A Fast-Fourier-Transform-Based Dynamic Likelihood Ratio Framework for Controlling False Positives in DNA Database...

Background/Objectives: Operational DNA databases traditionally rely on static locus-count thresholds to determine search eligibility and report matches. While computationally straightforward, these rigid criteria routinely discard high-value investigative leads from degraded forensic profiles while simultaneously permitting adventitious matches when common alleles are involved. To overcome the limitations of static rules, this study introduces an automated framework for dynamic likelihood ratio (LR) thresholding. Methods: Utilizing a Fast Fourier Transform (FFT) algorithm, the system calculates the Probability Mass Function (PMF) for any specific combination of shared loci in real-time, natively incorporating the Balding-Nichols model to account for population substructure. Instead of applying an arbitrary locus count or fixed LR cutoff, the framework defines admissibility based on a user-defined maximum upper bound of acceptable false positives at a specified confidence (probability) level (e.g., 95%). Results: This empowers database custodians to precisely predict and adapt their search criteria to match an acceptable administrative workload, dynamically adjusting the required LR threshold to the exact size of the searched database. This approach was validated through massive-scale empirical simulations across five reference population groups. Receiver Operating Characteristic (ROC) and Poisson distribution analyses reveal that static thresholds inevitably collapse under the multiplicity effect of large-scale comparisons; for instance, a static locus rule that maintains safety within a small DNA database yields an unmanageable false positive risk when scaled to larger DNA databases or international networks like the Prüm DNA Exchange. Conclusions: By explicitly coupling the decision threshold to the database size and the genetic rarity of the evidence, this dynamic framework provides a mathematically rigorous and scalable solution. Most notably, it identifies rare, low-locus matches that static rules typically discard, offering a method to maintain a predefined expected false positive rate.