Assigning Propositions for Likelihood Ratios

Assigning Propositions for 

Likelihood Ratios

Biological Data Interpretation & Reporting Subcommittee

Biology/DNA Scientific Area Committee

Organization of Scientific Area Committees (OSAC) for Forensic Science
Assigning Propositions for Likelihood Ratios

OSAC Proposed Standard

Assigning Propositions for Likelihood 

Ratios

Prepared by 

Biological Data Interpretation & Reporting Subcommittee

Version: 1.0

2018

Disclaimer:

This document has been developed by the Biological Data Interpretation & Reporting Subcommittee of 

the Organization of Scientific Area Committees (OSAC) for Forensic Science through a consensus 

process and is proposed for further development through a Standard Developing Organization (SDO). 

This document is being made available so that the forensic science community and interested parties can 

consider the recommendations of the OSAC pertaining to applicable forensic science practices. The 

document was developed with input from experts in a broad array of forensic science disciplines as well 

as scientific research, measurement science, statistics, law, and policy. 

This document has not been published by an SDO. Its contents are subject to change during the 

standards development process. All interested groups or individuals are strongly encouraged to submit 

comments on this proposed document during the open comment period administered by the Academy 

Standards Board (www.asbstandardsboard.org). 
Assigning Propositions for Likelihood Ratios

LR (E|H , I)2

H

I

1 and 2 are two mutually exclusive propositions, and

is the relevant information.

Foreword

When DNA testing data are generated from evidence and then compared to data from 

known individuals, it is necessary to provide a statistical statement for any comparison for 

which an individual cannot be excluded as a contributor (or possible contributor) to the 

DNA. One common

=

where:

Pr

(E|H1, I)

E

H

are the findings (e.g., DNA profile(s), presumptive test results, observations),

The terms Hp and Hd are often used in place of H1 and H2, and are assigned for the prosecution (p) 

and the defense (d), respectively. The arguments for the use of H1 and H2 in lieu of Hp and Hd, 

respectively, relate to avoiding any unintended assignment of propositions or scenarios to 

individuals such as the prosecution or defense. The arguments in favor of the alternative set, Hp 

and Hd, relate to directness of language. The exact propositions of the prosecution and defense may 

not be known, and in such circumstances, reasonable propositions consistent with both viewpoints 

should be selected for the analysis.

Cook et al. [5] and Evett et al. [7] classified propositions into four levels: from top to bottom these 

are offense, activity, source, and sub-source. This was expanded to include a sub-sub-source level 

and is explained in detail in Buckleton et al. [2], pp. 46-48. This document is limited to propositions 

at the sub-source and sub-sub-source levels.

The propositions in any given case depend on the knowledge of the case circumstances at the time 

the interpretation is carried out. Relevant information may include, but is not limited to, the 

following elements:

a) The alleged location, direction, and time of transfer

b) The location and time that the sample was taken

c) The genotypes of the person of interest (POI), the complainant, and proposed consensual 

partners, any persons who admit activity that could deposit DNA or have legitimate access 

to the sample, and any elimination samples such as scene of crime staff or lab staff

d) Evidence of opportunity for alternate donors may be relevant. In particular, the genotypes, 

ethnicity, or relationships1 of persons who could reasonably be alternative donors is 

relevant. Also relevant is information of those who could not reasonably be considered 

possible donors because of lack of opportunity.

1 There is a misperception that the likelihood ratio approach is unsuitable if any individuals within the pair of 
Assigning Propositions for Likelihood Ratios

propositions are related. This is not true as the likelihood ratio approach has been used for decades for paternity cases 

and missing persons. One could envisage two situations:

a) The known individuals are related and have been genotyped, or

b) One, or more, of the postulated unknown individuals is related to the genotyped individuals.
Assigning Propositions for Likelihood Ratios

e) Information of the results of other forensic analyses that suggest the presence at the scene 

of an alternatedonor.

When talking about the case information, it needs to be emphasized that one does not consider 

information such as prior conviction, motive, or a confession of the POI as relevant forensic 

information for the evaluation of the DNA results.

Keywords: statistics, likelihood ratio, propositions, DNA, DNA interpretation
Assigning Propositions for Likelihood Ratios

Table of Contents

Scope...........................................................................................................................1

Normative References ...........................................................................................1

Terms and Definitions............................................................................................1

Requirements.........................................................................................................2

Annex A (normative) Best Practice Recommendations............................................4

Annex B (informative) Bibliography .......................................................................6
Assigning Propositions for Likelihood Ratios

Assigning Propositions for Likelihood Ratios

1 Scope

This standard is to be used by laboratories for the assignment of propositions for the 

interpretation of DNA profiling evidence using likelihood ratios.

2 Normative References

There are no normative references.

3 TermsandDefinitions

For purposes of this document, the following definitions apply.

3.1

analysis

An interpretation and/or likelihood ratio calculation.

3.2

conditioning

The act of assuming one or more pieces of information when assigning a conditional probability. 

The information might be the profile of an individual, or profiles of a set of individuals, that are 

assumed to have contributed DNA to the evidentiary item under a particular proposition, or it 

might simply be the assumption that a particular proposition is true. Any events (or information) 

that have been used for conditioning are placed to the right of the conditioning bar in a conditional 

probability expression.

3.3

conditioning profile

The DNA profile of an individual assumed to be a contributor to the DNA (or DNA profile) obtained 

from an evidentiary item in both propositions, H1 and H2, of a pair of propositions.

3.4

evaluative analysis

An analysis using propositions that are used with the intent of producing an LR for reporting.

3.5

hierarchy of propositions

An organizational structure for propositions. Proposition pairs are classified by the level of

information they can provide to the trier of fact: offense (e.g., “Mr. X raped V”), activity (e.g., “Mr. X 

had intercourse with V”), source (e.g., “The semen came from Mr. X”), sub-source (e.g., “Mr. X is a 

contributor to this DNA.”), and sub-sub-source (e.g., “Mr. X is the minor contributor to this DNA 

mixture”). Further explanations can be found in Buckleton et al. [2], pp. 46-48.

3.5.1

sub-source level proposition

A proposition that specifies a defined set of assumed contributors (known or not) to the questioned 

DNA (evidentiary) sample.
Assigning Propositions for Likelihood Ratios

3.5.2

sub-sub-source level proposition

A proposition that specifies an assumed contributor (known or not) to one contribution of a 

questioned DNA (evidentiary) mixture (e.g., the major contributor of a two-person mixture).

3.6

intimate contributor

An individual from whose body a biological evidentiary item has been directly obtained.

3.7

probabilistic genotyping

The use of biological modeling (i.e., statistical modeling informed by biological data), statistical 

theory, computer algorithms, and/or probability distributions, to infer genotypes and/or calculate 

likelihood ratios.

3.8

probabilistic genotyping system

Software, or software and hardware, which utilizes a probabilistic genotyping approach to infer 

genotypes and/or calculate likelihood ratios.

3.9

proposition

A statement that is true or false, associated with the standpoint of one of the parties on a disputed 

issue of interest.

4 Requirements

Refer to Annex A, Best Practice Recommendations, for additional normative information on the 

following requirements.

4.1 The laboratory shall have a documented policy that outlines the difference between relevant 

and irrelevant information.

4.2 The laboratory shall have a documented policy on the reporting of results within the hierarchy 

of propositions. The policy shall define the level within the hierarchy of propositions (e.g., subsource or sub-sub-source) that the laboratoryreports.

4.3 The laboratory shall have a documented policy defining when a conditioning profile will be 

used. Support for the assumption of non-intimate conditioning contributors shall be documented 

in the case file.

4.4 Where multiple persons of interest (POIs) have LRs that support an association to a DNA 

mixture, within the capabilities of the approach used, an analysis shall be performed using 

proposition pairs that test whether the multiple POIs can be included together in the observed DNA 

profile.

4.5 If an analysis requires the number of contributors to be declared for each proposition or pair of 

propositions tested, then the laboratory shall have a documented policy regarding the assignment 

of the number of contributors for each proposition or pair of propositions.
Assigning Propositions for Likelihood Ratios

4.5.1 If an analysis requires a predefined number of contributors, then an assessment of the 

number of contributors shall be documented in the case file prior to comparison to any individuals 

who are not intimate or reasonably assumed (e.g., consensual partners) contributors.

4.5.2 If the approach used to calculate the LR cannot accommodate different numbers of 

contributors in H1 and H2, then the profile of the POI shall not be used in the initial assignment of 

the number of contributors.

4.5.3 Use of conditioning profiles in the contributor number assessment shall be documented in 

the case file.

4.5.4 If the laboratory allows for drop-in events in their probabilistic genotyping procedures, the 

laboratory shall have a documented policy regarding contributor number assumptions that require 

drop-in events.

4.5.5 Any reassessment of the number of contributors based upon a probabilistic genotyping 

system’s diagnostic calculations, or subsequent interpretations or LR calculations, shall be 

documented in the case file. This documentation shall include the reason for the change.

4.6 The laboratory shall have a documented policy on when and how propositions will include a 

relative of a conditioned donor within the set of unknowns.

4.7 Reporting only one, or a subset, of the LRs for evaluative analyses that have been conducted for 

multiple proposition pairs, differing by the conditioning profiles and/or the number of 

contributors, shall require documentation in the case file providing the reason the selected LRs 

were chosen.

4.7.1 Lacking any direction from either party, the laboratory shall formulate one or more 

reasonable proposition pairs that address each party’s assumed interests.

4.7.2 The laboratory shall reassess the data under a new pair of propositions if presented with a 

reasonable request (i.e., supported by the associated data, and presented in a timely manner) from 

either party regarding an alternate proposition pair.
Assigning Propositions for Likelihood Ratios

Annex A

(normative)

Best Practice Recommendations

A.1 Within the capabilities of the analysis approach used, the laboratory should report results for a 

pair of propositions that addresses the issue of interest. This level is the highest level in the 

hierarchy for which the forensic scientist can provide information. Hence, the laboratory should 

report results at sub-source level rather than sub-sub-source level.

A.2 If a single source profile is deduced from the mixture, even where sub-source propositions for 

mixtures are possible, then a sub-sub-source proposition pair may be used. However it is 

permissible, and may be advisable, to continue to operate at the sub-source level.

A.3 A profile should be assigned as a conditioning profile to a mixture when an individual is 

identified as an intimate contributor, or when it is reasonable to assume their presence based on 

case specific information, and the associated data supports the assumption. The conditioning 

profile could be from the complainant, POI, or other individual depending on the case scenario.

A.4 When conditioning on individuals in non-intimate samples, propositions that do not condition 

upon that individual’s profile may also be examined. A positive log(LR) value for an individual may 

be used as evidence of support for calculations that condition upon them.

A.5 The analysis should separate the propositions into their simplified constituents (i.e., simple 

proposition pairs2) when an LR favoring H1 has resulted from a compound proposition pair3

incorporating multiple POIs under H1 and none of the POIs under H2, in order to establish the 

weighting and the consequent probative value of the evidence per contributor under H1.

A.5.1 The results of the analyses using the simple proposition pairs should be included in the 

report unless the compound conclusion supports exclusion.

A.5.2 A simple proposition pair may include conditioning upon each POI separately in H1, where all 

other contributors are treated as unknowns. This could, however, contradict the assertions of the 

party represented by that proposition.

A.5.3 A simple proposition pair may include conditioning upon multiple POIs in H1 and one or a

subset of POIs in H2 with the goal of isolating the weight attributable to the POI not conditioned 

upon in H2. In the case of non-intimate samples, if a POI’s profile is assumed in both H1 and H2, then 

an LR shall also be calculated for a simple proposition pair with the POI not assumed in H2.

A.6 While the number of contributors to an evidentiary sample is strictly unknown, assessments of 

the number of contributors should involve profile traits such as

a) The number of clearly defined alleles;

b) The relative intensities of the results (e.g., relative peak heights);

2 simple proposition pair

A pair of propositions where no more than one POI in H1 is replaced with an unknown donor in H2 or vice versa.

3 compound proposition pair

A pair of propositions where more than one POI in H1 is replaced with unknown donors in H2 or vice versa.
Assigning Propositions for Likelihood Ratios

c) The relative proportions of peaksin expected artifact positions(e.g., STR reverse stutters);

d) Any assumptions regarding the contribution of a conditioning profile’s alleles; and

e) Any assumptions regarding rare genetic traits (e.g., tri-allelic genotypes).

Probabilistic methods may be used to provide estimated probabilities for the number of 

contributors.

A.6.1 A number of alternatives for the number of contributors may be used.

A.6.2 The number of contributors may be the same or different for H1 and H2.

A.6.3 For approaches that utilize probabilities, as opposed to probability densities, the number of 

contributors may be assigned values that maximize the probability of the evidence separately 

under H1 and H2. In such cases, the number of contributors under each proposition need not be the 

same within a given likelihood ratio.

A.6.4 Assigning the number of contributors may involve assessing possible drop-in events and also 

assessing or specifying the number of drop-in events allowed. Typically, if more than two drop-in 

events would be required, the assumed number of contributors should be increased [9, 11].

A.7 Investigative analyses4 should not be reported but retained in the case file. The report may 

include a comment that investigative analyses have been undertaken.

4 investigative analysis

An analysis using propositions that are used to determine the best pair(s) to use for an evaluative analysis.
Assigning Propositions for Likelihood Ratios

Annex B

(informative)

Bibliography

1] Buckleton,John, Bright,Jo-Anne, Taylor, Duncan, Evett,Ian, Hicks, Tacha,Jackson, Graham, 

and Curran, James. Helping formulate propositions in forensic DNA analysis. Science and 

Justice, 2014.

2] Buckleton,John, Bright,Jo-Anne, and Taylor, Duncan. Forensic DNA Evidence Interpretation, 

2nd ed. CRC Press, Boca Raton, 2016.

3] Buckleton,Johnand Curran,James. Adiscussion of themeritsofrandommannot excluded and 

likelihood ratios. Forensic Science International: Genetics, 2008.

4] Buckleton, John, Curran, James, and Gill, Peter. Towards understanding the effect of uncertainty 

in the number of contributors to DNA stains. Forensic Science International: Genetics, 2007.

5] Cook, R., Evett, Ian, Jackson, Graham, Jones, P., and Lambert, J. A hierarchy ofpropositions: 

deciding which level to address in casework. Sci Justice 1998.

6] European Network of Forensic Science Institutes, ENFSI guideline for evaluative reporting in 

forensic science, version 3.0, 2015.

7] Evett, Ian, Jackson, Graham, and Lambert, J. More on the hierarchy of propositions:exploring 

the distinction between explanations and propositions. Science & Justice 2000.

8] Gill, Peter and Haned, Hinda. A new methodological framework to interpret complex DNA 

profiles using likelihood ratios. Forensic Science International: Genetics, 2013.

9] Gill, Peter, Kirkham, A., and Curran,James, LoComatioN: A software tool for the analysis of low 

copy number DNA profiles. Forensic Science International, 2007.

10] Gittelson, Simone, Kalafut Tim, Myers, Steven, Taylor, Duncan, Hicks, Tacha, Taroni, Franco, 

Evett, Ian, Bright, Jo-Anne, and Buckleton, John. A practical guide for the formulation of 

propositions in the Bayesian approach to DNA evidence interpretation in an adversarial 

environment. Journal of Forensic Science, 2016.

11] Haned, Hinda, Slooten, Klaas, and Gill, Peter. Exploratory data analysis for the interpretation of 

low template DNA mixtures. Forensic Science International: Genetics, 2012.

12] Hicks, Tacha, Biedermann, Alex, de Koeijer,Jozias., Taroni, F., Champod, Christophe, and Evett, 

Ian. The importance of distinguishing information from evidence/observations when 

formulating propositions. Science and Justice 2015.

13] Federal Bureau of Investigation, Quality Assurance Standards for Forensic DNA Testing 

Laboratories, available at www.fbi.gov and www.swgdam.org

14] References at www.swgdam.org