HLTHINFO 730 Healthcare Decision Support Systems Lecture 6: Decision Trees

1 / 20

# HLTHINFO 730 Healthcare Decision Support Systems Lecture 6: Decision Trees - PowerPoint PPT Presentation

HLTHINFO 730 Healthcare Decision Support Systems Lecture 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)

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

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

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 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’

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
Decision Table example

d= doesn’t matter (True or False)

From van Bemmel & Musen, Ch 15

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