Bayes Rule Applied to Melanoma Detection
https://www.nature.com/articles/nature21056.epdf?author_access_token=8oxIcYWf5UNrNpHsUHd2StRgN0jAjWel9jnR3ZoTv0NXpMHRAJy8Qn10ys2O4tuPakXos4UhQAFZ750CsBNMMsISFHIKinKDMKjShCpHIlYPYUHhNzkn6pSnOCt0Ftf6
Melanoma is a form of skin cancer that causes cancerous skin lesions. These skin lesions look different from non-cancerous skin lesions; they are larger and asymmetric, with irregular borders. Recent developments in technology have allowed researchers to use machine learning and develop programs that can be used to identify cancerous skin lesions. In this article, researchers at Stanford input thousands of pictures of either cancerous or benign skin lesions, and created algorithms for the computer to distinguish between them. After this test set, researchers test the computer’s ability to distinguish between cancerous and noncancerous lesions with a test set of more lesions. Accuracy can be tested using sensitivity and specificity, which are the number of true positives/all positives and the number of true negatives/all negatives. The result of this machine learning algorithm is just as accurate as actual dermatologists.
Apps like these allow people to take pictures of lesions and get a result in the comfort and accessibility of their own home. This is especially important for people in rural areas who would otherwise not make the trek to see a doctor to get their skin checked. Though these programs have their benefits, they are not 100% accurate. They can give a negative result in people who do have a cancerous lesion, a false negative, or a positive result in people who do not have a cancerous lesion, a false positive. In statistics, a false positive is called a Type I error, and a false negative is a Type II error. Often, Type II errors are more harmful, as in this case (not diagnosing someone who has cancer). The probability of Type I and Type II errors are represented by ɑ and β, respectively. Reducing the probability of a Type I error will increase the probability of a Type 2 error, and vice versa. These probabilities can be calculated via Bayes’ Rule.
For example, assume the probability a patient has melanoma is 0.35. They take a picture with their app, which gives a positive result .80 of the time when the patient has melanoma and a negative result .90 of the time when they do not have melanoma.
When the app reports a negative result, the probability that the patient actually does not have melanoma can be solved using Bayes’ rule. 0.65*0.9/(0.65*.9+.35*.02)= 0.99.
When the app reports a positive result, the probability that the patient actually does have melanoma is 0.35*.8/(0.35*.8+0.65*0.1)=0.81. This particular program would be very good at ruling out melanoma, and okay at detecting it.
Researchers need to make decisions while training their program in order to find the appropriate balance between Type I and Type II errors. Though they stress the reduction of Type II errors, identifying a lesion as cancerous when it is not will have negative consequences too, such as inducing stress and doctors’ bills.