Skip to main content icon/video/no-internet
icon backReturn to Entries

Decision Trees, Construction

A decision model is a mathematical formulation of a decision problem that compares alternative choices in a formal process by calculating their expected outcome. The decision tree is a graphical representation of a decision model that represents the basic elements of the model. The key elements of the model are the possible choices, information about chance events, and preferences of the decision maker. The choices are the alternatives being compared in the decision model. The information consists of an enumeration of the events that may occur consequent to the choice and the probabilities of each of their outcomes. Preferences are captured by assessing utilities of each outcome that measure the desirability of each outcome. In addition to a utility, each outcome may be associated with a financial cost.

The decision tree is a convenient method, analogous to a high-level graphical language, of specifying the elements of the decision model in a way that leads naturally to a method for quantitatively evaluating the alternative choices, in a process known as averaging out and folding back the tree.

Formulating the Problem

Decision tree construction requires a properly formulated decision problem.

Decision Context

The first step is determining the context of the decision. This consists, at a minimum, of the clinical problem (e.g., chest pain), the healthcare setting (e.g., a hospital emergency room), and any characteristics of the patient to which the analysis is restricted (e.g., the age range, gender, or existing comorbid conditions). The context also specifies the timeframe being considered.

Specific Question

The second step is formulating a specific question that is to be answered by the decision analysis. It must be a comparison of specific alternative actions that are available to the decision maker. In healthcare decision making, choices generally involve diagnostic tests and treatments. An example of a clearly formulated decision is whether a patient with a suspected condition should be observed without treatment, given a diagnostic test, or treated empirically. Each choice must be unique. Choices may also contain combinations of actions with later decisions contingent on results of tests or outcomes of observation. These combinations of choices are referred to as policies. Typically, decision models involve multiple successive choices, which, in combinations, correspond to alternate policies. These combinations may differ according to the specific elements (e.g., one test or treatment as compared with another) or according to how these elements are applied (e.g., using differing rules for responding to the outcome of a diagnostic test or varying the amount of time before contingent action is taken). For these reasons, the number of decision alternatives that can be considered in a decision model can become very large as the number of combinations of the various factors increases.

Node Types

Standard decision trees contain three basic types of nodes. Decision nodes are typically represented by an open square, chance nodes by an open circle, and terminal nodes by rectangular boxes. Branches are represented as straight lines connecting nodes.

Overall Tree Structure

A simple decision tree is shown in Figure 1. By convention, the root of the tree is a decision node and is represented at the left of the figure, and the terminal nodes (referred to as the “leaves” of the tree) are at the right. According to conventions for drawing decision models that are published in the journal Medical Decision Making in the first issue of each year, lines representing branches of the same node are parallel and vertically aligned. Medical Decision Making also specifies that the branches should be attached to lines at right angles to nodes, as in Figure 1, but a common variation uses a fan of angled lines from each node leading directly to branches, as in Figure 2.

...

  • Loading...
locked icon

Sign in to access this content

Get a 30 day FREE TRIAL

  • Watch videos from a variety of sources bringing classroom topics to life
  • Read modern, diverse business cases
  • Explore hundreds of books and reference titles

Read next

More like this

Sage Recommends

We found other relevant content for you on other Sage platforms.

close

Have you created a personal profile? Login or create a profile so that you can save clips, playlists and searches

close
close
close Signed In to profile You are signed in as:
close
Logged in Institution Institution