Exclusion probabilities and likelihood ratios with applications to kinship problems

Area of Science:

• Forensic Genetics
• Statistical Genetics
• Biostatistics

Background:

• Statistical evidence in forensic genetics, such as paternity cases, can be reported using likelihood ratio (LR) or probability of not excluding a random man as father (RMNE).
• A long-standing debate exists regarding the merits of LR versus RMNE, particularly in DNA mixture interpretation, with no broad consensus reached.
• Understanding the relationship between these two common statistical measures is crucial for accurate forensic evidence reporting.

Purpose of the Study:

• To mathematically demonstrate the relationship between RMNE and LR in forensic genetics.
• To analyze the theoretical properties of LR in kinship cases.
• To provide practical implications for interpreting statistical evidence in forensic casework.

Main Methods:

• Mathematical derivation showing RMNE as a weighted average of inverse LR.
• Theoretical analysis of LR properties, including expected value and variance, for kinship cases.
• Illustrative examples using paternity cases to demonstrate findings.

Main Results:

• The RMNE is mathematically proven to be a weighted average of inverse likelihood ratios across all forensic contexts.
• The likelihood ratio favoring the correct hypothesis is, in expectation, greater than the reciprocal of the RMNE probability.
• While generally larger, LR can be smaller than the reciprocal of RMNE in non-pathological scenarios.

Conclusions:

• The study clarifies the statistical relationship between RMNE and LR, offering a theoretical basis for their comparison.
• Findings provide insights into the expected behavior of LR in forensic kinship analysis.
• The research has practical implications for forensic practitioners in reporting and interpreting statistical DNA evidence.