Abstract
Modeling the joint distribution of a binary trait (disease) within families is a tedious challenge, owing to the lack of a general statistical model with desirable properties such as the multivariate Gaussian model for a quantitative trait. Models have been proposed that either assume the existence of an underlying liability variable, the reality of which cannot be checked, or provide estimates of aggregation parameters that are dependent on the ordering of family members and on family size. We describe how a class of copula models for the analysis of exchangeable categorical data can be incorporated into a familial framework. In this class of models, the joint distribution of binary outcomes is characterized by a function of the given marginals. This function, referred to as a "copula," depends on an aggregation parameter that is weakly dependent on the marginal distributions. We propose to decompose a nuclear family into two sets of equicorrelated data (parents and offspring), each of which is characterized by an aggregation parameter (alphaFM and alphaSS, respectively). The marginal probabilities are modeled through a logistic representation. The advantage of this model is that it provides estimates of the aggregation parameters that are independent of family size and does not require any arbitrary ordering of sibs. It can be incorporated easily into segregation or combined segregation-linkage analysis and does not require extensive computer time. As an illustration, we applied this model to a combined segregation-linkage analysis of levels of plasma angiotensin I-converting enzyme (ACE) dichotomized into two classes according to the median. The conclusions of this analysis were very similar to those we had reported in an earlier familial analysis of quantitative ACE levels.
Full Text
The Full Text of this article is available as a PDF (231.4 KB).
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Abel L., Bonney G. E. A time-dependent logistic hazard function for modeling variable age of onset in analysis of familial diseases. Genet Epidemiol. 1990;7(6):391–407. doi: 10.1002/gepi.1370070602. [DOI] [PubMed] [Google Scholar]
- Abel L., Golmard J. L., Mallet A. An autologistic model for the genetic analysis of familial binary data. Am J Hum Genet. 1993 Oct;53(4):894–907. [PMC free article] [PubMed] [Google Scholar]
- Bonney G. E. Regressive logistic models for familial disease and other binary traits. Biometrics. 1986 Sep;42(3):611–625. [PubMed] [Google Scholar]
- Cannings C., Thompson E. A. Ascertainment in the sequential sampling of pedigrees. Clin Genet. 1977 Oct;12(4):208–212. doi: 10.1111/j.1399-0004.1977.tb00928.x. [DOI] [PubMed] [Google Scholar]
- Demenais F. M. Regressive logistic models for familial diseases: a formulation assuming an underlying liability model. Am J Hum Genet. 1991 Oct;49(4):773–785. [PMC free article] [PubMed] [Google Scholar]
- Elston R. C., Sobel E. Sampling considerations in the gathering and analysis of pedigree data. Am J Hum Genet. 1979 Jan;31(1):62–69. [PMC free article] [PubMed] [Google Scholar]
- Hsu L., Zhao L. P. Assessing familial aggregation of age at onset, by using estimating equations, with application to breast cancer. Am J Hum Genet. 1996 May;58(5):1057–1071. [PMC free article] [PubMed] [Google Scholar]
- Lalouel J. M., Rao D. C., Morton N. E., Elston R. C. A unified model for complex segregation analysis. Am J Hum Genet. 1983 Sep;35(5):816–826. [PMC free article] [PubMed] [Google Scholar]
- Liang K. Y., Beaty T. H. Measuring familial aggregation by using odds-ratio regression models. Genet Epidemiol. 1991;8(6):361–370. doi: 10.1002/gepi.1370080602. [DOI] [PubMed] [Google Scholar]
- Meester S. G., MacKay J. A parametric model for cluster correlated categorical data. Biometrics. 1994 Dec;50(4):954–963. [PubMed] [Google Scholar]
- Morton N. E., MacLean C. J. Analysis of family resemblance. 3. Complex segregation of quantitative traits. Am J Hum Genet. 1974 Jul;26(4):489–503. [PMC free article] [PubMed] [Google Scholar]
- Tiret L., Rigat B., Visvikis S., Breda C., Corvol P., Cambien F., Soubrier F. Evidence, from combined segregation and linkage analysis, that a variant of the angiotensin I-converting enzyme (ACE) gene controls plasma ACE levels. Am J Hum Genet. 1992 Jul;51(1):197–205. [PMC free article] [PubMed] [Google Scholar]
- Tosteson T. D., Rosner B., Redline S. Logistic regression for clustered binary data in proband studies with application to familial aggregation of sleep disorders. Biometrics. 1991 Dec;47(4):1257–1265. [PubMed] [Google Scholar]
- Trégouët D. A., Ducimetière P., Tiret L. Testing association between candidate-gene markers and phenotype in related individuals, by use of estimating equations. Am J Hum Genet. 1997 Jul;61(1):189–199. doi: 10.1086/513895. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Whittemore A. S., Gong G. Segregation analysis of case-control data using generalized estimating equations. Biometrics. 1994 Dec;50(4):1073–1087. [PubMed] [Google Scholar]
- Zhao L. P., Le Marchand L. An analytical method for assessing patterns of familial aggregation in case-control studies. Genet Epidemiol. 1992;9(2):141–154. doi: 10.1002/gepi.1370090206. [DOI] [PubMed] [Google Scholar]