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

General Protocol, Protocol Verification, and Case Record Requirements

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Draft 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 1.0

July, 2021

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

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

and the resulting claims are trustworthy.

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

General Protocol, Protocol Verification, and Case Record Requirements

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1 Foreword

2 Detailed and comprehensive protocols are needed to ensure that appropriate statistical 

3 calculations are performed consistently for evidentiary DNA profiles. These calculations 

4 are provided to aid in the assessment of an inclusion or positive association of a DNA 

5 profile with the profile of a known individual. Specific requirements for a laboratory’s 

6 protocol for performing statistical analyses, its verification, and requirements for case 

7 record documentation are provided. These requirements include documentation of when 

8 statistical calculations shall be performed and when they are not required; descriptions of 

9 the statistical methods available for use in the laboratory and relevant supporting 

10 information for their use; the use of assumptions in the calculations; documentation of the 

11 data used and relevant information for the calculations performed; and documented 

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

13

14 This standard addresses general requirements for calculations commonly performed in 

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

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

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

18 continuous or semi-continuous methods. This document applies to calculations resulting 

19 from the comparison of DNA profiles for identity testing (i.e., could the DNA have come 

20 from the same source?) as well as biological relationship testing (i.e., could the individuals 

21 be related?). While this standard applies directly to testing performed using the 

22 polymerase chain reaction (PCR) amplification of autosomal loci having short tandem 

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

24 testing and analysis. Additional information regarding the application of and specific 

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

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

27

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

Forensic DNA Testing Laboratories[1] 29 and the following ANSI/ASB Standards: (1) ANSI/ASB

30 Standard 018, Validation Standards for Probabilistic Genotyping Systems, First Edition, 

31 2020; (2) ANSI/ASB Standard 020, Standard for Validation Studies of DNA Mixtures, and 

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

33 Edition, 2018; (3) ANSI/ASB Standard 040, Standard for Forensic DNA Interpretation and 

34 Comparison Protocols, First Edition, 2019; (4) ANSI/ASB Standard 41, Assigning 

35 Propositions for Likelihood Ratios in Forensic DNA Interpretations, First Edition, 2020 and (5) 

36 ANSI/ASB Standard 123, Routine Internal Evaluation of a Laboratory’s Interpretation and 

37 Comparison Protocol as well as any current or future standards or recommendations that 

38 provide guidance for the appropriate use of specific statistical calculation methods and 

39 software. 

40

41 Keywords: statistics, statistical analysis, protocol, protocol verification, consistency, random 

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

43 ratio (LR), probabilistic genotyping, DNA profile, DNA mixtures
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44 Table of Contents

45

46 Foreword

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

48 and Case Record Requirements

49 Scope

50 Normative References

51 Terms and Definitions

52 Requirements

53 Annex A (informative)

54 Annex B (informative)

55 Bibliography
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56 Forensic Autosomal STR DNA Statistical Analyses - General Protocol, 

57 Protocol Verification, and Case Record Requirements

58 1 Scope

59 Forensic DNA testing requires that statistical calculations be performed on evidentiary 

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

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

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

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

64 requirements for the laboratory protocol for performing statistical analyses, verification 

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

66 pertinent information regarding the statistical calculations. This standard applies directly 

67 to testing performed using the polymerase chain reaction (PCR) amplification of autosomal 

68 loci having short tandem repeats (STR); many of the general requirements may also apply 

69 to other types of DNA testing and analysis. 

70 2 Normative References

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

72 references.

73 3 Terms and Definitions

74 For purposes of this document, the following definitions apply.

75 3.1

76 combined probability of exclusion (CPE)

77 The probability that a randomly selected, unrelated individual would be excluded as a 

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

79 each locus and subtracting the product from 1 (i.e., 1-CPI).

80

81 3.2

82 combined probability of inclusion (CPI)

83 The probability that a randomly selected, unrelated individual would be included as a 

84 possible contributor to a mixture; produced by multiplying the probabilities of inclusion 

85 from each locus.

86

87 3.3

88 conditioning

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

90 probability. The information might be the profile of an individual, or profiles of a set of 

91 individuals, who are assumed to have contributed DNA to the evidentiary item under a 

92 particular proposition, or it might simply be the assumption that a particular proposition is 
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93 true. Any events (or information) that have been used for conditioning are placed to the 

94 right of the conditioning bar in a conditional probability expression.

95 3.4 

96 likelihood ratio (LR) 

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

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

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

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

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

102 nomenclature is provided in Annex A.)

103

104 3.5

105 probabilistic genotyping

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

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

108 and/or calculate likelihood ratios.

109

110 3.6

111 proposition

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

113 disputed issue of interest.

114

115 3.7

116 random match probability (RMP)

117 The probability of randomly selecting an unrelated individual from the population who 

118 could be a potential contributor to an evidentiary profile.

119 4 Requirements

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

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

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

123 requirements.

124 4.1 The laboratory shall have and follow a protocol for performing statistical analyses that 

125 includes the following:

126

127 4.1.1 Descriptions of scenarios where statistical analyses must be performed and 

128 scenarios where statistical analyses are not required. 

129

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

131

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

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

135 available).

136

137 4.1.2 A requirement that any reported positive association of an evidentiary DNA profile to 

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

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

140 in the statistical calculation.

141

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

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

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

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

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

147

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

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

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

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

152

153 4.1.3 A requirement that statistical analyses shall only be performed on loci deemed 

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

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

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

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

158 be provided for that locus.

159

160 NOTE This requirement may not be applicable for some probabilistic genotyping software. 

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

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

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

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

165 explicit modelling of allelic dropout or other stochastic phenomena.

166

167 4.1.4 A description of statistical analysis methods available for use in the laboratory, to 

168 include the following: 

169

170 4.1.4.1 When statistical analyses are generated from manual calculations or software (e.g., 

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

172 used in the calculations including the following.

173

174 4.1.4.1.1 For a homozygous genotype at a locus.

175

176 4.1.4.1.2 For a heterozygous genotype at a locus.

177
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178 4.1.4.1.3 Where a theta (θ) correction factor(s) is used and provide the value of theta used 

179 in the calculation.

180

181 4.1.4.1.4 For the possible genotype combinations when data from more than one 

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

183

184 4.1.4.1.5 For combining genotype frequencies across multiple loci in a DNA profile.

185

186 4.1.4.1.6 For minimum allele frequencies, if used, for the population databases. 

187

188 4.1.4.1.7 For biological relationships, if used.

189

190 4.1.4.2 For calculations generated using probabilistic genotyping software, provide the 

191 following. 

192

193 4.1.4.2.1 References to the published literature, and any other relevant information (e.g., 

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

195 software for computing likelihood ratios. 

196

197 4.1.4.2.2 The statistical basis for defining inclusion, exclusion, inconclusive and 

198 uninterpretable when those terms are used by the laboratory. 

199

200 4.1.4.2.3 A requirement that when multiple persons of interest have likelihood ratios that 

201 support an association to a DNA mixture, within the capabilities of the approach used, an 

202 analysis shall be performed using proposition pairs that test whether the multiple persons 

203 of interest can be included together in the observed DNA profile. (note: borrowed from LR 

204 Props document -- need to be sure this stays consistent with that document as moves through 

205 the process)

206

207 4.1.4.2.4 A protocol regarding the use of replicate profile data, if performed by the 

208 laboratory.

209

210 4.1.4.3 A description of when each statistical method can be employed in the laboratory.

211

212 4.1.4.4 When multiple methods are available in the laboratory for calculating statistical 

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

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

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

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

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

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

219 laboratory. 

220

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

222 DNA profile; again, the protocol shall clearly define which calculation should be used. A 
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223 common scenario where this may be relevant is an assumed two-person contributor mixed 

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

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

226

227 4.1.5 The source of the population database(s) used in any statistical analyses.

228

229 4.1.6 Procedures describing when and how alternate databases and/or theta correction 

230 values shall be applied.

231

232 4.1.7 What types of assumptions can be made, when those assumptions can be made, and 

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

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

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

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

237 calculate likelihood ratios. The protocol shall provide information regarding the 

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

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

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

241 documented in the case record as required by 4.3.5.

242 4.1.8 A description of the appropriate validated software and version number to be used 

243 for each type of statistical analysis.

244 4.1.9 A description of when the variable input parameters should be modified and the 

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

246 analyst in the software. 

247 4.1.10 A requirement that statistical analyses be performed only at those loci common to 

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

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

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

251 4.1.11 A requirement that a new statistical analysis must be performed when subsequent 

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

253

254 4.1.12 A requirement that two or more conceptually different statistics shall not be 

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

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

257 combined probability of inclusion with a likelihood ratio. 

258

259 4.1.13 Statements of any known limitations for the use of any formulae and/or software 

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

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

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

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

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

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

266 is a reasonable risk that data are missing from a locus). 

267
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268 4.2 The laboratory shall verify and document that the protocols for performing statistical 

269 analyses generate appropriate values and are performed consistently within the laboratory 

270 for all types of DNA profiles typically encountered by the laboratory.

271 4.2.1 Verification of the protocols shall be performed on single source and mixed DNA 

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

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

274 statistical analysis protocol.

275 4.2.2 Verification of the statistical analysis protocol shall demonstrate that its use returns 

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

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

278 software).

279 4.2.3 Verification of the statistical calculations protocol shall demonstrate that its use with 

280 probabilistic genotyping software having an element of randomness results in consistent 

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

282 validation studies for both true contributors and non-contributors.

283 4.2.4 Verification shall include a demonstration of consistency among analysts in the 

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

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

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

287 within the laboratory.

288 4.2.5 Verification shall be performed on new, existing, and modified statistical 

289 interpretation protocols.

290 4.2.6 For verification of the Statistical Analyses protocol, the laboratory shall use data 

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

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

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

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

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

296 anticipated to be interpreted by the laboratory. 

297 4.2.7 The validation of the protocol shall be completed prior to implementation of the 

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

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

300 identified through this verification process. 

301 4.2.8 Any subsequent modifications to any DNA testing or data interpretation protocol 

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

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

304 as needed. 

305 4.2.9 Methods, equations, software, etc. shall not be used for statistical calculations without 

306 the prerequisite validation, protocol development and verification of the protocol for 

307 accuracy and consistency.

308 4.3 The laboratory shall document the following in the case record for each statistical 

309 analysis performed.

310

311 4.3.1 The population database(s) used and the source(s) of the database(s).

312
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313 4.3.2 The statistical analysis method(s) used, and, if applicable, the software program and 

314 version number used.

315

316 4.3.3 The theta correction factor value(s) used. 

317 4.3.4 The genetic loci and data used for statistical calculations. 

318 4.3.5 All assumptions made when performing the statistical analysis, including but not 

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

320 paternity or kinship analysis, any alleged or assumed biological relationships.

321 4.3.6 All statistical analyses performed, including analyses performed using different 

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

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

324 4.3.7 The actual value used by the analyst with each statistical analysis for any parameter 

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

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

327 4.3.8 Case-specific scenarios where calculations are not needed shall be documented in the 

328 case record.
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329 Annex A (informative)

330

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

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

333

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

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

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

337 (CPI/CPE): 

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

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

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

341 determination of the alleles and loci suitable for comparison, the risk of allele drop342 out and drop-in at each locus and across the profile, and the assumed number of 

343 contributors. None of these are interpretation methods and play no direct role in the 

344 interpretation of the DNA profile. 

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

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

347 different statistical calculations for a single profile per Requirement 4.1.12. 

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

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

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

351 purposes, causing that profile or locus to be reported as unsuitable for comparison, 

352 and thus inconclusive. 

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

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

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

356

357 Random Match Probability (RMP)

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

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

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

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

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

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

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

365 one or more assumed contributors in the determination of possible genotypes).

366 ii) May be used for multiple contributor profiles by considering the combinations of 

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

368 probabilities for all genotypes included at the locus. 

369 (1) Has sometimes been referred to as modified RMP or restricted RMP.
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370 b) The assumed number of contributors to the DNA mixture shall be assessed along 

371 with the genotypes from any assumed contributor(s) to limit, or restrict, the 

372 possible genotypes at a locus that are then used for the calculation of the RMP.

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

374 with a defined maximum number of contributors.

375 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] 376 for RMP calculations 

377 are:

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

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

380 isolated populations). 

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

382 is the frequency of allele Q at the same locus.

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

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

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

386 p is the frequency of the single obligate allele P. 

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

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

389 equations provide corrections for both homozygous and heterozygous profiles.

390 3) The RMP can be approximated by the estimated frequency of occurrence for a given 

391 genotype or set of genotypes, in a particular reference population, that make up the 

392 profile of a DNA contributor among random unrelated individuals. It is commonly 

393 reported as 1 in the number of individuals by inverting the resulting frequency after 

394 applying the product rule across all loci. 

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

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

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

398 evidence data alone. 

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

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

401 for the minor contributor(s)].

402 b) If a subset of loci are used to calculate the RMP, then the selection of loci used 

403 should be determined independently of (and even prior to) comparison to any 

404 reference profile. 

405 Likelihood Ratio (LR)

406 Some of the key features and use of the Likelihood Ratio method for STR DNA single source 

407 and mixture profiles are provided here:

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

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

410 and/or drop-in may have occurred.
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411 b) A probabilistic LR can be used for profiles where allele drop-out and/or drop-in may 

412 have occurred. 

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

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

415 3) The general equation for the LR is: 

416

417 where Pr = Probability, E = Evidence, Hp = Proposition of the prosecution, Hd = Proposition 

418 of the defense, and I = relevant Information in formulating the propositions and 

419 assigning the probabilities. Propositions may be referred to as prosecution/defense 

420 propositions, proposition 1/proposition 2, prosecution/alternate propositions, 

421 inclusionary propositions/exclusionary propositions or other terms that 

422 communicate the propositions are different from one another.

423

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

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

426 particular proposition is true. 

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

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

429 request of either party.

430 c) Propositions must be mutually exclusive. At least one element of the proposition 

431 must be different so that they may not both be true at the same time (e.g., 

432 Proposition 1 states the Person of Interest (POI) is the source of the DNA and 

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

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

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

436 a proposition.

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

438 propositions.

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

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

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

442 propositions. 

443 e) Consideration must be given to calculating a separate LR for each included 

444 contributor as well as an LR for the contributors together per requirement 4.1.4.2.3. 

445 This may prevent a major contributor from having undue influence on the weight of 

446 the evidence for a minor contributor. Conditioning profiles may be useful in this 

447 scenario.

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

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

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

451 0 and 1.
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452 h) The weights of the same genotypes may differ for different propositions in the 

453 probabilistic LR calculation.

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

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

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

457 1 is true rather than if Proposition 2 is true” or “It is LR times more likely that the DNA 

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

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

460 i) For a single source profile, often the LR and RMP values are numerically the 

461 reciprocal of each other; however, they answer fundamentally different 

462 questions. 

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

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

465 calculated.

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

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

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

469 limited range. 

470 6) A probabilistic LR calculation can return a value less than one (or negative logLR), 

471 which communicates that more weight of evidence is given to the defense or alternative 

472 proposition.

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

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

475 Neither proposition is supported over the other. 

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

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

478 prosecution proposition.

479

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

481 (CPE)

482 Some of the key features and use of the Combined Probability of Inclusion (CPI) and 

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

484 profiles are provided here:

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

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

487 DNA profiles.

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

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

490 no impact on the interpretation and ability to generate statistical frequency 

491 calculations.

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

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

494 calculated only for the two major contributors. 
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495 c) Rarely suitable for use with mixtures of three or more contributors, particularly 

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

497 possible exception of when two distinguishable major contributor profiles are 

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

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

500 dropped out at any locus.

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

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

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

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

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

506 for interpretation and comparison where there is no reason to expect that allele drop507 out might have occurred. (See 2b above.)

508 a) Data from loci with one or more alleles below the stochastic threshold shall not be 

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

510 (e) below). 

511 b) The assumed number of contributors to the DNA mixture using the entire DNA 

512 profile shall be assessed and then used for evaluating the prospect that all 

513 genotypes from all contributors are present at each locus.

514 c) This determination shall occur prior to comparison of the DNA profile data to the 

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

516 from other profiles). 

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

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

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

520 person mixtures), then the possibility that drop-out has occurred shall be 

521 considered and the CPI/CPE calculation shall not be used if there is some reasonable 

522 possibility that drop-out explains the paucity of alleles. Peak heights at other loci 

523 and total peak height values at each locus shall be taken into account when 

524 assessing the data and the possibility of drop-out. 

525 i) When the alleles from at least one contributor are below the stochastic threshold 

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

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

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

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

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

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

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

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

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

535 profile being rarer than it really is. Such a figure would be more prejudicial 

536 against the defendant. It is not generally accepted practice for rarer values to be 
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537 reported or presented in testimony when providing a statistical frequency for an 

538 individual who cannot be excluded as a possible contributor. 

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

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

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

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

543 is used).

544 4) The equations for CPI/CPE calculation are:

a) Probability of inclusion for a locus = (the sum of allele frequencies) 545 2 = (PA + PB + PC + 

... + PN)

2 546 , where PA, PB, PC and PN are the frequencies of alleles A, B, C and N, 

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

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

549 assumed number of contributors to the DNA profile.

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

551 and homozygous genotypes. 

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

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

554 incorporate the frequencies of homozygous genotypes included at that locus, 

555 however, individuals with homozygous genotypes could be excluded definitively 

556 from that locus during interpretation and comparison based on the assumed 

557 number of contributors. 

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

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

560 interpretation.

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

562 Annex B, Bibliography. 

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

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

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

566 as 1 in X number of individuals. 

567 a) The CPE is an approximation of the proportion of random individuals unrelated to a 

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

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

570 individuals, but is sometimes reported as a percentage. 

571 b) The CPI/CPE calculation is not appropriate for use when a non-contributing 

572 individual related to a true contributor to the DNA mixture cannot be excluded as a 

573 possible contributor to the DNA mixture. 

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

575 to the DNA mixture. 

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

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

578 on the questioned profile alone;
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579 a) Only one CPI/CPE frequency can be calculated for one mixed DNA profile.

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

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

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

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

585 Bibliography

586

587 1] Quality Assurance Standards for Forensic DNA Testing Laboratories, 

588 http://media.wix.com/ugd/4344b0_4a22824ce56f43d4b1a4d2486409f95d.pdf

589 2] Buckleton, John, Bright, Jo-Ann., and Taylor, Duncan A. (Eds.). Forensic DNA Evidence 

590 Interpretation. 2nd edition, CRC Press, 2016.

591 3] Balding, David J. and Steele, Christopher D. Weight-of-Evidence for Forensic DNA 

592 Profiles. 2nd edition, Wiley, 2015.

593 4] National Research Council (NRC II). The Evaluation of Forensic DNA Evidence. 

594 National Academy Press, 1996. (Available online at: 

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

596 5] Bieber, Frederick. R., Buckleton, John S., Budowle, Bruce, Butler, John M., and Coble, 

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

598 Interpretation, and Statistical Calculations Using the Combined Probability of 

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

600 6] Curran, James M. and Buckleton, John. “Inclusion Probabilities And Dropout.” J. For. 

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

602 7] Buckleton, John and Curran, James M. “A Discussion of the Merits Of Random Man 

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

604 348.

605 8] Bille, Todd W., Bright, Jo-Ann and Buckleton, John. “Application of Random Match 

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

607 474-85

608 9] Gittelson, Simone., Kalafut Timothy, Myers, Stephen, Taylor, Duncan, Hicks Tacha, 

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

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

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

612 186-195.

613 10]SWGDAM 2017 Interpretation Guidelines for Autosomal STR Typing by Forensic 

614 DNA Laboratories. https://1ecb9588-ea6f-4feb-971a615 73265dbf079c.filesusr.com/ugd/4344b0_50e2749756a242528e6285a5bb478f4c.p

616 df (October 2020)

617

618 ANSI/ASB Standards

619 11]ANSI/ASB Standard 018, Standard for Validation of Probabilistic Genotyping 

620 Systems, First Edition, 2020 

621 http://www.asbstandardsboard.org/wp-content/uploads/2020/07/018_Std_e1.pdf

622 (October 2020)

623 12]ANSI/ASB Standard 020, Standard for Validation Studies of DNA Mixtures, and 

624 Development and Verification of a Laboratory’s Mixture Interpretation Protocol, 
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625 First Edition, 2018 https://asb.aafs.org/wp626 content/uploads/2018/09/020_Std_e1.pdf (October 2020)

627 13]ANSI/ASB Standard 040, Standard for Forensic DNA Interpretation and Comparison 

628 Protocols, First Edition, 2019 

629 http://www.asbstandardsboard.org/wp-content/uploads/2019/10/Std_040_e1.pdf

630 (October 2020)

631 14]ANSI/ASB Standard 041, Assigning Propositions for Likelihood Ratios in Forensic 

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

633 added when available)

634 15]ANSI/ASB Standard 123, Routine Internal Evaluation of a Laboratory’s 

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

636 at ASB - link to be added when available)