1. RESEARCH POSTER PRESENTATION DESIGN © 2015
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Introduction
Materials and Methods
Non-linear power laws demonstrating predictable
distributions over multiple orders of magnitude have been
known since the late 19th century. One of the earliest
examples is “Zipf’s Law” for the distribution of words in a
language. Power laws are commonly observed in many
disciplines including physics (distribution of lunar crater
sizes), biology (allometric scaling), medicine (heart rate vs
time), and the social sciences (Pareto income distributions).
Power Law Example: Zipf’s Law for Word Frequency
(Montemurro MA. 2001)
Power Law Example: US City Population size
(Newman MEJ.2006)
Recent literature suggests that empirical power laws also
occur with adverse event data (Chen, et al. 2015; JM Bryan,
2015).
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 (see
Composite AE Profile Graph).
AE Profile Power Law Example with an Inflammatory Molecule
AE Profile Parameters for Evaluated Molecules
Results Conclusions
This investigation observed empirical statistical power law
behavior in AEPs across all evaluated therapeutic
domains and molecules. Similar to empirical power law
behavior in other areas of science (e.g., “Zipf’s Law”), this
finding suggests an underlying pattern and predictability to
the accumulation of adverse events from clinical research and
pharmacovigilance, which may be useful in our efforts to
streamline safety monitoring throughout a product’s
lifecycle.
References
1) Brown JH, et al. The fractal nature of nature: power laws,
ecological complexity and biodiversity. Phil. Trans. R.
Soc. Lond. B (2002) 357, 619–626.
2) Chen X, et al. Systematic Analysis of the Associations
between Adverse Drug Reactions and Pathways. BioMed
Research International Vole 2015, Article ID 670949, 12
pages http://dx.doi.org/10.1155/2015/670949.
3) Jonathon Bryan. Measuring the Relationship between
Innovative Drugs and AE_2015. The Brookings
Institution.http://www.slideshare.net/JonathanBryan5/mea
suring-the-relationship-between-innovative-drugs-and-
ae2015-50168899.
4) Montemurro MA. Beyond the Zipf–Mandelbrot law in
quantitative linguistics. Physica A 300 (2001) 567–578.
5) Newman MEJ. Power laws, Pareto distributions and
Zipf’s law. arXiv:cond-mat/0412004v3 [cond-mat.stat-
mech] 29 May 2006.
Acknowledgement(s)
Barbara Tong, PhD Global Biostatistics | Roche/Genentech
Gregory Bell MD VP PDS | Roche/Genentech
For this project, the author extracted adverse event report
listings in August 2015 from large, de-identified sponsor
internal post-marketing safety datasets for four marketed
products in the therapeutic areas of anti-infection, CNS
thrombolysis, oncology and inflammation. The number of
adverse events ranged between approximately 20,000 to
250,000 per molecule from multiple sources (spontaneous,
non-interventional programs, and clinical trials as well as
follow up cases) and over variable lifecycle times (5 years to
30+ years).
All adverse events were coded using the Medical Dictionary
for Regulatory Activities (MedDRA) and analyzed at the
preferred term (PT) level. PTs for each product were then
summarized and ranked in decreasing order of frequency of
occurrence within the dataset, to create the respective AEP.
This data was then transformed to a log-log scale in order to
estimate the power law scaling (α) and non-linear decay
constants (β) for each respective molecule. The general
power function shown below was fit using the SAS-JMP
11.1.1 statistical software.
𝑦(𝑥) = 𝛼𝑥−𝛽
(1)
An example of the overall AEP and power law fit are shown
in the AE Profile Graph for the Inflammatory Indication
molecule. Finally, the AEPs for all evaluated molecules were
plotted together on the same graph to visually determine if
there was similar power-law behavior across molecules. The
resulting parameters for the evaluated molecules are shown in
the corresponding table.
Based on the evaluation of the AEPs for molecules from this
Sponsor safety database, these results support the findings in
recent publications that adverse event profiles demonstrate
empirical power law behavior. In addition, a surprising
finding is that this behavior appears to be robust across
therapeutic class, historical period (e.g., data from 1970s,
80s, 90s, to 2015), mechanism of action, or delivery
mechanism. The relationship is such that all evaluated
molecule AEPs appear to follow one overall power law, as
shown below.
Composite AE Profile Power Law for all Evaluated Molecules
Implications for Future Research:
The observations from this investigation are based on a
relatively large data sample from a single sponsor. These
results suggest power law behavior may be a ubiquitous
feature of AE profiles.
However, this remains a hypothesis to be tested. One
potential way to do this would be to conduct a similar
experiment using a much larger safety database from a
Regulatory Body (egg, FDA’s Adverse Event Reporting
System) across many more molecules and diverse indications.
Discussion
Shaun Comfort, MD, MBA
Associate Director of Risk Management & Sr.SSL, Product Development Safety Science-IIDO | Roche/Genentech
Evidence for Empirical Power Law Scaling in Adverse Event Profiles
The goal of this work was to evaluate the claims in recent
publications, that non-linear power law relationships can be
observed in post marketing adverse event profile (AEP) data
(Chen, et al. 2015; JM Bryan, 2015).
Overall Objective
# Indication Route Events Alpha Beta
1 Oncology IV 268,512 0.047 -0.57
2 CNS IV 40,382 0.086 -0.75
3 Inflammatory SQ 124,576 0.031 -0.46
4 Anti-Infective PO 46464 0.058 -0.66
5 Ophthalmology ITV 19363 0.089 -0.83
Combined Data 499,297 0.058 -0.66
Disclosure(s)
Author(s) of this presentation have the following to disclose
concerning possible financial or personal relationships with
commercial entities that may have an interest in the subject
matter of this presentation:
• Shaun Comfort MD, MBA – Roche/Genentech Employee