci, MG1, MG2, and MG3. For the pooled case families, linkage analyses of Q1, but not AF, detected the flanking markers for MG1 and MG2 at the 0.05 and 0.01 levels, respectively. Overall, type 1 error rates were not elevated. The ability to analyze the disease quantitatively (Q1) and construct a data set more appropriate for linkage analysis (case families) enhanced the power to detect at least some of the major loci underlying the disease. © 1997 Wiley-Liss, Inc.     

Effect of linkage disequilibrium between markers in linkage and association analyses

Contributions to Group 17 of the Genetic Analysis Workshop 15 considered dense markers in linkage disequilibrium (LD) in the context of either linkage or association analysis. Three contributions reported on methods for modeling LD or selecting a subset of markers in linkage equilibrium to perform linkage analysis. When all markers were used without modeling LD, inflated evidence for linkage was observed when parental genotypes were missing. All methods for handling LD led to some decreased linkage evidence. Two groups performed a genome-wide association scan using either mixed models to account for known or unknown relatedness between individuals, trend tests or combination statistics. All methods failed to detect four of the eight simulated loci because of low LD in some regions. Three groups performed association analysis using simulated dense markers on chromosome 6, where a simulated HLA-DRB1 locus played a major role in disease susceptibility along with two additional loci of smaller effect. The overall conditional genotype method correctly identified both additional loci while a novel transmission disequilibrium test-statistic to combine studies with non-overlapping markers identified one HLA locus after stratifying on the parental HLA-DRB1 genotypes; LD mapping using the Malécot model mapped two loci in this region, even when using greatly reduced marker density. While LD between markers appears to be a nuisance that may cause spurious linkage results with missing parental genotypes in linkage analysis, association analysis thrives on LD, and disease genes fail to be detected in regions of low LD.     

Haplotype association analysis for late onset diseases using nuclear family data

In haplotype-based association studies for late onset diseases, one attractive design is to use available unaffected spouses as controls (Valle et al. [1998] Diab. Care 21:949-958). Given cases and spouses only, the standard expectation-maximization (EM) algorithm (Dempster et al. [1977] J. R. Stat. Soc. B 39:1-38) for case-control data can be used to estimate haplotype frequencies. But often we will have offspring for at least some of the spouse pairs, and offspring genotypes provide additional information about the haplotypes of the parents. Existing methods may either ignore the offspring information, or reconstruct haplotypes for the subjects using offspring information and discard data from those whose haplotypes cannot be reconstructed with high confidence. Neither of these approaches is efficient, and the latter approach may also be biased. For case-control data with some subjects forming spouse pairs and offspring genotypes available for some spouse pairs or individuals, we propose a unified, likelihood-based method of haplotype inference. The method makes use of available offspring genotype information to apportion ambiguous haplotypes for the subjects. For subjects without offspring genotype information, haplotypes are apportioned as in the standard EM algorithm for case-control data. Our method enables efficient haplotype frequency estimation using an EM algorithm and supports probabilistic haplotype reconstruction with the probability calculated based on the whole sample. We describe likelihood ratio and permutation tests to test for disease-haplotype association, and describe three test statistics that are potentially useful for detecting such an association.     

CAPL: a novel association test using case-control and family data and accounting for population stratification

The recent successes of GWAS based on large sample sizes motivate combining independent datasets to obtain larger sample sizes and thereby increase statistical power. Analysis methods that can accommodate different study designs, such as family-based and case-control designs, are of general interest. However, population stratification can cause spurious association for population-based association analyses. For family-based association analysis that infers missing parental genotypes based on the allele frequencies estimated in the entire sample, the parental mating-type probabilities may not be correctly estimated in the presence of population stratification. Therefore, any approach to combining family and case-control data should also properly account for population stratification. Although several methods have been proposed to accommodate family-based and case-control data, all have restrictions. Most of them require sampling a homogeneous population, which may not be a reasonable assumption for data from a large consortium. One of the methods, FamCC, can account for population stratification and uses nuclear families with arbitrary number of siblings but requires parental genotype data, which are often unavailable for late-onset diseases. We extended the family-based test, Association in the Presence of Linkage (APL), to combine family and case-control data (CAPL). CAPL can accommodate case-control data and families with multiple affected siblings and missing parents in the presence of population stratification. We used simulations to demonstrate that CAPL is a valid test either in a homogeneous population or in the presence of population stratification. We also showed that CAPL can have more power than other methods that combine family and case-control data.     

A case-control for the association between change in weight,family history and hypertension at different ages

To study the association between the changes of weight, family history and hypertension at different ages, a pair-matched case-control study was conducted in the outpatient service of department of internal medicine in Binjiang Hospital of Tianjin from 1994 to 1996. The cases were selected from 312 patients with hypertension diagnosed during 1994-1996 and identified newly in the survey. The controls were selected from other outpatients of no cardiovascular disease histories matched by age and sex. The conditional logistic regression model was used. The cases and controls were divided into two age groups under 59 years old, 60 and older. History of hypertension in the first degree-relatives was linked to hypertension, but family history of hypertension of groups under age 59, and at 60 and older was mainly hypertension history of parents and siblings, respectively. Other risk factors of developing hypertension were higher weight or body mass index (kg/m2) in the survey, higher degree of weight gain in comparison with the basic weight and early age at beginning weight gain in all two groups. However, the risk of developing hypertension for increasing weight and obesity increased with advancing age groups. The study further indicates that controlling body weight, decreasing the degree of weight gain, and delaying the beginning age of weight gain all contribute to the lower risk of suffering from hypertension and were effective measures of hypertension of the prevention and cure.     

Genome scan for association and linkage

In this paper, a genome search is performed on the GAW Problem 1 data, in an attempt to determine which, if any, of the marker loci are associated and/or linked with the disease. Since there was no clear indication from the data of the likely mode of inheritance, methods were used which did not require such assumptions to be made. A two-stage procedure was used to test for association. Firstly a standard unmatched case-control test was applied to all the loci. The family-based method of Self et al. [1991] was then applied to those loci which gave a positive result in the first stage. This procedure correctly detected loci 1 and 2, and that disease risk was increased for homozygote carriers of the disease allele at each locus, although a false positive result was also found. The affected sib pair method of Holmans [1993] was also applied to the data, although the sample contained far too few sib-pairs for such an analysis to be effective. This analysis failed to find any of the disease loci. ©1995 Wiley-Liss, Inc.     

On combining family and case-control studies

Studies to detect genetic association with disease can be family-based, often using families with multiple affected members, or population based, as in population-based case-control studies. If data on both study types are available from the same population, it is useful to combine them to improve power to detect genetic associations. Two aspects of the data need to be accommodated, the sampling scheme and potential residual correlations among family members. We propose two approaches for combining data from a case-control study and a family study that collected families with multiple cases. In the first approach, we view a family as the sampling unit and specify the joint likelihood for the family members using a two-level mixed effects model to account for random familial effects and for residual genetic correlations among family members. The ascertainment of the families is accommodated by conditioning on the ascertainment event. The individuals in the case-control study are treated as families of size one, and their unconditional likelihood is combined with the conditional likelihood for the families. This approach yields subject specific maximum likelihood estimates of covariate effects. In the second approach, we view an individual as the sampling unit. The sampling scheme is accommodated using two-phase sampling techniques, marginal covariate effects are estimated, and correlations among family members are accounted for in the variance calculations. The models are compared in simulations. Data from a case-control and a family study from north-eastern Italy on melanoma and a low-risk melanoma-susceptibility gene, MC1R, are used to illustrate the approaches.