Introduction

Genetic studies in founder populations have led to many successes in the identification of the mutations responsible for various rare monogenic diseases. Efficient linkage disequilibrium mapping strategies have been designed to take full advantage of the existence of unique founder mutations introduced only once in the populations and thus shared by virtually all the affected individuals. Indeed, the existence of founder mutations for rare mendelian diseases has been described in a wide range of populations, spanning from small strongly inbred isolates to much larger populations founded by a few thousand individuals, a few centuries ago. Heutink and Oostra1 have proposed to classify founder populations according to the number of generations since their foundation – very old isolates (>100 generations), young isolates (<100 generations) and very young isolates (<20 generations) – arguing that the older the populations, the better they are for localizing the mutation. The number of founders and the growth pattern of the population also have crucial consequences on genetic characteristics.

The genetic factors involved in complex diseases are alleles that are neither necessary nor sufficient for disease expression but that increase the risk, in often rather modest proportions and through complex interactions with many other genetic and environmental risk factors. The question as to whether these alleles are likely to be frequent or not is still open. Recent examples of both very frequent2 and rare susceptibility alleles3 have been described for various diseases. However, the frequencies are always higher than those for rare monogenic mutations. Further, in the case of relatively rare alleles, they are not present in all the affected individuals but only in a small subset. This change in characteristics of the genetic factors under study has called for the development of new mapping methods based either on linkage or/and on association information.

As in the case of outbred populations, the genetic study of complex traits in isolated populations requires a change in methodology compared with monogenic disease studies. Indeed, the probability of observing a founder allele, introduced only once in the population, when considering a common susceptibility allele, is likely to be negligible. Methodologies relying on that assumption are thus inappropriate. However, isolated populations may still present interesting features with regard to complex trait mapping. Environmental risk factors are generally more uniform in isolated populations than in large outbred populations and thus the genetic effects may be easier to identify in the former. Greater genetic homogeneity is also expected in these populations because of the limited number of founders (and thus a limited gene pool) and because of the absence of migration, which virtually rules out the risk of unidentified population stratification. Furthermore, the availability of extensive genealogical records can provide large genealogies, potentially very informative for linkage analysis. Finally, linkage disequilibrium may extend over larger regions than in outbred populations, increasing the power of association study for gene detection. We note that whereas these populations are alternatively described as ‘founder’ or ‘isolated’, the choice of ‘isolated populations’ better reflects the properties likely to be useful for complex trait mapping.

We do not intend to discuss whether isolated populations are the ‘El Dorado’ of genetic studies in this paper, many authors have discussed this issue before.1, 4, 5, 6, 7 As the number of genetic studies in isolated population is rapidly increasing and because the first successes are beginning to appear, we instead propose to review and discuss the statistical methods available for complex trait mapping in isolated populations, their advantages and their limitations.

Apart from their isolation, a key characteristic of these populations in terms of methodology is that, contrary to outbred populations, the probability for two random individuals to be related is not negligible. Further, inbreeding might also be present. In this case, not only are two individuals potentially correlated but the two alleles in a random individual may also be correlated. The existence of inter- and intra-individual correlations has important consequences on most mapping methods. In particular, the distinction between linkage information and association information might become tricky. We first review the methods for linkage studies of qualitative and quantitative traits and then focus on association studies. We show how classical methods might not be valid in isolated populations and present both the different strategies available to correct existing methods as well as the new methods specifically developed to make use of some particular properties of isolated populations. We separate the different methods depending on the extent of genealogical information available. We would like to note that the problem of correlations existing among random individuals is not specific to isolated populations but also concerns studies of extended genealogies in outbred populations. The problems and methods discussed in the present paper may thus be of a more general interest to human geneticists.

Linkage analysis

Qualitative traits

Linkage analysis allows a comprehensive scan of the entire genome for disease genes in a hypothesis-independent manner.8 It looks for shared segments of DNA among related patients that exceed the amount expected on the basis of their relationship pattern. In large outbred populations, this is usually performed on samples of independent affected sib-pairs. In isolated populations, affected sib-pairs are often not independent but related to an extent that depends on the demography of the population. Moreover, affected siblings and their parents may be inbred, resulting in an excess of shared segments of DNA on the entire genome as compared to what is expected in the absence of inbreeding. Not accounting for this increase in the expected sharing probability when performing a linkage test on inbred sib-pairs enhances the risk of falsely concluding linkage with a given region of the genome as shown by Génin et al9 in the situation where parents are not typed, and by Leutenegger et al10 in more general situations. Specific allele-sharing statistics have been proposed by McPeek11 for inbred pairs.

When genealogical data are available, one can use them to trace back the relationships between the different affected individuals and perform linkage analysis on extended pedigrees. The approach has in particular been very fruitful in Iceland where the strategy of using general families that extended beyond the nuclear family has led to the detection of significant linkage for a number of complex diseases.12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24 If additional replications of these findings in other populations are still required for validation, the success of this genealogical approach may be a consequence of the population history of Iceland, as explained by Gulcher et al.8 However, both the important sample sizes available in the different studies and the high density of markers used in the genome scans are certainly other key parameters of the success. We note that the genealogies used in these Icelandic studies are not extremely large. Affected individuals are related at five meioses at most (eg they are first or second cousins). One may then wonder whether going back further in the past is of additional usefulness in linkage analysis. Indeed the chance that affected individuals within the same pedigree share genetic risk factors identical by descent decreases rapidly when the relationship between these individuals becomes more remote and this is especially true for common risk factors. Even in the case of a simple dominant disease segregating in a pedigree, the evidence of linkage provided by a pair of distant affected relatives first increases with decreasing values of the kinship coefficient, reaches a maximum that depends on marker allele frequencies and then decreases.25 Further, pedigree complexity and inbreeding loops greatly increase the computational burden of linkage analysis and the different computer programs available are limited in terms of number of individuals to include in a single pedigree. Programs using exact multipoint estimation of identity by descent (IBD), where information provided by neighbouring markers is used to better estimate the IBD sharing at a given marker, such as Allegro,26 require 2N−F to be less than 26, where F and N represent the number of founders and nonfounders in the pedigree, respectively. Programs using Monte Carlo Markov Chain (MCMC) approaches to IBD estimation, such as Simwalk2,27 can analyse larger pedigrees but are also limited. Pedigrees and inbreeding loops have thus often to be broken into smaller units. Such breaking should be performed very carefully to minimize false specification of expected sharing probabilities and possibilities of spurious linkage detection.

When genealogical data are neither available nor reliable, one may opt for a strategy that consists in contrasting the observed sharing between pairs of affected relatives to the sharing observed over the whole genome. Indeed, genomic data can be used to estimate the separation distance between two affected individuals28, 29, 30, 31, 32 or the inbreeding coefficient of an individual.33

Quantitative traits

In the context of quantitative trait linkage analysis, variance component (VC) approaches are used on relatively large pedigrees. Briefly, the principle of VC is to consider that a phenotypic trait, Y, can be decomposed into the addition of a fixed effect, one (or several) quantitative trait locus (QTL) random effect(s) and an environmental random effect. Both the QTL and environmental effects are expected to have normal distributions with mean 0 and standard deviation, respectively, σg and σe. Assuming that the trait Y is approximately normally distributed in the population, it is possible to write the joint likelihood of a sample and test the existence of a QTL around the studied marker(s) by rejecting the null hypothesis σg2=0 (no linkage), using for example, a likelihood ratio test (LRT). To write the likelihood, the covariance between any pair of individuals in the sample must be available, which, in turn, requires the characterization of the IBD sharing for all the pairs in the sample. If exact multipoint IBD sharing estimation is limited to moderate-sized pedigrees as already noted for qualitative traits, approximate methods, such as correlation-based34 or MCMC35 algorithms, allow to use VC for much larger pedigrees. An illustration of the use of VC in isolated populations is the work of Williams-Blangero et al,36 who have conducted a linkage analysis on susceptibility to Ascaris infection (a roundworm) based on a 444-member pedigree from the Jirels, an isolated Nepalese population. Individuals were selected based only on pedigree informativeness and not with respect to Ascaris phenotype. Owing to a non-normal distribution of the trait, even after transformation, a robust test37 was chosen and P-values were validated using simulations. A total of 6209 pairs of relatives were informative for the analysis and allowed the detection of two QTLs, one on chromosome 1 and the other on chromosome 13. In inbred pedigrees, additional components of the variance are required to fully describe even simple models. Estimation of these components relies on the calculation of additional identity coefficients between the pairs of relatives, a task that can seriously increase the computational burden. However, as shown by Abney et al,38 given the low power to estimate these additional VCs, even in inbred samples, neglecting them in the analyses should not impact the power to detect linkage. Finally, VC approaches are not robust to departures from normality.39 When such a departure is due to a selective sampling (the trait is normal in the population but not in the selected sample), the regression-based method proposed by Sham et al40 and implemented in the software MERLIN-REGRESS is an interesting alternative available for pedigree data.

In extremely large and complex pedigrees, these methods may be computationally infeasible, especially in the context of genome screens. While analysing the Hutterite pedigree (see Table 2 for a brief description of the Hutterites) with a MCMC method for IBD-sharing estimation, Chapman et al41 had to break it into subpedigrees. As discussed for the qualitative traits, reducing pedigree complexity may entail a loss of power. Dyer et al42 showed how breaking a 1544 individual Hutterite pedigree into three subpedigrees, divided by 2 the relative efficiency to detect a QTL responsible for 20% of the phenotypic variance of a quantitative trait with a total heritability of 50%. However, these authors did not study the sensitivity of this result to the genetic model considered for the QTL. Recently, Falchi et al43 proposed a new systematic method for pedigree breaking that maximizes useful information for linkage while minimizing the burden in IBD calculation. They show that the loss of power when using subpedigrees depends on the genetic model.

Abney et al44 have proposed a regression-based linkage method for quantitative traits in complex and inbred pedigrees. The method relies on the existence of regions that are homozygous by descent (HBD, the two homologous regions are both copies of the same ancestral region) in inbred individuals, to detect QTLs that act recessively. HBD sharing is estimated using multipoint marker information and the complete pedigree information. Excess HBD sharing is expected for markers linked to QTLs acting recessively. The trait is regressed on different covariates including the HBD status. The test is equivalent to a t-test for the coefficient of the HBD covariate, corrected exactly for the known correlations among the individuals computed using the pedigree information. Abney et al44 also proposed a permutation test to correct for multiple testing over the genome that preserves the correlation structure of the data. Indeed, for permutation tests to be valid, the elements to be permuted must be exchangeable, which is not the case when individuals are related. In the VC context, Iturria et al45 have attempted to solve a similar problem by approximately maintaining the familial correlation structure. The procedure of Abney et al44 maintains this correlation structure in an exact manner provided that the genealogy is correctly specified and the trait under study has a multivariate normal distribution. This permutation procedure is extendable to a wide set of methods relying on similar linear models for the data, including VC approaches.

Association studies

Whereas linkage studies yield relatively broad locations for susceptibility loci, association studies may be used to test the role of particular candidate genes. As they are sensitive to ignored population substructures, case–control studies in outbred populations are used very cautiously and family-based association tests are often preferred to avoid the detection of spurious association. Yet, in the absence of population stratification, case–control tests are more powerful. They may thus regain interest in isolated populations.

Possible bias

Two tests are classically used to test for association, the case–control allele-based (CC-χ2allelle) and the case–control genotype-based (CC-χ2genotype) χ2 tests, which contrast allele or genotype frequencies between a sample of cases and a sample of controls. Under the null hypothesis of no association, CC-χ2allelle and CC-χ2genotype follow a χ2 distribution. However, for this null distribution to be valid, the cases and the controls must be independent, which might not be true in isolated populations. Bourgain et al46 have illustrated the increase of type I error (probability of detecting an association when there is no association) of the CC-χ2allelle test in samples drawn from the Hutterite population. Table 1 shows similar results for the CC-χ2allelle and CC-χ2genotype in two different samples: the highly inbred Hutterite sample and a non inbred sample of related cases and controls from the GAW12-simulated genealogies (see Box 1 for a brief description of the two data sets). When the probability to detect a false association is fixed at 5%, it is in fact greater than 10%, in both inbred (Hutterites) and noninbred samples (GAW12) with related individuals. Newman et al47 have illustrated the same problem in the case of quantitative trait analysis in Hutterite samples. Considering phenotypes such as IgE level, LDL or BMI and regressing the trait on age, sex and genotype, these authors showed how ignoring the pedigree structure increases the type I error by a factor of 10–20 (they observed an empirical type I error of 10–22% for a nominal type I error of 1%). Génin and Clerget-Darpoux48 focused on the problem of inbreeding in samples of independent individuals. When cases and controls are not correctly matched on the basis of inbreeding, the type I error of the CC-χ2genotype is modestly inflated. However, when cases and controls are correctly matched for inbreeding, inbreeding can increase the power of the test, especially for recessive or quasi-recessive disease susceptibility factors.

Table 1 Empirical type I error of the CC-χ2genotype, CC-χ2allele, CC-QLS and CC-corrχ2 tests using either the χ2 distribution or a resampling procedure to get significance. Nominal type I error is 5%
Full size table
Table 2 Box 1
Full size table

Caution with permutation procedures to assess significance

To perform valid tests, one might consider using classical test statistics and get accurate P-values by permutation strategies. However, as already outlined in the context of linkage analysis, existing correlations among individuals must be maintained when conducting a permutation procedure. In particular, the classical permutation test for qualitative traits, where statuses are randomly reassigned to genotypes to create dummy ‘null case control samples’ on which the statistic is computed (the permutation being repeated a large number of times to get the distribution of the statistic when there is no allele frequency difference between cases and controls), might not be valid. As an illustration, we present in Table 1 the type I error of this permutation strategy for the CC-χ2allele and CC-χ2genotype tests, in the Hutterite and GAW12 samples. Empirical type I errors are much larger than the expected 5%, demonstrating that such permutation strategies do not protect against spurious conclusions. The different solutions for performing valid tests of association depend on the amount of genealogical information available. We start by presenting the methods usable in the absence of genealogical information and end with methods that require the knowledge of the entire pedigree.

Genomic controls

Devlin and Roeder49 proposed the use of genomic controls (GC) to prevent from spurious signal detection in association studies. The primary concern of these authors was to control for population stratification, but they also recognized the impact of what they called ‘cryptic relatedness’ (unrecognized relationship among some individuals in the sample) on association studies. The general principle of GC approaches relies on the demonstration by Devlin and Roeder,49 that the effects of cryptic relatedness and population substructure on test statistics of interest are essentially constant across the genome, under certain conditions, and do not vary with individual locus properties (number of alleles, allele frequencies). Consequently, the test statistic inflation due to cryptic relatedness is the same for all markers throughout the genome. These authors suggested the use of null markers (eg, polymorphisms unlikely to affect susceptibility) across the genome to estimate the effects of confounding and to remove these effects from the association test statistics. In practice, when there is no association between the marker and the disease but cryptic relatedness is present, the CC-χ2allele statistic follows a χ2 distribution multiplied by a scaling factor λ. λ is constant over the genome and only depends on the relationship between all the individuals of the sample. λ is estimated using a robust estimator based on the median49 value or on the mean value50 of the CC-χ2allele statistics over all the control markers. Bacanu et al51 suggested that 70 markers should be used for a good estimation of λ. In their original paper, Devlin and Roeder proposed the GC approach for the Armitage's trend test,52, 53 a genotype-based association test that is robust to departure from HW but makes the assumption of additive effects for the two alleles of an individual. However, the GC principle is applicable to a wide class of statistics for marker association testing. Tzeng et al54 have recently proposed a method using GC in haplotype-based case–control analysis.

In 2002, Bacanu et al55 adapted GC for association studies of quantitative traits, using linear regression. A phenotypic trait is regressed on different environmental covariates and on one or several genotype covariates with possible interactions terms. Testing for association reduces to test whether the regression coefficients for the genotype covariates are significantly different from 0 using a t-test. As for the qualitative traits, Bacanu et al55 have shown that the inflation factor of the t-test, λ, due to population substructure or cryptic relatedness, only depends on the sample composition and not on the properties of the individual loci. λ can be estimated, as in the qualitative trait, using a robust estimator based on the median value of the t-test over all the control markers. The same principle can be used while simultaneously testing the effect of multiple loci with F-statistics.

TDT and related approaches

When parents are available, family-based association tests such as the TDT56 may also be considered though Spielman and Ewens57 underlined that the TDT is not a valid test of association if the families have affected members in multiple generations. Génin et al58 extended this result to samples of independent case–parent trios where cases or parents are inbred. However, the TDT remains a valid test for linkage and its power increases with the strength of association. To overcome the problem of meiose dependence that can arise when related affected are analysed simultaneously, different extensions of the TDT have been proposed, where an empirical robust variance is computed (see Clayton59 for the case of multiple affected sibs or Lake et al60 in more general situations such as pedigrees including multiple nuclear families). The FBAT software60, 61, 62 implements this latter approach and allows the inclusion of any type of family. The PDT63 is based on a similar strategy, but only considers two types of informative families (trios with an affected child and both parents genotyped and discordant sibships of at least one affected and one unaffected sib with different genotypes) and discards others even though they could bring additional information. This robust variance approach does not require the knowledge of the precise genealogical links between the individuals. However, when all the affected individuals in a sample are correlated within a single pedigree (as it is the case for instance with the Hutterite pedigree) and declared as such, the robust variance approach has virtually no power. Large pedigrees must thus be broken into smaller subpedigrees to use this approach. Neglecting the correlations between the different subpedigrees should not introduce a detectable bias in the test provided that most parent genotypes are available. This still needs to be demonstrated and the optimal breaking strategy remains to be defined.

Different extensions of the TDT have been proposed for haplotypes analyses where multiple linked loci are considered simultaneously. Apart from the problem of ambiguities in haplotypes assignments (see, for instance, Clayton64 or Zhao et al65), haplotypes analyses pose a multiple-testing problem that can be solved as in Clayton and Jones,59 who propose to test the global null hypothesis that all haplotype effects are 0. However, if the number H of haplotypes is large, this test may lack power as the number of degrees of freedom is H−1 and Clayton and Jones59 proposed to group haplotypes based on a similarity index defined as the length, around a focal point, of the continuous region over which haplotypes are identical by state. Bourgain et al66 proposed another approach, the Maximum Identity Length Contrast (MILC), which compares the mean lengths of haplotype identity among all transmitted haplotypes and among all nontransmitted haplotypes. More recently, Seltman et al67 proposed a grouping of haplotype based on their phylogeny and Zhang et al68 generalized the MILC approach. The impact of including related cases has only been evaluated in the context of MILC,69 where the authors have shown that closely related cases may be analysed simultaneously provided that one is not the parent of another. Indeed the null hypothesis tested by MILC is the absence of any genetic risk factor involved in the disease in the studied region and not a composite null hypothesis of no association or no linkage as for the TDT or related family-based association tests.

To our knowledge, there is no systematic power comparison of the TDT (or related approaches) and the GC tests in the context of cryptic relatedness. Bacanu et al51 extensively compare the two approaches for qualitative traits, in the presence of population stratification. They show that GC performs better than the TDT as long as the scenario is different from ‘a few highly differentiated subpopulations’. For the case of cryptic relatedness, they only note that the GC adjustment when notable levels of kinship are present in the sample has a substantial cost in power, because λ can become quite large. They suggest that family-based methods are likely to be more powerful in such situations. However, the need for genotype information on family members, such as parents or sibs, for the TDT to be most powerful, can drastically reduce the number of cases eligible for a study, a concern that may be particularly relevant for late-onset diseases. By allowing the recruitment of larger samples, case–control strategies may thus prove to be more efficient.

Association tests when the entire genealogy is available

When the genealogy is entirely known, it is preferable to use this information. Bourgain et al46 have recently proposed two methods for case–control association studies, suitable for any set of related individuals, provided that their genealogy is known: the case–control quasi-likelihood score test (CC-QLS) and the case–control corrected χ2 test (CC-corrχ2). The methods are suitable for large inbred pedigrees. The principle of the CC-corrχ2 is similar to GC as it consists in the computation of a correction factor, λ, for the CC-χ2allele test. The difference is that the value of λ is derived analytically using the extensive pedigree information. Bourgain et al46 showed that λ depends only on the values of all the kinship and inbreeding coefficients of the individuals included in the sample. CC-QLS and CC-corrχ2 have similar forms, but the CC-QLS actually compares allele frequencies in cases and controls estimated while taking into account the known correlations among the individuals, whereas CC-corrχ2 compares allele frequencies estimated by simply counting the number of alleles in each group. Bourgain et al46 showed that CC-QLS is asymptotically locally more powerful than CC-corrχ2. We present in Table 1 the empirical type I errors of these tests in the Hutterite and GAW12 samples. They are not significantly different from the nominal type I errors, showing that these tests correctly control for the presence of correlations among the individuals in the samples, provided that genealogical data are exhaustive. No power comparison of these latter approaches with GC has been published yet. However, when extensive genealogical information is available, exact computation of the correction factor as in CC-QLS or CC-corrχ2 should be more powerful. A test similar to CC-corrχ2 was used by Gretarsdottir et al14 and Styrkarsdottir et al17 in the Icelandic population.

Abney et al44 have proposed two different methods to test for association of quantitative traits in samples with known genealogy using the linear regression framework. Here again, the method roughly corresponds to an exact derivation of the inflation factor λ of the t-test described in Bacanu et al55 instead of an estimation through control markers as in the case of GC. More specifically, Abney et al proposed the ‘allele-specific HBD’ method (ASHBD) and the ‘general two-allele model’ method (GTAM). The ASHBD uses the same framework as the HBD linkage method described above, but models the effect of a particular allele rather than the effect of a main locus. The method also uses multipoint marker information to estimate the HBD status. Both inbreeding and a recessive effect of the allele at the locus tested are required for the ASHBD method to be of interest. GTAM is a single point method suitable for general genetic models and for inbred or outbred pedigrees. The model does not include an HBD status covariate but a covariate, indicating the number of alleles of a particular type at the locus tested and a second covariate modeling the genotypic effect. To test whether these two covariates have regression coefficients significantly different from zero, the method corresponds to an F-test corrected exactly for the known correlations among the individuals. The permutation procedure proposed to correct the HBD linkage test for multiple testing over the genome is also applicable to both the ASHBD and GTAM tests.

Conclusion

In reviewing the literature on isolated populations, the number of papers praising their merits for mapping genes involved in complex disease susceptibility is impressive. But it is also striking to note the lack of discussion about the need for specific statistical methods to correctly and best search for genetic risk factors in these populations. The review of the statistical methods, presented in this study, is not intended to be exhaustive. We only tried to present some of the available methods, their advantages and limits, for both linkage and association studies, and considering qualitative and quantitative complex traits. Our intention was to highlight the fact that if the features of population isolates may facilitate the identification of susceptibility factors for complex traits, these studies deserve particular care in the choice and design of statistical methods. To illustrate how the use of methods designed for outbred samples could lead to false conclusions when applied to isolated populations, we considered two extreme examples: a highly inbred isolate (the Hutterites) and data from noninbred extended genealogies where all the affected individuals were considered, including first- and second-degree relatives. As shown by Grettarsdottir et al,14 removing first- and second-degree relatives from the sample minimizes the bias in noninbred samples. However, since the number of cases may be limited in relatively small isolates, using methods allowing for an inclusion of all cases can be crucial.

Depending on whether extended genealogies are available or not, the methods that can be used differ. When the entire genealogy of the population is available, as it is the case in the Hutterite population, methods that take advantage of this information to characterize the correlations existing between the individuals and to account for them in the tests should obviously be preferred. When genealogies are not known or not accurate, then one may opt for methods that contrast what is observed at a given marker to what is observed on average over the whole genome. These GC approaches require additional genotyping of markers, but are probably a good alternative to extensive genealogical studies.