Page 195 - Assurance of Sterility for Sensitive Combination Products and Materials

176 Assurance of sterility for sensitive combination products and materials

7.2.4 Statistical analysis types
Before applying point estimates and confidence bounds to assurance of ste-
rility scenarios, one additional foundational concept is helpful. Statistical
analysis can be broadly broken up into two types. The simplest analysis is a
nonparametric analysis that does not make any assumptions about the un-
derlying statistical distribution and classifies the results as passing or failing
against a requirement. This type of data is called attribute data and statistical
analysis that is used to evaluate it is nonparametric analysis. The failure or
lack of failure of one package and the growth or nongrowth of an aseptic
process simulation test, are examples of this type of data. The point estimate
of a set of attribute data is a proportion as discussed above.
Parametric analysis is more complex than nonparametric analysis as it is
strongly dependent on the identification of the correct underlying statistical
distribution. Different distributions are described using different parame-
ters. An analogy to describe the concept of a parameter can be made using
geometry. The length of the side of a square is a parameter of a square. If
the length of the side of a square is known, everything about the square
is known. A rectangle has two parameters. The length of two sides fully
describes a rectangle. If the shape is unknown, the correct parameters to
describe it are also unknown. The most recognizable statistical parameters
describe the normal distribution. A normal distribution is most often pa-
rameterized using the mean and the standard deviation. In the parametric
analysis, the numeric values in a data set are used to estimate the appropriate
parameters for the specific distribution. If the distribution (the shape) and
the parameter estimates are known, this information can be used to estimate
performance and uncertainty.

7.2.4.1 Nonparametric analysis
The packaging and aseptic processing examples below use nonparametric
analysis. A bit of additional introduction is provided here to help the reader
get an intuitive understanding of this analysis. Imagine several experiments
where dozens, hundreds, and thousands of vials have been aseptically pro-
cessed and filled with growth media. The expected result for each of these
demonstrations is that none (zero) of the vials will show any evidence of mi-
crobial contamination. The expected result from the point estimate of all of
these data sets is zero, as 0 units with microbial growth divided by the num-
ber of units tested as part of the demonstration always equals zero. It should
be intuitive that thousands of samples provide more confidence than twenty
samples. The point estimate of zero does not depend on how many units