# Complex 2-stage risk-based surveillance - calculation of surveillance sensitivity

## Input Values

This page calculates the surveillance sensitivity for more complex, 2-stage, risk-based surveillance.

This analysis allows for clustering at the herd level, two risk factors (at herd and animal level) and/or a factor influencing the performance of the test. In addition, different test sensitivities can be applied to high-risk and low-risk animals (i.e. sensitivity is based on risk-group). If test sensitivity varies between groups but there is no difference in risk of disease use a relative risk value of 1. It assumes that the risk factors are independent 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).

Two risk factors are considered, one at the herd level and one at the animal level. For each risk factor the following information is required:

• The relative risk: this measures the risk of herds or animals being infected in the high-risk group, relative to the risk of herds or animals being infected in the low-risk group. For risk-based surveillance, this is usually greater than 1.
• The population proportion: this is the proportion of herds or animals from their respective populations that are in the high-risk group.
• The design prevalence at the herd and animal levels: this is the assumed prevalence of disease (proportion of infected herds and infected animals respectively), if the disease is present in the population. It is used as a standard by which the sensitivity of the surveillance can be evaluated.
• For the diagnostic test, performance depends on risk group:
• The sensitivity of the test for animals in the high risk group
• The sensitivity of the test for animals in the low risk group
• The numbers of high and low risk herds tested in the surveillance system
• The numbers of high and low risk animals tested in each herd (these are fixed across all herds)
• The prior confidence of freedom, to allow calculation of posterior confidence of freedom after completion of the surveillance.

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 herd-sensitivity achieved for sampling within sampled herds.
• For comparison, the surveillance system sensitivity and herd sensitivity achieved if representative sampling were used.
• The sensitivity ratio - This indicates how much more sensitivity the risk-based approach acheives, relative to a representative approach.
• Posterior confidence of freedom achieved for both risk-based and representative sampling.
• Effective probabilities of infection (EPI) for high-risk groups at both herd and animal levels are also shown. 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.

### Herd-level risk factor

Relative risk :
Population proportion in high risk group :
Design prevalence :

### Animal-level risk factor

Relative risk :
Population proportion in high risk group :
Design prevalence :

### Diagnostic test

Sensitivity in high risk group :
Sensitivity in low risk group :
High-risk herds tested :
Low-risk herds tested :
High-risk animals tested per herd :
Low-risk animals tested per herd :
Prior confidence of freedom :

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