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Basic fallacies in the formulation of the paternity index

C C Li¹, A Chakravarti

¹Department of Biostatistics, Graduate School of Public Health, University of Pittsburgh, PA 15261, USA.

American Journal of Human Genetics

|July 1, 1985

Summary

This study reveals flaws in calculating the paternity index, a genetic test for fatherhood. The current paternity index is not a reliable likelihood ratio and can lead to incorrect conclusions about paternity probability.

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Area of Science:

Forensic genetics
Statistical genetics

Background:

The paternity index is a commonly used metric in genetic testing to assess the probability of paternity.
Previous interpretations of the paternity index have been based on assumptions that are now being questioned.

Purpose of the Study:

To identify and address fundamental fallacies in the computation of the paternity index.
To critically evaluate the paternity index's validity as a likelihood ratio.
To propose an alternative method for calculating paternity probabilities based on genetic evidence.

Main Methods:

Analysis of the algebraic properties of the paternity index formula.
Comparison of the paternity index with the definition of a likelihood ratio.
Development of a revised formula for calculating paternity probabilities.

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Main Results:

The observed difference in mean paternity index between true fathers and nonfathers is an artifact of an algebraic identity, not indicative of actual paternity.
The paternity index does not function as a likelihood ratio.
Paternity index values less than one can lead to illogical conclusions regarding paternity probability.

Conclusions:

The current method for calculating the paternity index is flawed and requires re-evaluation.
A new formula based on prior and posterior probabilities, derived from genetic marker testing results, is proposed as a more accurate substitute for the paternity index.