Knox Statistic for Space-Time Clustering
The Knox approach is used to test whether there is a statistically significant cluster within a defined distance and time period. The pairs of points within the specified space and time intervals are counted and compared to the expected number of points within the same intervals. A P-value based on the poisson distribution is then calculated.
Input
Analysis
Low P-values indicate significant space-time clustering within the given time and distance intervals.
Formula
and V is the number of pairs (0,1,…, N_{11}-1) less than or equal to the observed pairs N_{11 }that are contained within the specfied time and distance parameters
Output
Example
For this example cases of an infectious disease during an outbreak over a period of 325 days will be considered. The data includes the X and Y coordinates in meters and the time in days, from the beginning of the epidemic, of the onset of each case. A sample of the input data file is shown in Table 1.
Table 1: Input File
X Y time 138902 58938 1 137625 59262 31 138431 58633 32 138637 58586 35 137738 58994 39 . . . . . . . . . 139641 61019 325
The disease is transmitted by a vector that is believed to operate over short distances (less than 35 meters). It is also believed that the symptoms of the victims would become evident within 5 days of infection. Consequently, we will use a space-time window of 35 meters and 5 days. The results of the Knox test are shown in Table 2.
Table 2: Output File
The input data file: epid.dat The output data file: epid.out DISTANCE TIME N11 N12 N21 N22 EN11 P 35.000 5.00 67 175 3507 39322 20.081 0.00000
The output shows that 67 pairs of points fell within the specified space-time window, and the expected number of points within this window (EN11) is calculated as 20.081. The very small P value indicates that there is significant clustering of cases within the space and time interval of 35 meters and 5 days.
References
Knox, G. (1964). The detection of space-time interactions. Applied Statistics 13:25-29.