An unconditional exact test for the Hardy-Weinberg equilibrium law: sample-space ordering using the Bayes factor

Area of Science:

• Forensic Genetics
• Statistical Genetics
• Population Genetics

Background:

• Forensic DNA analysis often assumes Hardy-Weinberg equilibrium (HWE).
• Existing statistical tests for HWE deviations have limitations, especially for multiallelic DNA loci.
• Accurate HWE testing is crucial for reliable forensic DNA evidence.

Purpose of the Study:

• To develop an exact statistical test for Hardy-Weinberg equilibrium (HWE) in biallelic DNA loci.
• To address limitations of existing HWE deviation tests, particularly for multiallelic cases.
• To introduce a significance index based on the Bayes factor for evaluating HWE.

Main Methods:

• Developed an exact test for HWE based on the Bayes factor (ratio of weighted likelihoods).
• The test is independent of asymptotic results and minimizes Type I and Type II errors.
• Applied sequential testing using chi-squared partition ideas for multiallelic loci and short tandem repeats.

Main Results:

• Presented an exact test for HWE in biallelic cases using the Bayes factor.
• Defined a significance index (P-value) based on weighted likelihoods.
• Demonstrated the test's utility on short tandem repeat loci using a Caucasian DNA database.

Conclusions:

• The proposed exact test provides a robust method for detecting HWE deviations in forensic genetics.
• The Bayes factor approach offers advantages over traditional methods, especially for complex genetic data.
• The test is applicable to both biallelic and multiallelic DNA loci, enhancing forensic inference accuracy.