The "Prior Odds" Fallacy
One of the increasingly common arguments I see defense experts make in our automobile collision practice and our aircraft crash practice involves the misuse of statistical evidence. Defense experts have taken the prior odds of a particular type of injury occurring in a certain type of accident and then applied that same statistical probability (which is often low) to support the defense argument that it is unlikely that a particular plaintiff suffered the injury she claims she suffered as a result of the accident. The fallacy arises from the fact that the expert is applying a probability rate derived from a large population group (everyone who was involved in a particular type of accident) to a very different and much smaller population group (individuals who claim they were in fact injured in that type of accident, who received medical treatment for their claimed condition, and then subsequently hired legal counsel and filed a lawsuit to recover damages for their claimed injuries). For example, let's assume an epidemiological study analyzes a large number of car crashes and concludes that less than 6% of vehicle occupants involved in rear impact collisions of less than 20 miles per hour had neck injuries that last more than six months. I have seen defense experts try to use this type of data to assert that it is extremely unlikely that a particular plaintiff really has the ongoing problems she claims to have because these types of symptoms usually resolve within six months. This is, however, complete statistical gibberish. The defense expert is applying the 6% statistical rate to a very different question, namely what percent of claimants who seek medical attention for their claimed continuing problems and subsequently file a lawsuit for their claimed continuing problems are really faking their injuries. The source study obviously never attempted to answer this question.
The "prior odds" statistical shell game only arises with injuries that are not objectively obvious and indisputable. A defense expert will not, for example, raise this argument where a car or aviation accident produces a compound fracture, paralysis or death. But these types of objective injuries do serve to illustrate the underlying illogic of the "prior odds" argument. Say, for example, that 6% of individuals who are involved in a vehicle rollover accident die. The forgoing defense experts are basically performing the equivalent of telling the deceased in a rollover accident that they cannot be dead because the vast majority of individuals survive rollover accidents.
Necessity is the mother of invention – in statistics as elsewhere. That is why it pays to think critically about what experts tell you, and do your research. An excellent article for further research on this subject is Forensic Epidemiology: A Systematic Approach to Probabilistic Determinations in Disputed Matters in the Journal of Forensic and Legal Medicine (2008) by Michael D. Freeman.