Page 192 - Assurance of Sterility for Sensitive Combination Products and Materials

Risk to the patient—Quantifying assurance of sterility 173

Fig. 7.2 Random mechanism for generating Table 7.2.

Fig. 7.3A shows the point estimates (the proportion of 1’s in each of the
columns) and the associated confidence intervals that were calculated above.
In all, 9 of 10 of the confidence intervals include the true value, 0.1. The
intent of the confidence interval is to clearly indicate the region where the
truth is likely to fall. The intervals that are shown are 90% intervals. About
90% confidence intervals are expected to contain the true value. In the case
of a proportion, the size of the interval is slightly dependent on the value of
the point estimate but it is very dependent on the sample size that was used
to calculate the proportion. The top data point in the graph shown in black
is the grand average for the table. The grand average was calculated using all
of the values in the table, 200 data points. It has a confidence interval that is
much smaller than the estimates for the groups of 20.
To provide a connection for the reader with the analysis in Section 7.3,
this same data is plotted in Fig. 7.3B in the format as forthcoming Figs. 7.4,
−9
7.5, 7.8, and 7.10, using 10 as an approximation for 0 and a log-based
x-axis scale.
Group 9 in Table 7.2 had an average of zero. The die was cast 20 times
and a 9 was never rolled. The confidence interval for sample 9 only extends
in the positive direction. A proportion is bound between 0 and 1. The upper
bound of this confidence interval includes the true value of 0.1. Sample 9
illustrates a very important truth in the context of discussions on PNSU*.
It is possible to get a proportion of 0, 0 positive results when the true pro-
portion in the population is nonzero. When the proportion of non-sterile
units in the population is very close to 0, as is the desired state for sterility
assurance as measured by PNSU*, a 0 proportion in the sample is very
likely unless the sample size is extremely large.