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Table 3 League table presenting the multiple score comparison (MSC) meta-analysis (lower-left half of the table) and the direct random effects meta-analysis (upper-right half of the table)

From: Large-scale external validation and comparison of prognostic models: an application to chronic obstructive pulmonary disease

Direct meta- analysis
MSC meta- analysis
  GOLD B-AE-D GOLD (2011–2016) DOSE BODEx SAFE eBODE BODE BODE updated ADO
   1 2 3 4 5 6 7 8 9 10
GOLD A AUC = 0.613 (1st Qu. 0.587, 3rd Qu. 0.637) ΔAUC = 0.030 (−0.005, 0.065) 0.017 (−0.005, 0.038) 0.036 (0.008, 0.064) 0.054 (0.029, 0.079) 0.047 (0.027, 0.068) 0.064 (0.004, 0.123) 0.071 (0.040, 0.102) 0.080 (0.041, 0.119) 0.090 (0.072, 0.109)
B-AE-D B ΔAUC = 0.010 (−0.010, 0.031)   −0.004 (−0.025, 0.017) 0.004 (− 0.012, + 0.020) 0.025 (0.011, 0.039) NA 0.069 (−0.016, −0.121) 0.079 (0.004, 0.154) 0.082 (−0.012, −0.152) 0.076 (0.051, 0.101)
GOLD (2011–2016) C 0.012 (−0.001, 0.024) 0.001 (− 0.019, 0.021)   0.009 (− 0.002, 0.021) 0.028 (0.017, 0.039) 0.055 (0.038, 0.072) 0.047 (0.016, 0.079) 0.059 (0.046, 0.073) 0.051 (0.027, 0.076) 0.067 (0.053, 0.080)
DOSE D 0.022 (0.006, 0.037) 0.011 (−0.007, − 0.029) 0.010 (− 0.005, 0.025)   0.018 (0.008, −0.029) NA 0.039 (0.007, 0.070) 0.033 (−0.000, 0.065) 0.043 (−0.002, 0.088) 0.061 (−0.044, −0.079)
BODEx E 0.041 (0.027, 0.055) 0.030 (0.014, 0.047) 0.029 (0.015, 0.043) 0.019 (0.005, 0.033)   NA 0.030 (−0.001, 0.061) 0.031 (−0.017, 0.079) 0.039 (−0.028, 0.105) 0.050 (0.034, 0.066)
SAFE F 0.061 (0.034, 0.087) 0.050 (0.018, 0.082) 0.049 (0.022, 0.076) 0.039 (0.010, 0.068) 0.020 (−0.009, 0.048)   NA 0.011 (−0.000, 0.023) 0.005 (−0.009, 0.018) −0.007 (−0.029, 0.015)
eBODE G 0.065 (0.046, 0.085) 0.055 (0.032, 0.078) 0.054 (0.034, 0.074) 0.044 (0.023, 0.064) 0.024 (0.007, 0.042) 0.005 (−0.025, 0.035)   −0.001 (−0.020, 0.017) 0.002 (−0.031, 0.034) 0.024 (−0.018, 0.066)
BODE H 0.068 (0.052, 0.084) 0.057 (0.034, 0.080) 0.056 (0.039, 0.074) 0.046 (−0.027, −0.065) 0.027 (0.009, 0.045) 0.007 (−0.019, 0.034) 0.003 (−0.016, 0.021)   0.005 (−0.006, 0.017) −0.004 (−0.023, 0.016)
BODE upd. I 0.076 (0.058, 0.095) 0.066 (0.041, 0.091) 0.065 (0.045, 0.085) 0.055 (−0.033, −0.076) 0.036 (0.015, 0.056) 0.016 (−0.012, 0.043) 0.011 (−0.009, 0.031) 0.008 (−0.005, 0.022)   −0.005 (−0.032, 0.022)
ADO L 0.083 (0.070, 0.096) 0.072 (0.052, 0.093) 0.071 (0.056, 0.087) 0.070 (−0.052, −0.089) 0.042 (0.026, 0.058) 0.022 (−0.005, 0.050) 0.018 (−0.003, 0.038) 0.015 (−0.002, 0.032) 0.007 (−0.012, 0.026)  
  1. Abbreviations: AUC area under the curve; the lower-left half of the table refers to the MSC meta-analysis. The upper-right half of the table refers to direct comparisons using conventional random effects meta-analysis. The first cell (first row, first column) gives a reference value (in boldface), namely the median and 1st and 3rd quartiles of the AUC of the GOLD classification across cohorts as an anchor to interpret the differences in AUC between the prognostic scores. In every other cell, each pair of scores is compared using the difference in AUC. Lower-left half of the table we report in the correspondent cell the difference between the AUCs of the score in the row and the score in the column; instead, for the upper-right half of the table we report the difference between the AUCs of the score in the column and the score in the row or the. We decided for this representation to make a visual comparison between direct and MSC comparison easier; in this way, it is enough to look at corresponding values mirrored at the main diagonal. The 95% confidence interval is indicated in parentheses. For better readability of the table the sign “+” is omitted, while the sign “–” is indicated
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