Making more accurate medical diagnoses using Bayes’ Theorem
Bayes’ Theorem is often applied in economic contexts, but it can also be applied to inform decisions in the healthcare industry. This study, conducted by Dujin et al., looks at how diagnostic-informed diagnosis of malaria in Kenya can improve accuracy in medical decision-making and ultimately reduce the probability of overdiagnosis and over-prescription. Dujin et al. ran diagnostic tests drawing data on socio-demographics, healthcare transactions, and medical outcomes. After testing the diagnostics on febrile patients in Kenya, they found statistics for malaria positivity and over-prescription. They concluded that digitized malaria diagnostics and understanding the entitlements for treatment for febrile patients could save costs and improve the quality of healthcare.
This study demonstrates that making a diagnosis and understanding the context and prior statistics of the patients and the population they come from can help make a more accurate diagnosis. This can also be understood through conditional probabilities in Bayes’ Theorem and could be a generalizable process effective for other diseases. To understand this through Bayes’ Theorem, the diagnostics, measured by statistics on several factors in malaria diagnosis, can be simplified to P(A | B) in which P(A) is the probability of having malaria and P(B) is the probability of having symptoms of fever. Bayes’ Theorem can help us find the probability of having malaria given the patient having a fever, distinguishing it from the confounding instances of a patient being febrile due to a different disease. This probability, when tested on a large, homogenous sample, can help improve the accuracy of malaria diagnosis, especially when healthcare personnel takes these statistics into consideration when giving diagnoses and prescriptions.
The Bayes’ Theorem setup can be more generalizable to any diseases that are often over-diagnosed and/or over-prescribed. This can be done by defining P(A) as the probability of having any disease A, represented as P (disease), and P(B) as the probability of experiencing symptoms associated with disease A, represented as P (symptoms). Then the probability of having disease A given symptoms would be:
P (disease | symptoms) = p (symptoms | disease) * p(disease) /p(symptoms)
= [p (symptoms | disease) * p(disease)] / [p(symptoms | disease) * p(disease) + p(symptoms | not disease) * p(not disease)]
By applying conditional probability, Dujin et al. took into consideration that their sample population was coming from Sub-Saharan Africa (SSA). This was important because SSA observes a disproportionately high percentage of malaria cases, and this, in turn, engendered more presumptive diagnoses and over-prescriptions of malaria that had both health and economic consequences. Therefore, a diagnostic test following a similar line of logic as Bayes’ Theorem above can help prevent false positives in both physical and mental health diagnoses. This is because applying Bayes’ Theorem would allow medical personnel to more actively take into consideration the setting and population of their clients and the prior probability of having the condition they are testing.
Source: https://bmcmedinformdecismak.biomedcentral.com/articles/10.1186/s12911-021-01600-z#Sec4