The product rule has been applied in odontology again, after years of research suggests that it shouldn't be.
We don't seem to learn from our lessons. Many years ago a paper was published that tried to establish the statistical basis for the individuality of the human dentition. It was flawed for a number of reasons but the main was that the statistics used the premises of the product ![Screen Shot 2014-08-08 at 13.13.09]()
rule. Whats this then? Simply its that you can consider the frequency of elements within a population and, if they are independent of each other, multiple these to give an overall occurrence rate. For example - if feature A occurs 1 in 100 people, and feature B occurs in 1 in 500 people then the total number of people exhibiting both features is 1 in 50,000. You can see how the product rule can quickly generate numbers that appear to demonstrate certainty. This approach is used in DNA - where the independence of the STR locations is assured. This is why you can often see reports that state the probability of the DNA sample being sourced from someone other that then suspect is 1.3 times 10-16, or no more frequent than 1 in 7.7 quadrillion individuals (7.7 million billion), which is more than a million times the population of the planet! Product rule and teeth So this seems an attractive prospect for dentistry? If the occurrence of someone missing an upper central incisor is 1 in 1000 and having a crown on the lower left first molar is 1 in 500 then surely we can treat these as independent? Rawson stated that the positions of teeth could be treated in this way. But they cant as neither is truly independent. For example, thinking about tooth position - if the upper left central incisor is rotated 5 degrees - then it is very likely that the upper right central incisor will also be rotated - the influencing factors are common and related. In the same way restorative treatments cannot be considered independent. If someone is at high risk of caries (dental decay) then it is a common risk for restorations of various types throughout the mouth. If you have one extracted tooth then it is plausible that you will have others. The decision to restore, the disease process and the treatment practices of dentists are not independent of each other. The product rule shouldn't be applied. In this current paper the authors argue that a variety of restorative treatments, extractions and prosthesis are independent findings and then use the proposed incidence of these in a population to ![Screen Shot 2014-08-08 at 14.46.40]()
support the certainty of their dental identification. Having looked at the case - I have no doubt that they have correctly identified the individual but the use of statistics to support this is inappropriate. For example - for a single dental feature they apply the product rule to argue the overall certainty - see table 2 here. However they have no data to support the actual occurrence in the population of these features - they simply state that an arbitrary number was used! There is no issue with the identification or that the number, type and complexity of the restorative care here clearly points to a common origin between antemortem records and the found remains. However, the stats aren't right and shouldn't have been applied - odontologists do themselves no favours by trying to replicate the mathematical certainty of DNA - and in doing so suggest that dental identifications are equal to or even superior to DNA identifications on a mathematical basis. There are lots of aspects of dental identifications that support their use, including the post-mortem survival of dental evidence and the expediency with which dental IDs can be deployed. There is no need for each forensic science to try and match the outcomes of others. Dental identifications should be reported with an appropriate conclusion level that reflects the certainty of the forensic dentist undertaking the assessment - its based on clinical and forensic experience and its opinion evidence and hence should be reported as such. Adding spurious stats to conclusion levels just simply doesn't work - either in identifications or bitemarks. Indeed there are cases where odonts have used numerical certainty on bitemark cases where this has been challenged or later discredited. A good example is the 1978 State v. Garrison. In his testimony, odontologist Homer Campbell stated that that the bitemark matched the defendant to a certainty of eight in one million.
rule. Whats this then? Simply its that you can consider the frequency of elements within a population and, if they are independent of each other, multiple these to give an overall occurrence rate. For example - if feature A occurs 1 in 100 people, and feature B occurs in 1 in 500 people then the total number of people exhibiting both features is 1 in 50,000. You can see how the product rule can quickly generate numbers that appear to demonstrate certainty. This approach is used in DNA - where the independence of the STR locations is assured. This is why you can often see reports that state the probability of the DNA sample being sourced from someone other that then suspect is 1.3 times 10-16, or no more frequent than 1 in 7.7 quadrillion individuals (7.7 million billion), which is more than a million times the population of the planet! Product rule and teeth So this seems an attractive prospect for dentistry? If the occurrence of someone missing an upper central incisor is 1 in 1000 and having a crown on the lower left first molar is 1 in 500 then surely we can treat these as independent? Rawson stated that the positions of teeth could be treated in this way. But they cant as neither is truly independent. For example, thinking about tooth position - if the upper left central incisor is rotated 5 degrees - then it is very likely that the upper right central incisor will also be rotated - the influencing factors are common and related. In the same way restorative treatments cannot be considered independent. If someone is at high risk of caries (dental decay) then it is a common risk for restorations of various types throughout the mouth. If you have one extracted tooth then it is plausible that you will have others. The decision to restore, the disease process and the treatment practices of dentists are not independent of each other. The product rule shouldn't be applied. In this current paper the authors argue that a variety of restorative treatments, extractions and prosthesis are independent findings and then use the proposed incidence of these in a population to 
support the certainty of their dental identification. Having looked at the case - I have no doubt that they have correctly identified the individual but the use of statistics to support this is inappropriate. For example - for a single dental feature they apply the product rule to argue the overall certainty - see table 2 here. However they have no data to support the actual occurrence in the population of these features - they simply state that an arbitrary number was used! There is no issue with the identification or that the number, type and complexity of the restorative care here clearly points to a common origin between antemortem records and the found remains. However, the stats aren't right and shouldn't have been applied - odontologists do themselves no favours by trying to replicate the mathematical certainty of DNA - and in doing so suggest that dental identifications are equal to or even superior to DNA identifications on a mathematical basis. There are lots of aspects of dental identifications that support their use, including the post-mortem survival of dental evidence and the expediency with which dental IDs can be deployed. There is no need for each forensic science to try and match the outcomes of others. Dental identifications should be reported with an appropriate conclusion level that reflects the certainty of the forensic dentist undertaking the assessment - its based on clinical and forensic experience and its opinion evidence and hence should be reported as such. Adding spurious stats to conclusion levels just simply doesn't work - either in identifications or bitemarks. Indeed there are cases where odonts have used numerical certainty on bitemark cases where this has been challenged or later discredited. A good example is the 1978 State v. Garrison. In his testimony, odontologist Homer Campbell stated that that the bitemark matched the defendant to a certainty of eight in one million.
In the instant case, Dr. Campbell obtained the figure of eight in one million not from personal mathematical calculations, but from "articles written in the journals of the American Academy of Forensic Sciences" and two books, and "there are articles written throughout the literature that do mention the possibility or the numerical values of finding two (sets of teeth) of the same."You can read more about the Garrison case here. The ABFO withdrew its bitemark "scoring" system many years ago. Opinion evidence needs to be clearly stated as such - it doesnt mean its wrong - but its for the trier of fact to determine the weight that should be placed on such testimony.