Power of the scan statistic for detection of clustering.

The scan statistic is the maximum number of events in an interval of fixed length w as the subinterval moves over the entire time frame. Previous research derived the null distribution of the scan statistic under the conditional model which assumed that the total number of events was fixed, and under the unconditional model which let the total number of events be a random variable. This paper derives approximations for the power of the scan test for a pulse alternative. Under this alternative, the relative risk of disease on a subinterval (tau, tau + w), tau unknown, is theta-fold as high as it is for other subintervals of length w. Two sets of approximations are given for each model. The first approximation gives highly accurate results, but requires use of a personal computer. The second procedure can be performed on a hand-held calculator and appears very accurate for the cases examined.

[1]  On the Distributions of Scan Statistics , 1984 .

[2]  R. Lancashire,et al.  Detection of minimal epidemics. , 1982, Statistics in medicine.

[3]  F. Hwang.  A Generalization of the Karlin-McGregor Theorem on Coincidence Probabilities and an Application to Clustering , 1977 .

[4]  Joseph Glaz,et al.  Approximations and Bounds for the Distribution of the Scan Statistic , 1989 .

[5]  J. Naus.  The Distribution of the Size of the Maximum Cluster of Points on a Line , 1965 .

[6]  Noel A Cressie.  Some properties of scan statistic on circle and line , 1977 .

[7]  Joseph Naus,et al.  Some Probabilities, Expectations and Variances for the Size of Largest Clusters and Smallest Intervals , 1966 .

[8]  Mark Berman,et al.  A Useful Upper Bound for the Tail Probabilities of the Scan Statistic When the Sample Size is Large , 1985 .

[9]  Joseph Naus,et al.  Probabilities for a $k$th Nearest Neighbor Problem on the Line , 1973 .

[10]  Joseph Naus,et al.  Approximations for Distributions of Scan Statistics , 1982 .

[11]  A Simpler Expression for $K$th Nearest Neighbor Coincidence Probabilities , 1975 .

[12]  S Wallenstein,et al.  An approximation for the distribution of the scan statistic. , 1987, Statistics in medicine.

[13]  Catherine Macken,et al.  Some statistical problems in the assessment of inhomogeneities of DNA sequence data , 1991 .

[14]  S Wallenstein,et al.  A test for detection of clustering over time. , 1980, American journal of epidemiology.

[15]  Joseph Naus,et al.  Tight Bounds and Approximations for Scan Statistic Probabilities for Discrete Data , 1991 .

[16]  S. Wallenstein,et al.  Probabilities for the Size of Largest Clusters and Smallest Intervals , 1974 .

[17]  Noel A Cressie,et al.  On some properties of the scan statistic on the circle and the line , 1977, Journal of Applied Probability.