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

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

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)
  1. D = disease status.
  2. *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.