Assessing probability of paternity and the product rule in DNA systems

The genetic resolution of paternity disputes begins with an intricate detection of inherited traits and finishes with a statistical inference (the probability of paternity, W). Notwithstanding some initial fanfare, statistical inference is a necessary component of DNA-based paternity tests because band patterns may be rare but not yet unique, and even rare events in a vacuum are meaningless. The genetic match must be combined with other evidence for relevancy, thus a Bayesian approach is preferred when computing W. This paper reviews the standard model used to compute W and discusses the model's various properties and assumptions. The standard model is extended to include DNA systems in which alleles are operationally continuous due to measurement error. This extension avoids problems associated with 'matched/non-matched' binned decisions. After outlining the model assumptions for a single DNA system, particular attention is given to the product rule-the procedure of multiplying intermediate probabilities across genetic loci to form a combined W. An empirical alternative to the product rule is also assessed and correlated with standard procedures.