T 43: Evidence for Empirical Power Law Scaling in Adverse Event Profiles
Principal Science Enablement Director
Genentech, A Member of the Roche Group United States
To evaluate recent published claims (Chen and Bryan 2015) that post-marketing adverse event data demonstrate empirical power law behavior.
The author examined spontaneous adverse events from large, de-identified sponsor internal post-marketing safety datasets (ranging between approximately 48,000 to 250,000 events per molecule) for 4 marketed products for anti-infection, thrombolysis, oncology treatment and inflammation.
All adverse event data for each molecular product was summarized and ranked in decreasing order of the proportion of total events.. The data was then transformed to log-log scales in order to estimate the non-linear decay constant for each respective molecule, using the SAS-JMP 11.1.1 statistical software. Finally, the AEPs for each molecule were plotted together on the same graph to visually determine if there was similar power-law behavior across molecules.
All evaluated AEPs demonstrated similar non-linear power law behavior. Specifically, despite the variation in mechanisms of action, dose, or route of deliver (e.g., Intravascular, Subcutaneous, Oral, Intravitreal, etc.) all AEPs demonstrated similar visual and numeric behavior with proportionality constants ranging between 0.03 and 0.08, and non-linear decay constants ranging between approximately -0.5 and -0.7. Visually, all AEPs could be superimposed on the same graph with one equation fitting all molecules with proportionality constant = 0.06 and decay constant = -0.7.
Based on the evaluation of spontaneous and clinical trial adverse event reports for molecules from this Sponsor safety database, these results support the findings in recent publications that adverse event profiles demonstrate statistical power law behavior. In addition, this behavior appears to be robust across therapeutic class, target patient population, mechanism of action, or delivery mechanism.
This investigation supports the finding of empirical statistical power law behavior in adverse event profiles and further suggests that this behavior is similar across therapeutic domains, molecule type, and the product lifecycle. Similar to empirical power law behavior in other areas of science (e.g., “Zipf’s Law” in human languages, distribution of lunar crater sizes, allometric scaling in biology, and Pareto income distributions), this behavior suggests an underlying pattern and predictability in the reporting and accumulation of adverse events from patients and their treatments.