HLTHINFO 730 Healthcare Decision Support Systems Lecture 6: Decision Trees

1. HLTHINFO 730Healthcare Decision Support SystemsLecture 6: Decision Trees Lecturer: Prof Jim Warren

2. Decision Trees • Essentially flowcharts • A natural order of ‘micro decisions’ (Boolean – yes/no decisions) to reach a conclusion • In simplest form all you need is • A start (marked with an oval) • A cascade of Boolean decisions (each with exactly outbound branches) • A set of decision nodes (marked with ovals) and representing all the ‘leaves’ of the decision tree (no outbound branches)

3. Example • Consider this fragment of the ‘Prostate Cancer Workup (Evaluation)’ decision tree from http://www.nccn.org/patients/patient_gls/_english/_prostate/contents.asp# The page also shows supporting text: “Additional testing is recommended for men expected to live 5 or more years or who have symptoms from the cancer. For example, if the tumor is T1 or T2, a bone scan is recommended if the PSA level is greater than 20 or if the Gleason score is greater than 8. A bone scan is also recommended if the man has any symptoms, or the cancer is growing outside the prostate (T3 or T4). A CT or MRI of the pelvis is recommended when the tumor is T1 or T2 and there is a 7% or greater chance of lymph node spread based on the Partin tables, or the tumor is growing outside the prostate (T3 or T4).”

4. KE problems for flowchart • The natural language may pack a lot in • E.g., “any one of the following” • Even harder if they say “two or more of the following” which implies they mean to compute some score and then ask if it’s >=2 • Incompleteness • There are logically possible (and, worse, physically possible) cases that aren’t handled • The ‘for example’ in the text is a worry • Inconsistency • Are we trying to reach one decision (which test) or a set of decisions • 1) whether to do a bone scan • 2) whether to do a ‘CT or MRI’

5. Let’s try it anyway • What’s said for ‘staging workup’ looks like this Legend S2 = step 2: ‘CT or MRI of pelvisBS = Bone scanS3 = step 3: ‘All others: no additional testing’LNS = ‘7% or greater chance of lymph node spread based on the Partin tables’ Please don’t decide your father’s Prostate follow-up from this! It’s unverified, and I don’t think a tumour can be ‘T1 or T2’ and ALSO ‘T3 or T4’ (but that’s what it says!) T1 or T2 Y N T3 or T4 PSA>20 BS S3 S2 Symptoms BS T3 or T4 LNS BS S3 S2

6. Decision Tables • As you can see from the Prostate example, a flowchart can get huge • We can pack more into a smaller space if we relinquish some control on indicating the order of microdecisions • A decision table has • One row per ‘rule’ • One column per decision variable • An additional column for the decision to take when that rule evaluates to true

7. Decision Table example d= doesn’t matter (True or False) From van Bemmel & Musen, Ch 15

8. Flowcharts v. Tables • Decision table is not as natural as a flowchart • But we’ve seen, a ‘real’ (complete and consistent) flowchart ends up very large (or representing a very small decision) • Decision table gets us close to production rule representation • Good as design specification to take to an expert system shell • Completeness is more evident with a flowchart • Decision table could allow for multiple rules to simultaneously evaluate to true • Messy on a flowchart (need multiple charts, or terminals that include every possible combination of decision outcomes) • Applying either in practice requires KE in a broad sense • E.g., may need to reformulate the goals of the guideline

9. On to production rule systems • In a production rule system we have decision-table-like rule, but also the decision outcomes can feed back to the decision variables • Evaluating some special decision rule (or rules) is then the goal for the decision process • The other rules are intermediary, and might be part of the explanation of how externally-derived decision variables were used to reach a goal decision • The inference engine of the expert system shell chooses how to reach the goal • i.e., with backward chaining, or forward chaining • Possibly with some direction from a User Interface (UI) manager component (e.g., we might group sets of variables for input into forms as a web page)

10. Boolean Algebra • To formulate flow chart decisions and (especially) decision table rows, can help to have mastered Boolean Algebra • Basic operators • NOT – if A was true, NOT A is false • AND – A AND B is only true if both A and B are true • OR – A OR B is true if either A, or B, or both are true (aka inclusive or) • This is not the place for a course on Boolean algebra, but a few ideas will help…

11. Notation • Alas there are a lot of ways the operators are written • NOT A might appear as A, ~A, A′ or ¬A • A AND B might appear as A.B, A·B, A^B or simply AB • A OR B might appear as A+B or AvB • We can use parentheses like in normal algebra • C(A+B) means the expression is True if and only if C is true AND either B is true OR C is true (or both) • It’s equivalent to CA + CB (C-AND-A or C-AND-B, evaluate AND before OR) • So AND is a bit like multiplication, whereas OR is a bit like addition • 1 + 1 ≥ 1 1 + 0 ≥ 1 (inclusive OR) • 1 x 1 ≥ 1 1 x 0 ≥ 1 (logical AND)

12. Think! • If you just keep your head and focus on the meaning in the clinical domain, you can usually find the Boolean expression you need • Be sure to be precise • “NOT (x>43)” is “x is NOT GREATER than 43” is “x<=43” (get your equals in the right place!) (with this advice, I won’t teach you De Morgan’s Law, truth tables, or Karnaugh maps, but feel free to look them up – they all Google well)

13. Venn diagrams • Visual representations of membership in sets • Can be very useful to decide what Boolean expression you need • Say A is the set of everything with two legs and B the set of everythingthat flies • A^B would be true for a parrot • A would be true for a human,B would be false • B would be true for a mosquito,A would be false A: 2 legs B: can fly Mossie Human Parrot

14. Decision Tree Induction • An alternative to knowledge engineering a decision tree is to turn the task over to a machine learning algorithm • The decision tree can be ‘induced’ (or inducted) from a sufficiently large set of example • The ID3 algorithm is the classic for inducing a decision tree using Information Theory • If I have 50 examples where the patients survived and 50 where they didn’t I have total (1.0) entropy and zero information • Given a set of potential decision attributes I can try to create more order (less entropy, more information) in the data

15. Example: Induced Decision Tree Of course they go and use ovals for listing the decision variables, put the test criteria on the arcs and put ‘leaf’ decisions in rectangles – notations vary; get used to it! From Chen et al, Complete Blood Count as a Surrogate CD4 Marker for HIV Monitoring in Resource-limited Settings, 10th Conf on Retroviruses and Opportunistic Infection, 2003.

16. Using Entropy measures in ID3 • For a decision node S with pp positive example (e.g., surviving patients) and pn negataive example • Entropy(S) = - pplog2 pp – pnlog2 pn • So with 15 survivors out of 25 patients • Entropy(S) = - (15/25) log2 (15/25) - (10/25) log2 (10/25) = 0.970 • I want to select a Boolean attribute A that splits S such that the two subsets are as ordered as possible, usually written…

17. ID3 continued • So if I have 20 available Boolean decision variables • I try splitting my cases, S, according to each, until I find the variable that gives the most Gain • I repeat this on each sub-tree until either every node if perfect (all survivors, or all deaths) or I run out of attributes • If my variables aren’t Boolean, then I have more work to do • Actually, the Gain equation works fine if the attribute is multi-valued (Day of Week would be OK, I just have a 7-way split in my tree) • For continuous values I have to ‘discretize’ – make one or more split points • e.g., SBP<140? – now I’ve made continuous-valued blood pressure into a Boolean • Can be done based on knowledge (e.g., clinical significance), or handed to an algorithm to search for the max Gain See http://dms.irb.hr/tutorial/tut_dtrees.php

18. Tools • You don’t find ‘pure’ ID3 too much • Other algorithms in a similar spirit to search for are C4.5 and Adaboost • Tools • Matlab implements decision tree induction • Weka toolkit (from Waikato Uni) has a variety of Java tools for machine learning • Try Pierre Geurts’ online decision tree induction applet, e.g., for ‘animal descriptions’ from http://www.montefiore.ulg.ac.be/~geurts/dtapplet/dtexplication.html#online

19. I de-selected ‘backbone’ from the available decision attributes, hit New Tree, then Build, and hit Zoom+ a couple times (note that the attribute order in the database effects how the decision nodes end up phrased)

20. Summary • Decision trees are a basic design-level knowledge representation technique for ‘logical’ (rule based, Boolean-predicate-driven) decisions • Decision tables let you compactly compile a host of decisions on a fixed set of decision variables • These take you very close to the representation needed to encode production rules for an inference engine • Rule induction from data provides an alternative to conventional Knowledge Engineering • Computer figures out rules that fit past decisions instead of you pursuing experts to ask them what rules they use