Eriksen, Poul Svante

Mogensen, Helle Smidt

Morling, Niels

Tvedebrink, Torben

English

The quantitative data observed from analysing STR DNA is a mixture of contributions from various sources. Apart from the true allelic peaks, the observed signal consists of at least three components resulting from the measurement technique and the PCR amplification:Background noise (random noise due to the apparatus used for measurements).Pull-up effects (more systematic increase caused by overlap in the spectrum)Stutters (peaks located four basepairs before the true peak).We present filtering techniques for all three technical artifacts based on statistical analysis of data from controlled experiments conducted at The Section of Forensic Genetics, Department of Forensic Medicine, Faculty of Health Sciences, Universityof Copenhagen, Denmark.The quantitative data observed from analysing STR DNA is a mixture of contributions from various sources. Apart from the true allelic peaks, the observed signal consists of at least three components resulting from the measurement technique and the PCR amplification:Background noise (random noise due to the apparatus used for measurements).Pull-up effects (more systematic increase caused by overlap in the spectrum)Stutters (peaks located four basepairs before the true peak).We present filtering techniques for all three technical artifacts based on statistical analysis of data from controlled experiments conducted at The Section of Forensic Genetics, Department of Forensic Medicine, Faculty of Health Sciences, Universityof Copenhagen, Denmark.</p

    Aalborg UniversitetStochastic filtering of quantitative data from STR DNA analysisTvedebrink, Torben; Eriksen, Poul Svante; Mogensen, Helle Smidt; Morling, NielsPublication date:2009Document VersionPublisher's PDF, also known as Version of recordLink to publication from Aalborg UniversityCitation for published version (APA):Tvedebrink, T., Eriksen, P. S., Mogensen, H. S., & Morling, N. (2009). Stochastic filtering of quantitative datafrom STR DNA analysis. Poster presented at ICFIS 2008 (International Conference on Forensic Inference andStatistics), Lausanne, Switzerland.General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            ? Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            ? You may not further distribute the material or use it for any profit-making activity or commercial gain            ? You may freely distribute the URL identifying the publication in the public portal ?Take down policyIf you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access tothe work immediately and investigate your claim.Downloaded from vbn.aau.dk on: November 28, 2020Stochastic filtering of quantitativedata from STR DNA analysisTorben Tvedebrinka, Poul Svante Eriksena,Helle Smidt Mogensenb, Niels Morlingba Department of Mathematical Sciences, Aalborg University, Denmarkb Section of Forensic Genetics, Department of Forensic Medicine, Faculty of Health Science, University of Copenhagen, Denmark.IntroductionThe quantitative data observed from analysing STR DNA is a mixture of contribu-tions from various sources. Apart from the true allelic peaks, the observed signalconsists of at least three components resulting from the measurement techniqueand the PCR amplification:• Background noise (random noise due to the apparatus used for measurements).• Pull-up effects (more systematic increase caused by overlap in the spectrum, seeright picture of Figure 1).• Stutters (peaks located four basepairs before the true peak - are proposed tooriginate from primer mispairings [1]).801006020400520 540 560 580 600 620 640Wavelength [nm]NormalisedflourescentintensityPull-up effectNoisePull-up effectDouble stutterNoiseStutterNoiseSmearFig. 1. Left: Picture of the non-signal components of a STR DNA trace. Right:Fluorescent dye bands where the colours under each curve indicate the amount ofspectral overlap between the various dyes.We present filtering techniques for all three technical artifacts based on statisticalanalysis of data from controlled experiments conducted at The Section of ForensicGenetics, Department of Forensic Medicine, Faculty of Health Sciences, Universityof Copenhagen, Denmarkb.The filterIn the sections below, we describe the methods used, in filtering the observed data.The samples were prepared as described in [5] and the data were analysed using athreshold of 5 rfu on peak heights and with no stutter filter or any other methodof pre-filtering.Figure 2 shows a flow chart of the filter, and in Section “Noise filter”, we describehow, the signal detection limit is determined. This limit is also used as thresholdwhen deleting signals. In Sections “Pull-up filter” and “Stutter filter”, the tworemaining filters based on regression for pull-up and stutters are presented.Filtered dataRaw dataDelete peaks below threshold after stutter correctionDetect and correct for stutter effectsDelete peaks below threshold after pull-up correctionDetect and correct for pull-up effectsDetect data above threshold limits and delete the restAttach noise medians to the remaining dataRemaining dataDetermine thresholds and noise mediansLocate off-ladder peaks not in pull-up positions of on-ladder peaksFig. 2. Flow chart of the filter.Noise filterThe peak height observations all fell in the interval from 5 rfu and upwards indi-cating that the noise distribution is a truncated positive valued distribution.Since the signal comprised both background noise and more systematic compo-nents, we removed all peaks on the allelic ladder and also off-ladder alleles inpossible pull-up position of the ladder on different fluorescent dye bands. Thisensures that the remaining points are pure noise as stutters and true peaks perdefinition fall on the ladder, and pull-up effects need therefore to be induced bypeaks on the ladder.Graphical inspections of the data indicated that the noise distribution is heavytailed. We investigated several heavy tailed distributions including the exponential,Fisher-Tippett, Pareto, Rayleigh, and Weibull. However, transforming the peakheight observations, h, by log(h − 4.5) indicated a sufficient fit to normality.In Figure 3, we stratified the observed peak heights by STR locus and plotted thetransformed heights, i.e. log(h − 4.5), against a standard normal distribution in aQQ-plot. This plot demonstrated that the noise (shifted by −4.5) followed a log-normal distribution with individual mean, µs, and variance, σ2s, for each locus s.These parameters determine the intercept and slope of the superimposed QQ-lineand are found byσs =xs(90%) − xs(50%)z(90%) − z(50%)and µs = xs(50%) − σsz(50%),where xs(q) and z(q) are the empirical and standard normal q-quantiles, respec-tively. We used these quantile estimators rather than the ordinary maximum like-lihood estimators in order to increase the robustness. Due to filtering, the noisefrom the true signal, the main interest of the noise distribution, is the upper tailas indicated by the chosen fractiles.The threshold was determined by three times the standard deviation implying thatca. 99.9% of the noise will be determined as noise by the filter. Hence, the locusspecific threshold is found asThreshold for locus s = exp(3σs + µs) + 4.5 .From Figure 3 it is clear that the fit to normality is poorer for the low values oflog(h − 4.5). However, the observations in this region are not of concern withrespect to noise filtering due to their limited height.True alleleOff-ladder alleleOn-ladder alleleLocus specific thresholdFixed 50 rfu thresholdQQ-lineStandard NormalPeakheight1025501504002000Threshold: 26.04D3Threshold: 79.61vWAThreshold: 29.49D16Threshold: 49.33D21025501504002000Threshold: 40.86AMEThreshold: 40.86D8Threshold: 46.02D21Threshold: 34.08D181025501504002000-3 -2 -1 0 1 2 3Threshold: 35.73D19-3 -2 -1 0 1 2 3Threshold: 44.8-3 -2 -1 0 1 2 3Threshold: 26.45FGATH01Fig. 3. QQ-plots of the observed signal. Note the different thresholds computedusing the locus itself as reference. For this particular sample, the fixed 50 rfu-threshold caused four drop-outs (D3, D8, D21 and D18) and two (D21 and D8)for the locus specific threshold (one true peak at locus D21 had height 21 rfu andwas embedded in the noise).Pull-up filterWe defined pull-ups as peaks not being true alleles or possibly stutters on a differentdye band than the parent peak within ±0.5 basepairs of the parent’s basepair.In Figure 4, we stratified the pull-up observations by transferring and receiving flu-orescent dyes. The magnitudes of the observed pull-up effects were in accordancewith the spectrum overlap in the right picture of Figure 1.Parent peak heightPull-uppeakheight41636641001441960 400 1600 3600416366410014419641636641001441960 400 1600 3600Yellow fluorescence dye → Blue fluorescence dye Yellow fluorescence dye → Green fluorescence dyeBlue fluorescence dye → Green fluorescence dye Blue fluorescence dye → Yellow fluorescence dyeGreen fluorescence dye → Blue fluorescence dye Green fluorescence dye → Yellow fluorescence dyeFig. 4. Pull-up effects stratified by overlapping fluorescent dyes. The superimposedlines indicate the estimated model for the directions of the different panels. Theplot is on square-root scale since this is the variance stabilising transformation.For predictive purposes, we fitted a linear model to the observed pattern in Figure4. Of the included data-points, only a limited subset comprised detectable pull-uppeaks, and the remaining observations were background noise in pull-up position.Our model takes this into account by having a noise dependent intercept, φNoise,s,for locus s. In the formulation of the model, the notation D → d reflects thatthe pull-up peak is located on fluorescent dye band d and the parent peak onfluorescent dye band D,φPull-up = αD→dφNoise,s + βD→dφParent. (1)The model is valid for both peak heights and areas replaced for φ in (1), whereφPull-up denotes the mean height or area of the pull-up peak and φParent is the ob-served peak height or area of the parent peak. The parameter estimates of αD→dand βD→d for peak heights are presented in Table 1.Table 1. Parameter estimates for the pull-up model (1) for peak heights.Dye→dye B→G B→Y G→B G→Y Y →B Y →GαD→d 1.047 0.958 1.069 0.955 1.125 1.018βD→d×102 0.951 0.566 0.319 1.081 0.000∗ 0.560Stutter filterAssuming additivity of the noise and stutter products, we take into account thatstutters from small peaks mainly consist of noise. The model for the expectedstutter height or area is given byφStutter = αsφNoise,s + βsφParent + γsb̃p · φParent, (2)where φNoise,s is the known median of the off-ladder peaks not in pull-up positionson locus s. In the latter term, b̃p is the basepair deviation from the mean basepair,b̃p = bp − b̄p. By including basepair in the model, we are able to have differentstutter percentages within the same locus for different alleles. It also means thatβs can be interpreted as an average stutter effect at a given locus s. The useof φStutter and φParent stresses that the model is valid for both peak heights andareas.The previously observed increase in stutter percentage as a function of allelic num-ber is captured in the positive estimates of γs in Table 2 and our estimates are inconcordance with the picture in [3, Figures 9-5, 9-6 and 9-7].Table 2. Parameter estimates for the stutter model (2) for peak heights.Locus D3 vWA D16 D2 D8 D21 D18 D19 TH01 FGAαs 0.935 0.867 0.988 0.911 0.916 0.954 0.870 0.934 1.034 1.015βs×102 6.929 6.100 5.255 7.525 4.798 6.182 6.531 6.413 1.567 5.751γs×102 0.101 0.202 0.218 0.090 0.092 0.082 0.181 0.192 0.067 0.138In Figure 5, we plotted the stutter peak heights predicted by the model againstthe observed stutter peak heights. The plot demonstrates that the model in (2) issufficient in order to describe the stutter behaviour.Observed stutter heightPredictedstutterheight2510022540025 100 225 400 25 100 225 4002510022540025 100 225 400D1925 100 225 400FGAD8 D21 D18D2D16vWAD3TH01Fig. 5. Predicted stutter peak heights plotted against observed stutter peak heightswith the identity line superimposed. The plot is on square-root scale as this is thevariance stabilising transformation.Additional examinations of the data made it clear that backstutters are present inthe data. The model for backstutters is based on the same idea as the filters forpull-up and stutters with a noise level and an additional effect from the parentalpeak, but the details are omitted owing to lack of space.ResultsWe have used our filter on 191 two-person mixtures. In Table 3, we have sum-marised the performance of the overall filter. It is worth emphasising that 179of the true alleles dropped out and that the stutter filter only let 32 stutters (25stutters and 7 backstutters) slip trough. In addition to the stutter peaks, another181 (128 drop-ins, 45 pull-ups and 8 smears) on-ladder peaks were classified asproper peaks by the filter.Table 3. Results for the overall filter. Smear is peaks ±3.5 bp from true peak.Classification Noise SignalTrue alleles 179 5562Stutters 3287 25Back-stutters 2231 7On-ladder alleles 16798 128Off-ladder observations 72961 275Smear positions 19302 545On-ladder smear 2460 8Off-ladder smear 16842 537Pull-up peaks 8034 198On-ladder pull-up peaks 1753 45Off-ladder pull-up peaks 6281 153The remaining peaks passing the filter were all detected to be off-ladder and thusremoved from the analysis afterwards. The data were also analysed following thestandard protocol of the Section of Forensic Genetics at University of Copenhagenb.Using the technique recommended by the manufacturer, 262 drop-outs were ob-served together with 26 stutters and 14 drop-ins.DiscussionThree times the standard deviation was also used in [4] for determining the limit ofdetection (LOD). However, the parameters µ and σ in [4] were based on negativecontrols and reagent blank samples, which implies that the parameters were com-puted for capillaries not containing the actual sample itself. This does not take thepossible differences between capillaries within a batch into account.An advantage of the locus specific threshold is that it enables the case worker toassess the noise level of the sample. Furthermore, in cases where the distributionof the transformed peak heights deviates substantially from normality, the samplemay be subject to extensive noise and/or contamination of some sort.ConclusionThe methodology of regression and distributional analysis of the noise yielded sa-tisfying results in order to deduce a stochastic filter for STR DNA samples.Comparisons of the results with those based on the recommendations of the man-ufacturer indicated that the number of drop-outs decreased by approximately 30%.Studies of different data sets supported this improvement and suggests that themethodology of the threshold determination is adequate for the noise filtering ofquantitative STR data.References[1] Butler, JM. 2005. ’Forensic DNA Typing, 2ed’. Elsevier Science and Techno-logy.[2] Gill, P., Curran, J., Elliot, K. (2005). ’A graphical simulation model of theentire DNA process associated with the analysis of short tandem repeat loci’.Nucleic Acids Research, 33(2): 632-643.[3] Applied Biosystems. 2006. AmpFℓSTR R© SGM Plus R© PCR Amplification KitUser’s Manual. Applied Biosystems.[4] Gilder, JR., Doom, TE., Inman, K., Krane, DE. (2007). ’Run-Specific Limits ofDetection and Quantitation for STR-based DNA Testing’. Journal of ForensicScience, 52(1): 97-101.[5] Tvedebrink, T., Eriksen, PS., Mogensen, HS., Morling, N. (2008). ’Evaluatingthe weight of evidence using quantitative STR data in DNA mixtures - Withnotes on handling missing data’. Manuscript in preparation.

Stochastic filtering of quantitative data from STR DNA analysis

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Stochastic filtering of quantitative data from STR DNA analysis

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