A Gamma model for mixture STR samples

1. A Gamma model for mixture STR samples Participants Dept. of Mathematical Sciences, Aalborg University: E.Susanne Christensen, Susanne G. Bøttcher Dept. of Forensic Genetics, University of Copenhagen: Niels Morling, Helle Smidt Mogensen Dept. of Statistics, Oxford University: Steffen L. Lauritzen This project investigates the behavior of the PCR Amplification Kit. A number of known DNA-profiles are mixed two by two in "known” proportions and analyzed. Gamma distribution models are fitted to the resulting data to learn to what extent actual mixing proportions can be rediscovered in the amplifier output and thereby the question of confidence in separate DNA -profiles suggested by an output is addressed. Short Tandem Repeats (STR) Abstract Human identity tests focus on Short Tandem Repeat markers (STR markers). STR markers are genetic loci consisting of repeated subunits, 2-8 base pairs in length. Discrimination between individuals is possible because the number of subunits present for a given marker varies from person to person. Simultaneous analysis of several STR markers allows for the compilation of a profile, which is almost unique to a given individual. Weight of DNA- British data DNA mixture output Estimates- Danish data Estimates- British data Amount of DNA- Danish data Source: Forensic DNA typing. J. M. Butler The QLB dataset Mixtures have been created from two contributors with known DNA profile, known mixture rates and known concentrations at 0.5 ng/µl, and seven different mixing proportions. Data have been processed by Genescan™ software, (Applied Biosystems). Systems analyzed are: D3S1358, vWA, D16S539, D2S1338, AMEL, D8S1179, D21S11, D18S51, D19S433,THO1,FGA. The constructed two-persons mixtures divides the persons in two groups, forming the mixtures: G.J and C.J, (involving three persons), and C.A, S.A, H.A and C.P, (involving four other persons). Observations in this British data are peak area. Std. residuals- Danish data Discussion The Cph-Crime-SGMP-Mix-Exp-2005-1 dataset The plots shows results from four systems only. In the QLB-data mixture C.J was consistently overestimated, S.A was overestimated in 9 of 10 markers, H.A was underestimated for 6 markers and mainly so for 3 others, and the C.P mixture was consistently underestimated for 2 markers and mainly underestimated for 3 markers. There is a slight tendency to decreasing std. residuals for increasing weight of DNA in the sample. The findings in Cph-Crime-SGMP-Mix-Exp-2005-1 data are not quite as consistent, but there is a clear tendency of over- or underestimation throughout the systems for any two persons, as there are systematic differences between individuals analyzed. The tendency to decreasing std. residuals for increase in amount in DNA is found in the Danish data as well. Data were created by an controlled laboratory experiment performed by Section of Forensic Genetics, University of Copenhagen to investigate the performance of the AmpF1STRSGM Plus PCR Amplification Kit (Applied Biosystems, CA, USA) in STR-profiling. Samples were created from 4 persons with known profiles. Mixtures of two contributors with different but known amounts of DNA were created as a full factor experiment. Also one-contributor samples were analyzed for all four persons in different concentrations. Every sample were analyzed twice. Observations used from this dataset are peak height, which are approximately proportional to peak area in this data. Std. residuals- British data Notation Conclusion The model seems logical and produces a fair fit to data. Residuals reveals the need for incorporation of a personal effect in the model, beyond what is included in amount of DNA present. The additional effect is seen in both one- contributor samples and in mixtures. There is no obvious difference in using mixing proportions or actual amount of DNA in the parameterization. In both cases it is seen, that some moderation from proportionality should be considered as residuals decrease with increasing amount of DNA in the sample. From the Danish data it is clear that a full understanding and modeling of the STR- amplification still is far from being obtained. It is however of great importance that this work is carried out in order to address the question of separation of DNA profiles from mixture samples. Model References J.M Butler, Forensic DNA typing. Elsevier, USA. 2005 B.S. Weir, C.M. Triggs, L.Starling, L.I. Stowell, K.A.J. Walsh, J.S. Buckleton, Interpreting DNA mixtures, J.Forensic Sci. 42(5), (1999), 987-995 J. Mortera, A.P.David, S.L. Lauritzen, Probabilistic expert systems for DNA mixture profiling, Theor. Popul. Biol. 63 (2003), 1919-205 R.G Cowell, S.L.Lauritzen, J.Mortera, Identification and separation of DNA mixtures using peak area information, Forensic Sci. Int. To appear. M.W. Perlin, B. Szabady, Linear mixture analysis, a mathematical approach to resolving mixed DNA samples, J. Forensic Sci. 45 (2001), 1372-1378 T. Wang, N. Xue, R. Wickenheiser, Least square deconvolution (LSD); a new way of resolving STR/DNA mixture samples, in: Proceedings of the 13’th International Symposium on Human Identification, October 7-10, Phoenix, AZ, 2002. I. Evett, P.Gill, J. Lambert, Taking account of peak ares when interpreting mixed DNA profiles, J. Forensic Sci, 43 (1998), 62-69 Future works A parameter of ’personal impact’ shall be incorporated in the model. The important question of ’drop-outs’, ’drop-ins’ and stutters shall be considered. Estimation of combined ’personal impact and amount DNA’ shall be considered for the purpose of separation of DNA –profiles in mixture DNA samples from crime scenes on basis of the model. Sensibility to the actual machine should be investigated, and influence of injection times be considered. A calibration algorithm for adaption to machinery will be constructed. Estimation Contact: E. Susanne Christensen, e-mail: susanne@math.aau.dk