Concept Architecture
Concept
Theoretically, a Decision Tree Model is a structured decision-analytic model that represents a sequence of healthcare decisions and uncertain events using a branching graphical framework. It is founded on decision analysis and expected utility theory and enables alternative clinical strategies to be evaluated by explicitly modelling decisions, probabilistic outcomes and terminal consequences. In health economics, decision tree models are widely used to estimate expected costs, health outcomes and cost-effectiveness for interventions with relatively short time horizons or non-recurring clinical events.
Mathematically, a decision tree model is represented as a directed acyclic graph consisting of decision nodes, chance nodes and terminal nodes. Expected values are calculated by assigning probabilities, costs and health outcomes to each branch and applying rollback analysis using expected value calculations. The optimal strategy is identified by maximising expected utility, expected net benefit or health outcomes, or by minimising expected costs according to the chosen decision criterion.
In practice, decision tree models are constructed from clinical pathways derived from trials, observational studies and expert knowledge. Branch probabilities are estimated from epidemiological or clinical evidence, while costs and utilities are obtained from economic and quality-of-life studies. The model is implemented by calculating expected outcomes through backward induction and is commonly used in health technology assessment, diagnostic evaluation, screening programmes and short-term economic evaluations.
Purpose
Used to compare alternative healthcare interventions by modelling clinical pathways, estimating expected costs and health outcomes, and determining the most cost-effective strategy under uncertainty.
Mathematical Formulae
Primary Formula
Expected value of a decision branch:
EV = ????� p?V?
where:
- EV = expected value
- p? = probability of outcome i
- V? = value associated with outcome i
Supporting Formulae
Expected cost:
E(C) = ????� p?C?
Expected health outcome:
E(H) = ????� p?H?
Incremental Cost-Effectiveness Ratio:
ICER = ?C / ?E
where:
- ?C = incremental cost
- ?E = incremental health outcome
Related Mathematical Methods
- Decision tree analysis
- Rollback analysis
- Expected value analysis
- Expected utility theory
- Cost-effectiveness analysis
- Probabilistic sensitivity analysis
Example
A decision tree compares standard care with a new diagnostic test.
For the new test:
- Correct diagnosis: probability = 0.90; cost = �1,100; QALYs = 8.8
- Missed diagnosis: probability = 0.10; cost = �2,800; QALYs = 6.2
Expected cost:
E(C) = (0.90 ? 1,100) + (0.10 ? 2,800) = �1,270
Expected health outcome:
E(H) = (0.90 ? 8.8) + (0.10 ? 6.2) = 8.54 QALYs
These expected values are compared with those of standard care to determine the preferred strategy and, where appropriate, calculate the ICER.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| SUMPRODUCT | =SUMPRODUCT(B2:B6,C2:C6) | Calculates expected costs, QALYs or utilities for decision tree branches. |
| IF | =IF(B2=1,C2,D2) | Represents conditional branching within the decision tree. |
| XLOOKUP | =XLOOKUP(MAX(E2:E5),E2:E5,A2:A5) | Identifies the preferred intervention based on expected value or net benefit. |
| Solver | Solver Optimisation | Supports optimisation of model parameters during calibration or scenario analysis. |
VBA (Optional)
Automate rollback calculations for complex decision trees and generate comparative cost-effectiveness results for multiple healthcare strategies.
Sources
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
- Sonnenberg FA, Beck JR. Markov Models in Medical Decision Making: A Practical Guide. Medical Decision Making. 1993.
- ISPOR-SMDM Modeling Good Research Practices Task Force. Modeling Good Research Practices. Value in Health.
Related Concepts (2)
Library
Publications
1
Conceptualizing a Model: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-2 — Roberts, Russell, Paltiel, Chambers, McEwan & Krahn, Task Force Report 2 ed., 2012 (Value in Health / Medical Decision Making)
Best-practice guidance on model conceptualisation — defining the decision problem, scoping, and choosing an appropriate model structure before implementation.
Journal ArticleView source →
Frequently Asked Questions (6)
What is a decision tree model?
A decision-analytic model built on the decision tree structure, with all possible patient pathways explicitly represented as branches to calculate expected cost.
Source: Weinstein & Fineberg 1980
How does a decision tree model handle time?
A decision tree model has no explicit clock, since it represents a sequence of events but does not track how long each takes or discount later costs and outcomes by their timing. This is why it fits short-horizon problems, where the passage of time can reasonably be ignored, and why long-term or recurring processes are usually modelled with a structure that advances in cycles instead. Analysts sometimes attach a longer-term extension to a tree to compensate for this limitation. Briggs and colleagues (2006) note this feature.
Source: Briggs et al. 2006
How does a decision tree model calculate expected cost?
A decision tree model calculates expected cost by assigning a cost to each pathway, weighting it by the probability of that pathway, and summing across all pathways for each strategy. The probability of a path is the product of the probabilities on its chance branches, and the expected cost of a strategy is the sum of its paths' costs weighted by their probabilities. The same is done for health effects, giving the expected cost and effect used to compute cost-effectiveness.
Source: Weinstein & Fineberg 1980
When is a decision tree model appropriate?
A decision tree model is appropriate for decision problems over a relatively short time horizon with a limited number of events that do not recur, where all pathways can be enumerated without the tree becoming unwieldy. It suits acute conditions or one-off decisions where the sequence of events is finite. Where events recur or the horizon is long, so that paths would multiply excessively, a state-transition or Markov model is usually preferred instead, as it handles time and recurrence more compactly.
Source: Weinstein & Fineberg 1980
What are the advantages of a decision tree model?
A decision tree model is transparent and easy to follow, since every pathway is laid out explicitly, making the structure, probabilities, and outcomes visible and the calculation straightforward. This clarity aids building, checking, and communicating the model. For suitable problems, it provides a clear and complete representation of the possible patient experiences and their expected costs and effects, which is why decision tree models are widely used for economic evaluation of shorter-horizon decisions.
Source: Weinstein & Fineberg 1980
What are the limitations of a decision tree model?
A decision tree model becomes impractical when events recur or the time horizon is long, because representing repeated events requires the tree to branch repeatedly, so the number of pathways grows rapidly and the model becomes unwieldy and hard to manage. It also lacks a natural way to represent the passage of time. For chronic conditions and long horizons, these limitations lead modellers to use Markov or state-transition models, which represent recurring events and time more efficiently.
Source: Weinstein & Fineberg 1980
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 21 Sep 2026
Content version: 1.0.0
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- Term code
- HE-EM-DM-019
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