Pairwise relatedness testing in the context of inbreeding: expectation and variance of the likelihood ratio
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ORIGINAL ARTICLE
Pairwise relatedness testing in the context of inbreeding: expectation and variance of the likelihood ratio Hilde Kjelgaard Brustad1 · Magnus Dehli Vigeland2 · Thore Egeland1 Received: 13 January 2020 / Accepted: 10 September 2020 © The Author(s) 2020
Abstract In this paper we investigate various effects of inbreeding on the likelihood ratio (LR) in forensic kinship testing. The basic setup of such testing involves formulating two competing hypotheses, in the form of pedigrees, describing the relationship between the individuals. The likelihood of each hypothesis is computed given the available genetic data, and a conclusion is reached if the ratio of these exceeds some pre-determined threshold. An important aspect of this approach is that the hypotheses are usually not exhaustive: The true relationship may differ from both of the stated pedigrees. It is well known that this may introduce bias in the test results. Previous work has established formulas for the expected value and variance of the LR, given the two competing hypotheses and the true relationship. However, the proposed method only handles cases without inbreeding. In this paper we extend these results to all possible pairwise relationships. The key ingredient is formulating the hypotheses in terms of Jacquard coefficients instead of the more restricted Cotterman coefficients. While the latter describe the relatedness between outbred individuals, the more general Jacquard coefficients allow any level of inbreeding. Our approach also enables scrutiny of another frequently overlooked source of LR bias, namely background inbreeding. This ubiquitous phenomenon is usually ignored in forensic kinship computations, due to lack of adequate methods and software. By leveraging recent work on pedigrees with inbred founders, we show how background inbreeding can be modeled as a continuous variable, providing easy-to-interpret results in specific cases. For example, we show that if true siblings are subjected to a test for parent-offspring, moderate levels of background inbreeding are expected to inflate the LR by more than 50%. Keywords Kinship analysis · Inbred founders · IBD triangle · Jacquard coefficients · Likelihood ratios
Introduction The conventional approach to forensic kinship testing includes formulating two hypotheses and calculating a likelihood ratio (LR) based on genetic data from genotyped individuals. Practice differs between countries and laboratories, but
Hilde Kjelgaard Brustad
[email protected] Magnus Dehli Vigeland [email protected] Thore Egeland [email protected] 1
Norwegian University of Life Sciences, 1432 Aas, Norway
2
Department of Medical Genetics, University of Oslo, PB 4956 Nydalen, 0424 Oslo, Norway
typically the LR or some version of it is included when the case is reported. The conclusion based on the LR may be flawed when the true pedigree connecting the individuals of interest differs from the pedigrees considered by the hypotheses. As an example, consider a standard paternity case, whe
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