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.
Low P-values indicate significant space-time clustering within the given time and distance intervals.
and V is the number of pairs (0,1,…, N11-1) less than or equal to the observed pairs N11 that are contained within the specfied time and distance parameters
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.
Knox, G. (1964). The detection of space-time interactions. Applied Statistics 13:25-29.