Decision Node

Concept

Theoretically, a Decision Node is a structural element within a decision tree that represents a point at which a decision-maker selects one of two or more available alternatives. It is a fundamental component of decision analysis and expected utility theory, distinguishing deliberate choices from uncertain events represented by chance nodes. In health economics, decision nodes represent alternative interventions, diagnostic strategies, treatment pathways or policy options whose consequences are subsequently evaluated through decision-analytic models.

Mathematically, a decision node is represented by a set of mutually exclusive decision branches. Unlike chance nodes, probabilities are not assigned directly to the outgoing branches because the branch is selected by the decision-maker. The optimal branch is identified by calculating the expected value of each alternative and applying a decision rule, such as maximising expected utility, maximising expected net benefit or minimising expected cost.

In practice, decision nodes are positioned at points where alternative healthcare strategies are available. Each branch is linked to subsequent chance nodes, terminal nodes or additional decision nodes. Expected costs, health outcomes and cost-effectiveness are calculated for each branch using backward induction, enabling the preferred intervention to be identified according to the chosen decision criterion.

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Purpose

Used to represent healthcare choices within decision-analytic models, compare alternative interventions and identify the strategy that maximises expected health benefit or economic value.

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Mathematical Formulae

Primary Formula

Optimal decision rule:

a* = arg max????? EV(a)

where:

• a* = optimal decision
• A = set of feasible alternatives
• EV(a) = expected value of alternative a

Supporting Formulae

Expected value of each decision branch:

EV(a) = ????� p?V?

where:

• p? = probability of outcome i
• V? = value associated with outcome i

Related Mathematical Methods

• Decision tree analysis
• Expected value analysis
• Expected utility theory
• Backward induction
• Bayesian decision analysis
• Cost-effectiveness analysis

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Example

A health authority must choose between two screening programmes.

• Programme A: expected value = 8.45 QALYs
• Programme B: expected value = 8.91 QALYs

Applying the decision rule:

a* = arg max(8.45, 8.91)

Programme B is selected because it produces the greater expected health outcome. The decision node therefore directs the model towards the branch representing Programme B.

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Excel Implementation

Function	Example Formula	Health Economics Application
MAX	=MAX(B2:B3)	Identifies the decision branch with the highest expected value.
XLOOKUP	=XLOOKUP(MAX(B2:B3),B2:B3,A2:A3)	Returns the preferred healthcare intervention.
SUMPRODUCT	=SUMPRODUCT(C2:C5,D2:D5)	Calculates the expected value associated with each decision branch.
IF	=IF(B2=MAX($B$2:$B$3),""Optimal"","""")	Identifies the optimal branch within the decision tree.

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VBA (Optional)

Automate rollback analysis of decision trees by calculating expected values and identifying the optimal branch at every decision node.

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Sources

• Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
• Raiffa H. Decision Analysis: Introductory Lectures on Choices Under Uncertainty. Addison-Wesley.
• TreeAge Software. Decision Tree Modeling and Analysis. User Documentation.
• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
• ISPOR-SMDM Modeling Good Research Practices Task Force reports.