Linkage Disequilibrium in Recently Admixed Populations

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1 Am. J. Hum. Genet. 60: , 1997 Mapping Genes Underlying Ethnic Differences in Disease Risk by Linkage Disequilibrium in Recently Admixed Populations Paul M. McKeigue Epidemiology Unit, Department of Epidemiology and Population Sciences, London School of Hygiene and Tropical Medicine Summary Where recent admixture has occurred between two populations that have different disease rates for genetic reasons, family-based association studies can be used to map the genes underlying these differences, if the ancestry of the alleles at each locus examined can be assigned to one of the two founding populations. This article explores the statistical power and design requirements of this approach. Markers suitable for assigning the ancestry of genomic regions could be defined by grouping alleles at closely spaced microsatellite loci into haplotypes, or generated by representational difference analysis. For a given relative risk between populations, the sample size required to detect a disease locus that accounts for this relative risk by linkage-disequilibrium mapping in an admixed population is not critically dependent on assumptions about genotype penetrances or allele frequencies. Using the transmission-disequilibrium test to search the genome for a locus that accounts for a relative risk of between 2 and 3 in a high-risk population, compared with a low-risk population, generally requires between 150 and 800 case-parent pairs of mixed descent. The optimal strategy is to conduct an - initial study using markers spaced at 10 cm with cases from the second and third generations of mixed descent, and then to map the disease loci more accurately in a subsequent study of a population with a longer history of admixture. This approach has greater statistical power than allele-sharing designs and has obvious applications to the genetics of hypertension, non-insulin-dependent diabetes, and obesity. Introduction Current attempts to map genes for complex traits are based on two main approaches: association studies using Received June 10, 1996; accepted for publication August 28, Address for correspondence and reprints: Dr. Paul M. McKeigue, Epidemiology Unit, Department of Epidemiology and Population Sciences, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, United Kingdom. pmckeigu@ lshtm.ac.uk 1997 by The American Society of Human Genetics. All rights reserved /97/ $ polymorphisms close to candidate genes or allele-sharing studies using affected sib pairs. Both these approaches have limitations: candidate gene studies depend on knowing which gene to look at, and allelesharing studies of a binary trait require very large sample sizes to detect a locus that contributes a recurrence risk ratio in siblings of <-1.5. An ideal method would combine the statistical power of association studies with the broad mapping resolution of linkage studies. Several authors have noted that it is possible to take advantage of the disequilibrium that results from recent admixture between two populations in which the frequencies of alleles influencing the trait are different (Chakraborty and Weiss 1988; Risch 1992; Stephens et al. 1994; Thomson 1995). Under these circumstances, linkage disequilibrium will be present over longer distances and the density of markers required for a whole genome search is less than in a population without history of recent admixture. Two previous groups have examined the statistical power and design requirements of this approach (Chakraborty and Weiss 1988; Stephens et al. 1994). These analyses were based on two assumptions that limit their application in practice. The first assumption was that disequilibrium between alleles at the marker locus and the disease locus can be measured directly because genotypes at the disease locus are easily distinguishable by the phenotypes they produce. This is an unrealistic model for the study of complex traits. In any case, if genotypes at a locus are easily distinguishable by the phenotypes they produce, the locus can be mapped by conventional linkage analysis. The second assumption made by these authors was that disequilibrium between unlinked genes could not be eliminated in the design of the association study. Gametic disequilibrium generated by admixture persists for a few generations, even when the loci are unlinked. Chakraborty and Weiss (1988) suggested that statistical tests based on the history of admixture could help establish whether disequilibrium between alleles was attributable to linkage, whereas Stephens et al. (1994) assumed that individuals whose ancestry included admixture within the last few generations would be excluded from the study. Neither of these measures is necessary if family-based study designs are used to test for association,

2 McKeigue: Mapping of Genes in Recently Admixed Groups as when analyzed correctly these studies detect disequilibrium only between linked genes (Ewens and Spielman 1995; Thomson 1995). A key advantage of family-based study designs is the ability to test for linkage disequilibrium in populations where admixture has occurred within the last few generations, because in such populations widely spaced markers can be used for a wholegenome search. The objective of this paper is to explore the practical possibilities for using linkage disequilibrium in recently admixed populations to map genes for complex traits and multifactorial diseases such as hypertension, diabetes, and obesity. The rationale for this approach is that admixture between populations that have markedly different disease rates or trait values for genetic reasons will generate linkage disequilibrium between genes influencing the trait and other alleles that have different frequencies in the two founding populations. A first step therefore is to consider the criteria for deciding whether ethnic differences in disease rates are likely to have a genetic explanation. Distinguishing between Genetic and Environmental Explanations for Ethnic Differences in Disease Rates Even where familial aggregation studies demonstrate that a trait has high heritability or high risk of recurrence in relatives of cases, it does not necessarily follow that ethnic differences in disease risk are attributable to genetic influences. The classical epidemiological approach to distinguishing between genetic and environmental explanations for between-population differences in disease rates is to study migrants (Reid 1971). When migrant groups living in the same environment have different disease rates that are not accounted for by adjusting for known environmental determinants of disease risk, genetic explanations should be considered. Genetic explanations are most likely where differences in disease rates persist even in migrants who have been settled outside the home country for several generations and where such differences are consistently found in all countries where the migrant group has settled. On these criteria, genetic factors are likely to underlie the high rates of coronary heart disease and non-insulin-dependent diabetes that have been reported in people of South Asian (Indian, Pakistani, Bangladeshi, and Sri Lankan) descent settled overseas (McKeigue et al. 1989). In contrast, genetic factors are unlikely to account for the low rates of coronary heart disease, colorectal cancer, and breast cancer in native Japanese compared with U.S. Whites; in second- and third-generation Japanese migrants to the United States, the rates of these diseases are close to those in U.S. Whites (Dunn 1975; Gordon 1982). The most-powerful technique for distinguishing between environmental and genetic explanations for ethnic differences in disease risk is to study populations in which the proportion of admixture of genes from highrisk and low-risk populations varies. If disease risk is correlated with the proportion of genes originating from the high-risk population, independently of environmental factors, this is consistent with genetic influences. Thus, in Mexican-Americans, prevalence of non-insulin-dependent diabetes is correlated with the percent of Native American admixture (Chakraborty et al. 1986). Some examples of ethnic differences in trait values that are likely to be attributable to genetic influences are listed in table 1. It is curious that hypertension, noninsulin-dependent diabetes, and obesity should be so prominent among the conditions for which genetic differentiation has apparently led to ethnic differences in disease risk. This may be because genes influencing risk of these diseases also influence traits on which there has been differential selection pressure, such as the ability to survive famine (Neel 1962). If there is less evidence of ethnic differences in cancer risk that are attributable to genetic influences, this may be because genes influencing cancer risk do not influence other traits on which there has been differential selection pressure. Whom to Study 189 European maritime expansion beginning in the fifteenth century led to admixture on a large scale with Native American, West African, and Pacific populations. Admixture in Asia has a longer history: thus, for instance, early Hindu sources refer to admixture between the inhabitants of Punjab and invaders from southwestern Asia who arrived around 1200 B.C. (Tinker 1989). It is not unusual for the offspring of mixed unions to form an endogamous subpopulation, isolated from the two founding populations by geographic or social barriers. An example is the Anglo-Indian population, descended from eighteenth-century intermarriages between Indian women and British officers of the East India Company (Younger 1987). Although searches of the whole genome may be feasible only in populations where admixture has occurred recently, studying populations with a longer history of admixture may help map disease loci more accurately. Because the power of the study depends on the relative risk between populations, the case definition and the distribution of cases by age and sex should be chosen to correspond with the categories that maximize the relative risk when the two populations are compared. For instance, to detect loci underlying the high rates of hypertension in people of West African descent compared with Europeans, the optimal group to study would be adult women, because the ethnic difference in blood pressure is largest in this group (Chaturvedi et al. 1993;

3 190 Table 1 Ethnic Differences in Disease Rates That Are Likely To Have a Genetic Component Am. J. Hum. Genet. 60: , 1997 DISEASE Non-Insulin-Dependent Diabetes Hypertension Obesity Coronary Heart Disease High-risk ethnic Many non-european groups, West Africans (Prineas Native Americans, South Asians groups including South Asians, West and Gillum 1985) Peninsular Arabs, (McKeigue et al. 1989) Africans, Peninsular Arabs, Pacific islanders, Aboriginal Australians, Pacific Aboriginal Australians, islanders, and Native West African women Americans (Zimmet 1992) (Hodge and Zimmet 1994); South Asians (central adiposity) (McKeigue et al. 1991) Low-risk ethnic Northern Europeans West African men groups (Miller et al. 1989) Typical relative risks 4 to 7 2 to 3 2 to 4 2 to 4 between high-risk and low-risk populations Manatunga et al. 1993) even though heritability of blood pressure is generally lower in adults than in children (Perusse et al. 1989). What Size of Relative Risk Should One Look For? On the assumption of a multiplicative model for the relative risks associated with combinations of genotypes at different loci, the relative risk associated with ethnicity can be partitioned into locus-specific relative risks: thus, two loci accounting for relative risks of 2 and 3 would generate a relative risk of 6. Usually we can only guess the number of loci likely to be involved, but the following argument suggests that loci where genetic variation accounts for ethnic differences in disease risk will generally be fewer in number than loci where genetic variation accounts for familial aggregation of disease risk within populations. Genes that underlie ethnic differences in the risk of a disease such as non-insulindependent diabetes are likely to influence traits for which differential selection pressure has occurred, such as ability to survive famine (Neel 1962). Presumably not all genetic loci influencing diabetes risk also influence traits on which there has been differential selection pressure, so only a subset of the loci where genetic variation influences the risk of diabetes will underlie ethnic differences in diabetes prevalence. For the examples in table 1, where the relative risks of disease in high-risk compared with low-risk populations are generally between 2 and 5, it is reasonable to begin by looking for loci where ethnic differences in allele frequencies account for relative risks of 2 to 3, about one-third to one-half of the observed ethnic difference in disease risk. It is possible that ethnic differences in disease risk depend on a balance between opposing effects at different loci: thus, in a population where selection pressure has led to high frequencies of an allele causing insulin resistance, there may have been selection for other traits such as increased beta-cell reserves, which allow glucose homeostasis to be maintained. In this case, the relative risk of diabetes attributable to a locus influencing insulin resistance could be larger than the total relative risk of diabetes between the two populations. Expected Frequency of Transmission of a Marker Allele from a Heterozygous Parent to Affected Offspring We first examine the properties of the transmissiondisequilibrium test, which tests for excess frequency of transmission of a marker allele to affected offspring from heterozygous parents (Ewens and Spielman 1995). The expected deviation from 50% transmission of the marker allele can be calculated for a simple two-locus model as follows, assuming random mating within the population under study. Suppose that there is linkage disequilibrium between alleles D1 and D2 which have frequencies PD and qd at a disease locus D, and alleles A1 and A2 which have frequencies PA and qa at a nearby marker locus A. With a gametic disequilibrium coefficient of A, the conditional probability R of a D1 allele given that the gamete carries an A1 allele is PD + A/PA, and the conditional probability S of a D1 allele given that the gamete carries an A2 allele is PD - A/qA. The expected frequency of transmission of the A1 al-

4 McKeigue: Mapping of Genes in Recently Admixed Groups lele from heterozygous parents to affected offspring is the probability H that the A1 allele is transmitted, given that the parental genotype is A1A2 and the offspring is affected. If gi is the risk of disease in individuals who have i A1 alleles, then from the rules of conditional probability we have ~qa + PAg2 (1) qa9g + g1 + PA92 If fi is the penetrance of the D genotype with i D1 alleles, then, assuming random mating, we can express gi in terms of fi, R and S as where g2= R2U + 2RV + W g= RSU + (R + S)V+ W, go = S2U + 2SV + W U = f2-2fi + fo, V = fi - fo, and W = fo. In an additive model, there is a linear relationship between penetrance and the number of copies of the D1 allele, so that U = 0 (Kempthorne 1969). In a fully recessive model, one copy of the D1 allele has the same genotypic value as no copies, so that V = 0. In a fully dominant model, one copy of the D1 allele has the same genotypic value as two copies, so that U + V = 0. Substituting the expressions for g2, g1, and go into equation (1) above, we have PD(PD + A/PA)U + (2PD + A/PA)V + W (2) PD(2PD + A/PA - A/qA)U + (4PD + A/PA - AlqA)V + 2W This expression depends only on the frequency of the D1 allele, the frequency of the marker allele A1, the gametic disequilibrium coefficient, and the penetrance ratios f[2fo and fi/fo. Thus, the expected transmission frequency does not depend on whether the disease is rare or common. When PA = qa = 0.5, equation (2) simplifies to 'l = A(PDU + V) (3) U +2PDV+W For an additive model, U = 0 and the expression simplifies further to =DAV (4) 2PDV + W' 191 Application of the Transmission-Disequilibrium Test to a Recently Admixed Population Consider two populations X and Y, where the frequency PDY of a disease-predisposing allele D1 in population Y is higher than the frequency PDX of this allele in population X, so that the relative risk of disease in population Y compared with population X is r. For simplicity, we restrict the analysis to an endogamous group formed by the offspring of mixed unions between population X and population Y. As noted earlier, this is not an unrealistic situation. The frequency of the D1 allele in this equally admixed population will be PD = (PDX + PDY)/2 - Suppose we examine a nearby marker locus A where the frequency of the A1 allele is higher (PAY) in population Y than in population X (frequency PAX). In the gametes that give rise to the first generation of mixed descent, the gametic disequilibrium coefficient is A1 = (PAY - PAX)(PDY - PDX)/4. After a further n - 2 generations of random mating, the disequilibrium coefficient A, - 1 in the gametes that produce the (n - 1)th generation of mixed descent will be An-1= (1-20)(1-0) 3A 1 where 0 is the recombination fraction between the two loci. The usual relation Ai + 1 = (1-0)Ai does not apply between the first and second generations, because the alleles are not in Hardy-Weinberg equilibrium until the second generation. If a transmission-disequilibrium test is applied to these parents and their affected offspring in the nth generation of mixed descent, the disequilibrium coefficient An in the gametes from heterozygous parents that produce these offspring will be An = (1-20)2(1-0)n 11/4pAqA Again the usual relation Ai + 1 = (1-0)Ai does not apply, because the test is restricted to parents heterozygous at the marker locus. In the gametes that give rise to these heterozygous parents, the disequilibrium coefficient is 114PAqA times the coefficient in the general population. In the gametes produced by these heterozygous parents, the disequilibrium coefficient is (1-20) times the coefficient in the parents themselves. Substituting these expressions for PD, PA, and A into equation (2) above gives the expected frequency of transmission of the A1 allele to affected offspring in the admixed population.

5 192 In practice, we would try to choose marker loci where certain alleles occur only in population X, or only in population Y. The optimal strategy is to use information from several closely spaced flanking markers, where necessary, to assign the parental alleles at each locus to X by descent or Y by descent. The transmission-disequilibrium test will then use at each locus only those parents who have one allele X by descent and one allele Y by descent. This assignment of marker alleles to X by descent or Y by descent is equivalent to using a marker locus A where the frequency PAX of the A1 allele in population X is 0 and the frequency PAY in population Y is 1. In an equally admixed population, this will be equivalent to PA = qa= 0.5, and the gametic disequilibrium coefficient in the first generation of mixed descent will be given by A = (PDY - PDX)/4. In practice, we would have no idea of the likely difference between allele frequencies PDX and PDY, but from epidemiological studies we will have an estimate of the relative risk r of disease in population Y compared with population X. The relationship between PDX and PDY is then YU + 2PDYV + W = r(p2xu + 2PDXV + W). Solving for PDY and substituting the result into equation (3) yields a value of HI in terms of r, the relative risk in population Y compared with population X, the frequency PDX of the disease predisposing allele in the low-risk population, and the risk ratios [2/fo and fi/fo. This transmission probability represents the maximal effect detectable in an equally admixed population, where the marker locus is close to the disease locus and the ancestry of parental alleles at the marker locus can be assigned accurately. If the effect of the D1 allele is additive, U = 0 and the expressions for PD and A simplify to and PD = [(r + 1)PDX + (r - 1)W/2V]/2 A = (r - 1)(2PDX + W/V)/8. Substituting these values for PD and A into equation (4), we have n = (r ) (5) 4(r +1)(5 Thus, with an additive model, an equally admixed Am. J. Hum. Genet. 60: , 1997 population, and markers that allow ancestry of parental marker alleles to be assigned accurately, the probability of transmission (and hence the sample size required to detect linkage) depends only on r, the relative risk between the two populations accounted for by the locus. For a given value of r, the required sample size is independent of any other assumptions about allele frequencies or penetrance. Sample Size For a given type I and type II error, the required sample size can be calculated from the standard test of the null hypothesis that a binomial probability is 0.5. Where the specific objective of the study is to detect loci that account for higher disease rates in one of the two founding populations, it is appropriate to use a one-sided test. For instance, in a study of a population of mixed Indian and European descent, we would plan to detect loci where alleles Indian by descent are transmitted to diabetic offspring more often than expected by chance, but we would probably ignore any loci where there was an excess transmission to diabetic offspring of alleles European by descent. With a one-sided type I error probability a and type II error probability of A, the required sample size n for a transmission probability HI is given by [0.5Za +H/(1 - Hi)Z1 12 n = Hl -0.5 (6) For an initial search of the whole genome, it is reasonable to set a type I error probability that will often generate one or two false-positive results, because any regions that show evidence of linkage disequilibrium will be followed up in further studies to map the loci more precisely. The threshold value of a that will yield one expected false-positive result in a whole genome search with closely spaced markers can be calculated from the formula given by Lander and Kruglyak (1995), which uses the crossover rate p between the genotypes being compared. In a study of the grandchildren of mixed unions, the crossover rate is 1, and setting the value of a to will give one expected false-positive result in a whole-genome search. In studies of populations with a longer history of admixture, the crossover rate will be higher. This will give finer mapping resolution but increase the effective number of independent statistical tests so that a lower value of a will be required to keep the expected number of false-positive results down to one. The sample sizes given here are based on a requirement of 90% power (i.e., i = 0.1), and a one-sided a of (equivalent to one expected false-positive result in a study of the grandchildren of mixed unions).

6 McKeigue: Mapping of Genes in Recently Admixed Groups On the assumption of an additive model, 633 case-parent pairs are required to detect a locus that accounts for a relative risk of 2 between the two founding populations, 381 case-parent pairs are required to detect a locus that generates a relative risk of 2.5, and 279 case-parent pairs are required to detect a locus that generates a relative risk of 3. The effects of assuming either a fully recessive model (fi = fo) or a fully dominant model (f2 = ft), and varying the frequency PDX of the D1 allele in population X are shown in table 2. To account for a relative risk of 2 in population Y compared with population X, two alternative values for the genotype risk ratio f2/fo are assumed: 5 and 10. The value of PDX is then allowed to vary from zero to the maximum possible value compatible with a relative risk of 2 between the two populations. Assuming a fully recessive model rather than an additive model reduces the required sample size by a fraction that depends on PDX. In the most extreme case, in which the D1 allele is absent in population X (i.e., PDX = 0), the Table 2 Sample Size Required To Detect a Locus That Generates a Relative Risk of 2 in Population Y Compared with Population X No. OF CASE-PARENT PAIRS f2/fo = 5 f2/fo = 10 PDX A. Fully Recessive Model (fo = fl) B. Fully Dominant Model (ft = f2) NOTE. -f2, fl, and fo are penetrances of genotypes D1D1, DID2, and D2D2, respectively. PDX is frequency of Di allele in population X. Sample sizes are based on 90% power and one-sided P-value of For an additive model and a relative risk of 2, required sample size is 633 case-parent pairs, whatever the values of [2, fi, fo, and PDXrequired sample size is reduced by about one-third. Assuming a fully dominant model rather than an additive model increases the required sample size, but, even on the most unfavorable assumption (a frequency of PDX so high that PDY is close to unity), the required sample size does not increase by more than about one-third. The power of the admixture disequilibrium study design is thus remarkably robust, whatever the underlying genetic model. For comparison, we can examine the power of an affected sib-pair study designed to detect such a locus, using the method described by Risch and Zhang (1995) for calculating the power of a study using pairs of sibs who have been selected on the values of a trait. The following calculations are based on 90% power to detect a locus where an additive genetic model with f2/fo = 5 generates a relative risk of 2 between population Y and population X, with a type I error rate equivalent to one expected false-positive result in a whole genome search. In this situation the required sample size depends critically on the frequency of the D1 allele: if the D1 allele is rare (which is possible in population X) or occurs with high frequency (which is possible in population Y), tens of thousands of sib pairs are required. Even in the most favorable situation, where the D1 allele frequency is -0.25, >1,500 affected sib pairs would be required: this is -10 times the sample size required for the admixture disequilibrium study design. Allele-sharing designs have less statistical power than association studies because large risk ratios between genotypes at a disease locus generate only modest recurrence risk ratios in relatives: thus, for an additive genetic model with f2/fo = 5 and a frequency of 0.25 for the D1 allele, the recurrence risk ratio in siblings is only 1.2. Misclassification of allele ancestry at the marker locus would seriously weaken the power to detect linkage disequilibrium in a recently admixed population. Thus, if the ancestry of 10% of alleles is misclassified, the gametic disequilibrium coefficient would be reduced by -20% and the sample size required to detect a disease locus would be increased by 56%. It is thus a crucial requirement of this design to be able to classify accurately the alleles at each locus as X by descent or Y by descent. What Markers Should Be Used and at What Density? In contrast to allele-sharing studies, marker loci for linkage-disequilibrium mapping do not have to be highly polymorphic: RFLPs would be suitable. The objective is to be able to classify the two alleles at a parental locus as XX by descent, XY by descent, or YY by descent. The first step in identifying such markers would be to assemble a bank of samples from each founding population and to look for marker alleles that occur in only

7 194 one of the two populations. Pooling of DNA samples from each population would speed this. The genetic distance between West Africans and Europeans is large enough for this to be feasible: '-8% of RFLPs with two or more alleles in Europeans have only one allele in West Africans (Poloni et al. 1995). Grouping the alleles at several closely spaced marker loci into haplotypes would allow ancestry of genomic regions to be assigned, since most haplotypes will contain at least one allele unique to one of the two founding populations. Groups of closely spaced microsatellite markers could be used to define such haplotypes. An alternative method of generating markers suitable for assigning ancestry would be to use representational difference analysis (Lisitsyn and Wigler 1993). Using pooled DNA from a large sample of individuals from population X to drive hybridization against DNA from population Y would detect base sequences present in population Y but absent in population X. By restricting the sample from population Y to two or three individuals, the chance of detecting base sequences that are rare in population Y (and therefore less useful for assigning ancestry) would be minimized. The strength of this approach is that it could be applied when the genetic distance between the two founding populations is too small for ancestry of genomic regions to be assigned using currently available markers. If base sequences that can be used to define ancestry exist, representational difference analysis can be relied on to detect them. The disadvantage of using representational difference analysis is that the base sequences would have to be mapped before they could be used as markers. The distance required between markers (or between groups of closely spaced markers used to define haplotypes) depends on the number of generations since admixture. Equations (5) and (6) show that the required sample size is approximately proportional to the square of the gametic disequilibrium coefficient A. In the grandchildren of mixed unions, the coefficient A2 will be decreased by a factor of (1-20) from its initial value A1 in their parents. After n generations since the mixed unions occurred (n > 2), the gametic disequilibrium coefficient An between marker locus and disease locus in the offspring of heterozygous parents will be (1-20)2(1-9)n - 3A1. Figure 1 shows the decay of the gametic disequilibrium coefficient A as a function of the distance from marker to disease locus and the number of generations since admixture. In the second and third generations of mixed descent, marker spacing of 10 cm will ensure that there is at least one marker locus at which A is within 20% of its initial value. In a population such as Anglo-Indians, where the main admixture occurred -10 generations ago (Younger 1987), marker spacing of o-4 cm would be necessary to ensure that the value of A was within 20% of its initial value. Interval E 0D._,l)._ _ 4- C 0 U- Al 1 Am. J. Hum. Genet. 60: , 1997 / /. ~~/ /.~ /: ///.1, I' / I-, / \,. \ IN, A2 A3 A5 A'-A Map distance (cm) from marker to disease locus Figure 1 Decay of gametic disequilibrium coefficient from its initial value as a function of distance between marker and disease locus and the number of generations since admixture. Al is the coefficient of disequilibrium in the gametes that produce the first generation of mixed descent, and A2, A3, A5, and Ajo are the coefficients of disequilibrium in the gametes from heterozygous parents that produce the 2d, 3d, 5th, and 10th generations of mixed descent. mapping techniques could maximize the information obtained at a given spacing of markers. Discussion In contrast to allele-sharing studies, which detect loci that contribute to familial aggregation of disease risk within populations, linkage-disequilibrium mapping in recently admixed populations would specifically detect the loci of genes that underlie ethnic differences in disease risk. One strength of the admixture disequilibrium mapping approach is that it is usually possible to assemble a sample in which several traits can be examined simultaneously. For instance, many populations with high rates of non-insulin-dependent diabetes also have high rates of hypertension and obesity. In an admixed population cases with more than one of these conditions are easy to find. The statistical analysis can then test for linkage disequilibrium with each condition separately, or with a combination of conditions such as diabetes and hypertension, which are likely to share genetic influences. With an allele-sharing design, the practical problems of identifying sib pairs affected with the same combination of conditions makes this more difficult. In the first generation of mixed descent, all individuals will have one allele X by descent and one allele Y by descent: all parents in this generation can therefore be included in a test of unequal transmission of alleles X by descent and Y by descent to affected offspring, pro- ""

8 McKeigue: Mapping of Genes in Recently Admixed Groups 195 vided that the ancestry of their alleles can be assigned accurately. In these first generation offspring of mixed unions it is sufficient to be able to identify one of the two alleles at each locus as X or Y by descent, because the ancestry of the other allele is then assigned by default. In subsequent generations where Hardy-Weinberg equilibrium is reached, only half the parents (in an equally admixed population) will have one allele X by descent and one allele Y by descent at any given locus. Thus, studying cases who are the grandchildren of mixed unions, rather than subsequent generations, not only maximizes the distances over which linkage disequilibrium can be detected but also doubles the effective sample size (number of heterozygous parents) obtained from a given number of affected offspring. The optimal design is therefore to conduct an initial study with the affected grandchildren of mixed unions and their parents. Regions of the genome that show evidence of linkage disequilibrium in such an initial study can then be examined in detail in a population with a longer history of admixture, which allows the disease loci to be mapped more accurately. Although the statistical power calculations in this paper are based on assuming random mating within an equally admixed population, the study design is valid even if there is nonrandom mating and unequal admixture between the two populations. For instance, cases who have one parent from population X and one parent who is the offspring of an XY union could be included, although such cases will contribute less information than those who have two parents of mixed descent. Admixture results in gametic disequilibrium between alleles at any pair of loci where the allele frequencies in the two founding populations are different, whether or not these loci are linked. With random mating, this gametic disequilibrium decays by a factor of (1-0) in each generation. If the loci are unlinked (O = 0.5), gametic disequilibrium will be halved in each generation. Thus, when admixture has occurred within the last two or three generations, disequilibrium between unlinked genes will be present, and population-based association studies cannot yield unequivocal evidence of linkage. The basis of the transmission-disequilibrium test's ability to eliminate disequilibrium between unlinked genes is that it uses information from heterozygous parents only. As noted earlier, when the parents are heterozygous at the marker locus, gametic disequilibrium decays by a factor of (1-20) in a single generation; when 0 = 0.5, the disequilibrium in the gametes produced by heterozygous parents is zero. Excess transmission of a marker allele from heterozygous parents to affected offspring is thus unequivocal evidence of linkage between the marker and an allele influencing susceptibility, even in a recently admixed population where stratification, nonrandom mating, and disequilibrium between alleles at unlinked loci are present (Ewens and Spielman 1995). Where parents are not available, as with diseases that affect mainly older adults, parental genotypes can be inferred from the genotypes of cases' sibs. The transmission-disequilibrium test is equivalent to analyzing a matched-pair case-control study in which the cases are the transmitted alleles, the controls are the untransmitted alleles, the exposure is the allele type, and each case is matched to a control within a stratum defined by the affected offspring-parent pair. As in a matched case-control study, conditional logistic regression (Breslow and Day 1980) can be used for the analysis, instead of a simple binomial proportion test; it is thus possible to test for gene-environment interactions, if covariates have been measured on the cases. Where suitable admixed populations exist, the main technical problem in undertaking a linkage-disequilibrium study is to assemble a set of markers from which ancestry of alleles can be accurately assigned to one of the two founding populations. It remains to be established whether the most efficient means of defining such markers is by haplotyping based on known microsatellite markers or by using representational difference analysis to detect base sequences unique to one of the two founding populations. If suitable markers can be identified, this analysis shows that linkage-disequilibrium mapping in recently admixed populations has much greater power than allele-sharing designs to detect loci contributing to ethnic differences in disease rates. With realistic sample sizes it is possible to detect loci that would account for one-third to one-half of the observed ethnic differences in prevalence of conditions such as hypertension, non-insulin-dependent diabetes, or obesity. Acknowledgments I am grateful to Tim Aitman and Steve Bennett for discussion and comments. References Breslow NE, Day NE (1980) Statistical methods in cancer research. Vol 1: The analysis of case-control studies. International Agency for Research on Cancer, Lyon, pp Chakraborty R, Ferrell RE, Stern MP, Haffner SM, Hazuda HP, Rosenthal M (1986) Relationship of prevalence of noninsulin-dependent diabetes mellitus to Amerindian admixture in the Mexican Americans of San Antonio, Texas. 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