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. 2022 Mar 21;22:274. doi: 10.1186/s12879-022-07274-w

Table 2.

Selected resultant rules from the ARM algorithm DESigFAR

(a) Rules for wave-1&2 local case rate; POI accessibility was used P
Antecedent Consequent Supp Conf Lev Imp
1 prop_higher_edu > 0.361 (p85) rate_local12 > 0.143 (p86) 10.73 0.33 5.98 0.18 3.34E−05
2 med_income > 18,518.024 (p62) rate_local12 > 0.136 (p85) 20.40 0.24 7.24 0.09 5.54E−05
3 med_area_home > 16.093 (p47) rate_local12 > 0.136 (p85) 26.44 0.23 8.43 0.07 6.08E−05
4 gender_ratio > 106.692 (p92) rate_local12 > 0.107 (p81) 9.88 0.57 6.33 0.36 1.48E−05
5 prop_over65 > 0.204 (p84) rate_local12 < 0.005 (p45) 25.42 0.76 10.35 0.31 6.96E−05
6 prop_private_resid > 0.101 (p66) rate_local12 > 0.046 (p63) 39.60 0.52 11.15 0.15 2.84E−06
7 prop_private_resid < 0.011 (p28) rate_local12 < 0.002 (p45) 43.51 0.74 16.71 0.28 1.14E−07
8 prop_industrial < 0.001 (p47) rate_local12 > 0.104 (p80) 33.96 0.34 12.94 0.13 3.96E−06
9 LU_entropy < 0.543 (p46) rate_local12 > 0.106 (p80) 29.65 0.30 9.50 0.10 6.50E−05
10 LU_entropy > 0.543 (p46) rate_local12 = 0.006–0.106 (p45-80) 54.87 0.47 15.52 0.13 1.60E−06
11 prop_rural_set < 0.008 (p56) rate_local12 > 0.038 (p60) 61.34 0.52 13.81 0.12 6.93E−05
(b) Rules for wave-1&2 imported case rate; POI accessibility was used
Antecedent Consequent Supp Conf Lev Imp P
1 prop_higher_edu > 0.364 (p85) rate_imported12 > 0.124 (p71) 24.89 0.78 15.77 0.49 6.85E−11
2 prop_higher_edu < 0.170 (p37) rate_imported12 < 0.039 (p50) 57.65 0.73 17.91 0.23 3.65E−07
3 med_income > 19,583.009 (p65) rate_imported12 > 0.110 (p70) 44.69 0.62 22.24 0.31 1.22E-15
4 med_income < 19,583.009 (p65) rate_imported12 < 0.110 (p70) 120.22 0.85 22.51 0.16 1.22E-15
5 med_area_home > 25.388 (p86) rate_imported12 > 0.169 (p78) 19.27 0.66 12.70 0.44 1.69E-12
6 gender_ratio > 94.842 (p64) rate_imported12 > 0.207 (p81) 26.22 0.32 10.36 0.13 6.60E−05
7 prop_over65 < 0.140 (p35) rate_imported12 > 0.083 (p65) 38.57 0.53 11.66 0.16 5.07E−05
8 prop_over65 > 0.140 (p35) rate_imported12 < 0.083 (p65) 100.87 0.72 11.69 0.08 5.07E−05
9 ave_household_size > 3.250 (p87) rate_imported12 > 0.110 (p70) 20.27 0.76 11.98 0.45 6.18E−09
10 den_population = 673.564–26,483.860 (p13-60) rate_imported12 > 0.084 (p66) 46.61 0.48 11.11 0.11 2.65E−05
11 den_public_trans < 3.592 (p25) rate_imported12 < 0.004 (p36) 33.98 0.63 14.57 0.27 1.77E−06
12 den_population < 673.564 (p13) rate_imported12 < 0.004 (p36) 18.89 0.70 9.22 0.34 3.94E−06
13 build_area_pp > 75.116 (p54) &prop_private_resid > 0.239 (p85) rate_imported12 > 0.184 (p80) 8.11 0.85 6.08 0.49 6.97E−05
14 prop_private_resid < 0.002 (p19) rate_imported12 < 0.005 (p36) 30.69 0.75 16.01 0.39 4.10E−09
15 prop_publicResid < 0.034 (p69) rate_imported12 > 0.103 (p69) 62.20 0.43 15.37 0.11 1.72E−08
16 prop_industrial < 0.000 (p43) rate_imported12 > 0.097 (p68) 44.29 0.49 13.89 0.15 1.39E−06
17 LU_entropy < 0.561 (p51) rate_imported12 > 0.099 (p68) 48.70 0.45 12.73 0.12 5.05E−05
18 LU_entropy > 0.561 (p51) rate_imported12 = 0.001–0.099 (p36-68) 46.64 0.44 13.70 0.13 6.21E−05
19 build_area_pp = 51.859–202.851 (p43-89) rate_imported12 > 0.105 (p69) 47.53 0.48 15.73 0.16 3.57E−07
20 build_area_pp > 71.028 (p53) &prop_rural_set > 0.026 (p66) rate_imported12 < 0.004 (p36) 26.61 0.69 12.69 0.22 1.88E−05
21 prop_agricultural > 0.055 (p81) rate_imported12 < 0.003 (p36) 25.97 0.63 11.25 0.27 2.23E−05
22 prop_gov_insti_faci > 0.030 (p41) rate_imported12 = 0.003–0.124 (p36-71) 62.21 0.49 16.38 0.13 3.90E−08
23 prop_transport > 0.121 (p50) rate_imported12 = 0.004–0.080 (p36-64) 43.70 0.40 12.51 0.11 4.34E−05
24 POI_pp_sports > 30.523 (p67) rate_imported12 > 0.196 (p80) 28.89 0.41 14.60 0.21 5.62E−08
25 POI_pp_telecom_elec > 25.431 (p76) rate_imported12 > 0.213 (p81) 24.73 0.46 14.51 0.27 5.34E−10
26 POI_pp_transport > 39.200 (p61) rate_imported12 > 0.188 (p80) 32.28 0.37 14.25 0.17 1.27E−07
27 POI_pp_mall_mkt > 10.941 (p75) rate_imported12 > 0.202 (p80) 25.16 0.45 14.06 0.25 1.15E−08
28 POI_pp_edu > 22.306 (p79) rate_imported12 > 0.187 (p80) 22.41 0.48 12.67 0.27 2.78E−08
29 POI_pp_telecom_elec < 6.513 (p36) rate_imported12 = 0.004–0.091 (p36-67) 48.88 0.64 25.23 0.33 1.78E−15
30 POI_pp_sports < 6.556 (p22) rate_imported12 = 0.004–0.108 (p36-70) 37.48 0.77 21.29 0.44 1.32E−13
31 POI_pp_edu < 3.533 (p20) rate_imported12 = 0.003–0.078 (p36-64) 32.83 0.75 20.52 0.47 8.59E−14
32 POI_pp_mall_mkt < 1.922 (p22) rate_imported12 = 0.003–0.083 (p36-66) 33.73 0.73 20.19 0.44 8.37E−12
33 POI_pp_transport < 4.899 (p9) rate_imported12 = 0.003–0.084 (p36-66) 18.09 0.89 12.07 0.59 1.59E−08
34 POI_pp_transport = 4.899–8.368 (p9-19) rate_imported12 = 0.003–0.084 (p36-66) 14.37 0.74 8.63 0.44 1.21E−05
(c) Rules for wave-3 local case rate; POI accessibility was used
Antecedent Consequent Supp Conf Lev Imp P
1 prop_higher_edu < 0.237 (p62) rate_local3 > 0.335 (p53) 75.42 0.57 14.15 0.11 7.00E−06
2 prop_higher_edu > 0.237 (p62) rate_local3 < 0.335 (p53) 58.31 0.71 13.93 0.17 7.00E−06
3 med_income < 15,406.084 (p39) rate_local3 > 0.335 (p53) 57.08 0.66 16.75 0.19 1.49E−06
4 med_income > 24,009.220 (p79) rate_local3 < 0.335 (p53) 38.57 0.84 13.99 0.31 3.40E−07
5 med_area_home < 13.826 (p27) rate_local3 > 0.340 (p54) 43.20 0.76 16.91 0.30 1.26E−08
6 med_area_home > 19.838 (p65) rate_local3 < 0.340 (p54) 56.62 0.75 15.50 0.20 5.08E−08
7 prop_over65 > 0.141 (p36) rate_local3 > 0.274 (p47) 85.51 0.61 10.65 0.08 8.15E−05
8 prop_over65 < 0.141 (p36) rate_local3 < 0.274 (p47) 44.95 0.61 10.53 0.14 8.15E−05
9 ave_household_size < 2.580 (p17) rate_local3 > 0.621 (p79) 18.74 0.43 9.54 0.22 2.66E−05
10 ave_household_size > 2.925 (p63) rate_local3 < 0.621 (p79) 78.93 0.91 9.95 0.11 8.13E−05
11 den_population > 21,684.808 (p53) rate_local3 > 0.267 (p47) 68.18 0.69 14.02 0.14 3.31E−05
12 den_road > 9.024 (p43) rate_local3 > 0.407 (p59) 59.85 0.49 11.28 0.09 5.28E−05
13 den_bldg > 0.136 (p43) rate_local3 > 0.411 (p59) 59.27 0.47 10.35 0.08 8.32E−05
14 den_population < 21,684.808 (p53) rate_local3 < 0.267 (p47) 66.24 0.58 14.34 0.13 3.31E−05
15 den_public_trans < 4.083 (p28) rate_local3 < 0.016 (p15) 23.50 0.40 14.24 0.24 9.33E-10
16 den_road < 9.024 (p43) rate_local3 < 0.407 (p59) 66.36 0.73 11.35 0.12 5.28E−05
17 den_bldg < 0.136 (p43) rate_local3 < 0.411 (p59) 64.66 0.72 10.38 0.12 8.32E−05
18 prop_higher_edu < 0.212 (p54) &prop_private_resid > 0.104 (p66) rate_local3 > 0.372 (p57) 17.56 0.94 9.55 0.39 3.17E−05
19 prop_private_resid < 0.021 (p36) rate_local3 < 0.041 (p16) 22.79 0.30 10.35 0.14 4.46E−05
20 prop_publicResid > 0.063 (p74) rate_local3 > 0.295 (p50) 40.41 0.74 12.49 0.23 6.57E−05
21 prop_publicResid < 0.063 (p74) rate_local3 < 0.295 (p50) 90.45 0.57 12.43 0.08 6.57E−05
22 med_income < 18,723.236 (p62) &prop_rural_set < 0.000 (p44) &prop_industrial < 0.008 (p69) rate_local3 > 0.428 (p63) 29.28 0.77 15.05 0.15 6.34E−05
23 build_area_pp < 61.380 (p50) rate_local3 > 0.222 (p38) 75.64 0.75 14.46 0.14 6.15E−06
24 build_area_pp > 61.380 (p50) rate_local3 < 0.222 (p38) 58.89 0.52 14.37 0.13 6.15E−06
25 med_income < 23,040.421 (p78) &prop_agricultural < 0.028 (p72) rate_local3 > 0.335 (p53) 72.65 0.64 20.12 0.09 5.81E−05
26 ave_household_size < 2.636 (p29) &prop_rural_set < 0.001 (p46) rate_local3 > 0.493 (p68) 25.71 0.65 13.15 0.17 5.45E−05
27 prop_shrubland < 0.009 (p30) rate_local3 > 0.570 (p76) 28.29 0.43 12.25 0.19 1.27E−05
28 prop_woodland < 0.012 (p22) rate_local3 > 0.409 (p59) 30.91 0.65 12.19 0.26 1.01E−05
29 prop_grassland < 0.000 (p16) rate_local3 > 0.500 (p68) 21.99 0.64 11.34 0.33 1.08E−05
30 prop_woodland > 0.322 (p82) rate_local3 < 0.409 (p59) 34.03 0.87 10.45 0.27 3.92E−05
31 prop_shrubland > 0.281 (p89) rate_local3 < 0.166 (p30) 16.40 0.71 9.31 0.40 1.54E−06
32 prop_open_recreation < 0.002 (p14) rate_local3 < 0.016 (p15) 13.07 0.44 8.31 0.28 9.22E−06
33 med_income < 17,081.439 (p53) &prop_open_recreation > 0.026 (p45) rate_local3 > 0.352 (p56) 49.42 0.71 18.23 0.11 1.03E−05
34 prop_higher_edu < 0.224 (p58) &prop_gov_insti_faci > 0.027 (p38) rate_local3 > 0.297 (p50) 54.45 0.74 17.12 0.12 6.17E−05
35 prop_transport > 0.141 (p55) rate_local3 > 0.382 (p57) 54.56 0.56 13.89 0.14 4.17E−05
36 prop_business > 0.039 (p84) rate_local3 > 0.518 (p71) 19.10 0.54 8.80 0.25 2.87E−05
37 prop_higher_edu < 0.222 (p58) &POI_pp_sports < 12.643 (p42) rate_local3 > 0.277 (p47) 49.14 0.79 16.23 0.13 7.74E−05
38 med_income < 19,861.505 (p65) &POI_pp_edu < 19.291 (p73) rate_local3 > 0.180 (p33) 94.43 0.80 15.87 0.06 2.84E−05
39 prop_higher_edu < 0.228 (p61) &POI_pp_mall_mkt < 9.663 (p69) rate_local3 > 0.233 (p39) 75.07 0.74 15.46 0.06 4.66E−05
40 POI_pp_transport < 16.809 (p38) rate_local3 > 0.191 (p35) 65.98 0.84 14.48 0.18 1.67E−07
41 POI_pp_telecom_elec < 6.955 (p37) rate_local3 > 0.193 (p35) 65.22 0.82 13.81 0.17 2.01E−06
(d) Rules for wave-4 local case rate; POI accessibility was used
Antecedent Consequent Supp Conf Lev Imp P
1 med_income < 12,559.030 (p7) rate_local4 > 0.831 (p79) 8.91 0.64 5.86 0.42 2.82E−05
2 med_income < 29,532.689 (p84) &prop_grassland < 0.007 (p31) rate_local4 > 0.852 (p80) 30.41 0.62 20.17 0.13 4.52E−05
3 med_income < 23,878.185 (p79) &den_bldg > 0.293 (p72) rate_local4 > 0.774 (p75) 29.22 0.65 17.99 0.13 5.12E−05
4 med_area_home < 15.641 (p45) rate_local4 > 0.299 (p29) 74.53 0.81 9.64 0.10 7.30E−05
5 med_area_home > 15.641 (p45) rate_local4 < 0.299 (p29) 45.56 0.37 9.68 0.08 7.30E−05
6 gender_ratio > 109.623 (p94) rate_local4 < 0.334 (p34) 10.16 0.79 5.84 0.45 5.99E−05
7 prop_over65 > 0.229 (p93) rate_local4 < 0.299 (p29) 11.05 0.78 6.81 0.48 2.32E−05
8 ave_household_size < 2.713 (p37) rate_local4 > 0.865 (p80) 27.87 0.38 12.90 0.17 2.34E−07
9 den_road > 16.383 (p71) rate_local4 > 0.722 (p72) 36.83 0.60 19.40 0.31 4.63E−12
10 den_bldg > 0.226 (p62) rate_local4 > 0.603 (p64) 50.39 0.60 18.56 0.22 3.09E−07
11 den_population > 26,219.620 (p60) rate_local4 > 0.466 (p46) 63.71 0.71 16.81 0.19 1.21E−06
12 den_public_trans > 95.120 (p92) rate_local4 > 0.780 (p76) 12.45 0.67 7.89 0.42 1.19E−05
13 den_road < 16.383 (p71) rate_local4 < 0.722 (p72) 128.58 0.84 19.36 0.13 4.63E-12
14 den_bldg < 0.226 (p62) rate_local4 < 0.603 (p64) 99.30 0.76 18.44 0.14 3.09E−07
15 den_population < 26,219.620 (p60) rate_local4 < 0.466 (p46) 75.80 0.61 16.78 0.14 1.21E−06
16 den_public_trans < 46.130 (p78) rate_local4 < 0.780 (p76) 136.41 0.85 15.26 0.10 4.31E-10
17 prop_private_resid > 0.087 (p64) rate_local4 > 0.731 (p73) 36.23 0.45 13.84 0.17 1.00E−06
18 prop_private_resid < 0.022 (p36) rate_local4 < 0.117 (p14) 22.60 0.29 11.64 0.15 2.50E−08
19 prop_publicResid > 0.042 (p70) rate_local4 = 0.168–1.073 (p16-87) 56.16 0.86 10.24 0.16 3.66E−05
20 prop_industrial < 0.000 (p36) rate_local4 > 1.033 (p86) 23.82 0.31 12.74 0.17 2.01E−07
21 LU_entropy < 0.548 (p47) rate_local4 > 0.863 (p80) 34.55 0.34 14.21 0.14 1.67E−07
22 LU_entropy > 0.548 (p47) rate_local4 = 0.140–0.863 (p14-80) 90.44 0.80 17.54 0.15 3.55E−08
23 build_area_pp < 58.100 (p47) rate_local4 > 0.222 (p21) 83.55 0.87 10.09 0.11 1.52E−05
24 build_area_pp > 58.100 (p47) rate_local4 < 0.222 (p21) 36.65 0.31 9.66 0.08 1.52E−05
25 prop_rural_set < 0.001 (p46) rate_local4 > 0.630 (p64) 50.56 0.52 15.79 0.16 4.68E−05
26 prop_agricultural > 0.017 (p64) rate_local4 < 0.430 (p43) 46.73 0.61 13.80 0.18 5.87E−06
27 prop_shrubland < 0.000 (p0) rate_local4 > 0.785 (p76) 27.11 0.71 17.92 0.47 4.93E−14
28 prop_agricultural < 0.001 (p40) rate_local4 > 0.766 (p74) 39.90 0.46 17.43 0.20 1.13E−08
29 prop_grassland < 0.004 (p23) rate_local4 > 0.848 (p80) 28.16 0.56 17.42 0.34 1.39E-13
30 prop_woodland < 0.016 (p25) rate_local4 > 1.282 (p90) 15.27 0.29 10.03 0.19 3.76E−08
31 prop_shrubland > 0.064 (p49) rate_local4 < 0.785 (p76) 101.16 0.90 15.67 0.14 2.93E−07
32 prop_grassland > 0.085 (p71) rate_local4 < 0.188 (p16) 20.40 0.32 9.55 0.15 6.50E−06
33 prop_open_recreation > 0.030 (p48) &LU_entropy < 0.551 (p49) rate_local4 > 0.804 (p78) 26.92 0.55 15.70 0.18 7.19E−06
34 prop_gov_insti_faci > 0.025 (p36) &LU_entropy < 0.546 (p47) rate_local4 > 0.765 (p74) 29.27 0.51 14.66 0.11 5.00E−05
35 prop_transport > 0.241 (p71) rate_local4 > 0.897 (p81) 25.98 0.43 14.55 0.24 3.65E−08
36 prop_business > 0.058 (p86) rate_local4 > 0.784 (p76) 18.49 0.65 11.61 0.41 1.45E−08
37 med_income < 24,082.337 (p79) &prop_rural_set < 0.001 (p46) &POI_pp_sports > 19.996 (p53) rate_local4 > 0.827 (p79) 19.48 0.68 13.18 0.22 4.62E−05
38 med_income < 24,082.337 (p79) &den_road > 10.205 (p48) &POI_pp_mall_mkt > 6.459 (p57) rate_local4 > 0.895 (p81) 18.62 0.63 13.02 0.22 4.56E−05
39 med_income < 23,241.294 (p78) &prop_rural_set < 0.002 (p49) &POI_pp_transport > 32.416 (p54) rate_local4 > 0.815 (p78) 18.37 0.70 12.49 0.24 6.88E−05
40 POI_pp_sports > 33.191 (p70) rate_local4 < 0.062 (p13) 22.58 0.35 14.17 0.22 8.48E−12
41 POI_pp_telecom_elec > 30.272 (p80) rate_local4 < 0.039 (p13) 19.74 0.45 14.04 0.32 3.55E−13
42 POI_pp_transport > 68.907 (p80) rate_local4 < 0.048 (p13) 19.71 0.45 14.01 0.32 7.44E−15
43 POI_pp_edu > 25.063 (p83) rate_local4 < 0.061 (p13) 15.92 0.40 10.72 0.27 2.21E−09
44 POI_pp_mall_mkt > 19.264 (p88) rate_local4 < 0.071 (p13) 12.77 0.48 9.31 0.35 2.60E−09
(e) Rules for wave-4 local case rate, excluding cases in the Dancing/Singing Cluster; POI accessibility was used
Antecedent Consequent Supp Conf Lev Imp P
1 prop_higher_edu < 0.346 (p82) &prop_rural_set < 0.000 (p43) rate_local4nondance > 0.389 (p53) 48.36 0.76 18.27 0.14 2.36E−05
2 prop_higher_edu < 0.342 (p81) &den_road > 11.532 (p53) rate_local4nondance > 0.421 (p58) 49.83 0.68 17.91 0.09 2.44E−05
(f) Rules for wave-3 local case rate; POI density was used
Antecedent Consequent Supp Conf Lev Imp P
1 POI_den_mall_mkt > 307.693 (p78) rate_local3 > 0.547 (p72) 24.39 0.53 12.21 0.26 5.24E−06
2 POI_den_sports > 882.075 (p78) rate_local3 > 0.528 (p71) 24.72 0.55 11.96 0.26 4.03E−06
3 POI_den_telecom_elec > 540.287 (p78) rate_local3 > 0.539 (p71) 24.30 0.53 11.95 0.26 2.43E−06
4 POI_den_transport > 1382.534 (p79) rate_local3 > 0.530 (p71) 24.57 0.54 11.70 0.26 1.18E−05
5 POI_den_edu > 611.274 (p81) rate_local3 > 0.558 (p74) 21.47 0.51 10.87 0.26 2.04E−05
(g) Rules for wave-4 local case rate; POI density was used
Antecedent Consequent Supp Conf Lev Imp P
1 POI_den_transport > 904.959 (p71) rate_local4 > 0.726 (p73) 36.27 0.60 19.27 0.32 1.95E−14
2 POI_den_mall_mkt > 208.752 (p73) rate_local4 > 0.753 (p74) 34.64 0.58 19.11 0.32 1.82E−11
3 POI_den_sports > 598.644 (p72) rate_local4 > 0.751 (p74) 34.76 0.58 19.11 0.32 9.18E−12
4 POI_den_telecom_elec > 374.340 (p72) rate_local4 > 0.741 (p74) 34.54 0.58 18.63 0.31 9.93E−12
5 POI_den_edu > 1372.584 (p94) rate_local4 > 0.751 (p74) 10.59 0.79 7.09 0.53 5.28E−07
(h) Rules for average waiting period; POI accessibility was used
Antecedent Consequent Supp Conf Lev Imp P
1 POI_pp_transport > 39.683 (p60) ave_waiting_period > 5.790 (p75) 22.98 0.34 9.81 0.14 6.65E−05
2 POI_pp_telecom_elec > 15.395 (p57) ave_waiting_period > 5.765 (p74) 24.76 0.33 9.65 0.13 7.16E−05
3 POI_pp_mall_mkt > 8.676 (p64) ave_waiting_period > 5.822 (p75) 20.26 0.33 8.90 0.14 0.0001
4 med_area_home > 17.644 (p50) ave_waiting_period > 5.807 (p75) 26.33 0.29 8.89 0.10 1.14E−05
5 med_income > 19,979.413 (p60) ave_waiting_period > 5.751 (p74) 21.18 0.33 8.39 0.13 9.48E−05
6 POI_pp_sports > 29.352 (p65) ave_waiting_period > 6.163 (p81) 16.16 0.27 8.26 0.14 1.53E−07
7 POI_pp_edu > 14.015 (p63) ave_waiting_period > 5.788 (p75) 20.68 0.31 7.75 0.12 0.0002
(i) Rules for median waiting period; POI accessibility was used
Antecedent Consequent Supp Conf Lev Imp P
1 med_area_home > 18.602 (p52) med_waiting_period > 4.392 (p67) 31.27 0.38 10.07 0.12 0.0002
2 med_income > 19,680.813 (p60) med_waiting_period > 5.030 (p82) 17.80 0.27 7.39 0.11 0.0002
3 build_area_pp > 57.721 (p46) med_waiting_period > 5.317 (p82) 19.22 0.18 6.54 0.06 0.0002

For clarity, the antecedent and consequent of each rule are put in separate columns. For example, rule 1 in Table 2a is “prop_higher_edu > 0.361 (p85) → rate_local12 > 0.143 (p86)”, where p85 means the 85th percentile of the variable among the 214 TPU-level areal units in Hong Kong. Variables in the rules are described in Table 1. Rules are shown together with the values of four RIMs: support (supp), confidence (conf), leverage (lev), and improvement (imp). P is the P value of each rule in the chi-square test described in the Methods. The full sets of resultant rules are shown in Table S2 in Additional File 1