Hello dear,

Theoricaly, I think the most important is Aria under curve (as an estimation of accuracy) ; but it highly depends on prevalnce in your population, as Zhu et al,(2010) reported: " A diagnosis for rare conditions in the population of interest may result in high sensitivity and specificity, but low accuracy. Accuracy needs to be interpreted cautiously".

For estimating suhc sample size, I recommend this article : (free to download):

Article Requirements for Minimum Sample Size for Sensitivity and Spe...

Best Wishes.

To address the error in the first answer, AUC-ROC is not an estimate of accuracy. Accuracy is influenced by prevalence of the groups. No where in the ROC graph is there any capacity to calculate accuracy as the two axis are sensitivity and 1-specificity - neither measure is affected by prevalence (although the power associated with an estimate will differ wildly is there is a big imbalance in group membership).

AUC has established and widely accepted metrics for calculating standard error to allow assessment of relative effect size for differences in AUC values. I am not aware of wide acceptance for error metrics for sensitivity and specificity.

The issue with sensitivity and specificity is that they are point estimates of one position in the ROC curves, leaving them highly sensitive to noise in the samples close to the decision line. AUC uses the full graph and so is a more stable measure.