# Introduction To 2 and 3 Person Mixtures How the RMP Can Help With Complex Mixtures.

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Introduction To 2 and 3 Person Mixtures How the RMP Can Help With Complex Mixtures

Restricted RMP (2 person mixture)

Mixture consistent with 2 contributors All alleles well above stochastic threshold – Lowest rfu value detected = 423 – Extremely clean baseline No drop out concerns at all No need for “Allele, Any” genotypes

Restricted RMP (2 person mixture) We can use a “Restricted” Random Match Probability ?! We will use PHR and P calculations to determine which combinations are possible – Remember the chart of all possible combinations for two contributors – Restrict the results by an expected PHR

Restricted RMP (2 person mixture) This is still just the RMP stat We have adopted the term “Restricted” RMP because we are restricting the genotypes calculated to only those that “fit” the data USACIL terms: – modified RMP = potential drop out so Allele, Anys – restricted RMP = No dropout concerns, reliable PHR and P for all contributors, so only the genotypes that make sense within the data

Restricted RMP (2 person mixture) We’ll look at 4 loci D3 vWA D5 FGA

Restricted RMP (2 person mixture) D3 50% PHR 75 MPH 0 MP No types assumed Shown in 2 places

Restricted RMP (2 person mixture) D3 50% PHR Possible types: – AA & BC only 1/3 15, 17 and 14(,14) – AB & BC only 2/3 15, 17 and 14, 15 15, 17 and 14, 17  

Restricted RMP (2 person mixture) Possible types: – AA & BC only 1/3 and – AB & BC only 2/3 and 14, 1715, 17 14, 1515, 17 14, 1415, 17   Locus, alleles and frequencies 2qr p 2 + p(1-p)Θ 2pq 2pr RMP for this pattern for all three population groups On the stat page you’ll see a line like this

Restricted RMP (2 person mixture) Drop PHr to 10% Now all 6 options

Raise PHr to 70% Now only 2 options Restricted RMP (2 person mixture)

vWA 50% PHR No types assumed 2 combinations 3 types possible Restricted RMP (2 person mixture)  Allele frequencies from pop database

D5 50% PHR No types assumed 2 combinations 4 types possible Restricted RMP (2 person mixture)

FGA 50% PHR No types assumed 5 combinations 6 types possible Restricted RMP (2 person mixture) 12 34 56  123 456  

Restricted RMP for the whole mixture 50% PHR 75 MPH 0 MP No types assumed

Restricted RMP (2 person mixture) Restricted RMP for the whole mixture 70% PHR 75 MPH 0 MP No types assumed

Conditioned RMP (2 person mixture) What if we condition the results upon a known contributor? Restrict the restricted RMP even more That term gets a bit confusing – rrRMP? – r 2 RMP?

Conditioned RMP (2 person mixture) We’re starting to run out of names for these stats Again this is simply the RMP stat (fine tuned a bit) At USACIL we’ve already defined modified RMP and restricted RMP We refer to this as a “conditioned” RMP

Conditioned RMP (2 person mixture) We’re only calculating a stat for the allowable probative genotypes – Intimate sample (whatever that is) – State assumption in report We’ll look at the same loci

Conditioned RMP (2 person mixture) Section 3.5 – SWGDAM Evidence items taken directly from an intimate sample, as determined by the laboratory, are generally expected to yield DNA from the individual from whom the sample was taken. If another source of DNA is present in sufficient quantity in such a sample, a mixture of DNA is likely to be detected. Based on this expectation, any DNA typing results from such a mixture that match a conditional known sample (e.g., from the victim) may be separated from the other mixture results to facilitate identification of the foreign alleles. The obligate alleles may effectively constitute a single-source profile (i.e., if there is one DNA contributor in addition to the individual from whom the sample was taken) or a mixture profile (i.e., if there are multiple additional DNA contributors). A similar state can exist when another known individual (i.e., consensual partner) is expected to have contributed biological material to the mixed sample.

An intimate sample in your lab is… 1.Internal body swab 2.#1 and external swab 3.#2 and underwear 4.#3 and outer clothing 5.Pretty much anything COC links to an owner Countdown 30 0 of 30

D3 50% PHR 75 MPH 0 MP Male assumed Conditioned RMP (2 person mixture) No change in options from before 15, 17 required But the 15, 17 isn’t in the stat

vWA 50% PHR 17(, 17) assumed Same combinations Conditioned RMP (2 person mixture) Now only 2 types in stat

D5 50% PHR 11, 13 assumed Dropped 1 combination Conditioned RMP (2 person mixture) 11, 12 is the only type that fits for foreign person

FGA 50% PHR 24, 26 assumed Started with 5 combinations & 6 types Conditioned RMP (2 person mixture)

Comparison of stats (Restricted vs. Conditioned) 50% PHR, no assumptions = 1 in 32 Billion 70% PHR, no assumptions = 1 in 640 Billion 50% PHR, Male assumed = 1 in 25 Quintillion – (7 loci had “combo” stats) Just for fun, CPI = 1 in 18 million

Restricted RMP (3 person mixture) The principle is the same as for a 2 person mixture Not concerned about drop out – At least for the loci where you’re going to use the restricted form of RMP – OK to mix and match the modified and restricted forms from locus to locus if needed

Restricted RMP (3 person mixture) Restrict the combinations to only those that are allowed by validated PHR etc. You may be able to restrict further based on a known (assumed) contributor – Conditioned RMP (Restricted Restricted RMP?) – Only the probative types are calculated

Restricted RMP (3 person mixture) You may be able to restrict even more if you can assume two people Consensual partner for example – Restricted Restricted Restricted RMP? – Conditioned Conditioned RMP? At USACIL this is defined as conditioned RMP, but conditions are stated in the report (2 people assumed present)

Restricted RMP (3 person mixture)

Mixture is consistent with 3 people Lowest rfu value is 448 (26 at FGA) Clean baseline We’re going to interpret this with only a 50% PHR requirement

Restricted RMP (3 person mixture) We’ll look at 4 loci D8 D21 D16 FGA

Restricted RMP (3 person mixture) D8 6 categories of combinations 42 different combinations possible ?!?! How crazy will this stat be? Does it = 1?

Restricted RMP (3 person mixture) Those 42 different combinations reduce to ten separate genotypes Is the stat 1.0? – Nope!! – 0.6273 for Caucasian

Restricted RMP (3 person mixture) D21 Similar to D8 – 5 Categories – 42 Combinations possible Reduces to 10 genotypes Does not equal 1 0.3861 for Caucasian

Restricted RMP (3 person mixture) D16 8 Categories possible “Only” 17 combinations

Restricted RMP (3 person mixture) D16 Really only 6 types to worry about Caucasian = 0.5170

Restricted RMP (3 person mixture) FGA Remember this? It’s actually not too bad 14 Combinations

Restricted RMP (3 person mixture) But 15 different genotypes possible Caucasian = 0.3494

Restricted RMP (3 person mixture) Stat for 3 person restricted RMP – Only the 50% PHR filter used – Makes no assumptions other than no drop out

Conditioned RMP (3 person mixture) Let’s restrict the restricted RMP based on assuming the presence of the Victim on her own vaginal swab – Restricted restricted RMP? – R 2 RMP? We’ve defined this as a conditioned RMP The RMP we’re about to look at is for two probative donors condition

Conditioned RMP (3 person mixture) D8 Known type of 10, 13 Now only 16 combinations viable – (Was 42!) The assumed profile (Ref 1) is the left most column

Conditioned RMP (3 person mixture) D8 – 10, 13 type assumed Those 16 combinations still have 10 genotypes – The same 10 genotypes – The stat didn’t change Note that there is still a 10, 13 type calculated 10, 13 for assumed (Ref 1)10, 13 also viable for one unknown contributor

Conditioned RMP (3 person mixture) D21 Known type of 28, 30.2 Now only 13 combinations viable – (Was 17) Still 10 genotypes total Again, we still must include 28, 30.2 in the stat as it “fits” as a probative type So even though we lost 4 viable combinations of contributors, the stat didn’t change

Conditioned RMP (3 person mixture) D16 Known type of 12 Now only 10 combinations viable – (Was 17) – (Now we’re rolling!) But still 6 types, no change in the stat

Conditioned RMP (3 person mixture) FGA Known type of 22, 25 Now only 7 combinations viable – (Was 14) – (So what?) But now only 9 types! – (Was 15!!)

Conditioned RMP (3 person mixture) Let’s compare the two stats For no assumptions other than 50% PHR – Caucasian is 1 in 85,000 – Restricted RMP Assuming the female on her own swab – Caucasian is 1 in 370,000 – Conditioned RMP So we made some progress

Conditioned RMP (3 person mixture) Let’s say that there is a consensual partner on the vaginal swab – Just state it in the report – (We do this routinely) Now what do we call it? – Restricted conditioned restricted RMP? – Conditioned conditioned RMP? We still just call it a conditioned RMP

Conditioned RMP (3 person mixture) Example wording: – “Assuming the presence of Bobbie Sue and her reported consensual partner Billy Joe, the remaining DNA profile is consistent with Suspect Miller.” Two young lovers with nothin’ better to do Just communicate with your investigators and prosecutors to be sure of your assumptions

Conditioned RMP (3 person mixture) Section 3.5 – SWGDAM Evidence items taken directly from an intimate sample, as determined by the laboratory, are generally expected to yield DNA from the individual from whom the sample was taken. If another source of DNA is present in sufficient quantity in such a sample, a mixture of DNA is likely to be detected. Based on this expectation, any DNA typing results from such a mixture that match a conditional known sample (e.g., from the victim) may be separated from the other mixture results to facilitate identification of the foreign alleles. The obligate alleles may effectively constitute a single-source profile (i.e., if there is one DNA contributor in addition to the individual from whom the sample was taken) or a mixture profile (i.e., if there are multiple additional DNA contributors). A similar state can exist when another known individual (i.e., consensual partner) is expected to have contributed biological material to the mixed sample.

Conditioned RMP (3 person mixture) Section 3.5.7 – SWGDAM Just state that you did so 3.5.7. Mixtures with a Known Contributor(s): The laboratory should establish guidelines for determining whether separation of a known contributor’s profile is applicable (e.g., based on the types of evidentiary items). 3.5.7.1. At a minimum, where there is no indication of sharing of the known and obligate alleles, the laboratory should separate out those alleles attributable to the known sample (e.g., victim, consensual partner, etc.). 3.5.7.2. To further refine the obligate alleles in a profile, the laboratory may establish guidelines for addressing potential sharing of alleles among the individual known to have contributed to a sample and the additional contributor(s).

Conditioned RMP (3 person mixture) D8 Known types of 10, 13 and 12, 13 Now only 4 combinations viable – (Was 42, then 16)

Let’s hope we have a lot less types in the stat now Only 4 genotypes to add up (Was 10!) What’s the new stat? (Finally it’s different!) – 27% of Caucasians included – (Was 63%) Conditioned RMP (3 person mixture)

D21 Known types of 28, 30.2 and 29, 30 Now only 10 combinations viable – (Was 17, then 13) We had a lot less genotypes with that last 4 allele pattern In this known mixture, both males are 29, 30 (Yay! Calculator worked!)

Will we get the same improvement as D16? Still the same 10 genotypes at this D21 locus as the first two times Conditioned RMP (3 person mixture)

D16 Known types of 12 and 11 (both homozygotes) Now only 3 combinations viable! – (Was 17, then 10) – (Now we’re rolling!) – (For real, this time)

This time we narrowed it down to only 3 genotypes for the third contributor No assumptions – Caucasian = 0.5170 (rRMP) Victim assumed – Same (cRMP) Victim and Consensual assumed – Less than 14% of Caucasians included Conditioned RMP (3 person mixture)

FGA Known types of 22, 25 and 24, 26 Two combinations viable – (Was 14, then 7) Unknown contributor is either 21, 21 or 21, 22

We went from 15 separate genotypes to 9 to 2 No assumptions – Caucasian = 0.3494 Victim assumed – Caucasian = 0.2355 Victim and Consensual assumed – Less than 10% of Caucasians included Conditioned RMP (3 person mixture)

RMP (3 person mixture) Results of all three scenarios for Caucasian 50% PHR – 1 in 85,000 Assuming female – 1 in 370,000 Assuming female and consensual partner – 1 in 47 Trillion Remember our old friend CPI? For the “indeterminate mixture” – 1 in 100,000

CPI vs. RMP (3 person mixture) CPI = 1 in 100,000 restricted RMP = 1 in 85,000 Why is CPI not the most conservative??

CPI vs. RMP (3 person mixture) The rRMP that we just did calculated all possible viable genotypes Turns out that all possible genotypes from the chart of possibilities are viable So for this example, the Unrestricted RMP is the same as the Restricted RMP And the exact same genotypes as CPI (Because we didn’t have to subtract any homozygotes.)

CPI vs. RMP (3 person mixture) But p 2 + p(1-p)Θ is used for homozygotes in the RMP (We were pulling out individual genotypes so we used the more complete formula) If you set Θ = zero, the rRMP and the CPI calculations give the exact same answer Remember, the inbreeding correction is designed to be conservative

Stutter Section 3.5.7 – SWGDAM 3.5.8. Interpretation of Potential Stutter Peaks in a Mixed Sample 3.5.8.3. If a peak is at or below this expectation, it is generally designated as a stutter peak. However, it should also be considered as a possible allelic peak, particularly if the peak height of the potential stutter peak(s) is consistent with (or greater than) the heights observed for any allelic peaks that are conclusively attributed (i.e., peaks in non-stutter positions) to the minor contributor(s).

Stutter In other words, make sure the sister allele of an observed minor allele isn’t hiding out in a (filtered) stutter peak Remember, we’re talking about a peak that was filtered in GMID and wasn’t called an allele In practice, this is pretty rare Requires a specific set of conditions

Stutter In general this requires: A large major/minor ratio (10:1? 20:1?) A large allowance for stutter – D18 is 17% in our lab – FGA is 17% But the true amount of stutter in the sample is relatively low (Otherwise high stutter + minor allele gets called by GMID)

Stutter Requires tall peaks on the right side of the egram – In our hands, if this “filtered” minor peak exists it tends to be on the right side – “Left side” minor allele + stutter = called peaks But we have an interpretation guideline that says if we have “blown out” data, we don’t use the minor Tall peaks on the right usually have blown out peaks on the left

Stutter Requires the detected minor peak to be above the stochastic threshold – Our lab used 300 rfu to define the stochastic threshold (homozygote threshold, Danger Zone…) – If <300 rfu we use Allele, Any so we’re covered If the detected minor peak is above 300 rfu, our 50% PHR expectation must be maintained AFTER correcting for stutter

Stutter In fact, this is so rare, that I couldn’t find an example to show you So I had to fake this data that you’re about to see We can use ArmedXpert to test this theory by editing the profile and adding the filtered allele stutter data to the locus of concern – First, we make a copy of the profile from the table – Then, edit the copy and test the stutter correction

Stutter Let’s look at D2 – We allow 11% stutter This was the closest “real” example that I could find, and I looked at a lot of mixtures 24 451 First, we have to make the stutter peak as big as possible 23 400 Make the called minor allele smaller, - maintain our 50% PHR

Stutter This is the “edited” data in ArmedXpert Although this looks like a 23, 24 is viable, remember that in real life the 24 wasn’t there

Stutter So click “Apply Stutter” to correct for stutter – Subtract 11% of 4213 rfu from 451 rfu If you correct for all possible stutter, the 24 allele drops below baseline

Stutter Correcting for all stutter (100%) is rather arbitrary Our TL has reviewed our mixture validation – 50% stutter correction is better – Preserves the expected 50% PHR

So, adjust the stutter correction to 50% of maximum stutter, or 5.5 % (D2 = 11% filter) Now you know you could have “missed” the true type Stutter

How to deal with it statistically? The 23 was >300 (and not in a stutter position from the major) so 23, Any not required 24 451 23 400

Stutter Just add a 24 allele into the stat (We can do it here by just typing it in)

Summary RMP is still a very powerful stat method (Provided you have the right calculator) You can deal with drop out You can deal with probative types only You can deal with “lost” stutter peaks But it still requires good, interpretable data

Summary RMP – single source stat or the generic term uRMP – kind of like CPI (sum ‘em, square ‘em, remove homozygotes where needed) mRMP – Allele, Any stat (add Allele, Anys to the uRMP calculation, think # of contributors) rRMP – restricted to viable types in mix calc (calculate 2pq and p 2 + p(1-p)Θ for each type) cRMP – restricted AND removes required type(s)

Summary Think of most of these RMP profile and statistics examples as a “partial deconvolution” technique We saw that CPI isn’t very useful (or conservative enough) But there are other ways Standby for Likelihood Ratios……

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