conditions of rules describing the subgroups are called the principal factors. The described iterative process was successful for data at stages B and C, but it turned out that anamnestic data on its own (stage A data) is not informative enough for inducing subgroups, i.e., it failed to fulfil the expert's criteria of interestingness.  Only after engineering the domain, by separating male and female patients, were interesting subgroups discovered. See Section 3.7 for more details on the expert's involvement in this subgroup discovery process.

Table 1: Induced subgroups in the form of rules. Rule conditions are conjunctions of principal factors. Subgroup A1 is for male patients, subgroup A2 for female patients, while subgroups B1, B2, and C1 are for male and female patients. The subgroups are induced from different attribute subsets with corresponding g parameter values

| A 1   | CHD   |
|-------|-------|
| A 2   | CHD   |
| B1    | CHD   |
| B2    | CHD   |
| C1    | CHD   |

given in column g .  The last column Sigcontains information about the significance of the rules computed by the χ 2 test.
Separately for each data stage, we have investigated which of the induced rules are the best in terms of the ROC space, i.e., which of them are used to define the ROC convex hull.

At stage B, for instance, seven rules are on the convex hull shown in Figures 4 and 5 for the TP/FP and the ROC space, respectively. Two of these rules, X1 and X2, indicated

| Expert Selected Subgroups          | g    | Sig   |      |
|------------------------------------|------|-------|------|
| positive family history AND        | 14   | 95%   |      |
| age over 46 year                   |      |       |      |
| body mass index over 25 kgm        | 9%   |       |      |
| AND                                | 8    |       |      |
| age over 63 years                  |      |       |      |
| total cholesterol over 6.1 mmolL   | AND  | 10    | 9.9% |
| age over 53 years AND              |      |       |      |
| body mass index below 30 kgm –2    | 9.9% |       |      |
| total cholesterol over 5.6 mmolL-1 | AND  | 12    |      |
| fibrinogen over 3.7 gL-1 AND       |      |       |      |
| body mass index below 30 kgm -     |      |       |      |
| left ventricular hypertrophy       | 10   | 9.9%  |      |

in the figures, are listed in Table 2. Notice that the expert-selected subgroups B1 and B2 are significant, but are not among those lying on the convex hull. The reason for selecting exactly those two rules at stage B are their simplicity (consisting of three features only), their generality (covering relatively many positive cases) and the fact that the used features are, from the medical point of view, inexpensive laboratory tests.

## 3.3  Statistical Characterization Of Subgroups

The next step in the proposed descriptive induction process starts from the discovered subgroups. In this step, statistical differences in distributions are computed for two populations, the target and the reference population. The target population consists of true positive case (CHD patients included into the analyzed subgroup), whereas the reference population are all available non-target class examples (all the healthy subjects).