3 ms·
Lets whip out Bayes' rule: P(Having cancer given positive) = P(Positive given having cancer) * P(Having Cancer) / P(Having a Positive in general) Lets say 1%
by blamestross 6y ago
Lets whip out Bayes' rule:
P(Having cancer given positive) = P(Positive given having cancer) * P(Having Cancer) / P(Having a Positive in general)
Lets say 1% true positive rate is a "useless test".
0.01 = 0.88 (Detection rate from paper) * X / 0.05 (inverse of specificity)
X = 0.0005
Incident rate of Stomach Cancer (most common) is 27,600 per year in US. The denominator for this fraction is iffy because there are a lot of biases on current detection rates. If we go ahead with "adults in the US" then the rate of cancer is 0.00014
[cite](https://www.cancer.org/cancer/stomach-cancer/about/key-statistics.html#:~:text=Stomach%20cancer%20mostly%20affects%20older,is%20about%201%20in%2095. https://www.cancer.org/cancer/stomach-cancer/about/key-stati...)
Basically, if we applied this test to all adults without other diagnostic factors. This would be worse than 1% true positive detection rate. I don't know about how effective intersecting with other diagnostic criteria would be on increasing the odds a patient actually have the disease and it might or might not still be useful after that.
This sort of study is mostly bullshit anyway. They took a relatively small pile of data, made a small classifier with high accuracy (maybe overtrained, maybe not) and really can't validate it.