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Table 1 Evaluation of ordinary kriging and ordinary cokriging with various combinatorial approaches (evaluation results of top 10 best methods for each class of PTB prevalence)

From: Spatial variations of pulmonary tuberculosis prevalence co-impacted by socio-economic and geographic factors in People’s Republic of China, 2010

Variable Covariable Type of detrending Anisotropy Model Prediction errors Rank
Mean RMS Meanstan RMSStan ASE RMS AbsMeanStan RMSStan RMSASE Total
Smear positive PTB prevalence HDI + Elevation Global TRUE K-Bessel 0.07657 94.16 0.0006996 1.031 91.36 44.5 14.0 14.5 15.5 88.5
HDI + Elevation Neighborhood TRUE K-Bessel −0.02200 94.12 −0.0002937 1.037 90.83 40.0 6.0 46.5 43.5 136.0
HDI + Elevation Local TRUE Stable −0.08795 93.82 −0.0009434 1.038 90.47 15.5 21.0 53.0 49.5 139.0
HDI + Elevation Local TRUE Gaussian −0.12560 93.95 −0.0013150 1.037 90.63 29.0 36.0 46.5 48.0 159.5
HDI Local TRUE Pentaspherical 0.05834 93.54 0.0006271 1.044 89.66 1.0 12.0 79.0 76.0 168.0
HDI Global TRUE Stable 0.27480 94.02 0.0027300 1.028 91.52 34.0 122.0 10.0 9.0 175.0
HDI Neighborhood TRUE Stable 0.24590 93.87 0.0025130 1.033 90.94 22.5 110.0 22.5 23.0 178.0
HDI + Elevation Neighborhood TRUE Gaussian 0.05429 94.30 0.0005347 1.038 90.88 68.0 10.0 53.0 55.0 186.0
HDI + Elevation Local TRUE Pentaspherical 0.19470 93.57 0.0021250 1.039 90.08 2.5 78.0 56.5 59.0 196.0
HDI + Elevation Global TRUE Stable 0.28060 94.13 0.0028940 1.031 91.33 41.5 131.0 14.5 15.5 202.5
Mycobacterium positive PTB prevalence HDI + Elevation Global TRUE J-Bessel 0.87820 151.0 0.00587800 1.089 138.2 8.0 105.0 1.0 1.0 115.0
  Global TRUE Stable 0.24530 152.7 0.00135700 1.100 138.5 139.0 16.0 12.5 11.0 178.5
HDI Global TRUE J-Bessel 0.25230 152.6 0.00124300 1.107 137.4 127.5 13.0 28.0 28.0 196.5
Elevation Global TRUE Hole Effect 0.84340 152.3 0.00561100 1.094 138.8 103.0 95.0 2.0 2.0 202.0
HDI Global TRUE Hole Effect 0.07334 152.8 −0.00008275 1.106 137.7 149.0 1.0 27.0 27.0 204.0
Elevation Global TRUE J-Bessel 0.85340 152.5 0.00544800 1.099 138.4 117.5 83.0 9.5 8.5 218.5
Elevation Global TRUE K-Bessel 0.46630 153.0 0.00294700 1.101 138.5 184.5 31.0 15.5 16.5 247.5
  Neighborhood TRUE Stable 0.32670 152.7 0.00200600 1.117 136.3 139.0 20.0 48.5 49.0 256.5
HDI Neighborhood TRUE J-Bessel 0.50320 152.3 0.00318000 1.121 135.4 103.0 37.0 64.0 63.5 267.5
HDI + Elevation Neighborhood TRUE J-Bessel 1.27800 151.5 0.00886400 1.110 136.1 21.0 197.0 32.5 30.0 280.5
Active PTB prevalence HDI + Elevation Global FALSE Pentaspherical 0.5921 426.5 0.003456 1.255 333.5 28.5 55.0 44.0 54.5 182.0
HDI Global TRUE Gaussian 0.9281 432.5 0.002311 1.235 348.0 156.5 27.0 7.0 6.0 196.5
HDI + Elevation Global FALSE Tetraspherical 0.8312 426.8 0.004003 1.251 335.2 39.0 76.0 38.5 46.5 200.0
HDI Global TRUE K-Bessel 1.1140 432.0 0.002998 1.236 347.3 144.5 42.0 9.0 7.5 203.0
HDI Global TRUE Hole Effect 0.4762 433.4 0.001026 1.240 347.2 171.5 7.0 14.5 13.5 206.5
  Global FALSE Tetraspherical 0.5214 426.5 0.003206 1.261 331.9 28.5 49.0 55.5 73.5 206.5
HDI Global FALSE Tetraspherical 0.5249 426.5 0.003222 1.261 331.9 28.5 50.0 55.5 73.5 207.5
HDI + Elevation Global FALSE Spherical 1.1160 427.2 0.004647 1.247 336.8 48.5 90.0 30.0 39.0 207.5
  Global FALSE Pentaspherical 0.2991 426.2 0.002701 1.265 330.4 23.0 32.0 70.5 83.0 208.5
   Global FALSE Spherical 0.7560 426.8 0.003742 1.257 333.4 39.0 65.0 46.0 59.5 209.5
  1. PTB, pulmonary tuberculosis; HDI, human development index; RMS, root-mean-square; MeanStan, mean standardized; RMSStan, root-mean-square standardized; ASE, average standard errors; AbsMeanStan, absolute value of MeanStan; RMSASE, difference value of subtracting ASE from RMS.