FPr, as assumed in the ROC analysis, but rather in terms of TP and FP in the so-called TP/FP space. The reason is the improved computational efficiency of computing the q o value which is used as a search heuristic for comparing the quality of rules for a given, fixed domain. For a fixed domain, the TP/FP space is as appropriate as the ROC space: the ROC space is namely equivalent to the normalized TP/FP space where Pos and Neg are normalization constants for Y and X axes, respectively. The TP/FP space and the ROC space are illustrated in Section 3.2 by Figures 4 and 5, respectively.

## 3. The Descriptive Induction Process

The induction of subgroups, described in Section 2.2, represents the main step of the proposed descriptive induction process. This step corresponds to the data mining step of the standard process of knowledge discovery in databases (KDD). The overall descriptive induction process, proposed in this paper, is comparable to the standard KDD process (Fayyad, Piatetsky-Shapiro, & Smyth, 1996), with some particularities of the task of subgroup discovery.

The proposed expert-guided subgroup discovery process consists of the following steps:
1. problem understanding 2. data understanding and preparation 3. subgroup detection 4. subgroup subset selection 5. statistical characterization of subgroups 6. subgroup visualization 7. subgroup interpretation 8. subgroup evaluation Section 3.1, illustrating steps 1 and 2, presents a medical problem used as a case study for applying the proposed descriptive induction methodology.  Tools for supporting subgroup detection and selection in steps 3 and 4 were described in detail in Sections 2.2 and 2.3, while the results of expert-guided subgroup detection and selection are outlined in Section 3.2. Methods and results of steps 5–8 for this domain are outlined in Sections 3.3–3.6, respectively.

The proposed descriptive induction process is iterative and interactive. It is iterative, since many steps may need to be repeated before a satisfactory solution is found. It is also interactive, assuming expert's involvement in most of the phases of the proposed descriptive induction process.  The expert's role in the patient risk group detection application is described in Section 3.7.