Likelihood ratio and posterior odds in forensic genetics: Two sides of the same coin

- Likelihood ratio (LR) and posterior odds (PO) are discussed in a forensic genetics context.
- Probabilistic models serve to illustrate the population-dependency of PO and LR.
- Valid PO can be derived empirically in the context of Forensic DNA Phenotyping.
- Owing to a lack of sensible priors, only LR, but not PO, is considered in DNA profiling.

It has become widely accepted in forensics that, owing to a lack of sensible priors, the evidential value of matching DNA profiles in trace donor identification or kinship analysis is most sensibly communicated in the form of a likelihood ratio (LR). This restraint does not abate the fact that the posterior odds (PO) would be the preferred basis for returning a verdict. A completely different situation holds for Forensic DNA Phenotyping (FDP), which is aimed at predicting externally visible characteristics (EVCs) of a trace donor from DNA left behind at the crime scene. FDP is intended to provide leads to the police investigation helping them to find unknown trace donors that are unidentifiable by DNA profiling. The statistical models underlying FDP typically yield posterior odds (PO) for an individual possessing a certain EVC. This apparent discrepancy has led to confusion as to when LR or PO is the appropriate outcome of forensic DNA analysis to be communicated to the investigating authorities. We thus set out to clarify the distinction between LR and PO in the context of forensic DNA profiling and FDP from a statistical point of view. In so doing, we also addressed the influence of population affiliation on LR and PO. In contrast to the well-known population dependency of the LR in DNA profiling, the PO as obtained in FDP may be widely population-independent. The actual degree of independence, however, is a matter of (i) how much of the causality of the respective EVC is captured by the genetic markers used for FDP and (ii) by the extent to which non-genetic such as environmental causal factors of the same EVC are distributed equally throughout populations. The fact that an LR should be communicated in cases of DNA profiling whereas the PO are suitable for FDP does not conflict with theory, but rather reflects the immanent differences between these two forensic applications of DNA information.