Conditional independence relations among biological markers may improve clinical decision as in the case of triple negative breast cancers.

The associations existing among different biomarkers are important in clinical settings because they contribute to the characterisation of specific pathways related to the natural history of the disease, genetic and environmental determinants. Despite the availability of binary/linear (or at least monotonic) correlation indices, the full exploitation of molecular information depends on the knowledge of direct/indirect conditional independence (and eventually causal) relationships among biomarkers, and with target variables in the population of interest. In other words, that depends on inferences which are performed on the joint multivariate distribution of markers and target variables. Graphical models, such as Bayesian Networks, are well suited to this purpose. Therefore, we reconsidered a previously published case study on classical biomarkers in breast cancer, namely estrogen receptor (ER), progesterone receptor (PR), a proliferative index (Ki67/MIB-1) and to protein HER2/neu (NEU) and p53, to infer conditional independence relations existing in the joint distribution by inferring (learning) the structure of graphs entailing those relations of independence. We also examined the conditional distribution of a special molecular phenotype, called triple-negative, in which ER, PR and NEU were absent. We confirmed that ER is a key marker and we found that it was able to define subpopulations of patients characterized by different conditional independence relations among biomarkers. We also found a preliminary evidence that, given a triple-negative profile, the distribution of p53 protein is mostly supported in 'zero' and 'high' states providing useful information in selecting patients that could benefit from an adjuvant anthracyclines/alkylating agent-based chemotherapy.