In the publication about “Likelihood ratios of quantitative laboratory results in medical diagnosis: The application of Bézier curves in ROC analysis” it was observed that when λ-weighted Youden indices are used, as defined by
Y (λ)=2*(λ*Se+(1-λ)*Sp)-1, with λ=1/(1+LR), the point on the ROC curve with the corresponding LR=(1-λ)/λ always is at the maximum of the λ-weighted Youden index.
In the technical report at doi:10.13140/RG.2.2.34168.90889 a proof is formulated that the above observation is generally valid.