Estimate the maximum detectable prevalence

Theory

Sampling a population and obtaining only negative results from all the samples does not necessarily mean that the population is free from the event under study. The event could exist below a given level of prevalence. That level depends on the number of individuals included in the sample, the population size and the sensitivity of the diagnostic method. When animals are sampled and 100% return a negative result the following values can be estimated: (1) the highest possible number of individuals having the event (or the maximum possible prevalence) in the population; and (b) the level of confidence with which it could be affirmed that the prevalence of the event is below a stated value. For estimating the maximum possible number of individuals with the event present in a population from which only negative results were obtained, the following formula is used:

Where:

CL The level of confidence.

n The number of individuals in the sample.

N The number of individuals in the population.

Se The sensitivity of the diagnostic method.

The level of confidence with which it can be affirmed - from a sampling having 100% negative results - that the prevalence of an event in a population is below a stated value is calculated as:

Where:

CL The level of confidence.

n The number of individuals in the sample.

N The number of individuals in the population.

e The number of individuals presenting the event in the population that can be detected.
e = N × expected prevalence × Se

Practice

Procedures performed by this module are useful only in the case of obtaining negative results from all individuals included in a random sample.

Sample size The number of individuals in the sample.
Acceptable values: any positive integer.

Population size The number of individuals in the population.
Acceptable values: any positive integer.

Sensitivity The probability that an individual having the event under study will be identified as positive by the diagnostic test.
Acceptable values: ≥ 0 and ≤ 1.

Level of confidence The confidence that the user wants to have in the results.
Acceptable values: 90%, 95% or 99%.

Minimum expected prevalence This procedure is used to estimate the level of confidence with which it could be affirmed (from a random sampling of size n with a diagnostic method of sensibility x from which 100% of the results were negative) that the prevalence of the event in the population is not greater than than a stated value.
Acceptable values: ≥ 0 and ≤ 1.


Instituto Nacional de Tecnología Agropecuaria	EpiCentre, IVABS, Massey University

CL	The level of confidence.
n	The number of individuals in the sample.
N	The number of individuals in the population.
Se	The sensitivity of the diagnostic method.

Sample size	The number of individuals in the sample. Acceptable values: any positive integer.
Population size	The number of individuals in the population. Acceptable values: any positive integer.
Sensitivity	The probability that an individual having the event under study will be identified as positive by the diagnostic test. Acceptable values: ≥ 0 and ≤ 1.
Level of confidence	The confidence that the user wants to have in the results. Acceptable values: 90%, 95% or 99%.
Minimum expected prevalence	This procedure is used to estimate the level of confidence with which it could be affirmed (from a random sampling of size n with a diagnostic method of sensibility x from which 100% of the results were negative) that the prevalence of the event in the population is not greater than than a stated value. Acceptable values: ≥ 0 and ≤ 1.