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HLTHINFO 730 Healthcare Decision Support Systems Lecture 6: Decision Trees

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## HLTHINFO 730 Healthcare Decision Support Systems Lecture 6: Decision Trees

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### HLTHINFO 730Healthcare Decision Support SystemsLecture 6: Decision Trees

Lecturer: Prof Jim Warren

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)

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).”

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’

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

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

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

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)

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…

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)

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)

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

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

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.

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…

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

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

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)

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

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