STATISTICAL TOPICS AND ANALYSIS IN RISK ASSESSMENT - Risk Management Applications in Pharmaceutical and Biopharmaceutical Manufacturing - page 84

TABLE 4.1 Comparison of Samples Sizes When
Estimating the Occurrence Rate for a Hazard

Occurrence Rate Confidence Interval

Sample P Sample Size N Range [ C ] at 95%

0.1 400 0.071-0.129

0.1 30 0-0.21

Is this range of any concern when applied to a risk assessment? It depends.
What if we took a sample of 30 instead of 400? For n = 400, we can assume
1.96 for a 95% CI, but for n = 30, we need to use the t distribution with a value
of 2.042. We will assume the same occurrence rate P = 0.1, or 10% T ,and
change N from 400-30.
So,

0.1

( 0.9 )

S p = =

0.055

30

95% CI = 1 ± 2.042 S p = 0.1 ± 2.042 × 0.055

95% CI = 0.1 ± 0.112

which changes the 95% CI range to

0-0.212

or

0%-21.2%.

What we originally thought had a probability of 0.1 could be as little as 0
or as high as 0.212 (if our sample size was 30) as summarized in Table 4.1.
Potentially an issue when attempting to assign an occurrence rate.
In the third case, we assume to have a reliable statistical model that can be
used to estimate probabilities. The most common models for laboratory data are
the normal distribution, the lognormal, and the exponential distribution.

4.12 CONCLUSION

While space does not permit an extended discussion of the common tools men-
tioned in ICH Q9, most readers have some prior knowledge even if in passing.
This chapter was not written to give the reader a full understanding but rather
to provide conceptual constructs and points to consider. However, the following
references will permit self-study for those needing an introduction or a refresher.
An Internet search will find many more.