Bayes’ Rule in Medicine
In class, we’ve discussed how Bayes’ rule can be used to evaluate a claim, given evidence related to that claim. Outside of the immediate context of networks, Bayes’ rule is relevant and essential to making diagnoses in the healthcare field. Certain conditions affect the probability of a patient having a certain disease, including demographics and lifestyle. Taking these factors into account allow physicians to make more accurate diagnoses regarding the conditions of their patients, compared to just using results from a medical test.
Tiemens, Wagenvoorde, and Witteman (2020) dive deeper into the usage of Bayes’ rule in the clinical setting, reiterating its importance and offering a guide on how to apply the often overlooked and abstract theorem to medicine. They argue that due to using Bayes’ rule incorrectly (or not using it at all), conditions such as depression have been both underdiagnosed and overdiagnosed.
The main focus of the paper was to not rely solely on a positive or negative test result to infer the presence of a disease. According to the researchers, a common mistake made by clinicians is not factoring in “the frequency of occurrence of the condition in the population of which the individual is a member.” For example, heart disease can be more prevalent in certain ethnic groups, or in groups of people who are sedentary. In class, this is known as Pr[A], or the probability that some claim is true. In the medical context, this probability is important because it essentially puts a different weight on a positive test result. If someone tests positive for a condition but the condition has low prevalence within the population, the probability of the individual having the condition is much lower compared to a scenario in which they tested positive and the condition had high prevalence.
Combining this information with the sensitivity of a test allows for a more accurate diagnosis of a medical condition. This correlates to Pr[B|A] and Pr[B] as we learned in class. Pr[B|A] would be the probability of a patient testing positive given that they have the condition, while Pr[B] would be the overall probability of a patient testing positive, regardless of whether or not they actually have the condition.
In other words, the entire formula would be given as follows: Pr[A|B] = Pr[A] * Pr[B|A] / Pr[B], or Pr[the patient has the condition given a positive test result] = Pr[the probability the patient has the condition] * Pr[the probability that the patient tests positive given that they have the condition] / Pr[the probability that the patient tests positive]. Ultimately, Bayes’ rule takes into account both the outside probability of having a certain condition and the sensitivity of a test for that condition. Using it can thus help doctors make a more informed diagnosis, rather than simply concluding that a positive result means that the patient has the disease.
Source: https://www.sciencedirect.com/science/article/pii/S2452301120300468#:~:text=Bayes’%20rule%20is%20designed%20to,of%20that%20test%3A%20its%20sensitivity