A parametric copula model for analysis of familial binary data

David Alexandre Trégouët, Pierre Ducimetière, Valéry Bocquet, Sophie Visvikis, Florent Soubrier, Laurence Tiret*

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

20 Citations (Scopus)

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 (α(FM) and α(ss), 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.

Original languageEnglish
Pages (from-to)886-893
Number of pages8
JournalAmerican Journal of Human Genetics
Volume64
Issue number3
DOIs
Publication statusPublished - 1999
Externally publishedYes

Fingerprint

Dive into the research topics of 'A parametric copula model for analysis of familial binary data'. Together they form a unique fingerprint.

Cite this