Conditional likelihood score functions for mixed models in linkage analysis.

Department of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden.
Biostatistics (Impact Factor: 2.24). 05/2005; 6(2):313-32. DOI: 10.1093/biostatistics/kxi012
Source: PubMed

ABSTRACT In this paper, we develop a general strategy for linkage analysis, applicable for arbitrary pedigree structures and genetic models with one major gene, polygenes and shared environmental effects. Extending work of Whittemore (1996), McPeek (1999) and Hossjer (2003d), the efficient score statistic is computed from a conditional likelihood of marker data given phenotypes. The resulting semiparametric linkage analysis is very similar to nonparametric linkage based on affected individuals. The efficient score S depends not only on identical-by-descent sharing and phenotypes, but also on a few parameters chosen by the user. We focus on (1) weak penetrance models, where the major gene has a small effect and (2) rare disease models, where the major gene has a possibly strong effect but the disease causing allele is rare. We illustrate our results for a large class of genetic models with a multivariate Gaussian liability. This class incorporates one major gene, polygenes and shared environmental effects in the liability, and allows e.g. binary, Gaussian, Poisson distributed and life-length phenotypes. A detailed simulation study is conducted for Gaussian phenotypes. The performance of the two optimal score functions S(wpairs) and S(normdom) are investigated. The conclusion is that (i) inclusion of polygenic effects into the score function increases overall performance for a wide range of genetic models and (ii) score functions based on the rare disease assumption are slightly more powerful.

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    ABSTRACT: In this paper we introduce two information criteria in linkage analysis. The setup is a sample of families with unusually high occurrence of a certain inheritable disease. Given phenotypes from all families, the two criteria measure the amount of information inherent in the sample for 1) testing existence of a disease locus harbouring a disease gene somewhere along a chromosome or 2) estimating the position of the disease locus. Both criteria have natural interpretations in terms of effective number of meioses present in the sample. Thereby they generalize classical performance measures directly counting number of informative meioses. Our approach is conditional on observed phenotypes and we assume perfect marker data. We analyze two extreme cases of complete and weak penetrance models in particular detail. Some consequences of our work for sampling of pedigrees are discussed. For instance, a large sibship family with extreme phenotypes is very informative for linkage for weak penetrance models, more informative than a number of small families of the same total size.
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    ABSTRACT: We consider stochastic processes occurring in nonparametric linkage analysis for mapping disease susceptibility genes in the human genome. Under the null hypothesis that no disease gene is located in the chromosomal region of interest, we prove that the linkage process Z converges weakly to a mixture of Ornstein-Uhlenbeck processes as the number of families N tends to infinity. Under a sequence of contiguous alternatives, we prove weak convergence towards the same Gaussian process with a deterministic non-zero mean function added to it. The results are applied to power calculations for chromosome- and genome-wide scans, and are valid for arbitrary family structures. Our main tool is the inheritance vector process v, which is a stationary and continuous-time Markov process with state space the set of binary vectors w of given length. Certain score functions are expanded as a linear combination of an orthonormal system of basis functions which are eigenvectors of the intensity matrix of v.
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