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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, MBAAssociate 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