Non-sterile (P) |
Non-sterile (P) |
Units |
Percent chance to fail sterility test (F) |
|
1:10,000 |
0.0001 |
1 |
0.01 |
|
1:1000 |
0.001 |
1 |
0.1 |
|
1:100 |
0.01 |
1 |
1.0 |
|
1:10 |
0.1 |
1 |
11.1 |
|
1:10,000 |
0.0001 |
5 |
0.05 |
|
1:1000 |
0.001 |
5 |
0.5 |
|
1:100 |
0.01 |
5 |
5.3 |
|
1:10 |
0.1 |
5 |
82.4 |
|
1:10,000 |
0.0001 |
10 |
0.10 |
|
1:1000 |
0.001 |
10 |
1.0 |
|
1:100 |
0.01 |
10 |
11.1 |
|
1:10 |
0.1 |
10 |
271.8 |
|
The above probability of a false negative sterility test F is calculated without respect to the sample volume tested. It is based on the number of units tested and the contamination rate P. Obviously, if a preparation has a contamination rate of P and N units are tested for sterility then the percent chance of correctly identifying a true sterility failure F is directly proportional to the volume of medium tested.
In this example I have highlighted the case where 1 in 1000 units are expected to be non-sterile. Ideally, a sterility test will correctly identify this level of contamination. However, the USP <71> test does not accomplish this. The chance of correctly identifying this level of contamination is 1, 0.5 and 0.1% when 10, 5 or 1 units are tested. Thus, even when 10 units are tested the USP sterility test will miss the contamination event 99% of the time.
Non-sterile (P) |
Non-sterile (P) |
Units |
Percent chance to fail sterility test (F) |
1:1000 |
0.001 |
1 |
0.1 |
1:1000 |
0.001 |
2 |
0.2 |
1:1000 |
0.001 |
3 |
0.3 |
1:1000 |
0.001 |
4 |
0.4 |
1:1000 |
0.001 |
5 |
0.5 |
1:1000 |
0.001 |
6 |
0.6 |
1:1000 |
0.001 |
7 |
0.7 |
1:1000 |
0.001 |
8 |
0.8 |
1:1000 |
0.001 |
9 |
0.9 |
1:1000 |
0.001 |
10 |
1.0 |
1:1000 |
0.001 |
20 |
2.0 |
1:1000 |
0.001 |
40 |
4.2 |
In this table it is shown that the chances of correctly identifying a contaminated lot when the contamination rate is 1 in 1000 as a function of sample size. When only a single unit is tested then the there is a 0.1% chance of an accurate result or a 99.9% chance of a False negative result. By expanding the test to include 40 units as the sample size the chance of correctly identifying the non-sterile lot slightly increases to about 4.2%.
Accordingly, any rational to justify a reduced number of units tested should take into account the limits of the statistical meaning of the USP sterility test.