Representing Decision Paths in an Influence Diagram by Decision Trees: Example of the ... according to the general order of the activities, and the decisions ...
Representing Decision Paths in an Influence Diagram by Decision Trees: Example of the Benefits of CT in Acute Abdominal Pain Ying-Lie O2, Job Kievit1, Jaap Sont1, Alex Meijer2, Koos Geleijns2 1
Department of Medical Decision Making, and 2Department of Radiology, Leiden University Medical Center, Leiden, the Netherlands
Introduction
Example
Influence diagrams are a powerful graphic representation for decision models, complementary to decision trees. An influence diagram depicts the associations between variables, decisions, and outcomes, as arrows between ovals, rectangles, and diamonds, respectively (figure 1). The main advantages of influence diagrams for (medical) decision making are: • An influence diagram can accommodate a large number of items and the complex associations between them, for instance the differential diagnosis, tests, treatments, decisions, and outcomes. • It primarily depicts the structure of the problem, without imposing any ordering. • Parts of an influence diagram can be adapted without affecting the remaining scheme. An important part of decision making are the decision paths. A disadvantage of influence diagrams is that the decision paths are invisible – except from the list of calculated values, it is not clear which information had led to the outcomes. Although in general an influence diagram cannot be transformed to decision trees, a decision path may.
The method is illustrated by an example on modelling the benefits of CT (computed tomography) in acute abdominal pain. Figure 1 represents a simplified model with 6 of the more than 20 possible diseases. The differential diagnoses concerns different tracts and either inflammatory or non-inflammatory diseases. The general order of the activities is as follows: 1. General tests such as AAP (acute abdominal pain) scoring, tests for inflammation, and other tests. 2. Diagnostic imaging according to the imaging policy. 3. Treatment according to the treatment policy.
Peritontitis
0,005
Urinary tract diseases
0,013
Gender
Appendicitis
Bowel Inflamm..
Peritonitis
AAP Scoring
General tests
Age
Acute Abdominal Pain
Bowel Diseases
Urinary Inflamm..
Test Inflamm..
Urinary Diseases
Urinalysis
Test Done
Diagnostic Imaging
Ultrasound
Diagnostic Laprascopie
MRI
MSCT
Imaging Done
Imaging Policy
Do Imaging
Treatment Policy
Do Treatment
0,044
Bowel diseases
Gender Age
Imaging Effects
Dose
Anatomic Region
Induced Cancer
Radiated Organs
0,116
Bowel inflammation
0,153
Urinary tract inflammation
0,446
US may be positive
0,911
MSCT positive
0,5
Peritonitis Outcome
Outcomes
0,895
US uncertain, MSCT positive
0,0
BowInflam Outcome
Appendicitis Outcome
0,404
Appendcitis
UrinInflam Outcome BowDis Outcome
Future Effects UrinDis Outcome
1,0
Probabilities
Disease Effects
Patient Risk
Figure 2: Probabilities of the diseases for positive tests of inflammation, and uncertain results of AAP scoring and the remaining general tests. Probabilities of appendicitis for different imaging policies (only US, decide MSCT, and always MSCT).
Health Effects
Figure 1: The most important part of an influence diagram of acute abdominal pain with a limited number of selected inflammatory and non-inflammatory diseases
Method The most important properties of influence diagrams and decision trees are summarised below: Influence diagram
Decision tree
Gender
The representation is network based, states and decisions are hidden inside the nodes.
The representation is tree-based, each state and decision is a branch.
There is no ordering between nodes.
There is a strict ordering between nodes.
The calculation propagates in all directions starting from the nodes which values are set.
The calculation is strictly in the direction from the root along the branches to the end nodes.
Allows complex associations between all nodes, only limited by the distinction of start nodes and end nodes.
Associations are restricted to a predecessor and a successor, thus not suitable for complex associations.
Complex problems can be represented in a compact way.
The tree expands rapidly because of its inherent property and repetition of branches.
Decision paths of different policies are only visible from the resulting values.
A partial conversion of the decision paths in the influence diagram to decision trees would take advantage of both methods. The conversion takes several steps: 1. The number of suspected diagnoses in the influence diagram are reduced by finding the most probable ones, or by ruling out others. After the general tests, appendicitis has the highest yet not convincing probability (figure 2).
Appendicitis
Gender Age
Acute Abdominal Pain
Peritonitis
AAP Scoring
General tests
Age
Test Inflamm.. Test Done
Diagnostic Imaging
Ultrasound
Diagnostic Laprascopie
MRI
MSCT
Imaging Done
Different policies, and the order of activities, are directly visible from the different branches.
2. All connected paths to these diagnoses, tests, decisions, and outcomes are traced, leaving out all other variables (figure 3). 3. These groups of nodes are then ordered according to the general order of the activities, and the decisions expanded (figure 4). 4. Node types (chance, decision, outcome) in the influence diagram translate to the same types in the decision tree, and each option of a decision in these becomes a branch (figure 5).
Imaging Policy
Do Imaging
Treatment Policy
Do Treatment
Imaging Effects
Dose
Anatomic Region
Induced Cancer
Radiated Organs
Appendicitis Outcome
Future Effects Peritonitis Outcome
Outcomes
Disease Effects
Patient Risk
Health Effects
Figure 3: The most important variables of the decision path of appendicitis, leaving out all other variables. AAP scoring General tests Appendicitis: uncertain Imaging policy: only US Ultrasound (US)
Imaging policy: decide MSCT Ultrasound (US) If US uncertain, then MSCT
Imaging policy: always MSCT MSCT
If positive, surgery Figure 4: Schematic representation of decisions in the imaging policy.
Conclusions
MSCT
Influence diagrams are preferred in modelling complex problems such as medical diagnosis. The hidden decision paths can be made explicit by conversion to decision trees, thus fully utilising both the advantages of influence diagrams and decision trees. Future work will investigate graphical tools to support the conversion and analysis of the mixed influence diagram – decision tree structure.
surgery Always MSCT
Appendicitis?
Genertal tests
positive
positive uncertain
positive Decide MSCT-ultrasound
uncertain negative
negative Only US
wait MSCT
uncertain negative
surgery no surgery
Appendicitis outcome Appendicitis outcome Appendicitis outcome
ultrasound
Figure 5: Part of the resulting decision tree, with emphasis on the imaging policy. This work was financially supported by the EC-EURATOM 6 Framework Programme (2002-2006) and forms part of the CT Safety & Efficacy (Safety and Efficacy of Computed Tomography (CT): A broad perspective) project, contract FP/002388.
