Multi-Criteria Decision Analysis

Multi-Criteria Decision Analysis: Concept Architecture

Orientation and learning roadmap

The page moves from defining a health care decision and its alternatives to recording performance against distinct criteria. It then demonstrates one additive scoring method, examines weights and uncertainty, and explains how the resulting comparison should inform deliberation.

Start with the decision, not a list of scores

An MCDA should answer a specific question for a stated decision maker and population. Selecting technologies for a national reimbursement decision, prioritizing local services, and weighing a medicine's benefits and harms are different problems; each can require different options, criteria, stakeholders, and constraints. The decision context also determines which information should remain outside a score, such as legal requirements or a fixed budget.

Specify the alternatives and the current practice or other relevant comparator before assessing performance. Agree on criteria that represent distinct objectives, define their direction and measurement, and explain why each belongs. Overlapping criteria can count the same benefit twice, while a missing criterion can conceal a trade-off that matters to the decision.

A useful decision record states:

• Decision question: What choice is being made, by whom, for which population and time horizon?
• Alternatives: Which feasible options, including current practice when relevant, are compared?
• Criteria: Which distinct consequences matter, how are they measured, and is higher or lower better?
• Stakeholders: Whose preferences inform trade-offs, and how were those people selected?
• Constraints: Which eligibility, capacity, budget, or ethical limits must be respected separately?

Show performance before applying preferences

The performance matrix places alternatives in rows and criteria in columns. Each entry records an alternative's estimated consequence on a defined scale, preferably with a source, population, time horizon, and uncertainty. Showing this matrix before aggregation allows a reader to see where one option improves a criterion and worsens another.

The values in this illustrative table are already on a common 0–10 preference scale for teaching purposes; they are not empirical evidence. In a real application, raw outcomes such as QALYs, serious adverse events, spending, or travel time first need clearly specified value functions if the selected method requires commensurable scores. A change from 4 to 8 on one criterion should not silently be treated as equivalent to the same change on another.

Criteria should be neither so broad that meaningful differences disappear nor so granular that the same consequence enters several times. Check whether differences in population or data quality make apparently comparable performance entries misleading. Record how uncertain or missing values were estimated, and preserve the unaggregated matrix alongside any summary.

How an additive model combines criteria

One common MCDA approach is an additive value model, but MCDA also includes other approaches such as outranking and reference-level methods. The chosen method should match the decision problem and the meaning stakeholders can give to trade-offs. An additive score is suitable only when its scaling and preference assumptions are defensible.

For alternative $a$ with $J$ criteria, an illustrative additive model is:

$$V(a)=\sum_{j=1}^{J}w_jv_j(x_{aj}),\qquad w_j\geq0,\quad\sum_{j=1}^{J}w_j=1.$$

Here $x_{aj}$ is alternative $a$'s performance on criterion $j$, $v_j$ maps that performance onto the chosen preference scale, and $w_j$ is the trade-off weight for a specified swing between stated reference and best levels on criterion $j$. A weight is not just an abstract statement that a criterion is “important”: it depends on the size and meaning of the performance range used to elicit it. Changing the ranges without reconsidering weights can change the model's meaning.

An additive model further assumes that the criteria and preference structure allow the specified aggregation. Strong interactions, noncompensable minimum standards, or a criterion that should never be traded away may call for another model or an explicit constraint. Normalizing numerical weights to sum to one does not validate those assumptions.

A worked comparison

This illustrative comparison shows how the same total can conceal opposing strengths. It uses already scaled preference scores to isolate the effect of the stated weights.

Suppose the decision team agrees on illustrative weights of 0.50 for health gain, 0.30 for equity reach, and 0.20 for implementation ease, using the common 0–10 preference scores above. The additive calculations are:

$$V(A)=0.50(8)+0.30(4)+0.20(6)=6.40,$$

$$V(B)=0.50(6)+0.30(8)+0.20(5)=6.40.$$

Under these particular assumptions, the alternatives tie. The equal total conceals a substantive difference: A scores higher on health gain and implementation ease, while B scores higher on equity reach. A different defensible weighting, performance estimate, or noncompensatory rule could change the ordering. A score of 6.40 is a model-specific preference summary; it is not a QALY total, cost-effectiveness ratio, or probability that an alternative is best.

How to elicit preferences and test uncertainty

Weights should reflect the stakeholders and decision remit. Elicitation can use stated trade-offs over concrete changes in outcomes, followed by checks for understanding and consistency. Report whose responses were used, whether preferences were pooled or displayed separately, and how disagreement was handled; an average weight vector can hide meaningful differences between groups.

Uncertainty enters both performance estimates and preferences. Sensitivity analysis should vary influential input values, scoring functions, weights, and structural choices, then show the conditions under which an alternative's rank or decision changes. Presenting only one set of weights and a final rank makes the result look more settled than the evidence supports.

1. Vary one influential assumption at a time to locate the trade-off or performance threshold where the preferred alternative changes.
2. Examine coherent scenarios that combine plausible changes in evidence, implementation, and stakeholder preferences.
3. Propagate quantified uncertainty where supported while keeping uncertain evidence distinct from disagreement about values.
4. Report the unaggregated consequences so decision makers can judge whether a stable rank still masks an unacceptable outcome.

A budget constraint requires particular care. Adding “cost” as a criterion is not necessarily equivalent to checking whether a portfolio is affordable within a fixed budget. When choosing several interventions, resource limits and opportunity costs may require an explicit constrained allocation analysis.

What MCDA can and cannot decide

MCDA organizes evidence and value judgments so that decision makers can inspect and challenge them. It does not replace the quality assessment of clinical evidence, create a universally valid set of weights, or establish that all relevant values are commensurable. The method is most useful when the model, participants, alternatives, scales, constraints, and uncertainty are transparent enough for a different team to reproduce the comparison.

In health technology assessment, MCDA may complement economic evaluation by making additional decision criteria explicit. If health gain, cost-effectiveness, budget impact, and affordability all appear, define their boundaries carefully to avoid counting the same effect or cost more than once. State whether the output is a ranking, a grouping, a structured deliberation aid, or an input to a further decision process.

Evidence used for this explanation

The ISPOR task force reports below set out the principal health care MCDA approaches and the sequence of implementation. They support the emphasis on transparent criteria, performance, preferences, uncertainty, and decision context.

• Thokala P et al. Multiple Criteria Decision Analysis for Health Care Decision Making: An Introduction, Report 1. Value in Health (2016);19:1–13.
• Marsh K et al. Multiple Criteria Decision Analysis for Health Care Decision Making: Emerging Good Practices, Report 2. Value in Health (2016);19:125–137. DOI: 10.1016/j.jval.2015.12.016.