Evaluating allelic drop-out probabilities using a Monte-Carlo simulation approach
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The document discusses methods for estimating drop-out probabilities in DNA mixtures, specifically focusing on two hypotheses regarding contributors to a sample. It employs Monte Carlo simulations to analyze allele distributions from experimentally simulated mixtures, ultimately estimating drop-out ranges based on observed alleles. The findings highlight the need to assess drop-out estimates separately under different hypotheses and emphasize the importance of qualitative data in the analysis.
![10 Estimating drop-out probabilities | Avila June 2013
Qualitative approach to the estimation of PrD
What are the probabilities of dropout that could have
led to observing the same number of alleles
recovered in the sample?
?
Build the empirical distributions of the numbers of alleles, conditioned
on the probabilities of dropout ranging in [0,1] using
Monte-Carlo simulations
We don’t know the probabilities of drop-out, but we can evaluate the
drop-out probabilities that could have led to a mixture similar to the
one we are investigating](https://image.slidesharecdn.com/5prdavila2013-140507021654-phpapp01/85/Evaluating-allelic-drop-out-probabilities-using-a-Monte-Carlo-simulation-approach-10-320.jpg)
![27 Estimating drop-out probabilities | Avila June 2013
5% - 95% percentiles of the distributions
Under Hp
5% 0.19
95% 0.45
Under Hd
5% 0.09
95% 0.41
The drop-out estimates
are given as a range:
lowest-highest value
[0.09,0.45]](https://image.slidesharecdn.com/5prdavila2013-140507021654-phpapp01/85/Evaluating-allelic-drop-out-probabilities-using-a-Monte-Carlo-simulation-approach-27-320.jpg)
Evaluating allelic drop-out probabilities using a Monte-Carlo simulation approach
- 1. 25 March 2013 Evaluating Drop-out Probabilities Hinda Haned
- 2. 2 Estimating drop-out probabilities | Avila June 2013 A three-person mixture sample: epithelial cells recovered from the victim of an assault two suspects are detained by the police
- 3. 3 Estimating drop-out probabilities | Avila June 2013 A three-person mixture Hypotheses Hp: the victim, suspect 1 and one unknown contributed to the sample Hd: the victim and two unknowns contributed to the sample Evaluation of the two hypotheses using likelihood ratios
- 4. 4 Estimating drop-out probabilities | Avila June 2013 Sensitivity analysis - LRmix LRs range from 103 to 107 : 103 PrD=0.99 107 PrD=0.41
- 5. 5 Estimating drop-out probabilities | Avila June 2013 Available methods Experimental mixtures (Perez et al, Coratian Med J, 2011) the levels of drop-out, based on large sets of DNA mixtures obtained in different conditions DNA quants Number of contributors Ratio of contribution Maximum likelihood principle LoComation software (Gill et al 2007) Drop-out probabilities that maximize the probability of observing the questioned epg
- 6. 6 Estimating drop-out probabilities | Avila June 2013 Available methods Experimental mixtures (Perez et al, Coratian Med J, 2011) the levels of drop-out, based on large sets of DNA mixtures obtained in different conditions DNA quants Number of contributors Ratio of contribution Maximum likelihood principle LoComation software (Gill et al 2007) Drop-out probabilities that maximize the probability of observing the questioned epg Methods derive estimates from empirical distributions
- 7. 7 Estimating drop-out probabilities | Avila June 2013 Qualitative approach to the estimation of PrD Relies on: the number of alleles observed in the sample the genotypes of the hypothesized contributors under H What are the probabilities of dropout that could have led to observing the same number of alleles recovered in the sample? ?
- 8. 8 Estimating drop-out probabilities | Avila June 2013 Qualitative approach to the estimation of PrD Relies on: the number of alleles observed in the sample the genotypes of the hypothesized contributors under H What are the probabilities of dropout that could have led to observing the same number of alleles recovered in the sample? ? What is the distribution of the number of alleles for the questioned sample, conditioned on PrD?
- 9. 9 Estimating drop-out probabilities | Avila June 2013 Qualitative approach to the estimation of PrD What are the probabilities of dropout that could have led to observing the same number of alleles recovered in the sample? ? We don’t know the probabilities of drop-out, but we can evaluate the drop-out probabilities that could have led to a mixture similar to the one we are investigating
- 10. 10 Estimating drop-out probabilities | Avila June 2013 Qualitative approach to the estimation of PrD What are the probabilities of dropout that could have led to observing the same number of alleles recovered in the sample? ? Build the empirical distributions of the numbers of alleles, conditioned on the probabilities of dropout ranging in [0,1] using Monte-Carlo simulations We don’t know the probabilities of drop-out, but we can evaluate the drop-out probabilities that could have led to a mixture similar to the one we are investigating
- 11. 11 Estimating drop-out probabilities | Avila June 2013 Monte Carlo method Any method which solves a problem by generating suitable random numbers and observing that fraction of the numbers obeying some property or properties.
- 12. 12 Estimating drop-out probabilities | Avila June 2013 Monte Carlo method Any method which solves a problem by generating suitable random numbers and observing that fraction of the numbers obeying some property or properties. Questioned sample properties: • three-person mixture: SGM+ • 33 alleles observed in the epg • profiles of victim and suspect available
- 13. 13 Estimating drop-out probabilities | Avila June 2013 Monte Carlo method Any method which solves a problem by generating suitable random numbers and observing that fraction of the numbers obeying some property or properties. Questioned sample properties: • three-person mixture: SGM+ • 33 alleles observed in the epg • profiles of victim and suspect available Simulate a large number of mixtures that have these properties
- 14. 14 Estimating drop-out probabilities | Avila June 2013 Important note! The hypothesized contributors change under Hp and under Hd: Derive distribution of the numbers of alleles under Hp and under Hd separately Yields two distributions, one under Hp and one under Hd
- 15. 15 Estimating drop-out probabilities | Avila June 2013 Mixture 33 alleles Victim Unknown Unknwon Hd Mixture 33 alleles Victim Suspect Unknown Hp Monte-Carlo simulation procedure
- 16. 16 Estimating drop-out probabilities | Avila June 2013 Victim Suspect Unknown By randomly sampling from the Dutch DNA frequencies fixed 36 alleles 17 alleles Step 1: simulate 1000 mixtures Mixture #1 51 distinct alleles Mixture #1000 53 distinct alleles Mixture #2 50 distinct alleles …
- 17. 17 Estimating drop-out probabilities | Avila June 2013 drop-out Victim Suspect Unknown Mixture #1 51 alleles Pr(D) # surviving alleles 0.01 51 0.02 50 … … 0.50 25 … 0.99 1 Step 2: Apply drop-out
- 18. 18 Estimating drop-out probabilities | Avila June 2013 Repeat the procedure 1000 times Simulate 1000 mixtures For each mixture, record the number of alleles obtained after the simulated drop-out procedure
- 19. 19 Estimating drop-out probabilities | Avila June 2013 Repeat the procedure 1000 times PrD sim1 sim2 sim3 sim4 sim5 sim6 sim7 sim8 sim9 sim10 … 0,01 51 50 49 50 53 54 45 47 51 51 … 0,03 50 50 44 44 51 39 47 51 44 50 … 0,05 46 44 44 40 44 41 41 50 41 51 … 0,09 38 48 43 41 42 33 40 41 40 38 … 0,17 38 37 33 44 37 51 46 39 36 44 … … … … … … … … … … … … … 0,89 7 6 9 6 5 3 7 10 9 7 … 0,91 6 8 9 7 8 5 4 5 3 3 … 0,93 8 4 3 3 7 8 5 2 4 7 … 0,95 5 0 7 4 3 4 2 3 8 4 … 0,97 1 3 0 1 2 2 0 0 2 2 … 0,99 0 1 1 1 0 3 0 0 2 0 …
- 20. 20 Estimating drop-out probabilities | Avila June 2013 We look at the distributions of the numbers of alleles obtained in the simulation procedure
- 21. 21 Estimating drop-out probabilities | Avila June 2013 We are only interested in those where we obtained 33 alleles (the number observed in the epg). Distribution of the numbers of alleles among the 1000 mixtures
- 22. 22 Estimating drop-out probabilities | Avila June 2013 Now we look at the distribution of the numbers of alleles and the corresponding drop-out probabilities
- 23. 23 Estimating drop-out probabilities | Avila June 2013 We are only interested in those where we obtained 33 alleles (the number observed in the epg). Distribution of the numbers of alleles among the 1000 mixtures Hp
- 24. 24 Estimating drop-out probabilities | Avila June 2013 The same procedure is carried out under Hd Victim Unknown 1 Unknown 2 By randomly sampling from the Dutch DNA frequencies fixed 19 alleles 35 alleles Mixture #1 49 distinct alleles Mixture #1000 48 distinct alleles Mixture #2 50 distinct alleles …
- 25. 25 Estimating drop-out probabilities | Avila June 2013 drop-out Victim Suspect Unknown Mixture #1 49 alleles Pr(D) # surviving alleles 0.01 48 0.02 47 … … 0.50 25 … 0.99 1 Apply drop-out The simulation procedure is repeated on a 1000 mixtures
- 26. 26 Estimating drop-out probabilities | Avila June 2013 Distribution of the numbers of alleles among the 1000 mixtures We are only interested in those where we obtained 33 alleles (the number observed in the epg). Hd
- 27. 27 Estimating drop-out probabilities | Avila June 2013 5% - 95% percentiles of the distributions Under Hp 5% 0.19 95% 0.45 Under Hd 5% 0.09 95% 0.41 The drop-out estimates are given as a range: lowest-highest value [0.09,0.45]
- 28. 28 Estimating drop-out probabilities | Avila June 2013 Sensitivity analysis
- 29. 29 Estimating drop-out probabilities | Avila June 2013 Sensitivity analysis vs. plausible ranges for PrD LR 107
- 30. 30 Estimating drop-out probabilities | Avila June 2013 Summary the ranges of the drop-out probability can be evaluated separately under Hp and Hd avoid reporting values of drop-out that are supported by one hypothesis but not by its alternative qualitative data only peaks slightly under threshold not taken into account Assess the uncertainty the data!
- 31. 31 Estimating drop-out probabilities | Avila June 2013 LRmix module Available in Forensim 4.1
- 32. 32 Estimating drop-out probabilities | Avila June 2013