Resource limitations (e.g. money, personnel) or other factors, however, may sometimes dictate a need to reduce the number of samples taken from a herd/flock from the minimum quantity identified in the Animal Sample Size Calculator. Use this Probability of Failure to Detect Diseased Animals calculator to evaluate how significant any deviations from your estimated minimum sample size compromise your ability to detect one or more diseased animals if they are present in the herd/flock from which the sample was taken.
It is noteworthy to point out that the this probability estimate, in turn, is used to establish the herd sensitivity of detection (HSe) for the disease in question:
HSe = 1- probability of failing to detect at least one diseased animal from those sampled
The HSe is the probability that an infected herd/flock will yield a positive result, i.e. one or more samples are positive to your screening test (taking into account its specific diagnostic Se), given that the herd/flock is infected at a design prevalence equal to or greater than the one set by you.
Tip: Since this calculator must use information from the Animal Sample Size Calculator in order to provide meaningful results, make sure to review its input values before proceeding.
This number corresponds to what the estimated probability is of failing to detect any positives (using your chosen test per its Se) from this particular sample size if repeatedly obtained randomly from this herd/flock population of animals with the specified prevalence of disease.
Herd Sensitivity of detection (HSe) is 1 minus this probability.
The values that populate the cells of the matrix are derived using the formula:
Probability of failure to detect disease (β) = [1 - (n · Se)/N]p · N
Herd sensitivity (HSe) of detection of disease is equal to 1 – β.