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Table 5 Observed disease status and Test 1 results.

From: Bias in trials comparing paired continuous tests can cause researchers to choose the wrong screening modality

Test 1 Observed Disease Status Probability
+ + { r [ 1 Φ ( x μ C 1 ) ] + r ( 1 ψ ) × [ Φ ( x μ C 1 , θ μ C 2 , ρ C ) Φ ( θ μ C 1 , θ μ C 2 , ρ C ) ] x < θ r [ 1 Φ ( x μ C 1 ) ] x θ MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@8C9B@
+ - { ( 1 r ) [ 1 Φ ( x μ N 1 ) ] r ( 1 ψ ) × [ Φ ( x μ C 1 , θ μ C 2 , ρ C ) Φ ( θ μ C 1 , θ μ C 2 , ρ C ) ] x < θ ( 1 r ) [ 1 Φ ( x μ N 1 ) ] x θ MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@93F0@
- + { r Φ ( x μ C 1 ) r ( 1 ψ ) Φ ( x μ C 1 , θ μ C 2 , ρ C ) x < θ r Φ ( x μ C 1 ) r ( 1 ψ ) Φ ( θ μ C 1 , θ μ C 2 , ρ C ) x θ MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@87CD@
- - { ( 1 r ) Φ ( x μ N 1 ) + r ( 1 ψ ) Φ ( x μ C 1 , θ μ C 2 , ρ C ) x < θ ( 1 r ) Φ ( x μ N 1 ) + r ( 1 ψ ) Φ ( θ μ C 1 , θ μ C 2 , ρ C ) x θ MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@8F01@
  1. Test 1 is + if the score on Test 1 is greater than x.