The likelihood ratio as a random variable for linked markers in kinship analysis.

Area of Science:

• Forensic Science
• Statistical Genetics

Background:

• The likelihood ratio (LR) is crucial for quantifying evidence in forensic kinship analysis.
• Understanding the theoretical properties of LR is essential for accurate interpretation.

Purpose of the Study:

• To investigate the theoretical properties of the likelihood ratio for pairwise kinship comparisons with linked markers.
• To derive exact expressions for the expectation and variance of the LR under various conditions.

Main Methods:

• Mathematical derivation of exact expressions for LR expectation and variance.
• Analysis of LR behavior with varying recombination rates for linked markers.

Main Results:

• The expected LR depends on allele frequencies solely through the number of alleles, even with linked markers and alternative true relationships.
• The expected LR is non-increasing with increasing recombination rates (0 to 0.5) when the tested relationship is the true one.
• Exact expressions derived can be used for precise software validation.

Conclusions:

• The study provides theoretical insights into LR behavior for linked markers in kinship analysis.
• Derived formulas facilitate software validation and power calculations in forensic genetics.
• The logarithm of the LR exhibits different statistical properties than the LR itself, aligning with its role as a weight of evidence.