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

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 & specificity^c	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.

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