Exact likelihood ratio calculations for pairwise cases

- Exact pairwise LR formula.
- Theoretical and practical discussion of mutation models: the relevance of 'detailed balance'.
- Freely available software: R library mut.

Some practical and theoretical aspects of evaluation of evidence based on the likelihood ratio (LR) in kinship cases are discussed. If relationships are complex or if complicating factors like mutation, correction for population structure or silent alleles need to be accounted for, available software may fail. We present an explicit general formula for non-inbred pairwise cases. Equipped with this formula it is possible to evaluate, say, how strongly a shared rare allele, points towards a specific relationship. Moreover, a general expression as the one presented, adds to the understanding of models and the underlying biological mechanisms. It is also useful for checking software and defining the limitations of programs. Some ideas for improving software may also be generated by the derivation of exact expressions.We argue that a proportional mutation model is well suited from a pragmatic point of view and derive some theoretical properties of this model. Several examples based on the general pairwise formula and its implementation in the freely available R package mut are presented.