Genetic Epidemiology 7:187-197 (1990)
Familial Resemblance of Plasma Apolipoprotein B: The Nancy Study Laurence Tiret, Josianne Steinmetz, Bernard Herbeth, Sophia Visvikis, Roger Rakotovao, Pierre Ducimetiere, and Francois Cambien lnstitut National de la Sante et de la Recherche Medicale (INSERM) U258, Hdpital Broussais, Paris (L. T., R.R., P. D., F.C.), and Centre de Medecine Preventive (J.S., B.H., S.V.) and INSERM U115 (B.H.), Vandoeuvre Ies Nancy, France The familial resemblance of plasma apolipoprotein B (apo B) was investigated in a sample of 102 families including 419 members who volunteered for a free health checkup in the Preventive Center of Vandoeuvre-12s-Nancy, France. The mean leve l s ( k S D ) o f a p o B were 141.0(+32.6), 121.8(?27.7), and98.6(+22.6)mg/dl in fathers, mothers, and offspring, respectively. The familial correlations were 0.04, 0.13, 0.21 ( P < .Ol), and 0.47 ( P < ,001) between spouses, father-offspring, mother-offspring, and siblings, respectively, after adjustment on age, body mass index, and sex. A genetic analysis was performed using the approach proposed by Bonney, which indicated that a recessive and a dominant major-locus model appeared nearly equally supported by the data. Under the recessive model, the frequency q of the most common allele was estimated as 0.825, with a mean difference of 60.4 mgidl between high and low homozygotes. Under the dominant model, q was estimated as 0.875, with a mean increase of 34.2 mgidl in heterozygotes and high homozygotes. However, the hypothesis of Mendelian transmission and the environmental hypothesis could not be formally tested because of great numeric difficulties encountered in the estimation of the three transmission probabilities. Given these analytical restrictions, we cannot conclude in favor of a major locus influencing apo B level in our population, even though the evidence is suggestive. The genetic heterogeneity underlying the familial aggregation of apo B level, suggested by several recent publications, might explain the difficulty in discerning a single major locus in a population sample of small nuclear families, not ascertained through patients enriching the sample in high values of apo B. These findings call into question the relevance of the approach through “healthy” populations in the search for major loci influencing biological traits. Received for publication February 15, 1989; revision accepted January 30, 1990. Address reprint requests to L. Tiret, INSERM U258, HGpital Broussais, 96 rue Didot, 75674 Paris Ctdex, France.
0 1990 Wiley-Liss, Inc.
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Key words: major gene determination, healthy population
INTRODUCTION
It is now well established that genetic factors are involved in the development of arteriosclerosis and coronary heart disease (CHD), through mechanisms affecting the levels of risk factors [Goldbourt and Neufeld, 19861. This evidence is strongly reinforced by the observation of genetic diseases, such as familial hypercholesterolemia (FH), characterized by an early and accelerated development of arteriosclerosis [Motulsky, 19891. Although the genetic abnormalities at the FH locus have a large effect on an individual’s cholesterol level, they do not make a large contribution to the cholesterol variability in the general population. Conversely, it is likely that minor but common genetic defects, alone or in association, could have a much greater impact on the incidence of CHD [Davignon et al., 19881. The familial resemblance of plasma lipoprotein levels, which are strongly related to CHD, has been demonstrated in several studies [Namboodiri et al., 1984; Iselius et al., 1985; Austin and Krauss, 1986; Friedlander et al., 19861. Among lipoprotein components, apolipoprotein levels have been shown to be better dicriminators of CHD than lipid levels [Avogaro et al., 1980; De Backer et al., 1982; Kukita et al., 1984; Sniderman et al., 1985; Durrington et al., 19881. The relationship between a parental history of early myocardial infarction and an elevated level of apolipoprotein B (apo B) [Kukita et al., 1984; Sniderman et al., 1985; Van Stiphout et al., 1986; Cambien et al., 19871 suggests an underlying genetic mechanism affecting the apo B level. Using complex segregation analysis, three studies have reported evidence for a major gene effect affecting the level of apo B [Amos et al., 1987; Hasstedt et al., 1987; Pairitz et al., 19881, whereas Beaty et al. [1986], in a single Amish pedigree, found significant evidence for polygenic effects, but not for a single locus effect. These studies were conducted among samples of families ascertained through probands with lipid abnormalities or with CHD. The purpose of this study was to assess whether or not a major gene effect could partly explain the level of apo B in a sample of nuclear families attending a preventive center for a free health checkup. MATERIAL AND METHODS Population Studied
The families were recruited in the Preventive Center of Vandoeuvre les Nancy, France, where members of families living in the Nancy area can obtain a free health examination [Deschamps, 19871. From January 1985 to June 1986,200 families composed of both parents aged 60 years or less and at least one offspring aged 10 or more agreed to participate in a study of familial cardiovascular risk factors. Plasma apo B was measured after fasting in a subsample of 102 families, including 419 members. The families were generally small, with the average number of offspring 2.1. Two fathers and one mother were receiving hypolipidemic drugs at the time of examination; none was well controlled by the treatment, and they were not removed from the study. Measurement of apo 6
Apo B level was measured in whole plasma, on a Cobas-Bio centrifugal analyzer (Roche Diagnostic) using immunoturbidimetric assays [Rifai and King, 19861. The
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immunoturbidimetric method has been shown to yield reliable results for routine assays of apo B, not only in normolipemic, but also in hyperlipemic sera [Siedel et al., 1988). The change in turbidity of the sample against a reagent blank was measured at 340 nm after 0.5 and 360 sec of incubation at 37°C. The 0.5 sec reading serves as a sampleplus-reagent blank. Sample values were calculated automatically by the Cobas-Bio DENS program (Data Evaluation for Nonlinear Standard Curves) to fit the standard curve values to a four-parameter logit-log curve model. Day-to-day imprecision (coefficient of variation) over 30 days was 4% at a concentration of 117 mg/dl. Statistical Methods
The first step of the analysis was to assess whether or not there was evidence for familial resemblance in apo B level. The second step was to determine if such a resemblance could be partly explained by the presence of a gene having a major effect on the phenotype. Adjustment for covariates. Analyses were performed on the residuals of apo B after linear adjustment on age, age2, sex, body mass index (BMI, computed as the ratio of weight to height2), BMI', age*sex, BMI*sex and age*BMI. Including interaction terms with sex allowed us to consider males and females simultaneously despite possible heterogeneity between sexes in the proportions of apo B variability explained by age and BMI. Computation of familial correlations. The maximum likelihood method proposed by Donner and Koval [ 19811 was used to compute the familial correlations jointly. Distribution of the trait is assumed to be multivariate normal within every family, with identical means, variances, and correlations among families. The parameters of this model were estimated as a restricted case of the more general model described in the next section. Modeling a major gene effect. An extension of the method proposed above, similar to the one proposed by Bonney [1984], was used to investigate the compatibility of the data with a major gene hypothesis. Under this model, variation among individuals for a quantitative trait is a consequence of a major gene effect and a residual variation, which could be attributable to polygenes and/or environmental factors, the detailed components of this residual variation not being analyzed. Let x = (xl,x2, x3, . . . xn) be the vector of phenotypes of a given family and g = (gl,82, 83, . . . gn) the vector of their major genotypes ( 1 indexing the father, 2 the mother, and 3 . . . n the offspring). Assuming a two-allele gene, there are three possible genotypes (aa, Aa, and AA) for each individual. If A is the allele associated with an elevation of the level of the trait, the contribution,mean effect, of the major genotype to the trait can be defined as the difference between the population mean of individuals having one (pAa)or two ( p A A ) copies of the A allele and that of individuals not having the A allele (pas). If 6, = p, - pas, we see that 6,, = 0, whereas 8Aaand SAA may differ from zero. Fixing EAa = 0 specifies the recessivity of the = 6 A A specifies dominance. major gene, The vector of residual phenotypes for a family after adjustment on major genotype is then y = x -ti,, where 6, = (Sg,, tig2,. . . S,,) is the familial vector of mean effects associated with the genotype. Let f(x I g ) be the conditional probability density of the phenotype vector x given the genotype g . The likelihood of a family may be written as:
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L(x) = X:$(x I g) P(g) = Xgl X g 2 C@ . . . X,,f(X
Ig) P(g1, 82, 83,
. . . gn).
In the case where the parents are genetically unrelated and the genotypes of the offspring are independent given the genotype of their parents, the joint probability of familial genotype is: P ( g l , g 2 , g 3 , . . . gn) = P(gl)P(g2)P(g3 I g I , 82) . . . P(gn 1 g I , g2).
The probability of the three possible genotypes in parents are determined by the Hardy-Weinberg proportions P(aa) = q2,P(Aa) = 2q( 1-q) and P(AA) = ( 1-q)2, where q is the frequency of the most common allele a. The conditional probabilities of the genotypes of the offspring, given the genotypes of their parents, are computed using the transmission probabilities (71, 72, and 73) which are the probabilities that individuals aa, Aa, and AA, respectively, transmit the a allele. Under the Mendelian hypothesis of inheritance, 71, 72, and 73 are equal to 1, 0.5, and 0, respectively. Fixing q = 71 = 72 = 73 specifies a nontransmitted environmental mixture of distributions. The conditional probability densityflx I g) is assumed to be n-variate normal, with mean vector ps and covariance matrix X.Because y = x - a, this is equivalent to saying that the conditional density of the residual vectory, given g, is the n-variate normal with residual mean vector paaand the same covariance matrix X.The elements of the n-vector paaare the residual means of the trait among fathers, mothers, and offspring, respectively, after adjustment for the major gene effect. The diagonal elements of 2 are the residual variances of the trait among fathers, mothers, and offspring, respectively, and the off-diagonal elements are the residual covariances among relatives. Residual familial correlations are derived from this matrix. In this model, fatheroffspring and mother-offspring correlations are estimated separately. Although the size of the vector paaand of the matrix X varies with the size of the family, the parameter values are assumed to be identical among families, whatever the size of the family. This model is equivalent to the class D regressive model introduced by Bonney [ 19861, specifying equal sib-sib correlations given major genotypes. The covariance matrix 2 is the same as that defined by Bonney [ 19841 in his regressive model, if one assumes equal sib-sib correlations and different father-child and mother-child correlations. The likelihood of a family is then a known function of the parameters paa,C, q, 6, and 7. All parameters defined above were estimated by maximizing the likelihood of the sample of families. The likelihood function was maximized using the program GEMINI [Lalouel, 19811. Different nested models were tested by comparing the likelihood L2 of a restricted model M2 with k2 parameters to the likelihood L, of a more general model M I with kl parameters, as 2(lnLl - InL2) is approximately distributed as a x2 with (k, - k2) df. When the models are not nested, an alternative test statistic based on Akaike’s information criterion (AIC) can be used to compare the fit of different models [Akaike, 19741. For a given model, this statistic is computed as AIC = -2 InL twice the number of parameters estimated. The model with the lowest AIC is considered to be the most parsimonious model providing the best fit to the data. For each individual in the sample, genotypic probabilities were computed under the major-locus model. The genotypic probability p i jthat an individual i has the genotypej given the family structure and phenotypes, is:
+
p.. 1J = L(x I g,
=j
) * P(g; = j ) / L f x ) .
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TABLE I. Mean Values (Standard Deviations) of Age, Body Mass Index (BMI), and Apolipoprotein B (apo B) Level in the Sample
Age Body mass index (kg/rn2) Apo B (mg/dl) Adjusted on covariatesa
Fathers
Mothers
Offspring
43.3 (5.3) (3.3) 25.1 141.0 (32.6) 116.0 (32.1)
41.0 (4.8) 23.6 (3.8) 121.8 (27.7) 114.7 (26.9)
15.4 (2.9) 19.4 (2.7) 98.6 (22.6) 113.9 (22.6)
"age, age2, sex, BMI, BMI', age*sex, BMI*sex, age*BMI.
RESULTS
The means and standard deviations (SD) of age, BMI, and apo B in the sample are given in Table I. The covariates explained 32.6% of the variability in apo B levels in the whole sample. The sex*BMI interaction was significant ( P < 0.05), whereas the sex*age and the BMI*age interactions were not. Variances among fathers, mothers, and offspring, respectively, were not much reduced after adjustment (Table I). The residuals from the regression were added to the mean of apo B in the sample (1 14.6 mg/dl) to obtain adjusted apo B levels. Adjusted apo B levels ranged from 43 mg/dl to 199 mg/dl. After adjustment, positive skewness (0.39) and kurtosis (0.59) of apo B level distribution were both significant. The familial correlations of adjusted apo B were strong among siblings (0.47; P < .OOl), moderate between mother and offspring (0.21; P < .Ol), and nonsignificant between father and offspring and between spouses (0.13 and 0.04, respectively). The model including familial correlations (model 1, Table 11) was much better supported by the data than the model assuming no familial resemblance (model 0) (x2 = 39.2 with 4 df; P < 0.001). The results of a series of analyses testing different genetic models are shown in Table 11. A model assuming a codominant major gene effect with residual familial correlations was first investigated. Exploration of the likelihood surface under this model showed two peaks, specifying different estimates of the parameters: under the first solution, the frequency q of the most common allele was estimated as 0.838 with a mean effect tiAaof - 2.0 mg/dl in heterozygotes (not significantly different from 0) and a mean effect tiAAof 62.9 mg/dl in high homozygotes; under the second solution, the frequency q of the most common allele was estimated as 0.875 with a mean effect tiAaof 36.0 mg/dl in heterozygotes and a mean effect 8 A A of 10.7 mg/dl in high homozygotes, indicating a model of overdominance, which seemed biologically unlikely. For this reason, the first solution was adopted for the comparison with further models. The codominant model (model 2) was better supported than the model stating no major gene effect (model 1) (x2 = 11.O with 3 df; P < .05). Residual familial correlations were significant, as shown by the comparison of model 3 to model 2 (x2 = 11.4 with 4 df; P < 0.05). The recessive model (model 4), assuming tiAa= 0, was associated with the same likelihood as the codominant model. Again, exploration of the likelihood surface under this model showed two maxima; under the first solution, the frequency q of the most common allele was estimated as 0.696 with a mean effect of 43.1 mg/dl in high homozygotes, whereas under the second solution q was estimated as 0.825 with a mean effect of 60.4 mg/dl. This second solution was adopted subsequently, as it was associated with lower variances of the parameter estimates and
39.2** 4 3,887.2
Ob
3,867.2
3 3,882.2
11.o*
(0.5) (.O) 3,856.2 1
(1.0)
(.O) (.O) (.O)
0.12 0.15 0.29 0.42 0.838 - 2.0 62.9
0.04 0.13 0.21 0.47 0.663 18.9 54.1 (1 .O) (0.5) (.O) 3,867.6 2 11.4* 4 3,885.6
(0
28.4 19.0 15.7
31.0 22.2 21.2
32.0 26.7 22.6
(1.0)
101.7 99.7 99.5
115.2 112.2 114.0
115.9 114.7 114.7
Model
(0.5) (.O) 3,856.2" 2 0 (NS) 1 3,880.2
(1.0)
0.11 0.15 0.28 0.42 0.825 (.O) 60.4
30.9 22.1 21.1
114.5 111.6 113.2
Recessive gene + residual correlations
4
+
3,881.2
1
-.O 0.10 0.44 0.875 (34.2) 34.2 (1.0) (0.5) (.O) 3,857.2 2 1 .O (NS)
-.O
29.1 21.6 17.7
108.1 106.5 106.9
Dominant gene residual correlations
5
0.697 (.O) 3,855.8 4 0.4 (NS) 1 3,881.8
(1.0)
0.807 (.O) 65.3
0.44
0.12 0.15 0.29
30.6 21.8 21.5
114.1 111.3 113.7
6 Same as model 4 with free transmission parameters
-.O -.O 0.11 0.46 0.863 (34.1) 34.1 (1.0) 0.537 0.518 3,856.6 5 0.6 (NS) 2 3,884.6
28.8 21.5 17.7
107.3 106.1 107.1
7 Same as model 5 with free transmission parameters
"Two peaks of the likelihood surface were observed; the solution shown in the table is the one associated with the greatest likelihood (see text). bModel 0 is without major gene and without familial correlations ( - 2 In L = 3906.4). *P < .05. **P < ,001. NS = not significant.
Df AIC
x2
72 73 -2 I n L Alternate model
71
&A,
6A,
Residual means Fathers Mothers Offspring Residual SD Fathers Mothers Offspring Residual correlations Spouses Father-offspring Mother-offspring Sib-sib 4
Codominant gene, no residual correlations
Codominant gene residual correlations
Familial correlations, no major gene
+
3
2
1
TABLE 11. Test of Genetic Hypotheses for Adjusted apo B in 102 Families, n = 419
3,885.0
0.11 0.14 0.28 0.44 0.836 (.O) 60.4 (0.836) (0.836) (0.836) 3.861.0
30.8 22.1 21.5
114.5 111.6 113.5
Environmental transmission
8
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a better likelihood. The dominant model (model 5), assuming 8 A a = tiAA,was also nearly equally supported by the data. Under this model, q was estimated as 0.875, with a mean effect of 34.2 mg/dl in heterozygotes and high homozygotes. Estimates of the residual spouses and father-child correlations were nearly zero, but with large standard errors (0.13 and 0.11, respectively). Comparison of the recessive and dominant models, using AIC statistic, indicated that the recessive model fit the data slightly better. To test the hypothesis of Mendelian inheritance, the transmission parameters were estimated under the recessive and dominant models (models 6 and 7). In both cases, 71 converged to its bound and was then fixed to 1. Because of numeric difficulties in estimating 72 and 73 simultaneously under the recessive model, we investigated a model in which 72 alone was left free, a possible approach suggested by Lalouel et al. [1983]. This resulted in an estimate of 72 of 0.697, compatible with the Mendelian expected value of 0.5 (x2 = 0.4 with 1 df; P > 0.05). Under the dominant hypothesis, 72 and 73 were estimated as 0.537 and 0.518, respectively, these values also being compatible with a Mendelian transmission (x2 = 0.6 with 1 df; P > .05). However, the convergence problems restrict the validity of the likelihood-ratio statistic. Again, model 6 (recessive) had a lower AIC value than model 7 (dominant). The model assuming an environmental mixture of two distributions was also investigated (model 8). Although it could not be formally tested against a more general model with free transmission probabilities because of numeric problems, the AIC value indicated that the fit of the environmental model was slightly worse than that of the model 6. Finally, when comparing all the models using the AIC statistic, the lowest AIC value occurred with the Mendelian recessive model (model 4). DISCUSSION
This study was based on a sample of families volunteering for a free health checkup. Although these families were probably not representative of the whole population of the region, depending on the bias that is associated with a free health checkup, recruitment for the study was not based on lipid abnormalities or cardiovascular diseases, as with the studies previously reported [Amos et al., 1987; Hasstedt et al., 1987; Pairitz et al., 19881. However, there is a likely selection bias in the opposite way, as one can hypothesize that individuals having cardiovascular disease or documented risk factors such as hyperlipidemia are medically followed elsewhere and probably do not attend the Preventive Center. For instance, it has been shown that adults attending the Preventive Center had a lower BMI than adults in the same age groups of the two study populations of the WHO Monica project close to the Nancy area (Tiret et al., unpublished). The genetic model used in this analysis, similar to the one proposed by Bonney [1984], assumed a major gene effect and possible residual covariances. The residual covariances are not explicitly modeled in terms of multifactorial inheritance, reflecting polygenic and/or culturally transmitted variation, as in the traditional mixed model. However, the class D regressive model, which is equivalent to our model, has been shown to be mathematically and numerically equivalent to the mixed model [Demenais and Bonney , 19891. In particular, major gene effects, when present, are correctly detected and estimated. The regressive model has the advantage of being more flexible than the mixed model, for example, allowing different father-offspring and mother-offspring correlations.
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TABLE 111. Phenotypic Values (Adjusted Apo B) and Genotypic Probabilities Under the Recessive and Dominant Models for Two Selected Families* Adjusted apo B (mgldl) Family 137 Father Mother Offspring Offspring Family 188 Father Mother Offspring Offspring
103.7 117.2 190.0 182.2 129.4 157.5 164.5 103.0
Genotypic probabilities Recessive model
Dominant model
aa 0.01 0.01 0.01 0.02 aa 0.40 0.37 0.38 0.43
aa 0.41 0.48 0.00 0.01 aa 0.73 0.08 0.01 0.98
Aa 0.97 0.98 0.01 0.01 Aa 0.59 0.30 0.16 0.57
AA 0.02 0.01 0.98 0.97 AA 0.01 0.33 0.46 0.00
Aa 0.47 0.42 0.96 0.95 Aa 0.27 0.92 0.93 0.02
AA 0.12 0.10 0.04 0.04 AA 0.00 0.00 0.06 0.00
*Rather favoring the former (family 137) or the latter model (family 188)
We experienced numeric difficulties in the analysis of these data. Multiple maxima were found in the likelihood, and several solutions appeared equally supported by the data; all suggested that the distribution of apo B is a mixture of two components. The recessive and the dominant models are detecting different components, with means separated by 60.4 mg/dl(2 to 3 residual SD) under the recessive model and 34.2 mg/dl (1 to 2 residual SD) under the dominant model. Comparison of the likelihoods of each family under the recessive and the dominant models, respectively, showed that the families favoring the recessive model were those with extreme apo B levels, such as Family 137, whereas families that supported the dominant model were those with moderately high apo B levels, such as family 188 (Table 111). This is explained by the fact that under the recessive model, q was estimated as 0.825, specifying a very low probability (0.03) of belonging to the upper distribution; therefore, only extreme apo B levels would fall in that distribution. On the other hand, under the dominant model, q was estimated as 0.875, specifying a higher probability (0.23) of belonging to the upper distribution. Great difficulties were also encountered in estimating the three transmission probabilities simultaneously. We had to fix one or two of these parameters; so the true likelihood of the unrestricted model would be better than the one obtained, and therefore the x2 for testing the Mendelian hypothesis would be larger, but with more degrees of freedom. As another consequence of these numeric problems, the environmental hypothesis could not be formally tested. Comparison of the likelihood under the different models, using the AIC statistic, indicated that the environmental hypothesis had a slightly worse fit than the hypothesis of transmission of a major effect. However, Demenais et al. [1986] showed that protection against the false inference of a major gene required estimation of the three transmission probabilities and testing both the hypothesis of Mendelian transmission and the hypothesis of no transmission of major effects. Because we were unable to fulfill these two conditions, we cannot conclude in favor of a major locus in our population, even though the evidence is suggestive. Using complex segregation analysis, Hasstedt et al. [ 19871and Pairitz et al. [ 19881 have both detected a codominant single major locus influencing the apo B level, with the frequency of the most common allele being 0.847 and 0.826, respectively. This
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major locus had similar effects on apo B level in both studies. The mean level (mg/dl) in low homozygotes was 110.5 in Hasstedt et al. [I9871 and 86.2 in Pairitz et al. [1988] and the separation between the low and middle means was 3 1.4 mg/dl and 43.3, respectively, whereas separation between low and high means was 97.6 and 103.2, respectively. Both studies included pedigrees ascertained through patients with coronary artery disease or lipid abnormalities, which might explain the detection of a third mode in the apo B distribution that was difficult to discern in our sample of families not ascertained through patients. For example, there were several individuals with sex- and age-adjusted apo B levels above 200 mg/dl in the sample of Hasstedt et al. [1987], whereas none was observed in our sample. Although we could not reach the same conclusion as the above-mentioned authors, some of our results are not in disagreement with their findings. First, the proportion of admixture in either of our models is comparable to that estimated by these authors. Second, in our data, the effect separating the two modes of the distributions under the dominant model is similar to that reported for heterozygotes in their codominant model, whereas the effect separating the two modes under the recessive model is slightly lower than that reported for high homozygotes. These findings suggest that the codominant hypothesis of inheritance is more likely, and because our sample was not sufficiently enriched in high values of apo B, the analysis lacked power to distinguish between the two upper distributions of heterozygotes and high homozygotes. These distributions were then mingled in one distribution, simulating either a recessive or a dominant model. The possibility that alleles situated at different loci may affect the level of apo B in different families is strongly supported by recent observations. Several studies have reported polymorphisms of the apo B gene that appear to correlate with lipids or apolipoproteins levels, and/or CHD [Law et al., 1986; Berg, 1986; Hegele et al., 1986; Talmud et al., 1987; Jenner et al., 1988; Rajput-Williams et al., 1988; Gavish et al., 1989; Myant et al., 19891. Recently, it has been suggested that mutations in the apoB-100 gene may be the underlying defect in some cases of familially trasmitted hypercholesterolemia [Chan, 19891. On the other hand, the genetic polymorphism of apolipoprotein E also correlates with apo B level by an indirect mechanism [Sing and Davignon, 1985; Ehnholm et al., 1986; Boerwinkle and Utermann, 19881. Other polymorphisms localized on the apo B gene or other genes and affecting the circulating level of apo B will probably be detected. The genetic heterogeneity underlying the familial aggregation of apo B level suggested by all of these publications might be an additional explanation for the difficulty in discerning a single major locus in a population not ascertained through patients, and composed of small nuclear families. In such conditions, larger samples would be required to detect the effect of few major genes and to test for genetic heterogeneity. In conclusion, although the evidence is suggestive, our study does not provide convincing evidence for a major locus influencing the apo B level in a sample of nuclear families not selected through affected individuals. The problems encountered in this analysis highlight the difficulties of the approach through “healthy” populations. Although this approach might appear attractive to epidemiologists, whose purpose is often to reach conclusions that can be extended to the whole population, the more traditional approach of geneticists based on selected large families might reduce the genetic heterogeneity and would increase the information about transmission, even at the expense of a relative loss of generality.
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ACKNOWLEDGMENTS
The authors thank Professor GCrard Siest and his collaborators at the laboratory of the Centre of MCdecine PrCventive de Vandoeuvre l&sNancy for their help during this study, Dr. Sandra Hasstedt, and Dr. Francoise Clerget-Darpoux for helpful comments. This work was supported by the Caisse Nationale d’Assurance Maladie des Travailleurs SalariCs and by INSERM. REFERENCES Akaike H (1974): A new look at the statistical model identification. IEEE Trans Automatic Control AC-19:719-723. Amos CI, Elston RC, Srinivasan SR, Wilson AF, Cresanta JL, Ward W,Berenson GS (1987): Linkage and segregation analyses of apolipoproteins A1 and B, and lipoprotein cholesterol levels in a large pedigree with excess coronary heart disease: The Bogalusa Heart Study. Genet Epidemiol4: 115-128. Austin MA, Krauss RM (1986): Genetic control of low-density-lipoprotein subclasses. Lancet 2592-595. Avogaro P, Bittollo Bon G, Cazzolato G, Rorai E (1980): Relationship between apolipoproteins and chemical components of lipoproteins in survivors of myocardial infarction. Atherosclerosis 37:69-76. Beaty TH, Kwiterovich PO, Jr, Khoury MJ, White S, Bachorik PS, Smith HH, Teng B, Snidennan A (1986): Genetic analysis of plasma sitosterol, apolipoprotein B and lipoproteins in a large Amish pedigree with sitosterolemia. Am J Hum Genet 38:492-504. Berg K (1986): DNA polymorphism at the apolipoprotein B locus is associated with lipoprotein level. Clin Genet 30515-520. Boerwinkle E, Utermann G, (1988): Simultaneous effects on the apolipoprotein E polymorphism on apolipoprotein E, apolipoprotein B, and cholesterol metabolism. Am J Hum Genet 42:104-112. Bonney GE (1984): On the statistical determination of major gene mechanisms in continuous human traits: Regressive models. Am J Med Genet 18:731-749. Bonney GE (1986): Regressive logistic models for familial disease and other binary traits. Biometrics 42~611-625. Cambien F, Warnet JM, Jacqueson A, DucimetiBre P, Richard JL, Claude JR (1987): Relation of parental history of early myocardial infarction to the level of apoprotein B in men. Circulation 76:266-271. Chan L (1989): Mutations in the apolipoprotein B-100 gene: An important underlying cause of familially transmitted hypercholesterolemia and premature arteriosclerosis? Am J Cardiol63:740-742. Davignon J, Gregg RE, Sing CF (1988): Apolipoprotein E polymorphism and atherosclerosis. Arteriosclerosis 8:1-21. De Backer H, Rosseneu M, Deslypere JP (1982): Discriminative value of lipids and apoproteins in coronary heart disease. Atherosclerosis 42: 197-203. Demenais F, Lathrop M, Lalouel JM (1986): Robustness and power of the unified model in the analysis of quantitative measurements. Am J Hum Genet 38:228-234. Demenais FM, Bonney GE (1989): Equivalence of the mixed and regressive models for genetic analysis. I. Continuous traits. Genet Epidemiol6:597-617. Deschamps JP (1987): Experience in France with periodic monitoring of family health. In Harris EK, Yasaka T (eds): “Maintaining a Healthy State Within the Individual.” New York: Elsevier Science Publishers BV (North-Holland), pp 3-8. Donner A, Koval JJ (1981): Multivariate analysis of family data. Am J Epidemiol 114:149-154. Durrington PN, Ishola M, Hunt L, Arrol S, Bhatnagar D (1988): Apolipoproteins (a) A l , and B and parental history in men with early onset ischaemic heart disease. Lancet 1: 1070-1073. Ehnholm C, Lukka M, Kuusi T, Nikkila E, Utermann G (1986): Apolipoprotein E polymorphism in the finnish population: Gene frequenciesand relation to lipoprotein concentrations.J Lipid Res 27:227-235. Friedlander Y, Kark JD, Stein Y (1986): Biological and environmental sources of variation in plasma lipids and lipoproteins: The Jerusalem Lipid Research Clinic. Hum Hered 36: 143-153. Gavish D, Brinton EA, Breslow JL (1989): Heritable allele-specific differences in amounts of apoB and low-density lipoproteins in plasma. Science 244:72-76. Goldbourt U, Neufeld HN (1986): Genetic aspects of arteriosclerosis. Arteriosclerosis 6:357-377. Hasstedt SJ,Wu L, Williams RR (1987): Major locus inheritance of apolipoprotein B in Utah pedigrees. Genet Epidemiol4:67-76.
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Hegele RA, Huang LS, Herbert PN, Blum CB, Buring JE, Hennekens CH, Breslow JL (1986): Apolipoprotein B-gene DNA polymorphisms associated with myocardial infarction. N Engl J Med 3 15: 1509-15 15. Iselius L, Carlson LA, Morton NE, Effendic S, Lindsten J, Luft R (1985): Genetic and environmental determinants for lipoprotein concentrations in blood. Acta Med Scand 217: 161-170. Jenner K, Sidoli A, Ball M, Rodriguez JR, Pagani F, Giudici G, Vergani C, Mann J, Baralle FE, Shoulders CC (1988): Characterization of genetic markers in the 3’ end of the apo B gene and their use in family and population studies. Atherosclerosis 69:39-49. Kukita H, Hiwada, Kokubu T (1984): Serum apolipoprotein A-I, A-I1 and B levels and their discriminative values in relatives of patients with coronary artery disease. Atherosclerosis 5 1:261-267. Lalouel JM (1981): GEMINI: A computer program for optimization of general nonlinear functions. Tech Rep 14, Department of Biophysics and Computing, University of Utah, Salt Lake City. Lalouel JM, Rao DC, Morton NE, Elston RC (1983): A unified model for complex segregation analysis. Am J Hum Genet 355316426, Law A, Wallis SC, Powell LM, Pease RJ, Brunt H, Priestley LM, Knott TJ, Scott J , Altman DG, Miller GJ, Rajput J, Miller NE (1986): Common DNA polymorphism within coding sequence of apolipoprotein B gene associated with altered lipid levels. Lancet 1:1301-1303. Motulsky AG (1989): Genetic aspects of familial hypercholesterolemia and its diagnosis. Arteriosclerosis 913-7. Myant NB, Gallagher J, Barbir M, Thompson GR, Wile D, Humphries SE (1989): Restriction fragment length polymorphisms in the apo B gene in relation to coronary artery disease. Atherosclerosis 77: 193-201. Namboodiri KK, Green PP, Kaplan EB, Momson JA, Chase GA, Elston RC, Owen ARG, Rifkind BM, Glueck CJ, Tyroler HA (1984): The Collaborative Lipid Research Clinics Program Family Study. IV. Familial associations of plasma lipids and lipoproteins. Am J Epidemiol 119:975-996. Pairitz G, Davignon J , Mailloux H, Sing CF (1988): Sources of interindividual variation in the quantitative levels of apolipoprotein B in pedigrees ascertained through a lipid clinic. Am J Hum Genet 43:3 1 1-321. Rajput-Williams J , Knott TJ, Wallis SC, Sweetnam P, Yarnell J, Cox N, Bell GI, Miller NE, Scott J (1988): Variation of apolipoprotein-B gene is associated with obesity, high blood cholesterol levels, and increased risk of coronary heart disease. Lancet 2: 142-1446, Rifai N, King ME (1986): Immunoturbidimetric assays of apolipoproteins A, AI, A11 and B in serum. Clin Chem 32:957-961. Siedel J , Schiefer S, Rosseneu M, Bergeaud R, De Keersgieter W, Pautz B, Vinaimont N, Ziegenhom J (1988): lmmunoturbidimetric method for routine determinations of apolipoproteins A-I, A-11, and B in normo- and hyperlipemic sera compared with immunonephelometry. Clin Chem 34: 1821- 1825. Sing CF, Davignon J (1985): Role of the apolipoprotein E polymorphism in determining normal plasma lipid and lipoprotein variation. Am J Hum Genet 37:268-285. Sniderman A, Teng B, Genest J , Cianflone K, Wacholder S, Kwiterovich P Jr (1985): Familial aggregation and early expression of hyperapobetalipoproteinemia. Am J Cardiol55:291-295. Talmud PJ, Barni N, Kessling AM, Carlsson P, Darnfors C, Bjursell G, Galton D, Wynn V, Kirk H, Hayden MR, Humphries SE (1987): Apolipoprotein B gene variants are involved in the determination of serum cholesterol levels: a study in normo- and hyperlipidaemic individuals. Atherosclerosis 67:81-89. Van Stiphout WAHJ, Hofman A, Kruijssen HACM, Vermeeren R, Groot PHE (1986): Is the ratio of apo B/apo A-I an early predictor of coronary atherosclerosis? Atherosclerosis 62: 179- 182.
Edited by I.B. Borecki and D.C. Rao
Familial Resemblance of Plasma Apolipoprotein B: The Nancy Study Laurence Tiret, Josianne Steinmetz, Bernard Herbeth, Sophia Visvikis, Roger Rakotovao, Pierre Ducimetiere, and Francois Cambien lnstitut National de la Sante et de la Recherche Medicale (INSERM) U258, Hdpital Broussais, Paris (L. T., R.R., P. D., F.C.), and Centre de Medecine Preventive (J.S., B.H., S.V.) and INSERM U115 (B.H.), Vandoeuvre Ies Nancy, France The familial resemblance of plasma apolipoprotein B (apo B) was investigated in a sample of 102 families including 419 members who volunteered for a free health checkup in the Preventive Center of Vandoeuvre-12s-Nancy, France. The mean leve l s ( k S D ) o f a p o B were 141.0(+32.6), 121.8(?27.7), and98.6(+22.6)mg/dl in fathers, mothers, and offspring, respectively. The familial correlations were 0.04, 0.13, 0.21 ( P < .Ol), and 0.47 ( P < ,001) between spouses, father-offspring, mother-offspring, and siblings, respectively, after adjustment on age, body mass index, and sex. A genetic analysis was performed using the approach proposed by Bonney, which indicated that a recessive and a dominant major-locus model appeared nearly equally supported by the data. Under the recessive model, the frequency q of the most common allele was estimated as 0.825, with a mean difference of 60.4 mgidl between high and low homozygotes. Under the dominant model, q was estimated as 0.875, with a mean increase of 34.2 mgidl in heterozygotes and high homozygotes. However, the hypothesis of Mendelian transmission and the environmental hypothesis could not be formally tested because of great numeric difficulties encountered in the estimation of the three transmission probabilities. Given these analytical restrictions, we cannot conclude in favor of a major locus influencing apo B level in our population, even though the evidence is suggestive. The genetic heterogeneity underlying the familial aggregation of apo B level, suggested by several recent publications, might explain the difficulty in discerning a single major locus in a population sample of small nuclear families, not ascertained through patients enriching the sample in high values of apo B. These findings call into question the relevance of the approach through “healthy” populations in the search for major loci influencing biological traits. Received for publication February 15, 1989; revision accepted January 30, 1990. Address reprint requests to L. Tiret, INSERM U258, HGpital Broussais, 96 rue Didot, 75674 Paris Ctdex, France.
0 1990 Wiley-Liss, Inc.
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Key words: major gene determination, healthy population
INTRODUCTION
It is now well established that genetic factors are involved in the development of arteriosclerosis and coronary heart disease (CHD), through mechanisms affecting the levels of risk factors [Goldbourt and Neufeld, 19861. This evidence is strongly reinforced by the observation of genetic diseases, such as familial hypercholesterolemia (FH), characterized by an early and accelerated development of arteriosclerosis [Motulsky, 19891. Although the genetic abnormalities at the FH locus have a large effect on an individual’s cholesterol level, they do not make a large contribution to the cholesterol variability in the general population. Conversely, it is likely that minor but common genetic defects, alone or in association, could have a much greater impact on the incidence of CHD [Davignon et al., 19881. The familial resemblance of plasma lipoprotein levels, which are strongly related to CHD, has been demonstrated in several studies [Namboodiri et al., 1984; Iselius et al., 1985; Austin and Krauss, 1986; Friedlander et al., 19861. Among lipoprotein components, apolipoprotein levels have been shown to be better dicriminators of CHD than lipid levels [Avogaro et al., 1980; De Backer et al., 1982; Kukita et al., 1984; Sniderman et al., 1985; Durrington et al., 19881. The relationship between a parental history of early myocardial infarction and an elevated level of apolipoprotein B (apo B) [Kukita et al., 1984; Sniderman et al., 1985; Van Stiphout et al., 1986; Cambien et al., 19871 suggests an underlying genetic mechanism affecting the apo B level. Using complex segregation analysis, three studies have reported evidence for a major gene effect affecting the level of apo B [Amos et al., 1987; Hasstedt et al., 1987; Pairitz et al., 19881, whereas Beaty et al. [1986], in a single Amish pedigree, found significant evidence for polygenic effects, but not for a single locus effect. These studies were conducted among samples of families ascertained through probands with lipid abnormalities or with CHD. The purpose of this study was to assess whether or not a major gene effect could partly explain the level of apo B in a sample of nuclear families attending a preventive center for a free health checkup. MATERIAL AND METHODS Population Studied
The families were recruited in the Preventive Center of Vandoeuvre les Nancy, France, where members of families living in the Nancy area can obtain a free health examination [Deschamps, 19871. From January 1985 to June 1986,200 families composed of both parents aged 60 years or less and at least one offspring aged 10 or more agreed to participate in a study of familial cardiovascular risk factors. Plasma apo B was measured after fasting in a subsample of 102 families, including 419 members. The families were generally small, with the average number of offspring 2.1. Two fathers and one mother were receiving hypolipidemic drugs at the time of examination; none was well controlled by the treatment, and they were not removed from the study. Measurement of apo 6
Apo B level was measured in whole plasma, on a Cobas-Bio centrifugal analyzer (Roche Diagnostic) using immunoturbidimetric assays [Rifai and King, 19861. The
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immunoturbidimetric method has been shown to yield reliable results for routine assays of apo B, not only in normolipemic, but also in hyperlipemic sera [Siedel et al., 1988). The change in turbidity of the sample against a reagent blank was measured at 340 nm after 0.5 and 360 sec of incubation at 37°C. The 0.5 sec reading serves as a sampleplus-reagent blank. Sample values were calculated automatically by the Cobas-Bio DENS program (Data Evaluation for Nonlinear Standard Curves) to fit the standard curve values to a four-parameter logit-log curve model. Day-to-day imprecision (coefficient of variation) over 30 days was 4% at a concentration of 117 mg/dl. Statistical Methods
The first step of the analysis was to assess whether or not there was evidence for familial resemblance in apo B level. The second step was to determine if such a resemblance could be partly explained by the presence of a gene having a major effect on the phenotype. Adjustment for covariates. Analyses were performed on the residuals of apo B after linear adjustment on age, age2, sex, body mass index (BMI, computed as the ratio of weight to height2), BMI', age*sex, BMI*sex and age*BMI. Including interaction terms with sex allowed us to consider males and females simultaneously despite possible heterogeneity between sexes in the proportions of apo B variability explained by age and BMI. Computation of familial correlations. The maximum likelihood method proposed by Donner and Koval [ 19811 was used to compute the familial correlations jointly. Distribution of the trait is assumed to be multivariate normal within every family, with identical means, variances, and correlations among families. The parameters of this model were estimated as a restricted case of the more general model described in the next section. Modeling a major gene effect. An extension of the method proposed above, similar to the one proposed by Bonney [1984], was used to investigate the compatibility of the data with a major gene hypothesis. Under this model, variation among individuals for a quantitative trait is a consequence of a major gene effect and a residual variation, which could be attributable to polygenes and/or environmental factors, the detailed components of this residual variation not being analyzed. Let x = (xl,x2, x3, . . . xn) be the vector of phenotypes of a given family and g = (gl,82, 83, . . . gn) the vector of their major genotypes ( 1 indexing the father, 2 the mother, and 3 . . . n the offspring). Assuming a two-allele gene, there are three possible genotypes (aa, Aa, and AA) for each individual. If A is the allele associated with an elevation of the level of the trait, the contribution,mean effect, of the major genotype to the trait can be defined as the difference between the population mean of individuals having one (pAa)or two ( p A A ) copies of the A allele and that of individuals not having the A allele (pas). If 6, = p, - pas, we see that 6,, = 0, whereas 8Aaand SAA may differ from zero. Fixing EAa = 0 specifies the recessivity of the = 6 A A specifies dominance. major gene, The vector of residual phenotypes for a family after adjustment on major genotype is then y = x -ti,, where 6, = (Sg,, tig2,. . . S,,) is the familial vector of mean effects associated with the genotype. Let f(x I g ) be the conditional probability density of the phenotype vector x given the genotype g . The likelihood of a family may be written as:
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L(x) = X:$(x I g) P(g) = Xgl X g 2 C@ . . . X,,f(X
Ig) P(g1, 82, 83,
. . . gn).
In the case where the parents are genetically unrelated and the genotypes of the offspring are independent given the genotype of their parents, the joint probability of familial genotype is: P ( g l , g 2 , g 3 , . . . gn) = P(gl)P(g2)P(g3 I g I , 82) . . . P(gn 1 g I , g2).
The probability of the three possible genotypes in parents are determined by the Hardy-Weinberg proportions P(aa) = q2,P(Aa) = 2q( 1-q) and P(AA) = ( 1-q)2, where q is the frequency of the most common allele a. The conditional probabilities of the genotypes of the offspring, given the genotypes of their parents, are computed using the transmission probabilities (71, 72, and 73) which are the probabilities that individuals aa, Aa, and AA, respectively, transmit the a allele. Under the Mendelian hypothesis of inheritance, 71, 72, and 73 are equal to 1, 0.5, and 0, respectively. Fixing q = 71 = 72 = 73 specifies a nontransmitted environmental mixture of distributions. The conditional probability densityflx I g) is assumed to be n-variate normal, with mean vector ps and covariance matrix X.Because y = x - a, this is equivalent to saying that the conditional density of the residual vectory, given g, is the n-variate normal with residual mean vector paaand the same covariance matrix X.The elements of the n-vector paaare the residual means of the trait among fathers, mothers, and offspring, respectively, after adjustment for the major gene effect. The diagonal elements of 2 are the residual variances of the trait among fathers, mothers, and offspring, respectively, and the off-diagonal elements are the residual covariances among relatives. Residual familial correlations are derived from this matrix. In this model, fatheroffspring and mother-offspring correlations are estimated separately. Although the size of the vector paaand of the matrix X varies with the size of the family, the parameter values are assumed to be identical among families, whatever the size of the family. This model is equivalent to the class D regressive model introduced by Bonney [ 19861, specifying equal sib-sib correlations given major genotypes. The covariance matrix 2 is the same as that defined by Bonney [ 19841 in his regressive model, if one assumes equal sib-sib correlations and different father-child and mother-child correlations. The likelihood of a family is then a known function of the parameters paa,C, q, 6, and 7. All parameters defined above were estimated by maximizing the likelihood of the sample of families. The likelihood function was maximized using the program GEMINI [Lalouel, 19811. Different nested models were tested by comparing the likelihood L2 of a restricted model M2 with k2 parameters to the likelihood L, of a more general model M I with kl parameters, as 2(lnLl - InL2) is approximately distributed as a x2 with (k, - k2) df. When the models are not nested, an alternative test statistic based on Akaike’s information criterion (AIC) can be used to compare the fit of different models [Akaike, 19741. For a given model, this statistic is computed as AIC = -2 InL twice the number of parameters estimated. The model with the lowest AIC is considered to be the most parsimonious model providing the best fit to the data. For each individual in the sample, genotypic probabilities were computed under the major-locus model. The genotypic probability p i jthat an individual i has the genotypej given the family structure and phenotypes, is:
+
p.. 1J = L(x I g,
=j
) * P(g; = j ) / L f x ) .
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TABLE I. Mean Values (Standard Deviations) of Age, Body Mass Index (BMI), and Apolipoprotein B (apo B) Level in the Sample
Age Body mass index (kg/rn2) Apo B (mg/dl) Adjusted on covariatesa
Fathers
Mothers
Offspring
43.3 (5.3) (3.3) 25.1 141.0 (32.6) 116.0 (32.1)
41.0 (4.8) 23.6 (3.8) 121.8 (27.7) 114.7 (26.9)
15.4 (2.9) 19.4 (2.7) 98.6 (22.6) 113.9 (22.6)
"age, age2, sex, BMI, BMI', age*sex, BMI*sex, age*BMI.
RESULTS
The means and standard deviations (SD) of age, BMI, and apo B in the sample are given in Table I. The covariates explained 32.6% of the variability in apo B levels in the whole sample. The sex*BMI interaction was significant ( P < 0.05), whereas the sex*age and the BMI*age interactions were not. Variances among fathers, mothers, and offspring, respectively, were not much reduced after adjustment (Table I). The residuals from the regression were added to the mean of apo B in the sample (1 14.6 mg/dl) to obtain adjusted apo B levels. Adjusted apo B levels ranged from 43 mg/dl to 199 mg/dl. After adjustment, positive skewness (0.39) and kurtosis (0.59) of apo B level distribution were both significant. The familial correlations of adjusted apo B were strong among siblings (0.47; P < .OOl), moderate between mother and offspring (0.21; P < .Ol), and nonsignificant between father and offspring and between spouses (0.13 and 0.04, respectively). The model including familial correlations (model 1, Table 11) was much better supported by the data than the model assuming no familial resemblance (model 0) (x2 = 39.2 with 4 df; P < 0.001). The results of a series of analyses testing different genetic models are shown in Table 11. A model assuming a codominant major gene effect with residual familial correlations was first investigated. Exploration of the likelihood surface under this model showed two peaks, specifying different estimates of the parameters: under the first solution, the frequency q of the most common allele was estimated as 0.838 with a mean effect tiAaof - 2.0 mg/dl in heterozygotes (not significantly different from 0) and a mean effect tiAAof 62.9 mg/dl in high homozygotes; under the second solution, the frequency q of the most common allele was estimated as 0.875 with a mean effect tiAaof 36.0 mg/dl in heterozygotes and a mean effect 8 A A of 10.7 mg/dl in high homozygotes, indicating a model of overdominance, which seemed biologically unlikely. For this reason, the first solution was adopted for the comparison with further models. The codominant model (model 2) was better supported than the model stating no major gene effect (model 1) (x2 = 11.O with 3 df; P < .05). Residual familial correlations were significant, as shown by the comparison of model 3 to model 2 (x2 = 11.4 with 4 df; P < 0.05). The recessive model (model 4), assuming tiAa= 0, was associated with the same likelihood as the codominant model. Again, exploration of the likelihood surface under this model showed two maxima; under the first solution, the frequency q of the most common allele was estimated as 0.696 with a mean effect of 43.1 mg/dl in high homozygotes, whereas under the second solution q was estimated as 0.825 with a mean effect of 60.4 mg/dl. This second solution was adopted subsequently, as it was associated with lower variances of the parameter estimates and
39.2** 4 3,887.2
Ob
3,867.2
3 3,882.2
11.o*
(0.5) (.O) 3,856.2 1
(1.0)
(.O) (.O) (.O)
0.12 0.15 0.29 0.42 0.838 - 2.0 62.9
0.04 0.13 0.21 0.47 0.663 18.9 54.1 (1 .O) (0.5) (.O) 3,867.6 2 11.4* 4 3,885.6
(0
28.4 19.0 15.7
31.0 22.2 21.2
32.0 26.7 22.6
(1.0)
101.7 99.7 99.5
115.2 112.2 114.0
115.9 114.7 114.7
Model
(0.5) (.O) 3,856.2" 2 0 (NS) 1 3,880.2
(1.0)
0.11 0.15 0.28 0.42 0.825 (.O) 60.4
30.9 22.1 21.1
114.5 111.6 113.2
Recessive gene + residual correlations
4
+
3,881.2
1
-.O 0.10 0.44 0.875 (34.2) 34.2 (1.0) (0.5) (.O) 3,857.2 2 1 .O (NS)
-.O
29.1 21.6 17.7
108.1 106.5 106.9
Dominant gene residual correlations
5
0.697 (.O) 3,855.8 4 0.4 (NS) 1 3,881.8
(1.0)
0.807 (.O) 65.3
0.44
0.12 0.15 0.29
30.6 21.8 21.5
114.1 111.3 113.7
6 Same as model 4 with free transmission parameters
-.O -.O 0.11 0.46 0.863 (34.1) 34.1 (1.0) 0.537 0.518 3,856.6 5 0.6 (NS) 2 3,884.6
28.8 21.5 17.7
107.3 106.1 107.1
7 Same as model 5 with free transmission parameters
"Two peaks of the likelihood surface were observed; the solution shown in the table is the one associated with the greatest likelihood (see text). bModel 0 is without major gene and without familial correlations ( - 2 In L = 3906.4). *P < .05. **P < ,001. NS = not significant.
Df AIC
x2
72 73 -2 I n L Alternate model
71
&A,
6A,
Residual means Fathers Mothers Offspring Residual SD Fathers Mothers Offspring Residual correlations Spouses Father-offspring Mother-offspring Sib-sib 4
Codominant gene, no residual correlations
Codominant gene residual correlations
Familial correlations, no major gene
+
3
2
1
TABLE 11. Test of Genetic Hypotheses for Adjusted apo B in 102 Families, n = 419
3,885.0
0.11 0.14 0.28 0.44 0.836 (.O) 60.4 (0.836) (0.836) (0.836) 3.861.0
30.8 22.1 21.5
114.5 111.6 113.5
Environmental transmission
8
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a better likelihood. The dominant model (model 5), assuming 8 A a = tiAA,was also nearly equally supported by the data. Under this model, q was estimated as 0.875, with a mean effect of 34.2 mg/dl in heterozygotes and high homozygotes. Estimates of the residual spouses and father-child correlations were nearly zero, but with large standard errors (0.13 and 0.11, respectively). Comparison of the recessive and dominant models, using AIC statistic, indicated that the recessive model fit the data slightly better. To test the hypothesis of Mendelian inheritance, the transmission parameters were estimated under the recessive and dominant models (models 6 and 7). In both cases, 71 converged to its bound and was then fixed to 1. Because of numeric difficulties in estimating 72 and 73 simultaneously under the recessive model, we investigated a model in which 72 alone was left free, a possible approach suggested by Lalouel et al. [1983]. This resulted in an estimate of 72 of 0.697, compatible with the Mendelian expected value of 0.5 (x2 = 0.4 with 1 df; P > 0.05). Under the dominant hypothesis, 72 and 73 were estimated as 0.537 and 0.518, respectively, these values also being compatible with a Mendelian transmission (x2 = 0.6 with 1 df; P > .05). However, the convergence problems restrict the validity of the likelihood-ratio statistic. Again, model 6 (recessive) had a lower AIC value than model 7 (dominant). The model assuming an environmental mixture of two distributions was also investigated (model 8). Although it could not be formally tested against a more general model with free transmission probabilities because of numeric problems, the AIC value indicated that the fit of the environmental model was slightly worse than that of the model 6. Finally, when comparing all the models using the AIC statistic, the lowest AIC value occurred with the Mendelian recessive model (model 4). DISCUSSION
This study was based on a sample of families volunteering for a free health checkup. Although these families were probably not representative of the whole population of the region, depending on the bias that is associated with a free health checkup, recruitment for the study was not based on lipid abnormalities or cardiovascular diseases, as with the studies previously reported [Amos et al., 1987; Hasstedt et al., 1987; Pairitz et al., 19881. However, there is a likely selection bias in the opposite way, as one can hypothesize that individuals having cardiovascular disease or documented risk factors such as hyperlipidemia are medically followed elsewhere and probably do not attend the Preventive Center. For instance, it has been shown that adults attending the Preventive Center had a lower BMI than adults in the same age groups of the two study populations of the WHO Monica project close to the Nancy area (Tiret et al., unpublished). The genetic model used in this analysis, similar to the one proposed by Bonney [1984], assumed a major gene effect and possible residual covariances. The residual covariances are not explicitly modeled in terms of multifactorial inheritance, reflecting polygenic and/or culturally transmitted variation, as in the traditional mixed model. However, the class D regressive model, which is equivalent to our model, has been shown to be mathematically and numerically equivalent to the mixed model [Demenais and Bonney , 19891. In particular, major gene effects, when present, are correctly detected and estimated. The regressive model has the advantage of being more flexible than the mixed model, for example, allowing different father-offspring and mother-offspring correlations.
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TABLE 111. Phenotypic Values (Adjusted Apo B) and Genotypic Probabilities Under the Recessive and Dominant Models for Two Selected Families* Adjusted apo B (mgldl) Family 137 Father Mother Offspring Offspring Family 188 Father Mother Offspring Offspring
103.7 117.2 190.0 182.2 129.4 157.5 164.5 103.0
Genotypic probabilities Recessive model
Dominant model
aa 0.01 0.01 0.01 0.02 aa 0.40 0.37 0.38 0.43
aa 0.41 0.48 0.00 0.01 aa 0.73 0.08 0.01 0.98
Aa 0.97 0.98 0.01 0.01 Aa 0.59 0.30 0.16 0.57
AA 0.02 0.01 0.98 0.97 AA 0.01 0.33 0.46 0.00
Aa 0.47 0.42 0.96 0.95 Aa 0.27 0.92 0.93 0.02
AA 0.12 0.10 0.04 0.04 AA 0.00 0.00 0.06 0.00
*Rather favoring the former (family 137) or the latter model (family 188)
We experienced numeric difficulties in the analysis of these data. Multiple maxima were found in the likelihood, and several solutions appeared equally supported by the data; all suggested that the distribution of apo B is a mixture of two components. The recessive and the dominant models are detecting different components, with means separated by 60.4 mg/dl(2 to 3 residual SD) under the recessive model and 34.2 mg/dl (1 to 2 residual SD) under the dominant model. Comparison of the likelihoods of each family under the recessive and the dominant models, respectively, showed that the families favoring the recessive model were those with extreme apo B levels, such as Family 137, whereas families that supported the dominant model were those with moderately high apo B levels, such as family 188 (Table 111). This is explained by the fact that under the recessive model, q was estimated as 0.825, specifying a very low probability (0.03) of belonging to the upper distribution; therefore, only extreme apo B levels would fall in that distribution. On the other hand, under the dominant model, q was estimated as 0.875, specifying a higher probability (0.23) of belonging to the upper distribution. Great difficulties were also encountered in estimating the three transmission probabilities simultaneously. We had to fix one or two of these parameters; so the true likelihood of the unrestricted model would be better than the one obtained, and therefore the x2 for testing the Mendelian hypothesis would be larger, but with more degrees of freedom. As another consequence of these numeric problems, the environmental hypothesis could not be formally tested. Comparison of the likelihood under the different models, using the AIC statistic, indicated that the environmental hypothesis had a slightly worse fit than the hypothesis of transmission of a major effect. However, Demenais et al. [1986] showed that protection against the false inference of a major gene required estimation of the three transmission probabilities and testing both the hypothesis of Mendelian transmission and the hypothesis of no transmission of major effects. Because we were unable to fulfill these two conditions, we cannot conclude in favor of a major locus in our population, even though the evidence is suggestive. Using complex segregation analysis, Hasstedt et al. [ 19871and Pairitz et al. [ 19881 have both detected a codominant single major locus influencing the apo B level, with the frequency of the most common allele being 0.847 and 0.826, respectively. This
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major locus had similar effects on apo B level in both studies. The mean level (mg/dl) in low homozygotes was 110.5 in Hasstedt et al. [I9871 and 86.2 in Pairitz et al. [1988] and the separation between the low and middle means was 3 1.4 mg/dl and 43.3, respectively, whereas separation between low and high means was 97.6 and 103.2, respectively. Both studies included pedigrees ascertained through patients with coronary artery disease or lipid abnormalities, which might explain the detection of a third mode in the apo B distribution that was difficult to discern in our sample of families not ascertained through patients. For example, there were several individuals with sex- and age-adjusted apo B levels above 200 mg/dl in the sample of Hasstedt et al. [1987], whereas none was observed in our sample. Although we could not reach the same conclusion as the above-mentioned authors, some of our results are not in disagreement with their findings. First, the proportion of admixture in either of our models is comparable to that estimated by these authors. Second, in our data, the effect separating the two modes of the distributions under the dominant model is similar to that reported for heterozygotes in their codominant model, whereas the effect separating the two modes under the recessive model is slightly lower than that reported for high homozygotes. These findings suggest that the codominant hypothesis of inheritance is more likely, and because our sample was not sufficiently enriched in high values of apo B, the analysis lacked power to distinguish between the two upper distributions of heterozygotes and high homozygotes. These distributions were then mingled in one distribution, simulating either a recessive or a dominant model. The possibility that alleles situated at different loci may affect the level of apo B in different families is strongly supported by recent observations. Several studies have reported polymorphisms of the apo B gene that appear to correlate with lipids or apolipoproteins levels, and/or CHD [Law et al., 1986; Berg, 1986; Hegele et al., 1986; Talmud et al., 1987; Jenner et al., 1988; Rajput-Williams et al., 1988; Gavish et al., 1989; Myant et al., 19891. Recently, it has been suggested that mutations in the apoB-100 gene may be the underlying defect in some cases of familially trasmitted hypercholesterolemia [Chan, 19891. On the other hand, the genetic polymorphism of apolipoprotein E also correlates with apo B level by an indirect mechanism [Sing and Davignon, 1985; Ehnholm et al., 1986; Boerwinkle and Utermann, 19881. Other polymorphisms localized on the apo B gene or other genes and affecting the circulating level of apo B will probably be detected. The genetic heterogeneity underlying the familial aggregation of apo B level suggested by all of these publications might be an additional explanation for the difficulty in discerning a single major locus in a population not ascertained through patients, and composed of small nuclear families. In such conditions, larger samples would be required to detect the effect of few major genes and to test for genetic heterogeneity. In conclusion, although the evidence is suggestive, our study does not provide convincing evidence for a major locus influencing the apo B level in a sample of nuclear families not selected through affected individuals. The problems encountered in this analysis highlight the difficulties of the approach through “healthy” populations. Although this approach might appear attractive to epidemiologists, whose purpose is often to reach conclusions that can be extended to the whole population, the more traditional approach of geneticists based on selected large families might reduce the genetic heterogeneity and would increase the information about transmission, even at the expense of a relative loss of generality.
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ACKNOWLEDGMENTS
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Edited by I.B. Borecki and D.C. Rao
