A Bayesian framework for estimating the incremental value of a diagnostic test in the absence of a gold standard

Table 1 Step-by-step calculation of Integrated Discrimination Improvement (IDI) when Test 2 (T2) has higher sensitivity than Test 1 (T1) ^*

T1, T2, D	Predicted probability conditional on T1 and T2 (P(D\|T1,T2))	Predicted probability conditional on T1 alone (P(D\|T1))	Difference	Weight (P(T1,T2\|D))	Contribution to IDI (weight × difference)
+ + +	0.96	0.75	0.21	0.56	0.12
+ - +	0.41	0.75	-0.34	0.14	-0.05
- + +	0.54	0.13	0.41	0.24	0.10
- - +	0.03	0.13	-0.1	0.06	-0.006
Incremental value among D + (Σweight × difference) = 0.17
+ + -	0.04	0.25	-0.21	0.01	-0.002
+ - -	0.59	0.25	0.34	0.09	0.03
- + -	0.46	0.87	-0.41	0.09	-0.04
- - -	0.97	0.87	0.1	0.81	0.08
Incremental value among D- (Σweight × difference) = 0.07
Overall incremental value = 0.24 (95% CrI: 0.10, 0.51)

D = disease status.
*S₁ = 0.7, C₁ = 0.9, S₂ = 0.8, C₂ = 0.9, π = 0.3. Median values of each parameter are listed here only for illustration purposes. Calculations take into account the entire posterior distribution of each parameter.

ISSN: 1471-2288