745

**Mixture models for linkage analysis of affected sibling pairs
and covariates**

**B. Devlin, B.L. Jones, S-A. Bacanu and K. Roeder**

### Abstract:

To determine the genetic etiology of complex diseases, a common study
design is to recruit affected sib/relative pairs (ASP/ARP) and
evaluate their genome-wide distribution of identical by descent
(IBD)-sharing using a set of
highly polymorphic markers. Other attributes or environmental
exposures of the ASP/ARP, which are thought to affect liability to
disease, are sometimes collected. Conceivably these covariates could
refine the linkage analysis. Most published methods for ASP/ARP
linkage with covariates can be conceptualized as logistic models in
which IBD-status of the ASP is predicted by pair-specific covariates.
We develop a different approach to the problem of ASP analysis in the
presence of covariates, one that extends naturally to ARP under
certain conditions. For ASP linkage analysis, we formulate a mixture
model in which a disease mutation is segregating in only a fraction
of the sibships, with sibships being unlinked.
Covariate information is used to predict membership within groups; in
this report, the two groups correspond to the linked and unlinked
sibships. For an ASP with covariate(s) *Z*=*z* and multilocus genotype
*X*=*x*, the
mixture model is , in which *g*_{0}(*x*) follows the distribution of
genotypes under the null IBD distribution
and allows for increased IBD sharing. Two mixture
models are developed. The `Pre-clustering' model uses covariate
information to form probabilistic clusters and then tests for excess
IBD-sharing independent of the covariates. The `Cov-IBD' model
determines probabilistic group membership by joint consideration of
covariate and IBD values. Simulations show that incorporating covariates
into linkage analysis can enhance power substantially.
A feature of our conceptualization of ASP
linkage analysis, with covariates, is that it is apparent
how data analysts might evaluate covariates prior to the linkage
analysis, thus avoiding the loss of power described by Leal and Ott [2000]
when data are stratified.

*Keywords:* clustering algorithms, mixing distribution,
score statistics, likelihood ratio, asymptotic distributions

*Heidi Sestrich*

*7/26/2001*
Here is the full .pdf text for this
technical report.