STATISTICAL TOPICS AND ANALYSIS IN RISK ASSESSMENT - Risk Management Applications in Pharmaceutical and Biopharmaceutical Manufacturing - page 83

value of 0.1 for the hazard. But is this the true value? How confident are we of
the value? Does this matter for a risk assessment?
For this, we need to calculate a confidence interval around the occurrence rate
determined for the potential hazard. For most cases, looking for a 95% confidence
interval is perfectly acceptable. This is shown as

95% CI = P ± 1.96 s p

where

=

S p standard error of the estimate

=

P occurrence rate sample probability

1.96 = normal Z score for 95% confidence

So

95% CI = 1 ± 1.96 s p

To calculate S p † , we use the following formula:

P ( 1 − P )
N

S p =

where

P = the occurrence rate sample probability
N = the number of samples taken
In this case, we know:

0.1
N = 400

P =

So,

0.1 ( 0.9 )
400

S p = = 0.015

Now

95% CI = 0.1 + 1.96 s p = 0.1 ± 1.96 × 0.015
95% CI = 0.1 ± 0.0294

So, we are 95% confident that the true occurrence rate is between

0.071 and 0.129

or

7.1% and 12.9%

† S P gives us a standard error based upon the sample size, N ,used.