Page 189 - Assurance of Sterility for Sensitive Combination Products and Materials

Risk to the patient—Quantifying assurance of sterility 171

to product built using this process. The population is all product built using
the processes and controls that generated the data set.
If the sample that was selected is representative of the population, the
sample results are only the most probable result for the larger population.
It is possible that the true result for the population is larger or smaller than
a point estimate derived from the sample. The single number, the sample
point estimate, does not provide any information about how different the
population may be. This is illustrated by an intuitive coin flip example.
A coin flipped once may result in a head. It may be accurately stated that
100% of the coin flips (in a sample size of one) resulted in heads. This factually
true statement does not provide any information about how likely a head will
be in future coin flips. In the technical world, it is appropriate to present data
in a format that includes a measure of the uncertainty when it is applied to
the population of interest. Answers are usually expressed as a confidence in-
terval or, if the risk is one-sided such as that for sterility, the UCB is reported.
7.2.2 Confidence interval example

Table 7.2 contains 10 columns of 20 randomly generated 0’s and 1’s. The
data could have been generated using a 10-sided die shown in Fig. 7.2. If
a nine is rolled a 1 is entered in the table. When any value between a 0 and
an 8 is rolled a 0 is entered.
Each entry in the table has a 10% chance of containing a 1 and a 90%
chance of containing a 0. In a very large number of rolls, 10% will have a
value of 1, as the true proportion of 1’s in the population is 10%. Imagine
the entries labeled ‘1’ represent a positive sterility test result, a non-sterile
unit, while a 0 entry is a negative sterility test result. The expected result is
that each column contains 10% 1’s, two results out of 20 with the value
of 1. In the case of 1’s and 0’s, an average of the column can be used to
represent the count of 1’s. In practice, most of the column averages are not
10% (0.1), the expected value. The actual column averages are shown at the
bottom of the table. Three of the columns have an average of 0.1. Others
columns have an average 0, 0.05, 0.15, and 0.20. These small samples have
a large amount of variability. The measured point estimate may not be the
true population proportion. The 90% confidence intervals for each column
are shown below the average values in the table. To the right of the main
table, the grand average of the table is shown along with its 90% confidence
interval. These intervals were calculated with the binomial formula.