Background: 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 United States Food and Drug Administration Adverse Event Monitoring System (US FDA AEMS). Methods: Six commonly used but pharmacologically different 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 modeled using the ZM law. Those medications that have a greater percentage of reported ADRs within their first ten ranks were also found to have a greater negative slope. Furthermore, a natural logarithmic transformation of both the reported FDA data and the ZM law-derived predicted values demonstrated a consistent near-linear relationship, which was statistically significant. The ratio of the coefficients of the ZM law, a·b−1, was also found to be a potentially useful index that 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 outcomes may be warranted.
Atlas et al. (Mon,) studied this question.