title: Inclusion probability with dropout: an operational formula.
abstract: In forensic genetics, a mixture of two or more contributors to a DNA profile is often interpreted using the inclusion probabilities theory. In this paper, we present a general formula for estimating the probability of inclusion (PI, also known as the RMNE probability) from a subset of visible alleles when dropouts are possible. This one-locus formula can easily be extended to multiple loci using the cumulative probability of inclusion. We show that an exact formulation requires fixing the number of contributors, hence to slightly modify the classic interpretation of the PI. We discuss the implications of our results for the enduring debate over the use of PI vs likelihood ratio approaches within the context of low template amplifications.
authors.affiliation: Département de chimie, biochimie et physique, Université du Québec à Trois-Rivières, 3351 boul. des Forges, CP 500, Trois-Rivières, QC, Canada G9A 5H7; Centre international de criminologie comparée, Université du Québec à Trois-Rivières, 3351 boul. des Forges, CP 500, Trois-Rivières, QC, Canada G9A 5H7. Electronic address: emmanuel.milot@uqtr.ca.
authors.forename: E
authors.initials: E
authors.lastname: Milot
authors.affiliation: Groupe de recherche PRIMUS, Faculté de médecine et des sciences de la santé, Université de Sherbrooke, 3001, 12e Avenue N., Sherbrooke, QC, Canada J1H 5N4. Electronic address: josiane.courteau@usherbrooke.ca.
authors.forename: J
authors.initials: J
authors.lastname: Courteau
authors.affiliation: Département de chimie, biochimie et physique, Université du Québec à Trois-Rivières, 3351 boul. des Forges, CP 500, Trois-Rivières, QC, Canada G9A 5H7; Centre international de criminologie comparée, Université du Québec à Trois-Rivières, 3351 boul. des Forges, CP 500, Trois-Rivières, QC, Canada G9A 5H7. Electronic address: frank.crispino@uqtr.ca.
authors.forename: F
authors.initials: F
authors.lastname: Crispino
authors.affiliation: Laboratoire de sciences judiciaires et de médecine légale, Ministère de la sécurité publique du Québec, 1701, rue Parthenais, Montréal, QC, Canada H2K 3S7. Electronic address: france.mailly@msp.gouv.qc.ca.
authors.forename: F
authors.initials: F
authors.lastname: Mailly
mesh_terms: D000483:Alleles; D045424:Complex Mixtures / Q000032:analysis*; D004247:DNA / Q000032:analysis* / Q000235:genetics; D016172:DNA Fingerprinting / Q000379:methods*; D053803:Forensic Genetics / Q000379:methods*; D006801:Humans; D016013:Likelihood Functions; D011336:Probability
chemical_list: D045424:Complex Mixtures; D004247:DNA
keywords: Dropout; Forensic mixture; Inclusion probability; Low-template DNA; Number of contributors; RMNE