Use of the Zipf-Mandelbrot Law in Modelling US FDA Adverse Reactions

Objective: The purpose of this preliminary study was to evaluate the use of the Zipf-Mandelbrot (ZM) law to mathematically model the percentage occurrence of adverse drug reactions (ADRs), as a function of rank, reported to the US FDA Adverse Event Monitoring System (AMES). Methods: Six commonly used hospital-based medications were examined. Nonlinear curve fitting of the two ZM coefficients was utilized to model the percentage occurrence of ADRs in a hierarchical or rank order for each drug examined. Results: The reported complications and their associated occurrence rates for all six medications were accurately modelled using the ZM law. Those medications which have a greater percentage of reported ADRs within their first ten ranks have a greater negative slope. Furthermore, a natural logarithmic transformation of both the reported FDA data and the predicted values utilizing the ZM law demonstrated a consistent statistically significant near-linear correlation. The ratio of the coefficients of the ZM law, a∙b^(-1), was also found to be a potentially useful index which allows for describing and comparing the overall shape of the medication-specific distributions. Conclusions: Based upon this preliminary examination, the ZM law appears to be applicable to the mathematical modeling of US FDA reported ADRs. Additional research to assess and utilize this law for the analysis, economic management, and possible improvement in patient outcome may be warranted.