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Tumor markers are substances that are found in blood, urine, or body tissues and that are used as indicators for tumors; elevated tumor marker values can indicate the presence of cancer, but there can also be other causes. We have used a medical database compiled at the blood laboratory of the General Hospital Linz, Austria: Several blood values of thousands of patients are available as well as several tumor markers. We have used several data based modeling approaches for identifying mathematical models for estimating selected tumor marker values on the basis of routinely available blood values; in detail, estimators for the tumor markers AFP, CA-125, CA15-3, CEA, CYFRA, and PSA have been identified and are analyzed in this paper. The documented tumor marker values are classified as "normal" or "elevated"; our goal is to design classifiers for the respective binary classification problems. As we show in the results section, for those medical modeling tasks described here, genetic programming performs best among those techniques that are able to identify nonlinearities; we also see that GP results show less overfitting than those produced using other methods.