Sumeet Dua and Mohit Jain

3.2.5. Decision Tree in Decision Analysis

A decision tree can be especially helpful to ophthalmologists, who need to manage difficult clinical problems.3 For example, if a student has an examination in the morning and have to decide whether to watch a soccer match or not, then a decision tree containing actions, events, and outcomes can be useful. In this case, the decision tree would contain two actions:

1. “Watch Soccer Match” or 2. “Do Not Watch Soccer Match.”

The events that influence the outcome of the actions are:

“Easy Questions” and “Difficult Questions,” and reflect the ease with which the student was able to complete the examination. Consider the decision tree in Fig. 3.1.

Once a student or ophthalmologist makes the decision tree, then he or she can add information, such as the cost of outcome and event probability. The cost will depend on the rank of the outcome or on which outcome is more important and can vary from person to person.

The outcome of the ranking system for our student example is shown in Fig. 3.2, in the rightmost column. Our first ranked outcome is “Fortunate,” for which we assigned a weight of 1.0; our second ranked outcome is “Right Decision,” for which we assigned a weight of 0.75. Our third ranked outcome is “Should Have Watched,” for which we assigned a weight of 0.5, and our

Watch Soccer Match

Difficult Questions Consequences

Fig. 3.1. Example of a decision tree.

94

Computational Decision Support Systems and Diagnostic Tools

Fig. 3.2. Example of a decision tree after assigning weight and rank to outcomes. Outcomes rank (1), (2), (3), and (4), based on weights (the cost of the outcome) of 1.0, 0.75, 0.5, and 0.0.

fourth ranked outcome is “Consequences,” for which we assigned a weight of 0.0. The weighting system is described below.

As the name indicates, event probability denotes the chance or probability that a particular event will occur. Let us continue with our example, and assume that if student watches soccer, then there is a 35% chance that the student will find the questions easy and a 65% chance that the student will find the questions difficult. If the student does not watch the soccer match, then there is a 60% chance that he or she will find the questions easy, and a 40% chance that the student will find the questions difficult. These event probabilities are shown below in Fig. 3.3.

Watch Soccer

Match

Difficult Questions Consequences (4) 0.0 (35%)

Easy Questions Should Have Watched (3) 0.5

Soccer Match

Fig. 3.3. Example of decision tree after assigning event probabilities.

95

Sumeet Dua and Mohit Jain

The final probabilities are calculated as:

“Watch Soccer Match”: 0.35 1 + 0.65 0 = 0.35 and

“Do Not Watch Soccer Match”: 0.6 0.5 + 0.4 0.75 = 0.3 + 0.3 = 0.6.

In this example, the student should choose “Do Not Watch Soccer Match,” since it has the highest weight.

For another example, consider a team of ophthalmologists that go to a city to perform cataract operations on several people. They must determine whether to include all the patients that need laser treatment to prevent blindness, because treating only the necessary people will save resources, time, and money. Fig. 3.4 shows a decision tree based on their actions, events, and outcomes.

First, a diagram of actions will be drawn (for example, in the above figure “Everyone” and “Not Everyone”), events (for example, in the above figure “Cataract” and “Not Cataract”), and outcomes (for example, in the above figure “Prevent Blindness,” “Waste of Time,” “Probable Blindness,” and “No Blindness or Waste of Time”). Based on the events and on personal perception, we determine how to rank the outcomes.

The ranks are described in Step 2.

Second, the outcomes of the events will be ranked, as shown in Fig. 3.5. In our example, the ophthalmologists rank the outcomes of the events as:

Rank 1. Not Everyone -> No Cataract -> No blindness, not examining people who do not have cataracts saves time and money. Rank 2. Prevention of Blindness -> The patient had cataracts removed after laser surgery.

Fig. 3.4. Example of decision tree with actions and events. The methodology for creating this tree consists of four steps, as defined below.

96

Computational Decision Support Systems and Diagnostic Tools

Fig. 3.5. Example of decision tree after assigning weight and rank to outcomes. The ranks are (1), (2), (3), and (4), and are based on weights (the cost of the outcomes) of 1.0, 0.75, 0.5, and 0.0.

Rank 3. Everyone -> No Cataract -> Waste of time. -> Since we have included everyone for examination, some people who do not have cataracts will be examined, which results in loss of time and money. Rank 4. Not Everyone -> Cataract -> Probable blindness, i.e. a person who has cataracts is not examined and may become blind because of not being included. “Not Everyone” ranks fourth since we do not want these cases to be missed.

The above ranking will vary from surgeon to surgeon. For a team, the surgeons will need to sit together and discuss which cases to give the best rank and which the least.

Our outcome ranking system, as explained above, is shown in Fig. 3.5 in the rightmost column. Our first ranked outcome is “No Blindness or Waste of Time,” which we assigned a weight of 1.0; our second ranked outcome is “Prevent Blindness,” which we assigned a weight of 0.75. Our third ranked outcome is “Waste of Time,” which we assigned a weight of 0.5, and our fourth ranked outcome is “Probable Blindness,” which we assigned a weight of 0.0.

Third, event probability will be determined, as shown in Fig. 3.6. Let us assume that if everyone is examined, the chance of an examined individual having a cataract is 50% and the chance of an examined individual not having a cataract is 50%.

Fourth, a numerical calculation will be made. The numerical calculation for the weighting is as described below:

“Everyone”: 0.5 0.75 + 0.5 0.5 = 0.375 + 0.25 = 0.625 and “Not Everyone”: 0.5 0 + 0.5 1 = 0.5.

97