Data-entropy analysis of renal transplantation data

The terms entropy and robustness are currently used by biomedical investigators to predict the risk of change in a system. The former is the mathematical identification of uncertainty about a system, while the latter is the likelihood of system stability. We conducted an entropy-based analysis of our renal transplantation data set.

The input variables in our model included donors and recipients, past medical history, and other clinical data. The output variables were 6- month, 1-year, and 2- year patient and graft survivals. Data-entropy analysis was performed with Ontonix s.r.l. software (www.ontonix.com).

The total input and output entropy was 13.14 and 1.54, respectively. The mean input and output robustness was 39.14% and 29.54%. The robustness amplification index was 0.75. The minimum entropy of the input variables was reported for a history of myocardial infarction (0.07), vascular disease (0.1), bladder residual (0.13), or urologic surgery (0.15). The minimum entropy of the output variables was 0.20 for 6-month patient survival; 0.22 for 1-year patient survival; 0.25 for 6-month graft survival; 0.27 for 1-year graft survival; 0.28 for 2-year patient survival; and 0.32 for 2-year graft survival.

Data-entropy analysis demonstrated a high stability of our transplantation data set. Nevertheless, long-term outcomes, especially those of graft survival, were slightly more unpredictable.