FAMILIAL AGGREGATION AND SEGREGATION ANALYSIS OF EOSINOPHIL LEVELS

To the Editor :

Holberg and colleagues describe the results of a segregation analysis of circulating eosinophil counts in white families from Tuscon, Arizona (Hispanic families were not analysed for segregation as there were no significant familial correlations in this group) (1). A principal conclusion of this article is that "multiple, relatively common genes [interact] to determine genetic susceptibility to asthma." While we believe that this is almost certainly true, we believe that the data presented in this article are subject to an alternative interpretation that the authors may wish to consider.

Holberg and her coauthors draw their conclusion after conducting two primary segregation analyses, one adjusted for age, sex, ethnic group, year and season of collection (Table 3) and the other adjusted for these covariates plus the presence of "currently active and nonactive physician-diagnosed asthma" (defined by questionnaire) (Table 4). While noting that "familial correlations were lower after this adjustment," the authors do not formally assess the significance of the reduction in familial correlations. That the familial correlations were slightly reduced suggests the possibility that asthma and circulating eosinophil counts may share some familial (genetic and/ or environmental) determinants. However, the major conclusions regarding possible segregation of a major gene are unchanged between the two models; an unrestricted model best fits the data. The authors conclude that the data derived from the model adjusting for current and past asthma (Table 4) suggest "an oligogenic mode of inheritance" and that their study "supports the notion of relatively common genes interacting to determine genetic susceptibility to asthma."

Our reservations about these conclusions stem from two sources. First, there is no convincing evidence presented that makes an oligogenic model any more likely than, say, a discrete environmental factors model or a discrete environmental factors plus polygenes model. One major common problem with segregation analysis, highlighted by this study, concerns the difficulty of choosing between alternative models. Despite the use of formal criteria such as the Aikaike information criterion (AIC) (2), the close overlap of distributions may mean that it is often difficult on theoretical grounds to reject or accept a restricted model in preference to a more general one. This certainly appears to be the case in the study of Holberg and colleagues, and we feel that it is important to explicitly acknowledge that segregation analysis often lacks power and that a variety of quite different biological models may all be reasonably consistent with the data.

Secondly, a critical point in their conclusions regarding the genetic susceptibility to asthma is not discussed by the authors. In effect, Holberg and colleagues (1) have investigated the extent to which additive major gene effects were shared between the phenotypes "circulating eosinophil count" and "physician-diagnosed asthma"; the original segregation model for eosinophil count (Table 3) was extended by adding terms for a second phenotype (asthma) (Table 4). Under such circumstances, a large reduction in the magnitude of either the estimates of familial correlations or, more specifically, the additive effects for a genotype, would suggest the sharing of familial determinants or a gene (respectively) affecting both phenotypes. The corollary to this is that the results presented in Table 4 reflect the evidence for familial/genetic determinants of eosinophil counts that are not shared with the determinants of asthma susceptibility; i.e., independent of asthma risk. Therefore, it is our belief that their conclusion that their study "supports the notion of relatively common genes interacting to determine genetic susceptibility to asthma" may not be warranted. Rather, we believe that their data support two principal conclusions:

1. It is unlikely that circulating eosinophil counts are determined by a simple biological modeleither genetic or environmental.
2. The familial determinants of circulating eosinophil counts that are independent of asthma susceptibility are just as complex as those shared with the determinants of asthma susceptibility.

Harvard Medical School, Harvard University, Boston, Massachusetts

Paul R. Burton

Department of Epidemiology and Public Health, University of Leicester, Leicester, United Kingdom

1. Holberg, C. J., M. Halonen, A. L. Wright, and F. D. Martinez. 1999. Familial aggregation and segregation analysis of eosinophil levels. Am. J. Respir. Crit. Care Med. 160: 1604-1610 [Abstract/Free Full Text].

2. Aikaike, H. 1977. On entropy maximization principle. In P. Krishnaiah, editor. Application of Statistics. North-Holland, London. 27-41.

From the Authors:

We would like to thank Drs. Palmer and Burton for their insightful comments on our article. (1). We are in agreement that the notion of shared familial determinants affecting both the eosinophil and asthma phenotype, although not explicitly mentioned in the text of our paper, is certainly a potential conclusion that could be drawn from the data. Further points raised revolve around our suggestion of a possible oligogenic mode of inheritance, and the idea of multiple relatively common genes interacting to determine genetic susceptibility to asthma.

We agree that sample size is an important issue in segregation analyses, where testing is based on "goodness of fit"; i.e., a failure to reject the null hypothesis. One can always fail to reject the null hypothesis that the data fit a certain model of inheritance if there is inadequate power. Our analyses illustrate the difficulties of distinguishing between models. For example, in the analysis shown in Table 3, the best fitting models which were not different from one another in terms of Aikaike's information criteria (AIC) (a difference greater than 2 being significantly different [2]), were represented by both the environmental and mendelian models. Further, in the analysis shown in Table 4, our conservative method of assessing degrees of freedom resulted in the rejection of the mendelian models, whereas a less conservative method would have failed to do so, leading to the inference of a major gene. No doubt including a larger number of families with more children would have resolved these issues. Our suggestion of an oligogenic model was associated with the finding in the Table 4 analysis that although all of the models tested were significantly different from the unrestricted model, the mendelian three-distribution model was significantly different from the nongenetic one-distribution model, as well as fitting the data better than the environmental models in terms of the AIC. This led us to surmise the existence of a more complex genetic model than a single major gene, one that is "possibly oligogenic." We also suggested "additional genetic (polygenic) and environmental components."

There is a very significant positive association between physician-diagnosed asthma and eosinophil levels (3). However, the analyses presented in Table 4, which adjust for asthmatic status, do appear to identify a group of individuals with very low Z-scores, mean 3.75, comprising only ~ 2% of the population. The lower scores necessarily imply that any asthmatics in this group would be in the lower eosinophil count range for asthmatics, which appears to be the case: of the 25 individuals who had a greater than 0.99 probability of being in this group (as calculated from the model parameters) only one had current asthma but had negligible eosinophil counts. These findings suggested to us that the majority of the population have the genetic potential to produce higher levels of circulating eosinophils regardless of their asthma status. The final paragraph of our paper, suggesting the possibility of multiple fairly common genes determining genetic susceptibility to asthma, was intended to lead on from the latter suggestion, and was not referring to multiple genes in the possible oligogenic model noted earlier in the paper. We failed to identify a rare gene associated with high eosinophil counts that might be associated with the high eosinophl counts in asthma. Nonetheless, the best fitting model of Table 4 indicated that 98% of the population was associated with higher eosinophil counts and with a more frequent allele, suggesting, since high eosinophil counts are associated with asthma, that this would be necessary but not sufficient for the manifestation of asthma. Other genes and environmental influences, not necessarily associated with eosinophil levels, would also be involved.

CATHARINE J. HOLBERG

Respiratory Sciences Center Department of Pediatrics University of Arizona Tucson, Arizona

FERNANDO D. MARTINEZ

Respiratory Sciences Center University of Arizona Tucson, Arizona

1. Holberg, C. J., M. Halomen, A. L. Wright, and F. D. Martinez. 1999. Familial aggregation and segregation analysis of eosinophil levels. Am. J. Respir. Crit. Care Med. 160: 1604-1610 .

2. Jones, R. 1993. Longitudinal Data with Serial Correlation: A State Space Approach. Chapman and Hall, London

3. Martinez, F. D., S. Solomon, C. J. Holberg, P. E. Graves, M. Baldini, and R. P. Erickson. 1998. Linkage of circulating eosinophils to markers in chromosome 5q. Am. J. Respir. Crit. Care Med. 158: 1739-1744 [Abstract/Free Full Text].