The Bayesian method is no stranger to the technology of Cell Culture Assay Testing, a "functional" biomarker. In fact, it is what gives credit to the accuracy of assay tests. The method has to do with "conditional probability." The probability that event E (an effect) and C (a cause) will both occur is the product of the event C occurring, times the conditional probability of an event E occuring (remember that in elementary statistics?). An example: The chances of being hit by a truck and bleeding to death is the product of the probability of being hit by a truck and the probability of bleeding to death if you get hit by a truck. Well, so what?
The Bayesian method turns this calculation around. That is, it tries to calulate the probability of C, given that E has occurred. Baye's Theorem is useful and reasonably well accepted for some applications such as testing whether the assumptions of probability are valid. For instance, if you flip 100 coins in the air at once, and only get tails 5 times, you have to assume that they aren't "fair" coins. The whole idea of it all, is to get more accuracy out of analysis.
The absolute predictive accuracy of cell culture assay tests varies according to the overall response rate in the patient population, in accordance with Bayesian principles. The actual performance of assays in each type of tumor precisely match predictions made from Bayes' Theorem. The theoretical expectations for cell death assays, based on Bayes' Theorem, are overall specificity for drug resistance of 0.92 and an overall sensitivity of 0.72.
Thus, the absolute probability of response with assay "sensitive" and "resistant" drugs varies according to the overall prior response probability in the patient population. Which means assay "resistant" patients have a below average probability of response and assay "sensitive" patients have an above average probability of response. Treatment with assay "sensitive" drug(s) is more likely to be associated with a favorable outcome than treatment with assay "resistant" drug(s).
Cell death assays are broadly applicable to a wide range of human neoplasms, ranging from low response rate tumors (like pancreatic cancer and Cholangiocarcinoma) to high response rate tumors (like acute lymphoblastic leukemia, breast cancer and ovarian cancer). In cases where more than one acceptable regimen exists, the physician can select the regimen containing the most favorable drugs and avoid the regimen containing the most unfavorable drugs.
Bayes' theorem is a tool for assessing how probable evidence makes some hypothesis. It is a powerful theorem of probability calculus which is used as a tool for measuring propensities in nature rather than the strength of evidence (Solving a Problem in the Doctrine of Changes).
Bayes' theorem describes the relationship between the accuracy of a predictive test (post-testing probability) and the overall incidence of what is being tested (pre-testing probability).
Bayes' theorem indicates that laboratroy assays will be accurate in the prediction of clinical drug resistance in tumors with high overall response rates in assays that are extremely specific for drug resistance (>99% specificity).
Post-test probability of response is independent of pre-test (expected) probability of response. Once identified, post-test response probabilities vary according to both assay results and pre-test reponse probabilities, precisely according to predictions based on Bayes' theorem. This allows the construction of a monogram for determining assay-predicted probability of response.
Assay Results and Bayes' Theorem:
http://weisenthal.org/figure06.htm