INTRODUCTION

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The inheritance of asthma is evident from its family concordance, with estimates of heritability as high as 60-70% (1, 2). The form of inheritance, however, is not well understood. It is unlikely to involve a single two-allele locus, but rather a polygenic or oligogenic mode of inheritance involving a number of intermediate or subphenotypes with roles in its pathogenesis (3), as well as environmental interactions. Such intermediate phenotypes may be associated with, for example, IgE levels (4, 5), bronchial hyperresponsiveness (6), or specific reactivity to aeroallergens (7).

High eosinophil counts are known to be related to asthma (8), suggesting therefore that this may be an intermediate phenotype for asthma amenable to genetic analysis. Eosinophils are major players in the pathogenesis of asthma and in immune responses to helminthic parasites (9, 10). The accumulation and activation of eosinophils during the late-phase allergic reaction with the release of toxic products, for example, eosinophilic cationic protein, is thought to be responsible for much of the tissue damage associated with chronic allergic reactions (11, 12). A number of cytokines, particularly interleukin 5 (IL-5) (13), as well as IL-3 and granulocyte-macrophage colony-stimulating factor (GM-CSF) (14), are known to influence eosinophil growth, maturation, and differentiation. In this context, a segregation analysis has indicated a major gene expressed in a codominant fashion, controlling IL-5 production in subjects infected with Schistosoma mansoni (15). Another study indicated familial aggregation of eosinophil levels in populations with a high incidence of parasitic helminths, although genetic and/or environmental factors were unresolved (16).

Few studies have assessed genetic and environmental effects of eosinophil levels in populations unaffected by helminths. One such study on blood cells in monozygotic and dizygotic twins indicated that the level of eosinophils fit a model with a heritability of 24%, with 76% of the variation being due to specific environmental influences. However, a model with only specific environmental effects fit the data equally well (17).

The aim of this study is to investigate whether there is familial aggregation of eosinophil levels in an unselected community population, and if so, to determine whether a Mendelian pattern of inheritance involving a major gene with two alleles can be detected.

	METHODS

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Families for this study were enrolled between 1980 to 1984 in the Tucson Children's Respiratory Study (CRS), a large longitudinal study investigating the risk factors for asthma and other acute and chronic lower respiratory illnesses in infancy and childhood (18). This study was approved by the Human Subjects Committee of the University of Arizona, and parents have signed consent forms at all phases of the study. Blood was drawn for an in-depth evaluation, including determination of eosinophil and serum IgE levels, of all consenting subjects when fathers, mothers, and children were at mean ages of 36, 33, and 8 yr, respectively. As one of our objectives was to assess genetic heterogeneity across ethnic groups, only families in which the biological parents declared they were either non-Hispanic white or Hispanic were included, these being the main ethnic groups in the Tucson area. There are too few representatives of other ethnic groups to consider them separately. There were 644 nuclear families, of 1,151 enrolled, with a total of 2,097 family members with information on eosinophil levels. These families comprised 97 families (333 members) with both parents Hispanic, 458 families (1,482 members) with non-Hispanic white parents, and 89 families (282 members) with one Hispanic and one non-Hispanic white parent.

Eosinophil levels were log₁₀ transformed owing to a positive skew and expressed as the number of eosinophils × 10⁶ L¹ (i.e., number per cubic milliliter). Percent eosinophils was based on a 300 count differential. Both measures were initially adjusted for age at the time of blood draw within sex and ethnic group and expressed as z scores. Because both season of the year and year of blood draw were significantly related to these z-score measures (p < 0.02 for season and p < 0.0001 for year), a further adjustment was made using a regression analysis employing dummy variables for season and year, and the final variables were expressed as z-scored residuals. Log₁₀ serum IgE levels were age and sex adjusted and expressed as z scores, as described previously (4).

Questionnaires administered at enrollment and during the in-depth evaluation, completed by parents for themselves and on behalf of family members, provided information on demographic variables. Current and past smoking habits and active or past physician-diagnosed asthma status (physician diagnosis with or without attacks in the past year) were assessed by questionnaires at the time of the in-depth evaluation.

Statistical Methods

Familial correlation coefficients were calculated using the program FCOR within the Statistical Analysis for Genetic Epidemiology (SAGE) software package (19).

To examine the fit of postulated genetic and nongenetic (environmental) models to the data we applied segregation analysis using regressive models for continuous traits (20) as previously described (4). Briefly, segregation analysis for continuous variables is a method of modeling data to test statistically whether a mixture of normal distributions fits the data better than a single distribution, and to detect Mendelian ratios in the transmission of a trait between generations. Essentially, the model translates assumptions about genetic and environmental trait determinants into mathematical equations with a number of model parameters that are estimated. Depending on the assumed correlations between siblings, there are several classes of regressive models for continuous traits. The class D model, used in these analyses, assumes that correlations between siblings are equal (i.e., do not depend on the rank of the sibling), but are not due to common parentage alone (21). Application of these models to continuous data has been shown to yield results equivalent to those of mixed models (22).

Regressive models, which are incorporated into the SAGE software package (19), assume the trait to be a linear function of the major genotypes, the phenotypes and genotypes of antecedents, and other covariates. Mendelian inheritance, if present, is presumed to be through a single autosomal locus with two alleles A and B. Therefore, three "types" of individual are assumed, labeled AA, AB, and BB. For genetic models these types correspond to the three possible genotypes and the means µ_AA, µ_AB, and µ_BB of these distributions are parameters estimated by the model.

Random mating and Hardy-Weinberg equilibrium proportions are assumed (23). Thus the frequency distribution of the types can be defined in terms of q_A, a model parameter for the frequency of allele A in the founders (in this case the parents), where the type frequencies are as follows:

Transmission parameters ( values) represent the probability of a parent of a given type transmitting allele A to his or her offspring. The probability of nonfounders (in this case the children) having each "type" is a function of allele transmission from parent to offspring. For Mendelian transmission the transmission parameters correspond to _AA = 1.0, _AB = 0.5, and _BB = 0.0. In addition, because the assumption of normality, conditional on type, is critical for the methods described above (20) the residual eosinophil z scores were simultaneously normalized using the standardized Box-Cox transform (24) as previously described by Martinez and colleagues (4). This transform is implemented within the SAGE software package (19), and computes two additional parameters ₁, a power transformation parameter and ₂, a constant. A residual variance, ², is also estimated as well as regression coefficients ( values) for any covariates included in the models.

Model parameters are constrained (fixed) to define each of three hypothetical genetic models, namely, Mendelian arbitrary (three distributions with three means µ_AA, µ_AB, µ_BB estimated), and dominant or recessive (each two distributions with two means estimated where µ_AA = µ_AB; µ_BB represents the allele A dominant model, and µ_AA ; µ_AB = µ_BB represents the allele A recessive [B dominant] model). The Mendelian codominant model is a special case of the Mendelian arbitrary model. In the codominant model µ_AB is distinct from the two homozygous means, µ_AA and µ_BB, indicating possible expression of both alleles. In addition, three nongenetic models are defined, namely, no major type or one distribution, and two environmental models. For the environmental models types are assumed to exist, possibly attributable to random environmental factors, but not to be transmitted from generation to generation. In the first environmental model transmission probabilities are thus made equal to the gene frequency, assuming no heterogeneity between generations. The second environmental model allows for heterogeneity, but no transmission, between generations. In this case transmission probabilities, but not the gene frequency, are constrained to be equal. The models are used to predict the distribution of the trait in the family data. An unrestricted model in which parameters are unconstrained represents the best fit to the observed data, given the model parameters. The different hypothetical models are tested against the general unrestricted model using likelihood ratio tests (see below). If the pattern predicted by the hypothetical model is not significantly different from the pattern predicted by the unrestricted model, this provides evidence in support of the hypothetical model. Alternatively, if the hypothetical model differs significantly from the unrestricted model then that hypothesis is rejected.

Evidence of a single major gene is considered to be present if three criteria are met (25), namely: (1) a model with more than one type fits the data significantly better than the "no major type" model; (2) the unrestricted model does not fit the data significantly better than the Mendelian model(s); (3) the unrestricted model fits the data significantly better than the environmental model. The specific inheritance mechanism is then tested by comparing the fit of the recessive and dominant models to that of the arbitrary model. If there is evidence of a major gene, significant residual family correlation parameters (spouse- spouse, parent-offspring, sibling-sibling) indicate an additional multifactorial component, representing genetic effects, probably polygenic, and/or the effects of a shared environment, beyond major gene segregation.

To evaluate specific hypotheses the likelihood ratio test was used by taking the difference between twice the negative of the log_e likelihoods of the models of interest. This difference has a ² distribution and can be used to give a probability level, with the degrees of freedom being the difference in the number of parameters estimated between models. When parameter estimates converge to bounds, probability was assessed at the midpoint of a range of degrees of freedom as described in detail previously (3, 26). The Akaike information criterion (AIC) was also used, as previously described (4), to assess which model best fit the data in cases of competing models where one was not a strict subset of the other, with the same number of parameters [AIC = 2 (ln-likelihood) + 2p, where p is the number of parameters estimated]. AICs were calculated with (AIC_max) and without (AIC_min) parameters that were fixed at a bound. Because conclusions were similar with both AIC calculations, only AIC_min is presented in Results.

Segregation analyses were performed within ethnic groups and for the total group, using both the z-scored residuals for the number of eosinophils × 10⁶ L¹ and percent eosinophils. Tests for heterogeneity between ethnic groups were performed as described previously (4). Active and past smoking were assessed as covariates, as well as active and past physician-diagnosed asthma and serum IgE levels. For this purpose we used option 3, in the SAGE program REGC, in which a major variate is adjusted for covariates (19). In Results the means of the type distributions are expressed as z scores that have been recalculated from the means of the Box-Cox transforms obtained from the different models, as previously reported (4). For models adjusted for covariates, the adjusted value was recalculated from the transformed means and further expressed as a z score of the adjusted mean and standard deviation calculated from the covariate coefficients of the model (19).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

A comparison of the familial characteristics of the 644 families included in the segregation analyses and the 507 families not included is presented in Table 1. Briefly, parents of families included were slightly, but significantly, older, more likely to be married, and to have at least one parent with some college education, when compared with parents of families not included. However, families included were not more likely to have parents with asthma or parents who smoked.

Results were entirely equivalent using either the number of eosinophils × 10⁶ L¹ or the percent eosinophils, and are presented for the former only. Table 2 shows the familial correlation coefficients for eosinophil levels adjusted for age, sex, and ethnic group (ZNEOS), and further adjusted for season and year of blood draw (ZREOS) for the total group, non-Hispanic white, Hispanic, and non-Hispanic white/Hispanic families, respectively. Significant familial correlations were noted only in the total group and in the non-Hispanic white group. Adjusting for season of blood draw (ZREOS) had the effect of decreasing the spouse-spouse correlations, which became nonsignificant in these groups. This adjustment had little effect on the other familial correlations in these groups. Thus, for the adjusted number of eosinophils × 10⁶ L¹ variable, ZREOS, spouse-spouse correlations are low and nonsignificant, whereas the parent-offspring and sibling-sibling correlations are significant and higher, indicating intergenerational transmission. Also, sibling-sibling correlations are higher than parent-offspring correlations, suggesting either dominance variance or additional family associations, over and above that due to common parentage. In addition, the mother-offspring correlation is significant and is higher than the father-offspring correlation, which is not significant.

Segregation analyses for each ethnic group showed that there was significant heterogeneity associated with ethnic group (² = 58.3, df = 28, p < 0.001, using the unrestricted model plus residual family correlations). Further analysis was limited therefore to non-Hispanic white families, that being the group with significant familial correlations indicative of possible genetic transmission.

Table 3 shows the results of fitting class D regressive models to the data of the non-Hispanic white families. Parameter estimates with residual family correlations (spouse-spouse, mother- and father-offspring, sibling-sibling) are shown. This segregation analysis demonstrated that all models were clearly significantly different from the unrestricted model and could therefore be rejected. Thus there is no evidence in this analysis of a single major gene with two alleles. However, genetic and nongenetic models with up to three distributions fit the data better than a model with one distribution (row 3 versus row 2 of Table 3, ² = 76.8, df = 2-3, p < 0.001; and row 5 versus row 2, ² = 77.4, df = 2-3, p < 0.001). Comparison of the three distributional genetic and nongenetic models without intergenerational heterogeneity indicated little difference in log_e likelihood, with the nongenetic environmental model having a marginally better fit, according to the AIC (3,903.6 versus 3,904.2). The nongenetic model allowing for intergenerational heterogeneity did not fit the data as well (AIC = 3,913.0). Thus, in this segregation analysis the data can be represented best by a model with more than one distribution that may be explained either by intergenerational transmission with no evidence for a major gene, or by nontransmissible environmental factors. However, comparison of the "no major type" model (row 2 of Table 3) with an equivalent model that excluded parent-offspring, spouse-spouse, and sibling-sibling correlations indicated a strong familial component (² = 55.9, df = 4, p < 0.0001). This residual familial component was significant over and above all seven models tested. Of the familial correlations, however, only the mother-offspring and sibling-sibling correlations were significant (² = 20.02, df = 1, p < 0.001; ² = 32.82, df = 1, p < 0.001, respectively). Thus over and above the evidence for more than one distribution there are significant familial correlations, likely representing a polygenic/ multi-factorial component with a strong maternal influence.

Neither active nor past smoking contributed significantly to the fit of the models (² = 0.0, df = 1, p > 0.975 for current and ² = 2.5, df = 1, p > 0.10 for past smoking). However, physician-diagnosed currently active asthma was significant (² = 18.0, df = 1, p < 0.001), while physician-diagnosed not currently active asthma was of borderline significance (² = 3.2, df = 1, p = 0.07). These results are reported for the no major type model plus residual family correlations and were entirely equivalent for the unrestricted model plus residual family correlations. A further segregation analysis was conducted, therefore, which included the two asthma variables as covariates. In the non-Hispanic white families the mean values for ZREOS for current and noncurrent physician diagnosed asthma and no asthma were 0.33, 0.16, and 0.14, respectively, p < 0.0001.

Table 4 shows the parameter estimates from segregation analysis of ZREOS, with residual family correlations (spouse- spouse, mother- and father-offspring, sibling-sibling), plus the covariates currently active and nonactive physician-diagnosed asthma. All familial correlations were lower after this adjustment (Table 4, row 2 versus Table 3, row 2). Again all models were significantly different from the best fitting unrestricted model, implying no evidence of a single major gene with two alleles. However, in this analysis, in contrast to the analysis presented in Table 3, the genetic (Mendelian) model with three-distributions is clearly significantly different from the one distribution model (Table 4, row 3 versus row 2, ² = 74.1, df = 3, p < 0.001) and at the same time fits the data better than the three distribution environmental model (AIC = 3,701.7 versus 3,715.2). The best fitting Mendelian dominant and recessive models are mirror images of one another in these analyses, representing a recessive model with a gene frequency ± standard deviation of 0.14 ± 0.16, where allele A is associated with low eosinophil levels, and a comparable dominant model with a gene frequency of 0.86 ± 0.16, in which case allele A is associated with a higher eosinophil level. A Mendelian recessive of high eosinophil levels model fit the data significantly worse (AIC = 3,756.4). Mendelian means decreasing (µ_AA  µ_AB  µ_BB) and increasing (µ_AA  µ_AB  µ_BB) models were similar in all respects to the best fitting Mendelian dominant (q_A = 0.86 for high allele A) and recessive (q_A = 0.14 for low allele A) models, respectively (AIC = 3,700.8 for both decreasing and increasing models). The three-distribution genetic model was not significantly different from the best fitting dominant or recessive, two-distribution models (² = 1.0, df = 1, p > 0.25 for both models), which have the lowest and identical AICs (3,700.7), representing the best fitting model(s) in terms of this criterion. The comparison of the best fitting Mendelian recessive of low eosinophil levels (or equivalent dominant of high) model with the no major type model (Table 4, row 4 versus row 2, ² = 73.1, df = 2, p < 0.001) indicates that this Mendelian model is significant in the presence of residual family correlations, i.e., in a mixed model context. We estimate from the Box-Cox transformed values of the means of the Mendelian recessive model (µ_AA = 1.44, µ_AB = µ_BB = 5.24, ² = 0.67) that approximately 30% of the covariate-adjusted eosinophil variability is accounted for by this model (27). A comparison of this model with an equivalent model excluding residual family correlations (² = 76.2, df = 4, p < 0.001) indicates that there are significant additional familial factors contributing to the inheritance of eosinophil levels.

While there is no support for a single major gene, these data show evidence of familial transmission of a major factor that does not fit a Mendelian pattern of inheritance. This suggests a more complex genetic model (possibly oligogenic) than a single major gene with residual family correlations. However, only the mother-offspring and the sibling-sibling correlations were significant residual family effects (² = 15.8, df = 1, p < 0.001; ² = 14.8, df = 1, p < 0.001, respectively, over and above Mendelian recessive of low, dominant of high model). Such additional familial factors may comprise both genetic (polygenic) and environmental components (i.e., polygenic/multifactorial), with a strong maternal influence. Results were fully equivalent with the addition of age- and sex-adjusted log₁₀ IgE levels, which was a significant covariate (² = 89.3, df = 1, p < 0.001) (Pearson  for ZREOS and age- and sex-adjusted log₁₀ IgE was 0.23, p < 0.0001). Results were also equivalent when adjusting for the two asthma covariates before the segregation analyses.

	DISCUSSION

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Our results demonstrate significant heterogeneity in the control of eosinophil levels by ethnic group. Familial correlations were significant only within the non-Hispanic white families and tests for heterogeneity between ethnic group were significant. This suggests that there are different genetic and/or other etiologic determinants associated with the eosinophil phenotype in non-Hispanic white and Hispanic families. Our segregation analyses were therefore limited to non-Hispanic white families.

After adjusting for variability associated with current and past asthma, our results indicate evidence of familial transmission of a major factor that does not fit a Mendelian pattern of inheritance. This suggests a more complex genetic model, possibly oligogenic, than a single major gene with residual family effects. Also, adjusting for total serum IgE levels did not alter this result. Alternatively, results may be influenced by other factors preventing clear detection of a major gene, for example, misclassification or confounding by other potential risk factors. The phenomenon of the removal of the effects of covariates allowing for the detection of additional genetic effects has been described in other studies (28). An oligogenic mode of inheritance is characterized by a few genes and is suggested in the analysis by the Mendelian models being significantly different from the nongenetic models (one distribution and environmental), but also being significantly different from the unrestricted model (3), as in our analyses. Our conservative method of assessing degrees of freedom results in the loss of 2 degrees of freedom for the latter comparison, owing to two of the transmission parameters in the best fitting unrestricted model being fixed at a boundary (_AA and _BB). With the addition of these two degrees of freedom the Mendelian model would, in fact, not be rejected; our cautious approach accounts for parameters that are initially free to vary and ultimately go to bounds. The best fitting models in terms of AIC were the Mendelian dominant of high and equivalent recessive of low eosinophil levels models (AIC = 3,700.7). These models were mirror images of one another with the same estimate of gene frequency for low eosinophil levels, q = 0.14. A recessive model for high eosinophil levels did not fit the data as well (AIC = 3,756.4). The parameter estimates of these models may correspond to global estimates of a few underlying oligogenes (29). Over and above these models were additional residual familial components associated with a strong maternal influence. Such components may represent genetic effects, probably polygenic and/or the effects of a shared environment.

While we have no definite explanation for the maternal influence on eosinophil levels in this population, we have also observed a similar influence in relation to FEV₁ in families with at least one member with asthma. We have previously discussed possible interpretations for such a maternal influence in association with subphenotypes of the asthmatic condition (26). Briefly, several other studies have shown a strong maternal influence on the immune parameters of their children, such as IgE and allergic sensitization, which has not been observed between fathers and offspring, leading to the suggestion of intrauterine environmental influences involved in the determination of asthma and the allergic phenotype. In addition there may be maternally influenced postnatal effects, as well as genetic transmission; the latter evidenced by studies demonstrating the transmission of atopy only through the maternal line.

Other genetic studies of eosinophil levels have shown sex-related effects. A twin study of the genetic and environmental effects on blood cells, by Dal Colletto and coworkers (17), assessed three components of variation, namely, those due to genetic differences, h², shared environmental factors, c², or nonshared or specific environmental influences, e². Interestingly, h² values for eosinophil levels in males, females, and combined, respectively, were 3, 24, and 24%, indicative of genetic sex differences, with the combined model being identical to the female model for all sources of variation. Although we detect a clear maternal offspring influence, we observed (data not shown) no major differences between sister and brother correlations for the z-scored residual eosinophil level, compared with the overall sibling-sibling correlation, or for correlations between mother and father with daughter or son, respectively.

Rodrigues and colleagues (15) performed a segregation analysis of IL-5 levels produced by peripheral blood mononuclear cells of Brazilian families infected with Schistosoma mansoni. This cytokine, IL-5, has a major role in eosinopoiesis, maturation, and activation (see above). They found clear evidence of a major gene of gene frequency q_A = 0.21 segregating in a codominant fashion and associated with low levels of IL-5 in ~ 4% of the population. However, the higher IL-5 levels in the other two distributions were closer to one another than to the low levels in ~ 4% of the population. Intriguingly, despite the difference in location and health status of the two populations, there is some comparability between these findings for IL-5 and our more cautious findings for eosinophil levels, which might suggest similar control of these phenotypes associated with eosinophil levels.

Of major interest is the fact that a number of studies have shown linkage of asthma-related phenotypes to markers in the segment of chromosome 5q containing the IL-5 structural gene (5, 6). Further, we have shown significant evidence of linkage, in the CRS population, among sibling pairs concordant for low levels of circulating eosinophils as a proportion of white blood cells, related to markers located in chromosome 5q31-33. This suggests that a locus or loci may be present in this region controlling for eosinophil levels (30). These findings were limited to non-Hispanic white individuals, in agreement with our segregation analyses. The Collaborative Study on the Genetics of Asthma has shown evidence of linkage between markers in chromosome 5q and asthma, also in non-Hispanic white families (31).

It may seem unusual that the recessive of low eosinophil levels model is associated with a low gene frequency estimate (q = 0.14), with a resulting homozygous phenotype for low eosinophil levels being present in only approximately 2% of the population. Given the association between high eosinophil counts and asthma (8), and their subsequent role in tissue damage and inflammation in the lung (32), the expectation might have been the identification of an infrequent allele associated with much higher than normal eosinophil counts. It seems unlikely, however, that asthma would occur in individuals with low eosinophil levels. This suggests that the majority of the population have the genetic potential to react to environmental stimuli with the production of high levels of circulating eosinophils.

These findings support the notion of multiple genes, each of perhaps relatively small individual effect, interacting to determine genetic susceptibility to asthma. In addition, it is likely that the genes involved would not be rare. Given four or five genes interacting to determine susceptibility to asthma, the contributing genes would need to be relatively common to give a prevalence of approximately 10% asthma in the population. The latter is close to the 9% prevalence for currently active physician-diagnosed asthma in the non-Hispanic white families included in this segregation analysis. We have previously concluded from a segregation analysis of physician-diagnosed asthma that the mode of inheritance is compatible with polygenes or oligogenes (3). Further, asthma is not a homogeneous condition, showing variability in symptoms, triggers, and age of onset, so it is likely, given this scenario, that different combinations of multiple genes may be involved in the pathogenesis of this complex phenotype.