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Tests for genetic linkage and homogeneity

M Lemdani¹, O Pons

¹Biométrie, Institut National de la Recherche Agronomique, Jouy-en- Josas, France.

|September 1, 1995

Summary

This study introduces likelihood ratio tests for genetic linkage analysis in heterogeneous family models. It details test statistics and their distributions, offering insights into linkage and homogeneity testing.

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Area of Science:

Genetics
Statistical genetics
Bioinformatics

Background:

Genetic linkage analysis is crucial for mapping genes associated with diseases.
Heterogeneous family models are necessary when dealing with mixed populations or varying linkage parameters.
Likelihood ratio tests provide a robust statistical framework for hypothesis testing in genetic studies.

Purpose of the Study:

To develop and evaluate likelihood ratio tests for genetic linkage in heterogeneous models.
To investigate the distributional properties of linkage and homogeneity test statistics under these models.
To compare the power of linkage and homogeneity tests through simulation.

Main Methods:

Utilized a heterogeneous model where the recombination fraction follows a binomial mixture distribution.
Considered families of unequal sizes with both known and unknown phase data.
Derived limit distributions for linkage test statistics and analyzed homogeneity test statistics.
Simulated critical values for homogeneity tests and conducted a simulation study to compare test powers.

Main Results:

The limit distributions of linkage test statistics were found to be a mixture of a mass at 0 and a chi-squared distribution (X2/1) in equal proportions.
Homogeneity test statistics were shown to converge to the supremum of Gaussian processes.
Simulation results provided insights into the power of both linkage and homogeneity tests.

Conclusions:

The developed likelihood ratio tests are suitable for genetic linkage analysis in heterogeneous family structures.
The distributional properties of the test statistics are well-defined, allowing for accurate statistical inference.
The study provides a comparative analysis of test powers, aiding in the selection of appropriate statistical methods for genetic mapping.

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