Estimating the optimal population upper bound for scan methods in retrospective disease surveillance

Correctly and quickly identifying disease patterns and clusters is a vital aspect of public health and epidemiology so that disease outbreaks can be mitigated as effectively as possible. The circular scan method is one of the most commonly used methods for detecting disease outbreaks and clusters in retrospective and prospective disease surveillance. The circular scan method requires a population upper bound in order to construct the set of candidate zones to be scanned, which is usually set to 50% of the total population. The performance of the circular scan method is affected by the choice of the population upper bound, and choosing an upper bound different from the default value can improve the method's performance. Recently, the Gini coefficient based on the Lorenz curve, which was originally used in economics, was proposed to determine a better population upper bound. We present the elbow method, a new method for choosing the population upper bound, which seeks to address some of the limitations of the Gini-based method while improving the performance of the circular scan method over the default value. To evaluate the performance of the proposed approach, we evaluate the sensitivity and positive predictive value of the circular scan method for publicly-available benchmark data for the default value, the Gini coefficient method, and the elbow method.