Fig. 2

Amount of separation of linear predictor values for cases and controls in hypothetical populations with different AUCs. Legend: AUC of population ‘A’ is 0.770; ‘D’ is 0.777; and ‘E’ is 0.795. Modeling is based on Approach II with the following specifications: Population ‘A’: ρ _Case  = 0.2, ρ _Control  = 0.2; μ _Cas e : (1, 2); μ _Control : (0, 0); σ _Cas e : (2, 2); σ _Control : (2, 2). Population ‘D’: ρ _Case  = 0.1, ρ _Control  = 0.1; μ and σ same like in ‘A’. Population ‘D’: ρ _Case =0.1, ρ _Control =0.1; μand σ same like in ‘A’. Population ‘E’: ρ _Case =-0.1, ρ _Control  = -0.1; μ and σ same like in ‘A’. Note: When the two linear predictor distributions are fully overlapping, for each chosen cut-off value on the range of linear predictor values, the proportion of false positives (controls labeled as high risk) equals true positives (cases labeled as high risk). This would result in an AUC of 0.5. Similarly when the two distributions are not overlapping, the AUC approximates 1