3.7 Examples of evaluation of cases given alleged activities
Once we have the data from the experiments, we can use them for the evaluation of the DNA findings. Below we present two examples of evaluation assuming that transfer/persistence/recovery and background are dependent (A). As recommended by the forensic community (e.g., ENFSI, ISFG), we have assessed the value of these findings considering the probability of the results given two alternative propositions and the case information. That is, the DNA results have been evaluated through the assignment of a likelihood ratio (LR). The LR measures the strength of support that the results give for one proposition compared to the other proposition. For the evaluation of our case scenario, we consider the alternative propositions Hp and Hd.
Example 1: : single source DNA profile of the trace that aligns with the DNA profile of the POI.
In this example, we consider that there is a single DNA profile aligning with the DNA profile of the POI. In general, if the source of the DNA is not contested, then we do not need to consider the source of the DNA. Here, we would like to tackle a more general situation where we should also consider that there is a possibility that the DNA came from an unknown person. In such as case, we need intermediate association propositions (i.e., sub-source level propositions). These intermediate association propositions are here: the DNA came from the POI or an unknown unrelated person. The likelihood ratio calculated for the comparison with STRmix™ is in the order of a million. All task relevant information available (e.g., unknown person is from the Swiss population, gloves were stolen given defense view) is taken into account in the evaluation and indicated in the formula by letter I.
Considering
E as the presence of a single DNA profile aligning with the reference profile of the POI, the likelihood ratio given activity level propositions can be developed as follows [
[48]Aitken C.G.G., Taroni F., Bozza S. Statistics and the Evaluation of Evidence for Forensic Scientists. 3 ed. Sons JW, editor. Chichester 2021.
]:
The upper part of the formula (i.e., the numerator) is developed considering prosecution proposition. It is the probability of obtaining a single source DNA profile aligning with the reference profile of the POI if s/he acted bare-handed. If this is true, then there are two possibilities: either DNA from POI was transferred/persisted/recovered or it did not. If there was DNA recovered from the POI given that activity, then as we have recovered no other DNA, it means that there was also no background. The first possibility can be expressed by the term .
Now, if we consider the second possibility and that there was no DNA recovered because of the POI opening/closing the door (this is indicated in our formula by there could still be DNA because of background, that is for unknown reasons. This single profile present as background would have to align with the DNA profile observed. To account for this we consider the LR calculated in STRmix™ with our intermediate association propositions. Combining the probabilities of our observations with the rarity of the profile, we obtain , where is the 1/LR calculated with the associated sub-source propositions.
The lower part of the formula is developed in a similar fashion, but we now consider the transfer of DNA through the gloves. In this case, one will assign the probability of no DNA transfer from the AO and DNA transfer from the POI detected as a single source profile ( based on our observations. We then add a second term, as there is the possibility that no DNA was recovered from either of AO or the POI given the activities and it is present as background ( would have to align with the DNA profile observed. As before to account for this we consider the LR calculated in STRmix™ with our intermediate association propositions. Combining the probabilities of our observations with the rarity of the profile, we obtain . The third possibility we consider is that the AO transferred DNA because of the activity and has a profile compatible with the trace; that the POI’s DNA has not been recovered because of the activities and there is no background (.
The LR formula is as follows:
which expresses in part the rarity of the profile obtained from the trace, is usually very small. Here it is neglected and we simplify the formula as follows:
This shows that when there are legitimate reasons for the POI’s DNA to be present, even if there is no agreement on the source of the DNA recovered, we can consider activity level propositions [
[47]- Hicks T.
- Buckleton J.
- Castella V.
- Evett I.
- Jackson G.
A logical framework for forensic DNA interpretation.
]. The terms of the likelihood ratio formula can be replaced by the numerical values summarized in
Table 5,
Table 6. The likelihood ratio obtained given activity level propositions is the following:
The numerical value obtained indicates that it is 3 times more likely to observe a single source profile matching the reference profile of the POI if she/he opened/closed bare-handed the door rather than if an AO opened/closed it wearing the POI’s worn gloves. In other words, if we refer to the verbal scale used by Marquis et al. [
[49]- Marquis R.
- Biedermann A.
- Cadola L.
- Champod C.
- Gueissaz L.
- Massonnet G.
- et al.
Discussion on how to implement a verbal scale in a forensic laboratory: Benefits, pitfalls and suggestions to avoid misunderstandings.
], these results provide limited support for the first proposition compared to the alternative.
Example 2: : DNA trace presenting a mixed DNA profile with a minor profile aligning with the DNA profile of the POI and major profile from an unknown source.
In this second example, we consider that we observe a mixed DNA profile with a minor contributor aligning with the reference profile of the POI. Like in the previous example, the trace is evaluated considering the two intermediate association propositions, namely: the DNA came from the POI and an unknown unrelated person or two unknown unrelated persons. These are the propositions used for the comparison of the DNA profiles with STRmix™. We take into account the same available information (e.g., the unknown persons are from the Swiss population, the gloves were stolen given defense view). The likelihood ratio calculated for the comparison with STRmix™ is of the order of a million.
Considering
E as the presence of a minor DNA profile aligning with the reference profile of the POI and of a major profile from an unknown source, the likelihood ratio general formula is as follows [
[48]Aitken C.G.G., Taroni F., Bozza S. Statistics and the Evaluation of Evidence for Forensic Scientists. 3 ed. Sons JW, editor. Chichester 2021.
]:
Similarly to the previous example, the upper part of the formula is developed considering prosecution proposition. It is given by the probability of obtaining a mixed DNA profile with a minor contributor aligning with the reference profile of the POI when s/he acted bare-handed. If this is true, then there are two possibilities: either DNA from POI was transferred/persisted/recovered or it did not. If it has been recovered because of her/his activity, as we have observed a mixed DNA profile, then it means that there was DNA of an unknown unrelated person as background. One must also consider the DNA profile characteristics: if the DNA has been transferred by the POI and that there is DNA as background, it means that the DNA comes from the POI and an unknown unrelated person. The probability of the DNA profiles given this proposition is equal to the numerator of the LR computed by STRmix™. We denote the numerator by the letter . The first possibility can be expressed by the term .
Now, if there was no DNA recovered because of the POI opening/closing the door (this is indicated in our formula by there could still be DNA because of background, that is for unknown reasons. This mixed DNA profile present as background would have to align with the DNA profile observed. To account for this, we consider this time the denominator of LR calculated in STRmix™ with our intermediate association propositions. Indeed, if the DNA has not been transferred by the POI and that there is DNA as background, it means that the DNA comes from two unknown unrelated persons. The probability of the DNA profiles given this proposition is equal to the denominator of the LR computed by STRmix™. We denote the denominator by the letter . We thus obtain for this term .
The lower part of the formula (i.e., denominator), is developed in a similar fashion, but we now consider the transfer of DNA through the gloves. In this case, one will assign the probability of no DNA transfer from the AO (our alternative offender) and DNA transfer from the POI detected as a minor contributor of a mixed DNA profile ( based on our observations. We then add a second term, as there is the possibility that no DNA was transferred from either the POI or the AO and it is present as background ( would have to align with the DNA profile observed with a probability . The third possibility we consider is that the AO DNA has been recovered as a major, that DNA transfer from the POI was detected as a minor contributor and there was no background (.
The LR formula is as follows:
As
is a million times smaller than the first term in numerator and the first term in the denominator, it can be considered as a negligeable factor, the formula can be simplified as follows:
As
appears in both the numerator and denominator the LR formula can be simplified as:
The terms of the likelihood ratio formula can be replaced by the numerical values summarized in
Table 5,
Table 6. Our likelihood ratio obtained given activity propositions is as follows:
As the LR is smaller than 1, we reverse the propositions as suggested in [
[47]- Hicks T.
- Buckleton J.
- Castella V.
- Evett I.
- Jackson G.
A logical framework for forensic DNA interpretation.
]. The value obtained indicates that the results (a two person mixed DNA profile with a minor contributor aligning with the reference profile of the POI) are 2 times more likely if an AO opened/closed the door wearing the POI’s gloves rather than the POI opened/closed it bare-handed. If using a verbal equivalent, one can say that these results support defense proposition rather than prosecution’s; this support can be qualified as limited [
[49]- Marquis R.
- Biedermann A.
- Cadola L.
- Champod C.
- Gueissaz L.
- Massonnet G.
- et al.
Discussion on how to implement a verbal scale in a forensic laboratory: Benefits, pitfalls and suggestions to avoid misunderstandings.
].