Health Economic Model

How a health economic model supports decisions

A health economic model brings together evidence about disease progression, treatment effects, costs and health outcomes within a consistent analytical structure. It allows decision makers to compare alternative interventions when no single study observes every relevant consequence, patient pathway or period of interest.

The model does not predict the future with certainty. It estimates expected outcomes under stated assumptions so that the consequences of alternative decisions can be compared transparently.

Defining the decision problem

A model should begin with a clearly specified decision problem because its structure and evidence requirements depend on the decision it is intended to inform. The population, interventions, comparators, perspective, outcomes and time horizon determine which costs and consequences belong in the analysis.

The decision problem commonly specifies:

• Population: The patients or population for whom the decision is being considered.
• Intervention: The technology, programme, service or policy being evaluated.
• Comparator: The relevant alternative, which may be current practice, another intervention or no intervention.
• Perspective: The viewpoint that determines which costs and outcomes are included.
• Outcomes: The health and economic consequences used to compare alternatives.
• Time horizon: The period over which relevant differences are captured.
• Decision setting: The jurisdiction, service context and policy question.

These elements should be internally consistent. The time horizon must capture important differences, while selected costs must reflect the analytical perspective.

Representing patient pathways and health outcomes

The model structure represents events, pathways or health states through which patients may move. It should capture differences that could affect the decision without adding complexity that does not improve the analysis.

Common structures include:

• A decision tree for a sequence of events over a relatively short period.
• A state-transition model for movement between health states over repeated cycles.
• A partitioned survival model deriving state occupancy from survival curves.
• A discrete-event simulation representing individual events and their timing.
• An individual-level simulation representing patient variation and history.
• A dynamic transmission model representing interactions between individuals.
• A hybrid model combining structures when one approach is insufficient.

The simplest structure capable of answering the decision question is generally preferred. Added complexity is justified only when it represents an important feature of the disease, intervention or decision.

Connecting model inputs to outcomes

A health economic model combines inputs from different sources because the required evidence is rarely contained in one dataset. Each input should have a clear definition, unit, source, applicable population and role.

Typical inputs include:

• Baseline risks or transition probabilities.
• Relative treatment effects.
• Event rates, survival estimates or progression parameters.
• Resource use and unit costs.
• Health-state utility values.
• Adverse-event frequencies, costs and health consequences.
• Treatment duration, discontinuation and adherence.
• Mortality risks and long-term outcomes.
• Implementation, monitoring and follow-up requirements.

Differences in population, setting, follow-up, outcome definition and study design may require adjustment, synthesis or explicit representation of uncertainty.

Calculating expected costs and outcomes

The model estimates expected costs and outcomes for each alternative. In a cohort model, an expected outcome can be calculated by weighting each possible result by its probability.

$$ E(O) = \sum_{i=1}^{n} p_i O_i $$

where (p_i) is the probability of outcome (i), (O_i) is its value and (n) is the number of possible outcomes.

Expected costs can be calculated as:

$$ E(C) = \sum_{i=1}^{n} p_i C_i $$

More complex models repeat these calculations across cycles, events, health states or simulated individuals and accumulate the results for each intervention.

Accounting for time

Time matters because costs and outcomes occur at different points and diseases and treatments can have long-term consequences. Cycle length, time horizon and treatment of recurring events should reflect the clinical process.

Future values may be discounted:

$$ PV(V_t) = \frac{V_t}{(1 + r)^t} $$

where (V_t) is the value in period (t), (r) is the applicable discount rate and (PV(V_t)) is its present value. The rates and sources should be reported explicitly.

Comparing alternative interventions

Results are compared incrementally because the decision concerns what is gained and what additional resources are required when one option replaces another.

$$ \Delta C = C_1 - C_0 $$

$$ \Delta E = E_1 - E_0 $$

When outcomes are quality-adjusted life years, an incremental cost-effectiveness ratio may be calculated:

$$ ICER = \frac{\Delta C}{\Delta E} $$

Net monetary benefit is:

$$ NMB = (\lambda \times E) - C $$

Incremental net monetary benefit is:

$$ INMB = (\lambda \times \Delta E) - \Delta C $$

A positive incremental net monetary benefit indicates cost effectiveness relative to the comparator at threshold (\lambda), subject to the evidence and assumptions.

Handling uncertainty

Model results are uncertain because evidence is incomplete and the model simplifies reality. Uncertainty should be examined rather than hidden within a single base-case result.

Important forms include:

• Parameter uncertainty in estimated model inputs.
• Structural uncertainty in representation of the disease and interventions.
• Methodological uncertainty from analytical choices.
• Heterogeneity in costs or outcomes between patient groups.
• Stochastic variability between otherwise similar individuals or events.

Deterministic sensitivity analysis changes selected inputs or assumptions. Probabilistic sensitivity analysis assigns distributions to uncertain parameters and samples from them to estimate joint uncertainty.

Checking whether the model is credible

Validation assesses whether the model is suitable for its purpose and whether calculations and behaviour are credible. It should accompany development, analysis and reporting.

Key checks include:

• Face validity: Experts assess whether structure, assumptions and results are reasonable.
• Internal validity: Formulae, code and data transformations are checked.
• External validity: Outputs are compared with relevant observed data.
• Cross-model validity: Results are compared with similar models.
• Predictive validity: Predictions are compared with later outcomes when possible.
• Extreme-value testing: Inputs are assigned extreme values to test logical behaviour.
• Traceability: Inputs, assumptions and calculations can be followed to reported results.

Agreement with observed data does not prove that every model component is correct. Validation should examine both results and their generating processes.

Making assumptions transparent

Every model contains assumptions because evidence is incomplete and reality cannot be represented fully. Assumptions may concern treatment duration, progression, extrapolation, adherence, resource use or mortality.

A defensible assumption should:

1. Address an identified gap.
2. Have a clinical, empirical or methodological rationale.
3. Be documented clearly.
4. Be tested when alternatives could change the result.
5. Be reviewed by appropriate experts.

Labelling an input as an assumption does not make it harmless. Influential assumptions require particular scrutiny.

A simplified worked example

Suppose current care costs £18,000 and produces 7.20 quality-adjusted life years, while a new intervention costs £21,500 and produces 7.45 quality-adjusted life years.

$$ \Delta C = £21{,}500 - £18{,}000 = £3{,}500 $$

$$ \Delta E = 7.45 - 7.20 = 0.25\ \text{QALYs} $$

$$ ICER = \frac{£3{,}500}{0.25\ \text{QALYs}} = £14{,}000\ \text{per QALY gained} $$

At a threshold of £20,000 per quality-adjusted life year:

$$ INMB = (£20{,}000 \times 0.25) - £3{,}500 = £1{,}500 $$

The positive incremental net monetary benefit supports cost effectiveness at this threshold, conditional on the model's evidence, structure and uncertainty.

Interpreting model results

A model result is a conditional estimate rather than a fact detached from its assumptions. Interpretation should consider expected health, expected cost, cost effectiveness, uncertainty, subgroup variation, affordability, equity and implementation.

A model can inform a decision without determining it. Decision makers may also consider budget impact, unmet need, feasibility and evidence quality.

Common modelling errors

Models can produce precise numbers even when their structure or inputs are inappropriate. Apparent precision should not be confused with validity.

Common errors include:

• Using an irrelevant comparator.
• Selecting a time horizon that omits important consequences.
• Combining incompatible evidence without justification.
• Double-counting costs, events or health effects.
• Extrapolating treatment effects without testing alternatives.
• Confusing average with incremental results.
• Reporting an ICER without uncertainty.
• Using probabilities inconsistent with cycle length.
• Applying discounting incorrectly.
• Treating calibration as proof of validity.
• Adding unsupported complexity.
• Failing to document assumptions and transformations.

What makes a model useful

A useful health economic model is proportionate to the decision, transparent enough to scrutinise and flexible enough to test important uncertainty. Its value comes from making the consequences of evidence and assumptions visible rather than producing one definitive number.

Another analyst should be able to understand how inputs become results, reproduce important calculations and identify where judgement affects the conclusion.