Reproductive outcome data are often screened for clusters of events, with a view toward determining the factors that may have caused the cluster. Clusters of interest could occur sporadically in time, or in a cyclical fashion. A test for either type of clustering should be easy to apply, and should have high power against alternatives of interest. We propose to investigate two statistics that satisfy the above requirements. The first is the scan statistic, which counts the number of events in every interval of prespecified length, s, and identifies a cluster as statistically significant at level Alpha if the maximum exceeds a critical value nAlpha. The second is the cusum statistic, which can be viewed as the maximum sum over arbitrary time intervals of """"""""excess' outcomes relative to some pre-set value. We plan to study the relationship between these statistics, to publish tables or simple formulas which will allow these statistics to be used on a routine basis, and investigate power gainst alternatives of epidemiologic importance. We plan to tabulate critical values of the scan statistic for N = 100 or more and to give a simple formula relating nAlpha, N, and s so that tables of critical values can be easily constructed. Algorithms will be developed that will allow power to be tabulated and the consequences of misspecifying is to be determined. We suggest a new modification of the cusum test procedure so that conventional percentage points can be determined given a specification of the minimum effect size that we want to detect. We plan extensive comparisons between the power of the cusum and scan statistics under various alternatives, and also between these and a statistic due to Chernoff and Zacks. We propose to give a series of tables and formulas such that the scan statistic can be applied to test for seasonal clustering, and compare the power of this test with other tests previously suggested for this purpose.
| Wallenstein, S; Naus, J; Glaz, J (1993) Power of the scan statistic for detection of clustering. Stat Med 12:1829-43 |
| Wallenstein, S; Gould, M S; Kleinman, M (1989) Use of the scan statistic to detect time-space clustering. Am J Epidemiol 130:1057-64 |
| Wallenstein, S; Weinberg, C R; Gould, M (1989) Testing for a pulse in seasonal event data. Biometrics 45:817-30 |
| Wallenstein, S; Neff, N (1987) An approximation for the distribution of the scan statistic. Stat Med 6:197-207 |
