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Table 2 Numerical illustration for calculating RPB of hypothetical continuous markers using data of three cancers as examples

From: Quantification of population benefit in evaluation of biomarkers: practical implications for disease detection and prevention

Biomarker/exposure characteristicsa Ratio of population benefit (RPB) Net benefit (NB)
(Threshold)b OR PAR% Sen. Spe. RPB RPB RPB NB NB NB
      (EA, f 0.03) (Breast ca, f 0.06) (Ovarian ca, f=0.15) (EA, f=0.03) (Breast ca, f=0.06) (Ovarian ca, f=0.15)
Fixed sensitivity (95%) 1.5 33.22 0.95 0.07 -0.456 -0.659 -0.812 -0.018 -0.046 -0.129
  2 48.88 0.95 0.09 -0.440 -0.641 -0.792 -0.017 -0.045 -0.126
  4 71.30 0.95 0.16 -0.389 -0.583 -0.728 -0.015 -0.040 -0.115
  10 84.46 0.95 0.29 -0.287 -0.466 -0.601 -0.011 -0.032 -0.095
  20 89.01 0.95 0.43 -0.187 -0.352 -0.475 -0.007 -0.024 -0.075
  50 92.25 0.95 0.61 -0.051 -0.196 -0.305 -0.002 -0.014 -0.048
Fixed specificity (95%) 1.5 2.59 0.08 0.95 -0.019 -0.032 -0.043 -0.001 -0.002 -0.007
  2 4.95 0.10 0.95 -0.013 -0.029 -0.041 -0.001 -0.002 -0.007
  4 12.67 0.17 0.95 0.006 -0.018 -0.036 0.000 -0.001 -0.006
  10 27.40 0.31 0.95 0.041 0.002 -0.028 0.002 0.000 -0.004
  20 41.15 0.44 0.95 0.074 0.021 -0.019 0.003 0.001 -0.003
  50 60.16 0.62 0.95 0.119 0.047 -0.008 0.005 0.003 -0.001
Balanced sensitivity & specificityc 1.5 14.83 0.54 0.54 -0.208 -0.316 -0.397 -0.008 -0.022 -0.063
  2 23.89 0.57 0.57 -0.178 -0.285 -0.366 -0.007 -0.020 -0.058
  4 42.57 0.64 0.63 -0.114 -0.222 -0.304 -0.005 -0.015 -0.048
  10 60.28 0.72 0.72 -0.030 -0.137 -0.218 -0.001 -0.010 -0.035
  20 70.68 0.78 0.77 0.024 -0.085 -0.166 0.001 -0.006 -0.026
  50 80.17 0.84 0.84 0.088 -0.020 -0.101 0.003 -0.001 -0.016
  1. Numerical relationships between Odds ratio and PAR% of continuous markers and their RPB based on the data of three studies.
  2. ca= cancer. EA= esophageal adenocarcinoma. f = loss-adjustment factor of quality-adjusted life year. NB= net benefit.
  3. OR= odds ratio. Sen.= sensitivity, Spe.= specificity.
  4. The disease prevalence of population used for the table = 0.01. As shown in the formula of RPB for continuous markers, disease prevalence w will directly affect the value of RPB.
  5. aHypothetical continuous biomarker/exposure with assumed distributions as described in Figure 1.
  6. bThreshold used for continuous biomarkers positive are the thresholds shown in Figure 1 (three vertical bars).
  7. cUsing a threshold that lead to sensitivity and specificity closest to the upper left corner of ROC curve coordinates for cutoff.