Page 196 - Assurance of Sterility for Sensitive Combination Products and Materials

Risk to the patient—Quantifying assurance of sterility 177

were included in the experiment. The numerator in this example is assumed
to be zero. While the point estimate is zero in every instance, the worst-case
estimate, the UCB of this estimate, is a nonzero positive value. The UCB is
very dependent on how many units were included in the sample.
The nonparametric analysis is often used to evaluate the results of the
aseptic process validations and for package integrity tests. Sample sizes per
batch traditionally do not exceed 10,000 units, and for combination prod-
ucts, the sample sizes can be below 100 units. Table 7.3 shows sample sizes
and the associated reliability of the result that can be claimed with high
confidence. The table includes three levels of confidence so the reader can
see that the conclusions are broadly applicable. With attribute data, hundreds
−2
of samples limit the reliability or PNSU* claim to the 10 level. Thousands
of samples raise the level of the PNSU* that can be demonstrated with
−3
high confidence to the 10 level. Demonstrating a PNSU* assurance level
−4
of 10 with high confidence would require nearly 30,000 samples if there
was not a single unit with evidence of growth.
One way to understand the UCBs associated with nonparametric sam-
pling is to consider drawing marbles out of an infinitely large bag. It is a
given that a certain percentage of the marbles are red; the rest are white.
Each draw has the same probability of getting a white or a red marble, as the
infinitely large bag has an unlimited supply of marbles. After 22 draws with
only white marbles being drawn (zero red marbles), what predictions can be
made about the percentage of red marbles? The 90% confidence, 90% reli-
ability location in Table 7.3 (bottom left corner of the table) indicates that
10% of the time 22 draws from the marble bag result in zero red marbles.
In other words, if a sample of 22 marbles is taken, and zero red marbles are
found, a statistical statement that there is at most 10% red marbles can be
made with 90% confidence. Each draw has a 90% chance of a white marble.
The chance of drawing two white marbles in a row is 0.9 × 0.9. The chance
22
of drawing 22 white marbles in a row is 0.9 , or 9.8%. As the percentage
of red marbles drops (as PNSU* drops) the chance of drawing many white
marbles in a row increases. To make a high confidence statistical statement
that the percentage of red marbles is low (the PNSU* is low), a very large
number of white marbles in a row needs to be drawn from the bag.

7.2.4.2 Parametric analysis
The terminal sterilization examples below use parametric analysis. A bit
of additional introduction is provided here to help the reader get an intui-
tive understanding of this analysis. The number of microorganisms that are