Relating Subjective and Objective Pharmacovigilance Association Measures - Clustering Challenges in Biological Network - page 281

Reaction Advisory Committee (ADRAC) database [13-15]. The basis for the re-
sults presented in this paper is another statistical approach based on an urn model
of the adverse event database that is non-iterative like the PRR method and is
therefore computationally simpler than the Bayesian and optimization-based ap-
proaches just described; further, this method has been found to be effective in
predicting subsequent regulatory actions on the basis of the AERS database [10].
Given a specified drug (Drug A) and adverse event (Adverse Event B) listed
in a spontaneous reporting database (e.g., the FDA's AERS database considered
here), all of the statistically-based methods listed above are closely related to the
two-way contingency table defined by the following four numbers of records:

1. N a = the number listing Drug A,
2. N b = the number listing Adverse Event B,
3. N ab = the number listing both Drug A and Adverse Event B, and
4. N = the total number of records in the database.

These numbers yield the following simple estimates of the probabilities p a of
observing Drug A in a randomly selected record, p b of observing Adverse Event
B, and p ab of observing both together:

p a = N a /N, p b = N b /N, and p ab = N ab /N. (15.1)

In the absence of any association between drugs and adverse events, we expect
the independence condition p ab = p a p b to hold. This observation motivates the
reporting ratio:

p a p b = NN ab

p ab

R ab =

N a N b ,

(15.2)

which has the value 1 if the empirical probability estimates defined in Eq. (15.1)
satisfy this independence condition. Unfortunately, terminology is not standard
in the pharmacovigilance literature, so the quantity R ab defined in Eq. (15.2) is
called the proportional reporting ratio by Gould [8] and the nonstratified rela-
tive report rate by DuMouchel [2]. Confusing the situation further, most authors
define the proportional reporting ratio as [4, 9]:
P ab = N ab ( N

− N a )

N ab ) .

(15.3)

N a ( N b −

The reporting ratio R ab defined in Eq. (15.2) is considered here because it remains
finite even in the limiting case where N ab = N b , in contrast to P ab which is not
well-defined for this case.
Nevertheless, it is well-known that even R ab behaves badly in these limiting
situations, motivating alternatives like DuMouchel's Bayesian shrinkage estimator