Evidence Against Linkage of Familial Combined Hyperlipidemia to the Apolipoprotein AI-CIII-AIV Gene Complex

	Abstract

Top Abstract Introduction Methods Results Discussion APPENDIX I APPENDIX II References

Key Words: familial combined hyperlipidemia • linkage analysis • apolipoproteins • complex traits

	Introduction

Top Abstract Introduction Methods Results Discussion APPENDIX I APPENDIX II References

 
Familial combined hyperlipidemia (FCHL) is a common inherited disorder estimated to cause approximately 10% of premature coronary heart disease.^{1 2} The original description of the disorder was characterized by the presence of elevated levels of plasma TC and TG or both in members of the same family.¹ The diagnosis of FCHL required, in addition to diagnosis of elevated TC or TG levels in the affected proband, the diagnosis of elevated levels of either TC or TG in at least one first-degree relative of the proband such that both lipid levels are elevated among members in the same family.¹ Subsequent studies also demonstrated increased level of apolipoprotein B (apoB) in families with FCHL.³ Although a dominant mode of inheritance was originally proposed,¹ the genetic, biochemical, and molecular basis of this disorder remains unknown. More recent complex segregation analyses also suggest that the mode of inheritance of apoB levels^{8 9} and of the bivariate distribution of TC and TG¹⁰ may be more complex than originally proposed, and thus the mode of inheritance of FCHL remains unresolved.

There is strong evidence to suggest that FCHL is caused by multiple genetic factors. For example, 1 of 20 FCHL patients recently examined had a mutation in the promoter of the LPL gene,¹¹ and most heterozygous parents of patients who are homozygous for the recessive disorder LPL deficiency have a lipid phenotype resembling that of mild FCHL.¹² However, this recessive disorder, with an estimated gene frequency of 0.1% and carrier frequency of 0.2%, is too rare to fully account for the estimated prevalence of 0.5% to 2% for FCHL.^{1 6} Two other loci that may also play a role in some FCHL families are the putative dominant locus suggested by complex segregation analysis of the small dense LDL phenotype^{13 14} and the codominant locus suggested by complex segregation analysis of apoB levels.¹⁵ A fourth locus that could also account for some cases of FCHL is a gene in the apolipoprotein AI-CIII-AIV gene cluster because transgenic mice with the human apo-CIII gene (APOCIII) develop hypertriglyceridemia,¹⁶ and a single nucleotide substitution in APOCIII is associated with hypertriglyceridemia in an Arab population.¹⁷ Support for a gene contributing to FCHL in the AI-CIII-AIV gene cluster is also suggested by reports of a positive association between FCHL and a 6.6-kb XmnI allele (the X2 allele) near the apo-AI gene,¹⁸ as well as by an association between FCHL and alleles in APOCIII.²⁰

The report of genetic linkage between FCHL and the apolipoprotein AI-CIII-AIV gene cluster on chromosome 11q23-q24 in a data set of seven small three-generation pedigrees¹⁹ is therefore of considerable interest. If FCHL is truly linked to this region, this finding could confirm the originally proposed dominant mode of inheritance, would identify a probable gene or set of genes responsible for the phenotype, and would provide the basis for genetic studies directed toward understanding the underlying biochemical basis of the disease. Three provisos need to be noted, however. First, confirmation of these results is important before dedication of resources toward biochemical or metabolic studies of this region. This is particularly important for a complex trait such as FCHL as confirmation of positive linkage results for such traits is not always easy to obtain. Second, in the study of Wojciechowski et al,¹⁹ only those pedigrees in which the affected proband carried the XmnI X2 allele in the genotype were used. Because this allele was positively associated with FCHL, the question of whether there is linkage to this region in families in which the proband does not carry this allele remains open. Positive or negative evidence of linkage in a separate set of families irrespective of the XmnI genotype would be important. Third, a recent study reported evidence against linkage of FCHL to this region.²¹ Unfortunately, the analyses used in this report did not account for reduced penetrance, sporadic cases, or other difficulties inherent in analysis of this complex trait. In principle it would have been possible to take such complexities into account with, for example, a full likelihood-based model; thus, the results must be interpreted with care until a more complete analysis can be performed.

The evidence for linkage of FCHL to the AI-CIII-AIV region must be viewed with caution. Attempts to map genes involved in complex diseases have demonstrated that confirmation is frequently difficult,²² unlike confirmation of results for traits with an established Mendelian mode of inheritance.^{23 24} In some recent studies of complex diseases, evidence for linkage has declined or disappeared when pedigrees giving initial evidence of linkage are extended,^{25 26} indicating that genetic heterogeneity is not always an explanation for the discrepancies among studies. It is therefore important to determine whether there is evidence for linkage of FCHL to the AI-CIII-AIV region in independent sets of pedigrees. We present here the results of such a linkage analysis with a highly polymorphic marker in the apolipoprotein CIII gene for a set of three large, well-characterized families.

	Methods

Top Abstract Introduction Methods Results Discussion APPENDIX I APPENDIX II References

 
Pedigrees
Three large pedigrees, previously ascertained for the study of severe hypertriglyceridemia,²⁷ were used in the current study. Individuals in the families of both parents of each proband had lipid levels characteristic of FCHL. Pedigrees of probands were extended to third-degree relatives (more than 6 years of age) of the proband, and the three largest pedigrees from the original nine that met the definition of FCHL were selected for further studies. As defined, such pedigrees were those in which at least one first-degree relative of the proband also had elevated TC or TG levels (above the 95th percentile), and in which both lipid levels were elevated in each pedigree. Although relationships among individuals in the extended pedigrees were available for all nine FCHL pedigrees in this earlier study, relatives more distant than first-degree relatives of probands were only sampled for the three pedigrees that had been selected for further study, so that lipid levels were only available for the members of the extended pedigrees of these three large pedigrees. It also should be noted that because of the definition of the phenotype, pedigree ascertainment followed a multiplex ascertainment scheme. Later follow-up identified additional fourth-degree relatives of the proband who had reached adulthood since the original study. Family 428 was ascertained through a proband (Fig 1, III-1) who had severe hypertriglyceridemia (TG levels >1000 mmol/L) and pancreatitis during pregnancy, was the niece of a survivor of a myocardial infarction, and was a participant in a separate study. Pedigrees 2100 and 2103 were ascertained through probands (Fig 1, III-20 and III-14, respectively) with very high TG levels exceeding 2000 mmol/L.²⁷ The size of the three pedigrees used in the linkage analysis was 54, 49, and 80 individuals for families 428, 2103, and 2100, respectively. DNA samples were available for 39, 27, and 64 individuals, and lipids were measured in 44, 43, and 67 individuals, respectively. All individuals for whom DNA samples were available had lipid measurements, but DNA samples were not available on all individuals for whom lipid measurements were available. Four individuals were on lipid-lowering medications (see Appendix I), but as three of these had elevated lipid levels even under medication, and the fourth had only one offspring, these individuals were not excluded from the analysis. The study was approved by the University of Washington institutional review committee, and procedures followed were in accordance with institutional guidelines. All subjects or their guardians gave informed consent.

View larger version (46K): [in this window] [in a new window]   Figure 1. Pedigrees used in linkage analysis. Slashes indicate deceased individuals; right-hand shading, TG levels; left-hand shading, TC levels; black, levels above the age- and sex-adjusted 95th percentile; dark gray, levels above the age- and sex-adjusted 90th percentile; stippled, levels below the age- and sex-adjusted 75th percentile. APOCIII genotypes are shown below individuals, with allele sizes increasing alphabetically. Relationships between letter representations and sizes of up to 27 observed alleles are for families 428 and 2103, alleles A–H=24 to 31, I=31.5, J–U=32 to 43, V=46; for pedigree 2100, A=20, B=21, C=21.5, D–J=22 to 28, K–M=32 to 34, N–O=36 to 37, P–Q=39 to 40, R–T=42 to 44, U–Z=46 to 51, a=55.

Unlike the study by Wojciechowski et al,¹⁹ the genotype of the apo-AI locus (eg, presence in the proband of the X2 allele as described under DNA methods) was not used to select pedigrees for inclusion or exclusion in the current study. However, because of suggestions of disequilibrium between the APOAI X2 allele and FCHL¹⁸ and to facilitate comparisons between the current and the previous study, the three probands (but not their family members) were typed for the same XmnI APOAI polymorphism.

Lipid Phenotypes
Fasting blood samples were drawn as described by Jarvik et al.²⁸ All lipid levels were measured in mmol/L. TC and TG levels were measured with enzymatic methods as described elsewhere.^{29 30} Total plasma apoB levels were measured by radioimmunoassay, as previously described.^{28 31} TG and TC levels were adjusted for age and gender through two different approaches. In one of the models used in the linkage analysis, which assumed exactly the same model, penetrances, and parameter values as did Wojciechowski et al,¹⁹ TG and TC levels were converted to the age- and sex- defined percentile levels of the Lipid Research Clinics.³² For all other models used in the linkage analyses lipid levels were adjusted for age and gender as determined by linear regression in the 487 control subjects described by Jarvik et al,²⁸ and adjusted to the mean for each distribution. For apoB levels, the gender-specific adjustments are described in Jarvik et al.²⁸ For TC levels, c, the gender-independent regression of TC levels on age, d, was c=147.9 + 1.05d.

Because the distribution of TG levels was skewed, analyses were performed on both the raw and log-transformed TG levels after adjusting for age and gender effects. However, as the results and conclusions were unaffected by the log-transformation, only analyses that used untransformed TG levels are reported. TG levels were eventually eliminated from the remaining linkage analyses on the basis of the results of principal component analyses (see below); thus details of the regressions involving TG levels are not reported.

Because of correlations among lipid levels, it is possible that a single locus may affect FCHL via the expression of several different lipid levels through a multivariate rather than univariate distribution of these levels. Although limited methods exist for obtaining models for use in linkage analysis from segregation analyses on multivariate phenotypes,³³ the very large number of parameters needed to describe transmission of such a multivariate distribution necessitates the use of data sets that are much larger than the one available for this study. Thus, to capture aspects of the multivariate distribution, the first principal component of the multivariate distribution was used to create a univariate distribution for use in the linkage analyses. The control population described by Jarvik et al²⁸ was used to define the multivariate distribution in the absence of availability of a large sample of unrelated cases, which would have been preferable. Lipid levels were adjusted for age and gender before estimation of the first principal component. The two bivariate distributions approximated through the first principal component were, first, TC and TG levels, which were the lipid levels originally used to define FCHL, and second, TC and apoB levels, which are known to be associated in FCHL.³ ApoB and TG levels are strongly correlated.³⁴ However, because there was relatively little variation in TG levels compared with apoB levels in the control subjects, it was expected that use of apoB rather than TG levels in principal component analysis might provide a more useful measure because of the variability in TC levels. Based on the results of the principal component analyses (described under Results), the two quantitative traits subsequently used in the linkage analysis were TC levels alone, and the first principal component of the bivariate distribution of apoB and TC levels, because only this latter bivariate distribution included a sizable contribution of both lipid levels in the first principal component, as defined by the normal control subjects.

DNA Polymorphisms
DNA was extracted from peripheral blood leukocytes by the proteinase K-phenol method on an Applied Biosystems Model 340A Nucleic Acids Extractor. For pedigrees 428 and 2103 alleles of the microsatellite (CTTT) tandem repeat polymorphism in intron 3 of the apolipoprotein CIII gene were detected by PCR amplification in the presence of radiolabeled dCTP as described elsewhere.¹⁹ A different set of primer pairs was used for pedigree 2100 because some members of this family had a base-pair change in the sequence complementary to one of the primers that resulted in failure to amplify alleles carrying the mutation. Alleles of the XmnI polymorphism located 2.5 kb 5' upstream of the apolipoprotein AI gene were detected by Southern blot analysis after digestion of genomic DNA (10 µg) with XmnI. The X1 (8.3 kb) and X2 (6.6 kb) alleles³⁵ were detected by hybridization with a full-length apolipoprotein AI cDNA probe.

Linkage Analyses
Two different approaches were used in the linkage analyses. The first approach was to compute lod scores³⁶ under the assumption of a Mendelian dominant mode of inheritance with known parameter values. Several different models were used in this analysis, including one identical to that used by Wojciechowski et al.¹⁹ The lod score approach, which is based on maximum likelihood methods, has the advantage of higher power than other methods of analysis when the genetic model is approximately correct^{37 40} and should give positive evidence of linkage even if parameter values of the model are not precisely correct.³⁸ This approach also has the advantage of being able to make full use of the information in the extended pedigrees used in the current study and is therefore preferred when there is prior support for the assumed mode of inheritance. In the current case, there is such prior support from both positive evidence of linkage from a previous analysis¹⁹ using one of the models also used here, and from segregation analyses of various components of the phenotype.^{1 8} However, inaccurate parameterization of the model may cause overestimation of the recombination fraction,³⁹ and may produce lod scores that are artificially low at small recombination fractions, thereby leading to false rejection of the hypothesis of linkage of FCHL to the candidate region. Care must be taken in the interpretation of negative lod scores at small recombination fractions with candidate genes, and interpretation requires careful consideration of the effects of violation of assumptions.

A second approach to linkage analysis was also used. This latter analysis uses the approach suggested by Haseman and Elston,⁴¹ which involves regression of the squared trait difference in unselected sib pairs on the number of marker alleles shared identical-by-descent. This approach does not require the assumption of a known mode of inheritance with known parameter values, as is necessary with the lod score analyses. The regression analysis was therefore used to make sure that false rejection of linkage of FCHL to the candidate region did not occur simply because our assumptions about the mode of inheritance or associated parameter values used in the lod score analyses were incorrect: in the presence of a gene in the region, this regression analysis could produce positive evidence of linkage (a regression line with significant negative slope) even if the lod score method failed to give positive results because of severe model misspecification. We stress that such severe model misspecification is unlikely in this study because of other information supporting the assumed mode of inheritance, including the previous study reporting positive evidence of linkage with one of the models also used here. Therefore, discordant results between the two analysis approaches were not expected. However, we also felt that it was important to present this alternative analysis because of inherent uncertainties in interpretation of linkage analyses of this complex trait. The disadvantages of this regression analysis are reduced power compared with the lod score method,^{37 40} and inability to use the full information contained in the extended pedigree structures because of the necessity that the pedigrees be broken into nuclear family units for analysis. Although extensions now exist to this method that allow analysis of extended pedigrees,⁴² these extensions are only valid when applied to large numbers of independent pedigrees⁴³ and thus could not be used here because only three large pedigrees were available.

Three models were used in the lod score analyses because the parameter values describing inheritance of FCHL are unknown. In all three models, the disease gene frequency was assumed to be 0.005, as was assumed in the analysis by Wojciechowski et al.¹⁹ For model 1, the mode of inheritance, parameter values, and penetrance functions were identical to the values used by Wojciechowski et al:¹⁹ individuals with TG or TC levels or both exceeding the age and gender adjusted 95th percentiles were considered to be affected in the analysis; individuals for which both TG and TC levels fell below the 75th percentile were considered to be unaffected; and the remaining individuals were considered to be unknown with respect to the disease phenotype. A dominant mode of inheritance was assumed, with two risk categories. A sporadic rate of 2% was assumed for the normal genotype for individuals in whom both TG and TC levels exceeded the 95th percentile. A sporadic rate of 5% was assumed for all other individuals. A 99% penetrance of the genotypes bearing the disease gene was assumed for both risk categories. Computations were performed with the LINKAGE package.⁴⁴

This first model was chosen for purposes of trying to replicate the results of Wojciechowski et al.¹⁹ However, because FCHL is characterized by elevated levels of quantitative traits, we also used two additional models that were based on quantitative measures of lipid levels. These two models (models 2 and 3) were both based on use of TC, TG, and apoB levels, all of which are associated with FCHL. For lod score analyses of these models, a version of LIPED⁴⁵ modified to handle large numbers of marker alleles and different alleles in different pedigrees⁴⁶ was used.

The genotypic means and standard deviations used to describe inheritance of quantitative lipid levels in models 2 and 3 used in the lod score linkage analyses were derived by commingling analysis with the program NOCOM.⁴⁷ A mixture of normal distributions was fit to the appropriate distribution in the 487 control subjects described by Jarvik et al²⁸ under the constraint of Hardy-Weinberg equilibrium. Model 2 in the lod score analyses was based on a genetic model that was fitted to the quantitative distribution of TC alone. Model 3 was based on a genetic model fit to the first principal component defined by the bivariate distribution of TC and apoB. In both cases lipid levels were adjusted for age and gender effects as described above before analysis with NOCOM. Note that although commingling analysis is not segregation analysis (no comparison of the fit to the data of genetic versus nongenetic models is obtained), past genetic modeling,¹ segregation,¹⁵ and linkage¹⁹ analyses of these phenotypes suggest that FCHL and lipid levels that are used to define FCHL are inherited in a dominant or codominant fashion, consistent with the results obtained by commingling analysis. The use of commingling analysis to choose parameters for the models used in the linkage analysis in this case was necessitated by the size of the available sample, which was too small to obtain accurate parameter estimates of the large number of parameters required in a formal segregation analysis.

The regression-based linkage analyses were performed on the same two quantitative traits as were used in models 2 and 3 in the lod score analyses, but without the underlying assumption necessary for the lod score analyses of known parameter values defining the mode of inheritance, including genotypic means, standard deviations, and allele frequencies of the trait locus. SIBPAL from the S.A.G.E. genetic analysis package version 2.0^48-50 was used for linkage analyses with quantitative sib-pair methods after breaking the extended pedigrees into nuclear families.

Marker allele frequencies used in the linkage analyses were estimated by direct count from the observed alleles in the families because of the need to provide allele frequencies that are similar to the true frequencies when there are missing marker data.⁵¹ Allele frequencies estimated in this fashion for related individuals are unbiased, although the variances of the estimates are incorrect.⁵² To reduce computation time in the lod score analyses, marker alleles were recoded when possible with methods suggested by Braverman⁵⁵ to reduce the apparent number of alleles segregating in the pedigree. A single additional allele was used to account for all remaining unobserved alleles. Marker allele frequencies used in the resulting analyses corresponded to those of the original alleles.

Ascertainment Bias
Bias in the expected lod score introduced by the pedigree selection scheme used by Wojciechowski et al¹⁹ was one possible explanation for discrepancies between our results and theirs. To explore this possibility, a study of the effect on linkage analysis results of FCHL pedigree ascertainment through marker genotype in the proband was undertaken. To document that ascertainment through proband marker genotype could produce biased results, analytic results were obtained for linkage analysis with an unlinked marker (recombination fraction of 1/2) on the smallest possible FCHL pedigree. This smallest pedigree was used because its size allowed direct computation of all possible genotypic outcomes, and therefore, exact computation of expected lod scores under different ascertainment schemes.

The FCHL pedigree consisted of two parents and two affected siblings, one of whom was the proband. Parents were assumed to be deceased and with unknown disease and marker phenotype information, as is typical of this disorder. Note that for such a pedigree to enter into a mapping study, the definition of the FCHL¹ implies that both siblings must be affected because a first-degree relative of the proband must also have elevated lipid levels. For the linkage analyses with this pedigree, a single, diallelic, unlinked marker was assumed, which was in linkage equilibrium with the trait locus. In computing lod scores, only the disease model parameters used by Wojciechowski et al¹⁹ (model 1, here) were used, but the allele frequencies at the marker locus were allowed to span the range from 0 to 1.

Two ascertainment schemes were compared. For unselected ascertainment, a=u, no selection on the basis of proband marker genotype was used to determine which FCHL pedigrees to include in the linkage analysis. For selected ascertainment, a=s, pedigrees were only included in linkage study if the proband had marker genotype 1/2 or 2/2. We assume in all cases that the pedigree was ascertained using multiplex ascertainment, as is implicit in the definition of FCHL, before the marker genotyping used to exclude pedigrees in which the proband had genotype 1/1, under selected ascertainment.

For each ascertainment scheme, a, and true marker allele frequency, q, the expected lod score, Elod(a, q), was computed for a range of recombination fractions, . Details of the lod score computations in this case are given in Appendix II. Given the expected lod score under each ascertainment scheme, for a given marker allele frequency and a given recombination fraction, the bias, B(q), was computed as B(q)=Elod(a=s,q)-Elod(a=u,q).The percent bias was computed by dividing the bias by Elod(a=u,q). The expectation and bias were also computed for assumed marker allele frequencies that were 5% higher or lower than the true frequencies. This was done to determine whether use of incorrect frequencies would accentuate the bias. Note that in this case the same incorrect marker allele frequency was used in computing lod scores for both selected and unselected pedigrees.

	Results

Top Abstract Introduction Methods Results Discussion APPENDIX I APPENDIX II References

 
Lipid Phenotypes and DNA Polymorphisms
Cholesterol and apoB levels both contributed substantially to the first principal component of the bivariate distribution of the two quantitative traits in the control subjects. The first principal component, which explained 88.7% of the total variance, was

where z is the synthetic variable, and b' and c' are age- and gender-adjusted apoB and TC levels, respectively. For the bivariate analysis of TC and TG levels in the control subjects, the value of the TG component in the first principal component was less than 1% of that of the TC component. Because this model is thus almost identical to that obtained by using TC alone, the first principal component from this bivariate distribution was not used in further analyses. The resulting parameters obtained from NOCOM for TC levels and for the first principal component of the joint distribution of TC and apoB levels that were used in models 2 and 3 in the lod score analyses of FCHL are given in Table 1.

Figure 1 shows the three pedigrees used in the current study along with the APOCIII genotypes. As shown in Table 2, lipid levels of sampled individuals are clearly elevated in many members of these families. Appendix I gives the actual lipid levels and ages of all sampled individuals. Among sampled individuals who are the descendants of the founders in the pedigrees, 28 of 127 (or 22%) had TC levels above the 90th percentiles described for age and gender. For TG levels, 41 of these 127 individuals (32%) had levels exceeding the 90th percentile. No formal test was done to determine whether the lipid levels were significantly higher than expected in the total data set because the within-family dependencies would violate assumptions of such tests. However, among the unrelated spouses who married into the pedigrees and who would be expected to be representative of control subjects, a total of 5 of 27 (19%) had TC levels above the 90th percentile and 2 of 27 (7%) had TG levels above the 90th percentile. Two of the three probands had the X2 allele at the APOAI locus: the proband of pedigree 428 (III-1 in Fig 1) was heterozygous for the X2 allele, and the proband of pedigree 2103 (III-14) was homozygous for the X2 allele. The proband of pedigree 2100 (III-20) was an X1 homozygote.

Linkage Analyses
Table 3 gives the results of the lod score linkage analyses of APOCIII with FCHL. With model 1, the model used by Wojciechowski et al,¹⁹ the three pedigrees combined give significant evidence against linkage (lod <-2) to this region to a recombination fraction of more than 10%. Family 2100 alone provides significant evidence against linkage to a recombination fraction of more than 5% with model 1, and family 428 provided strongly suggestive evidence against close linkage of FCHL to this region with a lod score of -1.56 at 0% recombination. Although model misspecification alone could produce artificially small lod scores at low recombination fractions, thus making these results potentially difficult to interpret, parameter misspecification of a susceptibility locus should produce suggestive or significantly positive lod scores at moderate recombination fractions, with only a modest decline in the maximal lod score expected compared with that if the model parameters are exactly correct.³⁹ The negative lod scores for all three models across much of the range of recombination fractions are therefore consistent with absence of a susceptibility locus in the region. Only model 2 for family 2100 gives very small positive lod scores, and only at high recombination fractions. However, the expected lod score in the presence of linkage for this large pedigree is almost four times the maximum observed in Table 3, so that these small positive lod scores are unlikely to indicate the presence of linkage. Inspection of the pedigrees also identifies a number of apparent recombination events in affected individuals as defined under model 1. For example, affected individual II-10 in pedigree 2100 transmitted different alleles at APOCIII to each of two affected children, and affected siblings II-1 and II-8 in pedigree 428 are discordant for their APOCIII alleles. It should be noted that the offspring in pedigree 2100 who received different alleles from affected parent II-10 are the proband and his sibling.

Failure to find evidence within these families for a gene for FCHL in this region was also obtained with the other genetic models used. For model 2, which was based only on TC levels, both family 2100 and 428 gave significant evidence against close linkage of FCHL and APOCIII with lod scores below -2. For model 3, which incorporated a measure of both TC and apoB levels, total lod scores remained significantly negative, although family 2100 became essentially uninformative. Family 2103 was essentially uninformative for all three models.

Linkage analysis with the sib-pair regression method also gave no indication that a locus that has significant effects on either TC levels alone or on the first principal component of bivariate apoB and TC levels is closely linked to the AI-CIII-AIV region. For the first principal component of apoB and TC, the slope of the regression line was -0.104 (P=.46); for TC levels alone, the slope was -0.170 (P=.43), neither of which is statistically significant.

Ascertainment Bias
Figure 2 shows expected lod scores for the nuclear FCHL pedigree under both presence and absence of selection of probands through marker genotype, as well as the resulting biases in the expected lod scores. The expected lod scores are biased when marker genotypes in the proband are used to determine which FCHL families to include in a linkage study (Fig 2c and 2d). As can be seen, for an unlinked marker the expected lod scores for the affected sib-pair situation are negative for both unselected pedigrees (Fig 2a) and those selected on the basis of marker genotype (Fig 2b). However, when the expected lod scores for the selected pedigrees are compared with those for the unselected pedigrees, it is clear that they differ, introducing a bias (Fig 2c). This bias is positive when the frequency of allele 1 is less than about 0.65, with greatest bias for moderate marker allele frequencies. Although the absolute magnitude of the effects are small per pedigree for the small pedigree considered, the percent bias is as high as 16.9% for intermediate marker gene frequencies at low recombination fractions (Fig 2d).

View larger version (34K): [in this window] [in a new window]   Figure 2. Expected lod scores, bias, and percent bias expected for affected sibling pair family. Lod scores and bias (but not percent bias) have been multiplied by 1000 for display purposes. q, frequency of allele 1. a, Expected lod score when there is no selection on marker genotype in proband. b, Expected lod score when families in which probands with marker genotype 1/1 are excluded. c, Bias in lod score, comparing selected with unselected pedigrees. d, Percent bias in lod score for selected vs unselected pedigrees.

Use of incorrect marker allele frequencies accentuated the bias. Overestimation of the frequency of marker allele 1 caused the bias to become positive at all recombination fraction/gene-frequency combinations, whereas underestimation of the frequency of allele 1 caused the bias to become negative at all such combinations. For example, the percent bias for computations performed for q=0.4 and =0.05 was 16.8 for the true marker allele frequency of q=0.4, but was -77.1 when the true frequency for q was 0.45, and was 290.3 when the true frequency was 0.35. It is worth noting that when the true frequency for allele 1 was overestimated, not only was the bias positive, but the expected lod scores for the selected ascertainment scheme were positive for the whole range of parameter values evaluated. In contrast, under unselected ascertainment but slight overestimation of q, the lod scores were negative for most parameter values, only exceeding zero for small q.

	Discussion

Top Abstract Introduction Methods Results Discussion APPENDIX I APPENDIX II References

 
The results presented here suggest that FCHL is not linked to the AI-CIII-AIV gene cluster in this particular set of FCHL families. This is in contrast to the results of Wojciechowski et al,¹⁹ who presented significant positive lod scores in a linkage analysis with markers in this region. The quantitative sib-pair approach used here also did not confirm the weakly positive suggestion of linkage of LDL-cholesterol levels and two diallelic markers in APOCIII,²⁰ although this may be a reflection of the difference in the phenotype used for the analysis. This difficulty in confirming an initial report of positive evidence of linkage is similar to results obtained for other complex diseases, including bipolar disorder^{26 56} and schizophrenia.^{57 58} As described below, there are a number of explanations for our failure to replicate the earlier positive report of linkage of FCHL to the AI-CIII-AIV region, including a false-positive result by chance, genetic heterogeneity, and variability in pedigree selection.

In any linkage analysis a positive result may be obtained by chance. Although it may seem unlikely that a lod score of 3.0 (a likelihood ratio of 1000:1) or above could be a "false positive," it is important to remember that this critical value of 3.0 was chosen with a predefined testwise false-positive rate of about 2% to 5% under the assumption of the existence of the disease locus.³⁶ If the existence of a disease locus is not well established, a lod score of 3.0 or above may not represent the same overall false-positive rate. Some failures to replicate initial results of linkage analysis with complex diseases have, indeed, been shown to be initial false-positive results. For example, an early report of linkage of Alzheimer's disease to chromosome 21⁵⁹ was not confirmed.⁶⁰ This report of linkage to chromosome 21 was later shown to be a false positive when a gene for this disorder was mapped to chromosome 14⁴⁶ and the defect in the original families used to support a chromosome 21 location was subsequently also found to map to chromosome 14.⁶¹

In the absence of definitive evidence for a Mendelian mode of inheritance for FCHL, the interpretation of a positive lod score is not straightforward.²² The probability of incorrectly accepting a conclusion of linkage, given a nominally significant lod score, will generally exceed that for genetic disorders with clear Mendelian modes of inheritance. Recent reevaluation of difficulties that arise in linkage analysis of complex traits suggests that inflated positive evidence of linkage can result from poor parameter specification, particularly if there are interactions between misspecified parameter values in both the disease locus and the marker locus.^{62 63} Although often assumed to be known, parameter values such as marker gene frequencies, marker-disease haplotype frequencies, and the parameters of the mode of inheritance of the trait are, in reality, only estimated; often such estimates are based on small sample sizes in populations other than those used in the particular linkage analysis.

As in other complex diseases for which confirmation has been difficult, another possible explanation of differences between results from different studies is that there is genetic heterogeneity: defects in different loci can independently cause the disorder. Genetic heterogeneity is highly probable for a complex, relatively common disease such as FCHL, and there is already strong evidence to suggest that FCHL is genetically heterogeneous.^{11 12} The possibility of genetic heterogeneity was the reason Wojciechowski et al¹⁹ used only those pedigrees in their linkage analysis in which the proband carried the 6.6-kb XmnI APOAI (X2) allele because there was some evidence that there was an association between the disease and this allele. It was thought that selection on the basis of this allele might enrich the sample for pedigrees potentially linked to this region. However, our analyses do not confirm the results reported by Wojciechowski et al,¹⁹ even for pedigrees in which the proband had the APOAI X2 allele. Specifically, family 428, in which the proband was homozygous for the X2 allele, gave consistently negative evidence for linkage to this region for a variety of models. Although one possible explanation for this is that our trait model in linkage analysis was inaccurate because we did not perform a segregation analysis, it should be noted that a recent large simulation suggested that linkage analysis is more likely to succeed in the absence than in the presence of a complex segregation analysis.⁶⁴ It is therefore important to consider not only the APOAI genotype of the proband, but also other differences between the two studies.

In addition to the differences in pedigree selection on the basis of the APOAI genotype, our pedigrees are much larger than those analyzed by Wojciechowski et al.¹⁹ Large pedigrees may be advantageous in that each pedigree by itself may provide sufficient evidence to detect or reject evidence of linkage in the presence of genetic heterogeneity. Analyses in large pedigrees are also less likely to be affected by artifacts introduced by possible biases in pedigree selection introduced by ascertainment through a proband of a particular genotype. However, in large pedigrees it is also possible that two different genetic causes of the disease may be segregating in the same pedigree, which would tend to reduce evidence of close linkage. In the large pedigrees used here, both parents of each of the probands had elevated lipid levels, raising this possibility. However, there is little evidence of linkage heterogeneity within the families studied because in the pedigrees with strongly negative results, the results on both sides of each of the families were similar.

A final possibility that might explain the discrepancies between the two studies is that the pedigrees were selected differently in the two studies. Wojciechowski et al¹⁹ included in their linkage analyses only those pedigrees in which the proband had the X2 allele. Such pedigree ascertainment added to prior selection on the basis of multiple family members with an unusual phenotype (as is implicit in the definition of FCHL) violates the requirement that ascertainment of families should depend only on one of the two loci used in such a linkage analysis.^{65 66} As demonstrated by our computations of expected lod scores in a small family with FCHL, there can be a positive bias introduced by selecting on the proband marker genotype, in particular when the marker allele frequencies are even slightly misspecified, as is probably typical in most studies. This bias could cause a shift in the lod score distribution so that the type I error associated with a positive lod score is increased. The precise value of the bias that may have been introduced into the study of Wojciechowski et al¹⁹ cannot be determined because of unknowns in the model parameters and because the excluded pedigrees were not presented, nor is it possible to prove that a bias in either direction necessarily occurred because of their sampling scheme. However, a small simulation study on their published pedigrees suggests that in the absence of linkage the ascertainment procedure may have increased the fraction of lod scores exceeding 1 by about 38% (details not shown). Extension of the original pedigrees would supply independent meioses, which could be used to confirm or reject the original results without the difficulty of trying to evaluate possible differences in phenotype definitions or selection criteria among studies.

Given the complexity of FCHL, it is perhaps not surprising that two linkage analyses failed to reach similar conclusions about the existence of a gene contributing to this disease in the AI-CIII-AIV region. Although replication of the negative results presented here is as important as replication of a positive report of linkage for a complex disease such as FCHL, these negative results do indicate that further work will need to be done to identify the location(s) of gene(s) contributing to FCHL. Careful evaluation of the sensitivity of the results to the clinical phenotype, the parameter assumptions, and the sampling methods will most likely be needed to reconcile differences among studies. It also may be necessary to obtain consensus on possible subtypes of the disease as defined by molecular and clinical studies, as well as to obtain better estimates of parameters that describe the mode of inheritance of the disorder. It is also likely that many more loci will need to be tested before the genomic location(s) of genes contributing to this disorder are identified.

	APPENDIX I

Top Abstract Introduction Methods Results Discussion APPENDIX I APPENDIX II References

 
Table 4

	APPENDIX II

Top Abstract Introduction Methods Results Discussion APPENDIX I APPENDIX II References

 
Computation of lod scores for the nuclear pedigree with and without exclusions based on proband genotype was performed as follows. We assume that the pedigree consists of two parents with complete missing data, and two affected siblings, one of whom was the original proband, as described elsewhere. Given a population frequency, q, for marker allele 1, genotype probabilities of the proband for pedigrees selected for inclusion in a linkage analysis were computed as shown in Table 5. Genotype probabilities of the sibling, conditional on the proband's genotype, were computed with probabilities shown in Table 6.

For each ascertainment scheme, a, and true marker allele frequency, q, the expected lod score, Elod(a,q), was computed for recombination fraction, , as:

(1)

where genotypes 1/1, 1/2, and 2/2 are indexed 1, 2, and 3, respectively, g_p=i represents genotype i in the proband, g_s=j represents genotype j in the sibling, and lod(g_s=i, g_p=j,q) is the lod score computed for recombination fraction and marker allele frequency q, for the joint genotypic combination in which the sibling has genotype i and the proband has genotype j. The first part of the equation (1) under the summations is therefore the quantity computed in Table 6, the second part is the quantity computed in Table 5, and the last part is the lod score, conditional on the particular genotypes in the two siblings. Lod scores at specific recombination fractions for each joint genotype combination were obtained for model 1 with LIPED⁴⁵ as described previously.

	Selected Abbreviations and Acronyms

 

apoB = apolipoprotein B FCHL = familial combined hyperlipidemia LPL = lipoprotein lipase TC = total cholesterol TG = triglyceride

	Acknowledgments

 
Part of this work was performed during Dr. Austin's tenure as an Established Investigator of the American Heart Association. This work was supported by US Public Health Service Grant HL30086. A portion of this study was performed in the University of Washington Medical Center Clinical Research Center, NIH RR 37. Some of the results in this paper were obtained by using the program package S.A.G.E., which is supported by US Public Health Service resource grant RR03655 from the Division of Research Resources. We thank M. Farrell showing us his files used to perform linkage analysis of FCHL with the APO AI-CIII-AIV region, and S-W Guo and M. Yang for help in performing computations.

	Footnotes

 
Reprint requests to Ellen M. Wijsman, PhD, Division of Medical Genetics, University of Washington, BOX 357720, Seattle, WA 98195-7720.

Divisions of Medical Genetics (E.M.W., G.P.J., S.S.D.) and Metabolism, Endocrinology, and Nutrition (J.D.B.), Department of Medicine, School of Medicine; Department of Biostatistics (E.M.W.) and Department of Epidemiology (M.A.A.), School of Public Health and Community Medicine; and Department of Genetics (A.G.M.), School of Arts and Sciences, University of Washington, Seattle.

Received March 19, 1996; accepted September 30, 1997.

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