This paper introduces SSTBoost, a predictive classification methodology designed to target the accuracy of a modified boosting algorithm towards required sensitivity and specificity constraints. The SSTBoost method is demonstrated in practice for the automated medical diagnosis of cancer on a set of skin lesions (42 melanomas and 110 naevi) described by geometric and colorimetric features. A cost-sensitive variant of the AdaBoost algorithm is combined with a procedure for the automatic selection of optimal cost parameters. Within each boosting step, different weights are considered for errors on false negatives and false positives, and differently updated for negatives and positives. Given only a target region in the ROC space, the method also completely automates the selection of the cost parameters ratio, tipically of uncertain definition. On the cancer diagnosis problem, SSTBoost outperformed in accuracy and stability a battery of specialized automatic systems based on different types of multiple classifier combinations and a panel of expert dermatologists. The method thus can be applied for the early diagnosis of melanoma cancer or in other problems in which an automated cost-sensitive classification is required.