Table 2.
Numerical illustration for calculating RPB of hypothetical continuous markers using data of three cancers as examples
|
Biomarker/exposure characteristics
a
|
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 | |
Numerical relationships between Odds ratio and PAR% of continuous markers and their RPB based on the data of three studies.
ca= cancer. EA= esophageal adenocarcinoma. f = loss-adjustment factor of quality-adjusted life year. NB= net benefit.
OR= odds ratio. Sen.= sensitivity, Spe.= specificity.
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.
aHypothetical continuous biomarker/exposure with assumed distributions as described in Figure 1.
bThreshold used for continuous biomarkers positive are the thresholds shown in Figure 1 (three vertical bars).
cUsing a threshold that lead to sensitivity and specificity closest to the upper left corner of ROC curve coordinates for cutoff.