That is a vital question in pain management and the opioid crisis, because millions of pain patients undergo drug tests regularly. The answer is not just a matter of looking at the accuracy of the test.
In a simple situation, like a toss of a coin or a roll of a die, computing the probability of an outcome is elementary. Most people realize that a toss of a coin has an equal chance of coming up heads or tails.
But drug testing is not as simple. It is an example of a conditional probability. A drug test that is 95% accurate will not find drug users 95% of the time. That is because the test is applied to both drug users and non-users. We have use a calculation known as Bayes’ Theorem to determine the real probabilities.