Conditional non-independence of radiographic image features and the derivation of post-test probabilities – A mammography BI-RADS example

Bayes' theorem has proven to be one of the cornerstones in medical decision making. It allows for the derivation of post-test probabilities, which in case of a positive test result become positive predictive values. If several test results are observed successively Bayes' theorem may be used with assumed conditional independence of test results or with incorporated conditional dependencies. Herein it is examined whether radiographic image features should be considered conditionally independent diagnostic tests when post-test probabilities are to be derived. For this purpose the mammographic mass dataset from the UCI (University of California, Irvine) machine learning repository is analysed. It comprises the description of 961 (516 benign, 445 malignant) mammographic mass lesions according to the BI-RADS (Breast Imaging: Reporting and Data System) lexicon. Firstly, an exhaustive correlation matrix is presented for mammography BI-RADS features among benign and malignant lesions separately; correlation can be regarded as measure for conditional dependence. Secondly, it is shown that the derived positive predictive values for the conjunction of the two features "irregular shape" and "spiculated margin" differ significantly depending on whether conditional dependencies are incorporated into the decision process or not. It is concluded that radiographic image features should not generally be regarded as conditionally independent diagnostic tests.