Applying Bayes’ Rule in Drug Screening
Many jobs in the workplace require a drug-free environment and a common way companies implement this is through drug screening. Drug screening can be done in different ways but it is often done using urine or blood samples. Looking at the statistics that are provided by testing sites present this process as highly accurate, meaning that the percentage of sensitivity(true positives) and specificity(true negatives) are extremely high. However, when applying Bayes’ rule, we can find that the probability of a randomly selected individual with a positive result being an actual drug user is lower than expected, regardless of the given sensitivity and specificity being really high.
http://corysimon.github.io/articles/why-cocaine-users-should-learn-bayes-theorem/
The article linked above talks about why cocaine users should learn about the Bayes theorem. Even if the cocaine screening process has 99% specificity and 99% sensitivity, given a population of 0.5% cocaine users, the probability of correctly identifying a cocaine user as positive is only 33%. Bayes Rule represents the probability of event A occurring given the probability of event B which can be represented as:
In this case event A refers to the probability of being a drug user, while event B refers to the probability of testing positively when getting screened. P(B|A) would equal the sensitivity of the screening, which is very high of 99%. P(A) would equal the probability of an individual being a drug user, and when assuming 0.5% of the general population are cocaine users, P(A) = 0.005. P(B) would equal the probability of getting tested positively, which would equal P(A)*P(B|A) + P(NOT A)*P(B|NOT A). When inputting the numbers, we can calculate P(B) = 0.005*0.99 + 0.995*0.01 = 0.0149. Now we can calculate P(A|B) which would be 0.99*0.005/0.0149 = approximately 0.33. This means that the probability of cocaine’s screening process correctly identifying a cocaine user is only 33%, a shockingly low number.
The article attributes the low probability to the relatively small sample size because cocaine users are not prevalent around the world, thus the number of false positives would outnumber the number of true positives. If companies were to enforce a drug-free environment in the workplace, I believe that a heavy reliance on screening is not promising. Though the article makes a sarcastic comment that cocaine users should be taking advantage of such screening processes, there are many limitations on only relying on drug screening processes.