What is discrimination index (discrimination power; probability of discrimination Pj) – in forensic science

The ability of a given test to individualize evidence. In forensic science, this term is usually associated with blood and DNA typing, but the idea can be applied to any analysis that results in a classification or categorization of physical evidence. The terms are used in different but closely related ways. First, the discrimination index is the probability that any two people selected at random in a given population will have different blood types. The discrimination index is also referred to as the discrimination power. In the U.S. Caucasian population, approximately 42 percent have the ABO blood group type of A, 43 percent O, 12 percent B, and 3 percent AB. The discrimination index of the ABO blood group system is approximately 0.60, meaning that there is a 60 percent chance that any two people selected at random will have a different ABO type. Similarly, the isoenzyme system PGM has 3 types (discounting subtypes), 1-1 59 percent, 2-1 35 percent, and 2-2 6 percent and a discrimination index of 0.52. Thus, PGM has a lower discrimination index and is less likely to distinguish two individuals selected at random. Another way to state this would be to say that PGM has a lower power of discrimination. This is attributable to the fact that nearly two-thirds of the population is PGM type 1-1. Thus, if only one system can be typed, it would be wiser to select the ABO system since it has the higher discrimination index and is more likely to distinguish two individuals.

In contrast, the probability of discrimination (Pj) of a given system looks at the probability that any two people selected at random will have the identical type. Thus, a low Pj is desirable since this would mean that the odds of two people having identical types would be low. For the ABO system, the Pj is approximately 0.40, meaning the probability that two people selected at random will have the same ABO type is 40 percent. Note that the discrimination index and the probability of discrimination are related; they must both add up to one. For the ABO system, this calculation would be 0.60 + 0.40 = 1.00. This makes sense; the chance that any two people selected at random will have either identical types or different types must be 100 percent. This is like flipping a coin the chances that it comes up either heads or tails is 100 percent since those are the only two possible outcomes.

The more types there are within a given system and the more widely spread the frequencies are, the lower the Pj, and by typing more systems, the Pj increases. For example, the Pj of the PGM system is about 0.48, meaning that there is a 48 percent chance that two people selected at random would have the same type. This is not a very good system by itself, but if both PGM and ABO are typed, the cumulative Pj becomes 0.40 x 0.48, or 0.19. This means that there is about a 20 percent chance that any two people selected at random will have the same ABO and PGM type. The actual Pj for any system varies by race and other factors, but the calculation method is the same.

Another less confusing way to express the same idea is to look at frequencies in the population and come up with a one-in number. For example, assume a bloodstain is typed as ABO type A and PGM 1-1. In the example population used, the combined frequencies are 42 out of 100 for ABO type A and 59 out of 100 for PGM type 1-1. To get the combined frequencies, these values are multiplied together (42/100 x 59/iooj or 0.42 x 0.59) to obtain a value of .25 percent, meaning that 25 people per hundred would be expected to have this combination of types (25 percent). This can be restated as l-in-4. Because this is a relatively large number, it is not very useful for forensic work. However, it is not unexpected since both types are very common. If a bloodstain were found to have the rarest types, AB and 2-2, the same calculation using those frequencies (4/ioo x 6/ioo) leads to a value of 0.0024, meaning that 2 people per thousand would be expected to have this combination. Thus, discrimination index (discrimination power) and the probability of discrimination depend on the number of different systems typed, the number of variants of each system, and the frequencies of those variants.

DNA typing has largely replaced the typing of blood for groups such as ABO and PGM, but the same principles apply. Using the 13 short tandem repeats (STRs) commonly typed in forensic labs, it is possible to obtain powers of discrimination that exceed the population of the planet by several orders of magnitude. For example, using STR frequencies for African Americans, typing the first three produces a power of discrimination of about one in a million while typing all 13 leads to figures smaller than one in a trillion. This is remarkable considering that the population of earth is less than 10 billion, a hundred times smaller than a trillion. There are many issues related to these assumptions, such as the dependability of frequencies and population genetics, but the reliability of these calculations has been generally accepted.