Page 206 - Assurance of Sterility for Sensitive Combination Products and Materials

Risk to the patient—Quantifying assurance of sterility 185

For Case 6, with 300 trials (3 × 100) and an acceptance number of zero,
Eq. (7.1) reduces to Eq. (7.2) as x is zero.
P x () = q n (7.2)

Eq. (7.2) can be rearranged as Eq. (7.3).
 Ln   Px () 

    (7.3)
q = e  n 
Using the data in Case 6 and assuming a 95% level of confidence yields
05
.
q = e ( Ln[ ]/300 ) = .99064
0
PNSU* is the probability of a non-sterile unit (p), and by definition
p = 1 − q. The UCB of PNSU* = 1 − 0.990064 = 0.009936, 9.9E−03.
If the true value of the PNSU* is 9.9E−03 with a 95% UCB, there is a
5% chance that a test sequence could pass. That is, there is a 5% chance that
the result required by the standard, 0 contaminated units in 300 trials, would
be observed. In other words, the confidence is 95% that the true value of the
PNSU* is <9.9E−03. Referencing back to the marble example, if in truth
just under 1% (0.99%) of the marbles in the bag are red, the probability of
drawing 300 white marbles in a row is 5%. The confidence is 95% that the
true percentage of red marbles is <9.9E−03.

7.3.3.1 Conclusion—Point estimates and confidence
bounds—Aseptic processing
The statistical point estimates for the PNSU* when zero contaminated units
−9
are found during the testing is zero, show as 10 in Fig. 7.5. When a single
−5
contaminant is found the point estimates are in the 10 range. The UCB for
−4
most of the cases are in the 10 range, the exception being Case 6 where it was
one to two orders of magnitude higher. For Case 6, statistics cannot exclude
−2
the possibility that the true PNSU* is in the 10 range. For the other cases,
−3
−4
statistics cannot exclude the possibility that the true PNSU* in the 10 –10
range. The sample size is the factor driving these confidence bounds.
In summary, the point estimates and UCB for each of the cases shown
in Table 7.7 are shown graphically below in Fig. 7.5.
• For aseptic process simulation tests with zero failures (e.g., Table 7.7,
Cases 2 and 4–6), zero out of “n” failures provides a point estimate of
−2
−9
−4
zero (shown as 10 in Fig. 7.5). The UCBs range from only 10 to 10 .
• For aseptic process simulation tests with one failure being acceptable
followed by retests with no failure (e.g., Table 7.7, Cases 1 and 3), the
−5
−4
point estimate is only in the 10 –10 range and the upper 95% confi-
−4
−3
dence bound is in the 10 –10 range.