Formula Derivation and Validation of Probability of Exclusion in the Cases of Standard Triplet Parentage Testing

Abstract

Objective To derive and experiment validate the probability of exclusion （PE） formulas in the cases of standard triplet parentage testing. Methods The formulas were derived voluntarily based on the PE definition: PE=■Pi2（1-Pi）2+■PiPj（1-Pi）3+■PiPj（1-Pj）3+■PiPj（Pi+Pj）（1-Pi-Pj）2. This formula was compared with the 5 formulas （1）-（5） reported previously, and the PE values of 19 autosomal STR loci in AGCU EX20 system were calculated. Based on 1 000 samples of single-parentage cases and 1 000 unrelated individuals, the real experiment was designed and the real experiment results of PE were calculated. Ten million pairs of simulated biological mother and son and 10 million random individuals were gained by random simulation method, and the simulated experiment was designed and the simulated values of PE were calculated. In 19 STR loci, the sum of all allele frequency （S） was calculated, and the formula values of PE were compared with the values of real and simulated experiments. Results If S=1, the calculation values of formula （1）, （2）, （5） and （6） were quite the same, which accord with the double verification of real and simulated experiments. If S≠1, there was a minor error in the calculation results of formula （1）, （2）, （5） and （6）, while which had a large error in formula （3） and （4）. Conclusion The formula （6） derived in present study and the classical formulas （1）, （2） and （5） can be applied to the standard triplet parentage testing. The S value has a certain influence on PE calculation.

Keywords

•  forensic genetics; parent-child relations; probability of paternity exclusion; triplet; formula