Non-sterile (P) |
Non-sterile (P) |
Units |
Percent chance to fail sterility test (F) |
Percent False NegativeResult |
1:10,000 |
0.0001 |
1 |
0.0 |
99.99 |
1:1000 |
0.001 |
1 |
0.1 |
99.90 |
1:100 |
0.01 |
1 |
1.0 |
99.01 |
1:10 |
0.1 |
1 |
9.5 |
90.48 |
1:10,000 |
0.0001 |
5 |
0.0 |
99.95 |
1:1000 |
0.001 |
5 |
0.5 |
99.50 |
1:100 |
0.01 |
5 |
4.9 |
95.12 |
1:10 |
0.1 |
5 |
39.3 |
60.66 |
1:10,000 |
0.0001 |
20 |
0.2 |
99.80 |
1:1000 |
0.001 |
20 |
2.0 |
98.02 |
1:100 |
0.01 |
20 |
18.1 |
81.87 |
1:10 |
0.1 |
20 |
86.5 |
13.54 |
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 refer to 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 2, 0.5 and 0.1% when 20, 5 or 1 units are tested. Thus, even when 20 units are tested the USP sterility test will miss the contamination event 98% of the time
Non-sterile (P) |
Non-sterile (P) |
Units |
Percent chance to fail sterility test (F) |
Percent False NegativeResult |
1:1000 |
0.001 |
1 |
0.1 |
99.9 |
1:1000 |
0.001 |
2 |
0.2 |
99.8 |
1:1000 |
0.001 |
3 |
0.3 |
99.7 |
1:1000 |
0.001 |
4 |
0.4 |
99.6 |
1:1000 |
0.001 |
5 |
0.5 |
99.5 |
1:1000 |
0.001 |
6 |
0.6 |
99.4 |
1:1000 |
0.001 |
7 |
0.7 |
99.3 |
1:1000 |
0.001 |
8 |
0.8 |
99.2 |
1:1000 |
0.001 |
9 |
0.9 |
99.1 |
1:1000 |
0.001 |
10 |
1.0 |
99.0 |
1:1000 |
0.001 |
20 |
2.0 |
98.0 |
1:1000 |
0.001 |
40 |
3.9 |
96.1 |
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 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 3.9%.
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.