An approximation for the distribution of the scan statistic.

Area of Science:

• Epidemiology
• Biostatistics
• Spatial Statistics

Background:

• Scan statistics are used to detect disease clusters in time.
• Calculating exact probabilities for these clusters is computationally challenging with large datasets.
• Existing approximations may lack accuracy for hypothesis testing.

Purpose of the Study:

• To develop a more accurate and computationally feasible approximation for scan statistics.
• To provide a reliable method for hypothesis testing of temporal disease clusters.
• To address limitations in current probability calculations for scan statistics.

Main Methods:

• The study utilizes a 'moving window' approach to scan a time period T.
• An asymptotic upper bound approximation is derived for cluster probability calculations.
• The method is validated for both fixed and Poisson distributed event numbers (N).

Main Results:

• A novel approximation for scan statistic probabilities is presented.
• This approximation is computationally efficient and serves as an upper bound.
• It demonstrates improved accuracy for hypothesis testing compared to existing methods.

Conclusions:

• The proposed approximation offers a practical and accurate solution for analyzing temporal disease clusters.
• This method is particularly useful when dealing with large numbers of events.
• The approach was illustrated using data on spontaneous abortions in New York City.