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Table 4 Sensitivity to prior distribution for the case when both sensitivity and specificity of the second test are better than the first test (true values are S 1 = 0.7, C 1 = 0.9)

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

Conditional Independence Model
Prior information on T1 sensitivity and specificity IDI (True value 0.3) AUCdiff(True value 0.14)
Bias Length Coverage Bias Length Coverage
Informative priors centered at true values* 0.001 0.43 1 -0.003 0.14 0.99
Degenerate priors at true values: S1 = 0.7, C1 = 0.9 0.006 0.19 0.95 -0.001 0.07 1
Degenerate priors, but not at true values: S1 = 0.8, C1 = 0.925 -0.17 0.08 0 -0.07 0.04 0
Informative priors covering but not centered on true values (centered on S1 = 0.8, C1 = 0.925) -0.16 0.42 0.99 -0.07 0.15 1
  1. *S1 ~ Beta(58.1, 24.9) (95% CrI 0.6, 0.8), C1 ~ Beta(128.7, 14.3) (95% CrI 0.85, 0.95).
  2. S1 ~ Beta(8.6, 1.4) (95% CrI 0.6, 0.99), C1 ~ Beta(38.1, 2.4) (95% CrI 0.85, 0.99).