# Simple 2-stage risk-based surveillance - calculation of surveillance sensitivity based on herd testing data

## Input Values

This page calculates the surveillance sensitivity for simple risk-based surveillance with 2-stage sampling, for instance, a survey in which high-risk herds are preferentially targeted for testing, but with representative sampling of animals within selected herds. The analysis is based on actual sampling results for each herd, assuming that all results are negative.

This analysis assumes 2-stage sampling to account for clustering of disease (for example at the herd, flock or village level) and that the effective specificity of the surveillance system is equal to one (all positives are followed up to ensure that they are not false positives).

One risk factor is considered, for which the following information is required:

• The relative risk: this measures the risk of herds in the high-risk group being infected, relative to the risk of herds in the low-risk group being infected. For risk-based surveillance, this should usually be greater than 1.
• The population proportion: this is the proportion of herds from the entire population that are in the high-risk group.

In addition, the following parameters are required:

• The design prevalence: this is the assumed prevalence of disease, if the disease is present in the population. It is used as a standard by which the sensitivity of the surveillance can be evaluated. Values must be entered for both herd- and animal-level design prevalence.
• The individual animal test sensitivity: this is the sensitivity of the test performed on individual animals.
• Prior confidence of freedom: this is the estimated confidence that the population was free of disease (at the design prevalence) before the surveillance was done and is used to estimate confidence of freedom following completion of the surveillance.
• Detailed data on the number of animals tested in each herd, including: number tested, risk group, herd id (optional) and herd size (optional).

Outputs include:

• The sensitivity of the surveillance system, or in other words, the probability that the surveillance system would detect at least one infected animal if disease was present at the specified design prevalence.
• The probability of freedom, or confidence that the disease is NOT present at the design prevalence (equivalent to the negative predictive value of the surveillance system).
• The sensitivity of the system and confidence of freedom for assumed representative sampling.
• The sensitivity ratio - This indicates how much more sensitivity the risk-based approach acheives, relative to a representative approach.
• Effective probabilities of infection (EPI) for high-risk and low-risk herds. EPI values approaching 100% suggest that, based on the values used for relative risk, population proportions and design prevalence, close to 100% of herds (or animals) in the high-risk group are expected to be infected. If this is unreasonable you may need to review the input values. Values over 100% mean that the model is invalid and processing will be stopped, with an error message. Input values must be changed to ensure EPI values are appropriate.
• Numbers of high-risk and low-risk herds tested and the total.
• A summary of herd-sensitivities achieved in tested herds.
• Herd-sensitivity achieved in individual herds.

Relative risk :
Population proportion in high risk group :
Herd-level design prevalence :
Animal-level design prevalence :
Test sensitivity :
Prior confidence of freedom :

Paste herd testing data in the space below. Data columns can be in any order but must include columns for number tested (labeled 'Tested') and risk group (labeled 'Risk'). 'Risk' must be coded as high-risk = 1 and low-risk = 0. Columns for herd id, and herd size (labeled 'HerdSize') are optional. A header row specifying column names must also be included.

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It provides a range of epidemiological tools for the use of researchers and epidemiologists, particularly in animal health.