br This table can also be used in
This table can also be used in determining the optimal number of features considering the opportunity cost for the change in FA or ac-curacy with respect to number of features. We have used an arbitrary order of removing the features for this experiment because enumerating all combinations for feature Calcipotriol is not pragmatic. To demonstrate a practical implementation we have used two test cases in Section 4.2,where selection of features is based on various objectives corre-sponding to cost and comfort for clinical tests.
4.2. Potential application: test selection using cost and comfort
The algorithm designed in Section 3.3 can be used for personalized selection of test schedule for individual patients. In this section, we present two such application based on two common concerns of pa-tients while undergoing medical diagnosis: cost and comfort.
For the application involving cost of tests, the prices have been
Accuracy and sensitivity for unskewed data for different features.
Feature Threshold Post Initial Post Initial Post Initial Post Initial No
FA FA FN FN Accuracy Accuracy Sensitivity Sensitivity
Cost and discomfort index indicative values.
Feature no. Feature description Cost Discomfort
taken in INR from sources: [51,52]. It is understood that the prices are only indicative, and will vary across diagnostic centers. Also, for the study only relative prices are important. For the application involving comfort preferences, in absence of standard measures, we consider some natural values for discomfort index (values between 1 to 10). The values for different test are are listed in Table 5. For this study, we assume the setting where a budget is imposed on the total cost or discomfort during tests performed for diagnosis. Such a constraint can be imposed due to economic condition of a patient, or as decided by insurance provider, or due to a limit on total budget (as set
by world bank, government health organization etc.) for a medical project. The obvious objective is to minimize the false abnormal rate, under the constraints that false normal is zero and the total cost of tests is less than or equal to the budget. However, heartwood is easy to see that this problem is NP-Hard, since it involves enumerating all test combinations which satisfy the constraint (assuming the false normal can always be made zero using Algorithm 1), and evaluating the false abnormal rate for these combinations. While approaches for tacking this problem will be studied in another work, in this work we follow the following heuristic scheme:
1. Set budget on total cost or discomfort value of patient as constraint. Start with a full set of features. 2. Prepare the feature set by either greedily selecting the tests (cost constraint) or greedily deselecting the tests (choice constraints).
3. For each option adjust threshold to make FN = using algorithm 1; Calculate FA. 4. Choose the option corresponding to minimum FA (False abnormal rate).
Due to the greedy nature of the algorithm described above, it is clear that complexity is linear in the number of features, so long as we evaluate a constant number of feature combinations.
For the application related to costs, we assume a budget of INR 2000 (against a total cost of all 15 tests INR 6250). Fig. 3 enumerates a total 12 options (columns) for selecting tests, and Fig. 4 shows the corre-sponding false abnormals out of total 738 patients (test set data). In this case option 8 produces a minimum number of FA and 100% sensitivity,
Fig. 3. Total possible enumeration for a budget constraint INR 2000.