OSAC 2021-S-0021 Forensic Autosomal STR DNA Statistical Analyses -

General Protocol, Protocol Verification, and Case Record Requirements

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OSAC 2021-S-0021

Forensic Autosomal STR DNA 

Statistical Analyses - General 

Protocol, Protocol Verification, 

and Case Record 

Requirements

Human Forensic Biology Subcommittee

Biology Scientific Area Committee

Organization of Scientific Area Committees (OSAC) for Forensic Science
OSAC 2021-S-0021 Forensic Autosomal STR DNA Statistical Analyses -

General Protocol, Protocol Verification, and Case Record Requirements

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OSAC Proposed Standard

OSAC 2021-S-0021

Forensic Autosomal STR DNA 

Statistical Analyses - General Protocol, 

Protocol Verification, and Case 

Record Requirements

Prepared by 

Human Forensic Biology Subcommittee

Version 2.0

November 2022

Disclaimer:

This OSAC Proposed Standard was written by the Human Forensic Biology Subcommittee of 

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

process that includes an open comment period. This Proposed Standard will be submitted to a 

standards developing organization and is subject to change. 

There may be references in an OSAC Proposed Standard to other publications under 

development by OSAC. The information in the Proposed Standard, and underlying concepts and 

methodologies, may be used by the forensic-science community before the completion of such 

companion publications.

Any identification of commercial equipment, instruments, or materials in the Proposed Standard 

is not a recommendation or endorsement by the U.S. Government and does not imply that the 

equipment, instruments, or materials are necessarily the best available for the purpose.

To be placed on the OSAC Registry, certain types of standards first must be reviewed by a 

Scientific and Technical Review Panel (STRP). The STRP process is vital to OSAC’s mission of

generating and recognizing scientifically sound standards for producing and interpreting forensic

science results. The STRP shall provide critical and knowledgeable reviews of draft standards or 

of proposed revisions of standards previously published by standards developing organizations 

(SDOs) to ensure that the published methods that practitioners employ are scientifically valid, 

and the resulting claims are trustworthy.
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The STRP panel will consist of an independent and diverse panel, including subject matter 

experts, human factors scientists, quality assurance personnel, and legal experts, which will be 

tasked with evaluating the proposed standard based on a comprehensive list of science-based 

criteria. 

For more information about this important process, please visit our website at: 

https://www.nist.gov/topics/organization-scientific-area-committees-forensic-science/scientifictechnical-review-panels
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Foreword

Detailed and comprehensive protocols are needed to ensure that appropriate statistical 

calculations for evidentiary DNA profiles are performed consistently by qualified analysts. 

These calculations are provided to aid in the assessment of an inclusion or positive 

association of a DNA profile with the profile of a known individual. Specific requirements 

for a laboratory’s protocol for performing statistical analyses, its verification, and 

requirements for case record documentation are provided. These requirements include 

documentation of when statistical calculations shall be performed and when they are not 

required; descriptions of the statistical methods available for use in the laboratory and 

relevant supporting information for their use; the use of assumptions in the calculations; 

documentation of the data used and relevant information for the calculations performed; 

and documented verification and consistency of use of the protocol in the laboratory.

This standard addresses general requirements for calculations commonly performed in 

forensic DNA testing laboratories. These include the likelihood ratio (LR), the random 

match probability (RMP), and the combined probability of inclusion/exclusion (CPI/CPE). 

This document applies to any manual calculations or software using fixed formulae and 

continuous or semi-continuous (also termed discrete) methods. This document applies to 

calculations resulting from the comparison of DNA profiles for identity testing (i.e., could 

the DNA have come from the same source?) as well as biological relationship testing (i.e., 

could the individuals be related?). While this standard applies directly to testing performed 

using the polymerase chain reaction (PCR) amplification of autosomal short tandem repeat 

loci (STR), many of the general requirements may also apply to other types of DNA testing 

and analysis. Additional information regarding the application of and specific 

requirements for the various statistical calculation methods routinely used in forensic DNA 

testing laboratories may be found in Annex A and the Bibliography (Annex B).

This standard is to be used in conjunction with the FBI’s Quality Assurance Standards for 

Forensic DNA Testing Laboratories[1] and the following ANSI/ASB Standards and Best 

Practice Recommendations: (1) ANSI/ASB Standard 018, Validation Standards for 

Probabilistic Genotyping Systems, First Edition, 2020; (2) ANSI/ASB Standard 020, 

Standard for Validation Studies of DNA Mixtures, and Development and Verification of a 

Laboratory’s Mixture Interpretation Protocol, First Edition, 2018; (3) ANSI/ASB Standard 

040, Standard for Forensic DNA Interpretation and Comparison Protocols, First Edition, 

2019; (4) ANSI/ASB Best Practice Recommendation 114, Best Practice Recommendations for 

Internal Validation of Software Used in Forensic DNA Laboratories, First Edition, 2022; (5) 

ANSI/ASB Standard 41, Assigning Propositions for Likelihood Ratios in Forensic DNA 

Interpretations, First Edition, 2020 and (6) ANSI/ASB Standard 123, Routine Internal 

Evaluation of a Laboratory’s Interpretation and Comparison Protocol as well as any current 

or future standards or recommendations that provide guidance for the appropriate use of 

specific statistical calculation methods and software. 
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Keywords: statistics, statistical analysis, protocol, protocol verification, consistency, random 

match probability (RMP), combined probability of inclusion or exclusion (CPI/CPE), likelihood 

ratio (LR), probabilistic genotyping, DNA profile, DNA mixtures

Table of Contents

Foreword

Forensic Autosomal STR DNA Statistical Analyses - General Protocol, Protocol Verification, 

and Case Record Requirements

Scope

Normative References

Terms and Definitions

Requirements

Annex A (informative)

Annex B (informative)

Bibliography
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Forensic Autosomal STR DNA Statistical Analyses - General Protocol, 

Protocol Verification, and Case Record Requirements

1 Scope

Forensic DNA testing requires that statistical calculations be performed on evidentiary 

DNA profiles that are established as relevant in the context of the case to aid in the 

assessment of an inclusion or positive association with a known individual. Calculations 

commonly used are the likelihood ratio (LR), random match probability (RMP), or 

combined probability of inclusion or exclusion (CPI/CPE). This standard provides general 

requirements for the laboratory protocol for performing statistical analyses, verification 

and consistency of use of the protocol, and documentation in the case record of all 

pertinent information regarding the statistical calculations. This standard applies directly 

to polymerase chain reaction (PCR) amplification of autosomal short tandem repeat loci 

(STR); many of the general requirements may also apply to other types of DNA testing and 

analysis. 

2 Normative References

There are no normative reference documents. Annex B, Bibliography, contains informative 

references.

3 Terms and Definitions

For purposes of this document, the following definitions apply.

3.1

combined probability of exclusion (CPE)

The probability that a randomly selected individual would be excluded as a contributor to 

the mixture; produced by multiplying the probabilities of inclusion from each locus chosen 

for inclusion and subtracting the product from 1 (i.e., 1-CPI).

3.2

combined probability of inclusion (CPI)

The probability that a randomly selected individual would be included as a possible 

contributor to a mixture; produced by multiplying the probabilities of inclusion from each 

locus chosen for inclusion.

3.3

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, who 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 
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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.

3.4 

likelihood ratio (LR) 

The ratio of two conditional probabilities of the same event under mutually exclusive 

hypotheses. The general formula is: LR= Pr (E|H1, I)/Pr (E|H2, I). For DNA testing, a 

statement of comparison of the probability of the evidence (E) (i.e., the DNA profile), given 

two competing hypotheses, inclusionary (H1) or exclusionary (H2) for an individual or 

specific sets of individuals, and in the context of relevant information (I). (Note: alternative 

nomenclature is provided in Annex A.)

3.5

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.

3.6

proposition

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

disputed issue of interest.

3.7

random match probability (RMP)

The probability of randomly selecting an individual from the population who could be a 

potential contributor to an evidentiary profile.

4 Requirements

Refer to Annex A, Information on Random Match Probability (RMP), Likelihood Ratio (LR) 

and Combined Probability of Inclusion or Exclusion (CPI/CPE), for additional information 

regarding the statistical values applicable to autosomal DNA testing and the following 

requirements.

4.1 The laboratory shall have and follow a protocol for performing statistical analyses that 

includes the following:

4.1.1 Descriptions of scenarios where statistical analyses must be performed and 

scenarios where statistical analyses are not required. 

NOTE No statistical analysis is required for an exclusion determined manually. 

NOTE Statistical analyses on the evidentiary DNA profile are not required, but may be 

performed, when a comparison has not been made to known reference data (e.g. to provide 
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important or relevant information for a particular case when no reference sample is 

available).

4.1.2 A requirement that any reported positive association of an evidentiary DNA profile to 

the DNA profile from a known individual be supported by a statistical analysis. The data 

from each locus used for comparison and for stating a positive association shall also be 

included in the statistical calculation.

NOTE This does not apply to the inclusion of an individual whose DNA is reasonably 

expected to be present on the item of evidence based on how and from where the biological 

sample was collected, as defined by the laboratory protocol and/or as documented in the 

case record for a specific case scenario (e.g., swabbings of an area of an individual’s body; 

clothing worn in close contact with the individual’s body). 

NOTE Statistical analyses are not required in support of a positive association between 

two sets of evidentiary data, but may be calculated and provided (e.g., DNA profiles in 

common between two blood stains of unknown origin found at two different crime scenes 

to aid in assessing the possibility they may be from the same individual). 

4.1.3 A requirement that statistical analyses shall be performed only on loci deemed 

suitable for comparison based upon the laboratory’s documented interpretation and 

comparison protocol (e.g., where stochastic phenomena such as allelic drop-out, allelic 

drop-in, or stutter are not explicitly accounted for in the statistical model being used). If the 

data at a locus have been deemed unsuitable for comparison, then no statistical value can 

be provided for that locus.

NOTE This requirement is not applicable for probabilistic genotyping software. This 

requirement is meant to eliminate the practice of omitting loci which do not exhibit the 

alleles of one or more individuals when compared to the known reference standard. 

Although such practice has been historically labelled as neutral or conservative, it typically 

is not, and can be especially problematic with interpretation methods that do not allow 

explicit modeling of allelic dropout or other stochastic phenomena.

4.1.4 A description of statistical analysis methods available for use in the laboratory, to 

include the following: 

4.1.4.1 When statistical analyses are generated from manual calculations or software (e.g., 

RMP, CPI/CPE, and LR not from probabilistic genotyping software), provide all equations 

used in the calculations including the following.

4.1.4.1.1 For a homozygous genotype at a locus.

4.1.4.1.2 For a heterozygous genotype at a locus.

4.1.4.1.3 When a theta (θ) correction factor(s) is used and provide the value of theta used 

in that calculation.
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4.1.4.1.4 For the possible genotype combinations when data from more than one 

contributor (i.e., mixture) are present at a locus. 

4.1.4.1.5 For combining genotype frequencies across multiple loci in a DNA profile.

4.1.4.1.6 For minimum allele frequencies, if used, for the population databases. 

4.1.4.1.7 For biological relationships, if used.

4.1.4.2 For calculations generated using probabilistic genotyping software, provide the 

following. 

4.1.4.2.1 References to the published literature, and any other relevant information (e.g., 

technical and/or user’s manual), for the equations and the calculations used by the 

software for computing likelihood ratios. 

4.1.4.2.2 The statistical basis for defining inclusion, exclusion, inconclusive and 

uninterpretable when those terms are used by the laboratory. 

4.1.4.2.3 A requirement that when multiple persons of interest have likelihood ratios 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 persons 

of interest can be included together in the observed DNA profile. 

4.1.4.2.4 A protocol regarding the use of replicate profile data, as defined by, and if 

performed by, the laboratory.

4.1.4.3 A description of when each statistical method can be employed in the laboratory.

4.1.4.4 When multiple methods are available in the laboratory for calculating statistical 

values and more than one may be appropriately used for a particular case sample scenario 

and/or DNA profile per 4.1.4.3, then the protocol shall state which statistical analysis 

method shall be used and/or how to determine which method will be used. For example, 

the protocol may permit the use of RMP and LR calculations for single source DNA profiles; 

in this situation, the protocol shall clearly define which calculation should be used under 

which scenario to ensure reliability based on validation studies and consistency within the 

laboratory. 

Similarly, a CPI/CPE, RMP and/or LR calculation may be appropriate for use for a mixed 

DNA profile; again, the protocol shall clearly define which calculation should be used. A 

common scenario where this may be relevant is an assumed two-person contributor mixed 

DNA profile obtained from a vaginal, oral or breast swab where the DNA profile from the 

known female contributor is available and each of the approaches may be applicable. 

4.1.5 The source of the population database(s) used in any statistical analyses.
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4.1.6 When and how alternate population databases and/or theta correction values shall 

be applied.

4.1.7 What types of assumptions can be made, when those assumptions can be made, and 

how they shall be incorporated into the statistical analysis. Such assumptions may include, 

but are not limited to, the number of contributors, the presence of possible artifacts (e.g., 

stutter) and/or stochastic effects, and the presence of assumed contributors. In addition, 

the protocol shall also define the use of conditioning information in propositions used to 

calculate likelihood ratios. The protocol shall provide information regarding the 

appropriate situation for the use of assumptions (and/or conditioning information used in 

the proposition for an LR) permitted in the laboratory that may impact the statistical 

analyses. Assumption(s) used that may impact the statistical analyses shall be documented 

in the case record as required by 4.3.5.

4.1.8 A description of the appropriate validated software and version number to be used 

for each type of statistical analysis.

4.1.9 A description of when the variable input parameters should be modified and the 

appropriate values to be used for any parameter or input value that can be changed by the 

analyst in the software. 

4.1.10 A requirement that statistical analyses be performed only at those loci common to 

both profiles (e.g., when one of the profiles used for comparison has data at fewer loci than 

the other profile in the comparison, as in a partial, incomplete profile or data from different 

multiplex kits) for non-probabilistic genotyping (e.g., manual) methods.

4.1.11 A requirement that a new statistical analysis must be performed when subsequent 

review of the profile data alters how it is used in the original statistical analysis. 

4.1.12 A requirement that two or more conceptually different statistics shall not be 

combined. Specific examples include not multiplying a random match probability with 

either a combined probability of inclusion or a likelihood ratio, and not multiplying a 

combined probability of inclusion with a likelihood ratio. 

4.1.13 Statements of any known limitations for the use of any formulae and/or software 

based on external or internal validation studies, and situations where profile data cannot 

be used for statistical calculations shall be clearly defined in the protocol. Some possible 

limitations include the number of contributors that may be assumed when using certain 

formula(e) or software, limitations established through the laboratory validation studies, 

functions that have not been validated by the laboratory, and when data are insufficient for 

using the statistical analysis method (e.g., the inability to use CPI/CPE calculations if there 

is a reasonable risk that data are missing from a locus). 
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4.2 The laboratory shall verify and document that the protocols for performing statistical 

analyses generate appropriate values and are performed consistently within the laboratory 

for all types of DNA profiles typically interpreted and compared by the laboratory.

4.2.1 Verification of the protocols shall be performed on single source and mixed DNA 

samples of known origin that are different from those used in the initial validation studies 

for the amplification kit and/or statistical analysis software or used to establish the 

statistical analysis protocol.

4.2.2 Verification of the statistical analysis protocol shall demonstrate that its use returns 

the same value within the laboratory for the same DNA profile when using procedures 

without an element of randomness (e.g., Popstats or non-probabilistic genotyping 

software).

4.2.3 Verification of the statistical calculations protocol shall demonstrate that its use with 

probabilistic genotyping software having an element of randomness results in consistent 

values between different runs with the same inputs, as defined by the laboratory based on 

validation studies for both true contributors and non-contributors.

4.2.4 Verification shall include a demonstration of consistency among analysts in the 

laboratory for the calculated statistical values using examples representative of the range 

of samples handled by the laboratory. The laboratory shall define the acceptable range of 

variability in the statistical values generated for use in the evaluation of the consistency 

within the laboratory.

4.2.5 Verification shall be performed on existing, modified, and new statistical analysis 

protocols.

4.2.6 For verification of the statistical analyses protocol, the laboratory shall use data 

generated and processed under similar testing conditions to those routinely used by the 

laboratory. The data for all contributors to the DNA used in the verification shall be known 

and available for the assessment of the data and the proposed statistical analyses protocol. 

DNA data from different sets of contributors than used in the initial validation studies shall 

be used to verify the protocol. These supplemental data sets shall span the range of data 

anticipated to be interpreted by the laboratory. 

4.2.7 The verification of the protocol shall be completed prior to implementation of the 

protocol for casework. Additional validation studies and/or protocol development shall be 

necessary if deficiencies in the protocol or inconsistencies within the laboratory are 

identified through this verification process. 

4.2.8 Any subsequent modifications to any DNA testing or data interpretation protocol 

shall include an evaluation for its impact on DNA statistical calculations. These 

modifications shall be updated in the relevant protocol(s) addressing these requirements, 

as needed. 
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4.2.9 Methods, equations, software, etc. shall not be used for statistical calculations without 

the prerequisite validation, protocol development and verification of the protocol 

according to the requirements of this standard.

4.3 The laboratory shall document the following in the case record for each statistical 

analysis performed.

4.3.1 The population database(s) used and the source(s) of the database(s).

4.3.2 The statistical analysis method(s) used, and, if applicable, the software program and 

version number used.

4.3.3 The theta correction factor value(s) used. 

4.3.4 The genetic loci and data used for statistical calculations. 

4.3.5 Assumptions made when performing the statistical analysis, including but not limited 

to number of contributors and/or assumed contributors, and in the case of paternity or 

kinship analysis, any alleged or assumed biological relationships.

4.3.6 All statistical analyses performed, including analyses performed using different 

assumptions and/or different propositions (e.g., conditioning on different DNA profiles), 

regardless of whether the statistical analysis is reported by the laboratory. 

4.3.7 The actual value used by the analyst with each statistical analysis for any parameter 

or input value that can be changed in the software (e.g., random number seeds, number of 

Markov Chain Monte Carlo iterations, probability of drop-out and/or drop-in).

4.3.8 Any interpreted and compared profile for which a calculation is not needed, based on 

case-specific scenarios, shall be documented in the case record.
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Annex A (informative)

Information on Random Match Probability (RMP), Likelihood Ratio (LR) 

and Combined Probability of Inclusion or Exclusion (CPI/CPE)

Additional information regarding the three major types of statistical values calculated for 

forensic STR DNA profiles is provided below. It should be noted that for Random Match 

Probability (RMP), Likelihood Ratio (LR) and Combined Probability of Inclusion/Exclusion 

(CPI/CPE): 

1) These three terms refer only to statistical values and their respective calculations. 

2) The use of all three statistical calculation methods requires prior independent 

interpretation of the STR DNA profile, which includes (but is not limited to) 

assessment of stutter, determination of the alleles and loci suitable for comparison, 

the risk of allele drop-out and drop-in at each locus and across the profile, and the 

assumed number of contributors. None of these statistical calculation methods are 

interpretation methods and play no direct role in the interpretation of the DNA 

profile. 

3) A single statistical calculation method must be used across all loci that are suitable 

for comparison in a given profile; it is not permissible to combine any of these 

different statistical calculations for a single profile per Requirement 4.1.12. 

4) There may be situations where the insufficiency of data and/or the inability to 

perform a statistical calculation for a profile or for one or more loci within a profile 

precludes that profile or locus, respectively, from being used for comparison 

purposes, causing that profile or locus to be referred to as unsuitable for 

comparison, and thus inconclusive. 

5) The calculated values are estimates and will vary depending on the allele frequency 

database used, the quality of the DNA profile, the number of loci having data, the 

model and formula(e) used and many other variables that impact the calculations. 

Random Match Probability (RMP)

Some of the key features and use of the Random Match Probability statistical calculation 

method for STR DNA single source and mixture profiles are provided here:

1) The RMP may be used for single source profiles and for some mixtures. 

a) For mixtures, the RMP may be calculated for one contributor to a mixture, a subset 

of contributors, or for the combined genotypes of all contributors. Within a mixture: 

May be used for single source profiles that may be resolved (e.g., single major or 

minor contributor; deduced single contributor when using the genotypes from one 

or more assumed contributors in the determination of possible genotypes). May be 

used for multiple contributor profiles by considering the combinations of possible 

genotypes at a locus (e.g., two contributor profiles) by summing the probabilities for 

all genotypes included at the locus. Has sometimes been referred to as modified 

RMP or restricted RMP.
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b) The assumed number of contributors to the DNA mixture and the genotypes from 

any assumed contributor(s) limit, or restrict, the possible genotypes at a locus that 

are then used for the calculation of the RMP.

c) It may be practical to limit the RMP calculation to profiles, or the portion of a profile, 

with a defined maximum number of contributors.

d) The RMP can be used for profiles where stochastic effects may be present. 

2) The equations using Recommendation 4.1 of the NRC II (1996)[4] for RMP calculations 

are:

a) p2 + p(1-p)θ for homozygous loci, where p is the frequency of allele P at a single 

locus and θ = 0.01 (for most populations in the United States) or 0.03 (for some 

isolated populations). 

b) 2pq for heterozygous loci, where p is the frequency of allele P at a single locus and q 

is the frequency of allele Q at the same locus.

c) For single alleles at a locus for which the second allele cannot be determined (e.g., 

due to possible allele drop-out or allele masking at a possible shared allele), one of 

the three following equations may be used: a) 2p; b) 2p-p2 or c) p2 + 2p(1-p), where 

p is the frequency of the single obligate allele P. Note: the equations in b) and c) are 

two notations of the same equation. 

d) The product rule is used to calculate the RMP across multiple loci.

e) Equations using Recommendation 4.2 of the NRC II (1996) may also be used. These 

equations provide corrections for both homozygous and heterozygous profiles.1

3) The RMP can be estimated by the frequency of occurrence for a given genotype or set of 

genotypes, in a particular reference population, that make up the profile of a DNA 

contributor among random unrelated individuals. It is commonly expressed as 1 in the 

number of individuals by inverting the resulting frequency after applying the product 

rule across all loci. 

4) The RMP is calculated for the genotypes of the single source or mixed evidentiary DNA 

profile independently of (and even prior to) comparison to the profile from any known 

individual (other than assumed contributors) since the calculation is based on the 

evidence data alone. 

a) If a subset of loci in the evidence profile is used to calculate the RMP, then the 

selection of those loci used should be determined independently of (and even prior 

to) comparison to any reference profile. 

b) It is necessary to calculate different RMP values for a DNA mixture when different 

profiles can be resolved [e.g., one RMP for the major contributor(s), and one RMP 

for the minor contributor(s)].

Likelihood Ratio (LR)

1 Equations 4.1a and 4.1b are identical algebraically to equations 4.10a and 4.10b when theta is 

zero. However the interpretation of these two sets of equations is fundamentally different. 

Equations 4.1 represent the probability of occurrence of a genotype in a population, whereas 

equations 4.10 represent the probability of occurrence of a genotype in a population GIVEN that 

this genotype has been observed in a known individual. The latter is often referred to as a 

conditional match probability.
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Some of the key features and use of the Likelihood Ratio method for STR DNA single source 

and mixture profiles are provided here:

1) The LR may be used for single source profiles and mixtures. 

a) A probabilistic (semi-continuous, continuous) LR can be used for profiles where 

allele drop-out and/or drop-in may have occurred. 

b) A binary LR (non-probabilistic LR) cannot be used for profiles where allele drop-out 

and/or drop-in may have occurred.

2) The LR is a ratio of probabilities of observing the evidence (i.e., DNA profile obtained) 

under opposing propositions. It is NOT a measure of frequency or a probability. 

3) The general equation for the LR is: 

 

1

2

Pr(

Pr(

E H LR

E H

  )

=

  )

where Pr = Probability, E = Evidence, H1 = Hypothesis 1, H2 =Hypothesis 2, and I= 

relevant Information in formulating the propositions and assigning the 

probabilities. Propositions may be referred to as prosecution/defense 

propositions (Hp/Hd, respectively), proposition 1/proposition 2, 

prosecution/alternate propositions (Hp/HA, respectively), inclusionary 

propositions/exclusionary propositions or other terms that communicate the 

propositions are different from one another.

a) A proposition represents the set of contributor(s), known and unknown, who may 

have contributed to the observed DNA profile. There is no requirement that a 

particular proposition is true. 

b) The propositions depend on case information and the claims (or reasonably 

assumed claims) of each of the parties. The propositions may be changed at the 

request of either party.

c) By definition, the two propositions must be mutually exclusive. At least one element 

of the proposition must be different so that they may not both be true at the same 

time (e.g., Proposition 1 states the Person of Interest (POI) is the source of the DNA 

and Proposition 2 states a random, unrelated person in the population is the source 

of the DNA), or the value of the LR will equal 1.

d) A particular contributor genotype may be known or assumed to be a contributor in 

a proposition.

i) A conditioning profile is a profile that is assumed to be present in both 

propositions.

ii) A conditioning profile may be a profile assumed to be present due to the 

collection and/or origin of the evidence item (e.g., intimate sample) or it might 

simply be the assumption that a particular profile is present under a given set of 

propositions. 

e) To prevent a major contributor from having undue influence on the weight of the 

evidence for a minor contributor, consideration must be given to calculating a 

separate LR for each included contributor as well as an LR for the contributors 
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together per requirement 4.1.4.2.3. Conditioning profiles may be useful in this 

scenario.

f) For a binary LR calculation, the weight given to a plausible genotype is 1 and the 

weight given to an implausible genotype is 0 (hence the name “binary”).

g) For a probabilistic LR calculation, the weight given to a genotype can vary between 

0 and 1.

h) The weights of the same genotypes may differ for different propositions in the 

probabilistic LR calculation.

4) An LR is reported as a ratio of the probabilities of the evidence given the propositions, 

and not as a ratio of the probabilities of the propositions. For example, appropriate 

statements include: “The evidence is LR times more likely to be observed if Proposition 

1 is true rather than if Proposition 2 is true” or “It is LR times more likely that the DNA 

profile would be observed if Proposition 1 is true rather than if Proposition 2 is true”. 

a) It is expressed as an LR; it is NOT expressed as 1 in X number of individuals. 

i) For a single source profile, when theta is equal to zero, often the LR and RMP 

values are numerically the reciprocal of each other; however, they answer 

fundamentally different questions. 

5) A given LR is only for the propositions stated under the relevant information. If the 

propositions change or if the relevant information changes, then a new LR must be 

calculated.

a) The value of the LR will change when the data and/or propositions change.

i) LRs generated under the same set of propositions using probabilistic genotyping 

software with an element of randomness will generally vary within an expected 

limited range. 

6) An LR calculation can return a value less than one (or negative logLR), which 

communicates that more weight of evidence is given to the proposition in the 

denominator.

7) A probabilistic or a binary LR calculation can return a value of one (or logLR of 0), 

which communicates that equal weight of evidence is given to both propositions. 

Neither proposition is supported over the other. 

8) A probabilistic or a binary LR calculation can return a value greater than one (or 

positive logLR), which communicates that more weight of evidence is given to the 

proposition in the numerator.

Combined Probability of Inclusion (CPI) and Combined Probability of Exclusion 

(CPE)2

2 While there is limited support for the continued use of CPI/CPE by forensic DNA testing 

laboratories, it is recognized that some laboratories are still using this calculation for their 

casework. This section is provided as guidance for those laboratories as well as for laboratories 

interested in assessing their prior practices and protocols for the use of CPI/CPE in older casework 

(e.g., cold cases, postconviction review). CPI may be used in a case where there is no other available

statistical calculation available for use; however, the CPI calculation shall be used according to the 

guidance provided in this annex and the Bieber et al. reference in the Bibliography.
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Some of the key features and use of the Combined Probability of Inclusion (CPI) and 

Combined Probability of Exclusion (CPE) statistical calculation method for mixed STR DNA 

profiles are provided here:

1) Also referred to as Random Man Not Excluded (RMNE).

2) Only appropriate use is to provide statistical calculations for a limited subset of mixed 

DNA profiles.

a) Most applicable for use with profiles generated from the amplification of sufficiently 

high amounts of DNA such that stochastic effects, if present, are negligible, and have 

no impact on the interpretation and ability to generate statistical frequency 

calculations.

b) Generally, most applicable for use with DNA profiles from two-person DNA mixtures 

or three-person mixtures having two major contributors, where the CPI/CPE is 

calculated only for the two major contributors. 

c) Rarely suitable for use with mixtures of three or more contributors, particularly 

when amplified with high sensitivity kits using recommended procedures, with the 

possible exception of when two distinguishable major contributor profiles are 

present. It can only be used with mixtures of three or more contributors when high 

levels of DNA are observed and no contributor is reasonably expected to have 

dropped out at any locus.

d) Commonly used for indistinguishable mixed DNA profiles (i.e., unable to associate 

alleles into genotypes for the contributors due to similarities in peak heights and the 

inability to assume the genotypes of one of the contributors).

3) May ONLY be used for profiles where there is very high confidence that all alleles, and 

thus all genotypes, for all contributors are present at each of the loci with data available 

for interpretation and comparison, and where there is no reason to expect that allele 

drop-out might have occurred. (See 2b above.)

a) Data from loci with one or more alleles below the stochastic threshold cannot be 

used for comparison or for calculating the CPI/CPE (with the one exception stated in 

(d) below). The assignment of the number of contributors to the DNA mixture using 

the entire DNA profile is critical for evaluating the prospect that all genotypes from 

all contributors are present at each locus.

b) This determination has to occur prior to comparison of the DNA profile data to the 

profile from any known contributor (i.e., independently of any knowledge of data 

from other profiles). 

c) If all alleles at a locus are above the stochastic threshold, but there are only a limited 

number of alleles as compared to the maximum expected allele count based on the 

assumed number of contributors (1-2 alleles in 2 person mixtures; 1-4 alleles in 3 

person mixtures), then the CPI/CPE calculation cannot be used if drop-out best 

explains the paucity of alleles. Peak heights at other loci and total peak height 

values at each locus are taken into account when assessing the data and the 

possibility of drop-out. 
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i) When the alleles from at least one contributor are below the stochastic threshold 

at multiple loci, it is reasonable to assume that the alleles for that individual will 

be below the stochastic threshold at all loci based on the mixture ratio of the 

contributors’ DNA; thus, CPI/CPE cannot be used for this profile, even for the 

one or few loci with all alleles above the stochastic threshold as it is more likely 

that alleles are missing than the assumption that all alleles are present.

ii) If one or more alleles are missing from a locus, the CPI/CPE value resulting from 

the use of the existing alleles would underestimate the proportion of possible 

contributors as compared to the calculation using all of the alleles from all of the 

contributors. That is, the value calculated would give the appearance of the 

profile being rarer than it really is; this would overstate the value of the evidence 

and could be more prejudicial. It is not generally accepted practice for rarer 

values to be reported or presented in testimony when providing a statistical 

frequency for an individual who cannot be excluded as a possible contributor. 

d) Loci with one or more peaks below an RFU-defined stochastic threshold may be 

used in the CPI calculation ONLY if the total number of alleles present at each locus 

is consistent with all alleles being present for the assumed number of contributors 

(e.g., six alleles are present at a locus and the assumption of three total contributors 

is used).

4) The equations for CPI/CPE calculation are:

a) Probability of inclusion for a locus = (the sum of allele frequencies)2 = (PA + PB + PC + 

... + PN)

2, where PA, PB, PC and PN are the frequencies of alleles A, B, C and N, 

respectively, observed at the locus, where it is assumed that all alleles from all 

contributors to the DNA mixture are present, based on the data observed and the 

assumed number of contributors to the DNA profile.

i) The value at each locus is the cumulative frequency of all possible heterozygous 

and homozygous genotypes. 

ii) For profiles where the maximum allele count is observed based on the assumed 

number of contributors to the DNA mixture, the CPI/CPE calculation would still 

incorporate the frequencies of homozygous genotypes included at that locus, 

however, individuals with homozygous genotypes could be excluded definitively 

from that locus during interpretation and comparison based on the assumed 

number of contributors. 

b) The Combined Probability of Inclusion (CPI) is the product (i.e., multiplied together) 

of each of the probabilities of inclusion calculated from each locus used in the 

interpretation.

c) CPE = (1 – CPI); other equations are available in the publications referenced in 

Annex B, Bibliography. 

5) The CPI value is an approximation of the proportion of random individuals unrelated to 

a true contributor in the mixture who would be expected to be included as possible 

contributors to the DNA mixture from the random population. It is commonly reported 

as 1 in X number of individuals. 
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a) The CPE is an approximation of the proportion of random individuals unrelated to a 

true contributor in the mixture who would be excluded as contributors to the DNA 

mixture from the random population. This value may be expressed as Y out of X 

individuals, but is sometimes expressed as a percentage. 

b) The CPI/CPE value is appropriate for use when related individuals are contributors 

to the DNA mixture. 

c) The CPI/CPE calculation cannot be used to consider the possibility/compute the 

probability that an untested relative may be a contributor to the DNA mixture. 

6) The CPI/CPE is calculated for the mixed DNA profile independently of (and even prior 

to) comparison of the profile from any known individual since the calculation is based 

on the questioned profile alone;

a) Only one CPI/CPE frequency can be calculated for one mixed DNA profile.

b) A CPI/CPE calculation is based on the questioned profile alone. It should never be 

based on the profile of an individual who cannot be excluded as a contributor.

Additional information regarding CPI/CPE calculations and uses is available in publications 

referenced in Annex B, Bibliography.
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Annex B (informative)

Bibliography

1] Quality Assurance Standards for Forensic DNA Testing Laboratories, 

https://www.fbi.gov/file-repository/quality-assurance-standards-for-forensic-dnatesting-laboratories.pdf/view (May 2022)

2] Buckleton, John, Bright, Jo-Ann., and Taylor, Duncan A. (Eds.). Forensic DNA Evidence 

Interpretation. 2nd edition, CRC Press, 2016.

3] Balding, David J. and Steele, Christopher D. Weight-of-Evidence for Forensic DNA 

Profiles. 2nd edition, Wiley, 2015.

4] National Research Council (NRC II). The Evaluation of Forensic DNA Evidence. 

National Academy Press, 1996. (Available online at: 

https://www.nap.edu/read/5141/).

5] Bieber, Frederick. R., Buckleton, John S., Budowle, Bruce, Butler, John M., and Coble, 

Michael D. “Evaluation of Forensic DNA Mixture Evidence: Protocol for Evaluation, 

Interpretation, and Statistical Calculations Using the Combined Probability of 

Inclusion.” BMC Genet., vol. 7, no. 1, 2016, pp .125.

6] Curran, James M. and Buckleton, John. “Inclusion Probabilities And Dropout.” J. For. 

Sci., vol. 55, no. 5, 2010, pp. 1171-1173.

7] Buckleton, John and Curran, James M. “A Discussion of the Merits Of Random Man 

Not Excluded and Likelihood Ratios.” For. Sci. Int: Gen., vol. 2, no. 4, 2008, pp. 343-

348.

8] Bille, Todd W., Bright, Jo-Ann and Buckleton, John. “Application of Random Match 

Probability Calculations to Mixed STR Profiles.” J. For. Sci., vol. 58, no. 2, 2013, pp. 

474-85

9] Gittelson, Simone., Kalafut Timothy, Myers, Stephen, Taylor, Duncan, Hicks Tacha, 

Taroni, Franco, Evett, Ian W., Bright, Jo-Ann, and Buckleton, John. “A Practical Guide 

for the Formulation of Propositions in the Bayesian Approach to DNA Evidence 

Interpretation in an Adversarial Environment.” J. For. Sci. vol. 61, no. 1, 2016, pp. 

186-195.

10]SWGDAM 2017 Interpretation Guidelines for Autosomal STR Typing by Forensic 

DNA Laboratories. https://1ecb9588-ea6f-4feb-971a73265dbf079c.filesusr.com/ugd/4344b0_50e2749756a242528e6285a5bb478f4c.p

df (May 2022)

ANSI/ASB Standards and Best Practice Recommendations

11]ANSI/ASB Standard 018, Standard for Validation of Probabilistic Genotyping 

Systems, First Edition, 2020 

https://www.aafs.org/sites/default/files/media/documents/018_Std_e1.pdf (May 

2022)
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12]ANSI/ASB Standard 020, Standard for Validation Studies of DNA Mixtures, and 

Development and Verification of a Laboratory’s Mixture Interpretation Protocol, 

First Edition, 2018 

https://www.aafs.org/sites/default/files/media/documents/020_Std_e1.pdf

(May 2022)

13]ANSI/ASB Standard 040, Standard for Forensic DNA Interpretation and Comparison 

Protocols, First Edition, 2019 

https://www.aafs.org/sites/default/files/media/documents/Std_040_e1.pdf (May 

2022)

14]ANSI/ASB Standard 041, Assigning Propositions for Likelihood Ratios in Forensic 

DNA Interpretations, First Edition, 20xx, (currently in progress at ASB - link to be 

added when available)

15]ANSI/ASB Standard 123, Routine Internal Evaluation of a Laboratory’s 

Interpretation and Comparison Protocol, First Edition, 20xx, (currently in progress 

at ASB - link to be added when available)

16]ANSI/ASB Best Practice Recommendations 114, Best Practice Recommendations for 

Internal Validation of Software Used in Forensic DNA Laboratories, First Edition, 

2022 (October 2022 – link to be added when available)