Table 7.

Summary of sample size formulae to estimate the probability of disease freedom or estimate surveillance system sensitivity.

Study design	Outcome	Arguments	References
Representative sampling	Probability of disease freedom assuming imperfect test sensitivity and perfect test specificity.	The assumed population size, an estimate of the prior probability that the population is free of disease, an estimate of the probability of disease introduction, the population level design prevalence, the desired probability that the population is free of disease, the sensitivity of the diagnostic test used at the surveillance unit level.	(22, 23)
Representative sampling	Surveillance system sensitivity assuming a single risk factor and varying test sensitivity.	The assumed population size, the population level design prevalence, the desired surveillance system sensitivity, the sensitivity of the diagnostic test used at the surveillance unit level.	(24, 25)
Representative sampling	Surveillance system sensitivity assuming two stage sampling, imperfect test sensitivity and perfect test specificity.	The number of clusters in the population, the number of surveillance units within each cluster, the cluster level design prevalence, the desired cluster level sensitivity, the population level design prevalence, the desired population level sensitivity, the sensitivity of the diagnostic test used at the surveillance unit level.	(24–27)
Representative sampling	Surveillance system sensitivity, imperfect test sensitivity and imperfect test specificity.	The assumed population size, the population level design prevalence, the desired population level sensitivity, the desired population level specificity, the sensitivity of the diagnostic test at the surveillance unit level, the specificity of the diagnostic test at the surveillance unit level.	(26–28)
Representative sampling	Surveillance system sensitivity assuming pooled sampling giving rise to imperfect test sensitivity and imperfect test specificity.	The number of surveillance units that contribute to each pool, the population level design prevalence, the sensitivity of the diagnostic test at the pooled level, the specificity of the diagnostic test at the pooled level, the desired population level sensitivity.	(29)
Risk-based sampling	Surveillance system sensitivity assuming imperfect test sensitivity and perfect test specificity.	The population level design prevalence, relative risk estimates for each strata, the population proportions for each strata, the surveillance proportions for each strata, the desired population level sensitivity, the sensitivity of the diagnostic test at the surveillance unit level.	(5)
Risk-based sampling	Surveillance system sensitivity assuming risk-based 2-stage sampling on one risk factor at the cluster level assuming imperfect test sensitivity and perfect test specificity.	Relative risk values for each strata in the population, the population proportions in each strata, the planned number of units to be sampled from each strata, the cluster level design prevalence, the desired cluster level sensitivity, the surveillance unit level design prevalence, the sensitivity of the diagnostic test at the surveillance unit level, the desired surveillance system (population-level) sensitivity.	(5)
Risk-based sampling	Surveillance system sensitivity assuming risk-based 2-stage sampling on two risk factors at either the cluster level, the unit level or both, imperfect test sensitivity and perfect test specificity.	The number of risk strata defining the relative risk values at the cluster level, the population proportions at the cluster level, the planned surveillance proportions at the cluster level, the cluster level design prevalence, the desired cluster level sensitivity, the number of risk strata defining the relative risk values at the surveillance unit level, the population proportions at the surveillance unit level, the planned surveillance proportions at the surveillance unit level, the surveillance unit level design prevalence, the sensitivity of the diagnostic test at the surveillance unit level, the desired surveillance system (population-level) sensitivity.	(5)