Page 214 - Assurance of Sterility for Sensitive Combination Products and Materials

Risk to the patient—Quantifying assurance of sterility 193

The number of recovered microbes is a sample from a Poisson distri-
bution (Eq. 7.4). A single parameter lambda fully describes the distribution.
The value of lambda is also the average value of the Poisson distribution.
Assuming the true average number of microbes per unit after a half-cycle
is one (lambda is one), the probability of getting a zero result in a single
sample can be calculated using the Probability Mass Function (PMF) for the
Poisson distribution shown in Eq. (7.5). Given a k of zero (zero microbes),
the equation reduces to 1 over e. There is a 36.788% of a value of zero on
any sample.
λ k × e −λ (7.5)
P =
k
where k!
k is the number of observations.
P k is the probability of k observations.
Basic probability theory states the probability of getting a zero twice in two
attempts is P k × P k . The probability of getting zero 3 times in a row is 0.367888
cubed or 4.98%. There is less than a 5% chance of getting three zero values in
three consecutive attempts if the true value of lambda is as large as one. The
upper 95% confidence bound of this estimate is the average (λ) is <1.
The spore-log-reduction (SLR) for the fraction negative results are de-
fined in Eq. (7.6). The log of the final population is required to be zero.
The log of zero is undefined and the standard states that the SLR can be
reported as “>log N 0 ” if one is used for N U , the final population.

SLR = log N 0 − log N U (7.6)
where
N 0 is the initial population,
N U is the final population.
Using one for the value of N U is conservative as the upper 95% confi-
dence bound for lambda is <1. The analysis above supports that the 95%
confidence for the average value of N U is <1.
The required initial bioburden load of one million spores and the re-
quired final result of one are substituted into Eq. (7.6). The result is a spore
log reduction of 6. There is 95% confidence that the spore log reduction is
demonstrated in Section A is at least 6.

7.3.5.2 Section B
The definition of D-value requires that if ETO exposure time is doubled,
the SLR also doubles from 6 to 12. The standard requires at least doubling