Modelling

Why this matters in health economics

Almost every important funding decision in health has to be made on incomplete evidence. A trial follows patients for two years; the drug will be taken for twenty. A study is run in one country's hospitals; the decision is for another country's clinics. A new test is compared against placebo; the real choice is against three treatments already in use. A model is the structured way of bridging those gaps — of taking what is known and reasoning carefully to the quantity a decision-maker actually needs: the lifetime cost and health consequence of choosing option A over option B. Without a model, the alternative is not "unmodelled certainty"; it is an implicit, undocumented model in someone's head, with none of the assumptions visible and none of them testable.

For a director, this is where public money is committed at scale. When a national payer decides to reimburse a medicine, fund a screening programme, or reconfigure a service, the number that anchors the decision — the incremental cost per quality-adjusted life year (QALY) — almost always comes out of a model, not a trial. The economic evaluation concepts that number expresses (QALYs, incremental cost-effectiveness ratios, thresholds, perspective) belong to Chapter 2.1 — Economic Evaluation and are assumed here; this chapter owns the machinery that produces the estimate. If the machinery is wrong, the threshold is being applied to a fiction.

The stakes are therefore both financial and ethical. A model that overstates benefit funds something that displaces better uses of the same budget — the opportunity cost falls on unnamed patients elsewhere. A model that is opaque cannot be challenged, and unchallengeable analysis is where capture, wishful thinking, and vendor optimism hide. The discipline of modelling — declaring structure, testing every assumption, and quantifying what you do not know — is what turns a persuasive slide into evidence a public body can defend.

Core concepts

Decision analysis is the formal framework underneath all of this: laying out the options, the chance events that follow each, the probabilities of those events, and the value of each outcome, then computing the expected value of each option. A health economic model is decision analysis applied to a health choice, with cost and health outcome as the values being weighed. The foundational text for the field is Briggs, Sculpher and Claxton's Decision Modelling for Health Economic Evaluation, whose framework this chapter follows.

The simplest structure is the decision tree: a branching diagram from a decision node through chance nodes to final outcomes, each branch carrying a probability and each endpoint a cost and a health payoff. Trees are clear and quick, and they suit decisions that resolve over a short, fixed horizon — an acute event, a diagnostic pathway. Their weakness is time: a tree has no natural way to represent events that recur, conditions that persist, or risks that change year after year, because every possibility must be drawn as an ever-branching path.

For chronic disease, the workhorse is the Markov chain, or Markov cohort model. It represents a disease as a set of mutually exclusive health states — for example well, complication, dead — and moves a hypothetical cohort between them in fixed time cycles according to transition probabilities. Accumulating cost and quality of life across many cycles yields lifetime totals. Its defining simplification is the Markov assumption: transitions depend only on the current state, not on history, so a standard model cannot "remember" how long a patient has been ill. Analysts work around this with tunnel states or time-dependent transitions, but the assumption is the first thing a reviewer should interrogate.

When patient history, individual characteristics, or interactions matter too much to lose, modellers turn to individual-level simulation. Microsimulation runs patients through the model one at a time, each carrying attributes (age, risk factors, event history) that shape their trajectory, so heterogeneity and memory are preserved. Where patients also compete for shared, constrained resources — beds, theatres, staff, a transplant waiting list — discrete-event simulation adds queues and timing, modelling the system rather than a lone patient. These methods buy realism at the price of data hunger, run time, and a harder job explaining the result.

No model output is a single certain number, and pretending otherwise is the cardinal sin of the field. Sensitivity analysis asks how the conclusion moves when inputs change. Deterministic sensitivity analysis varies one or a few parameters across plausible ranges (often shown as a tornado diagram). Probabilistic sensitivity analysis assigns each uncertain parameter a probability distribution and, using Monte Carlo sampling, runs the model thousands of times to produce a distribution of results — summarized as the probability that an option is cost-effective at a given threshold. Uncertainty that remains after this can be valued: value of information analysis estimates what it would be worth to commission more research before deciding, turning "we're not sure" into a number a research budget can act on.

A model is only as trustworthy as its validation. Face validity asks whether the structure and results make clinical sense; internal validity (verification) checks the model does what its equations intend, free of coding error; cross-validity compares results against other models of the same problem; and external validity tests predictions against real outcomes the model did not use as inputs. Finally, the modelling toolkit sits inside the broader machinery of health technology assessment (HTA) — the process by which bodies such as England's NICE, Germany's IQWiG, Canada's CDA-AMC, Australia's PBAC, and the United States' ICER weigh evidence for funding decisions worldwide.

Best practices

1. Decide trial-based versus model-based before you build anything. A within-trial analysis alongside a randomized controlled trial is the right tool when the trial's horizon, comparators, and population match the decision. A model is required when — as is usual — the decision outstretches the trial: lifetime consequences, comparators never trialled head-to-head, or a target population different from those enrolled. Most real decisions need both: the trial anchors short-term effect, the model extrapolates it. State which you are doing and why on the first page.

2. Let the decision problem choose the model type, never the reverse. A short, acute, non-recurring decision suits a decision tree; a chronic condition with recurring events suits a Markov model; strong patient heterogeneity or event memory pushes to microsimulation; constrained shared resources and queuing push to discrete-event simulation. Choosing a structure because it is familiar, or because a vendor already owns one, is how models come to mis-fit the question they are meant to answer.

3. Fix the time horizon long enough to capture all relevant differences. The horizon must run until no further meaningful differences in cost or health accrue between the options — for a lifelong condition, that means a lifetime. Truncating early flatters interventions whose costs land upfront and whose benefits arrive late (prevention, cure), and it is one of the most common ways a model quietly biases its own answer. Justify the horizon explicitly against the disease's natural history.

4. Choose model structure to reflect the disease, and name the assumptions it forces. Health states must be clinically meaningful, mutually exclusive, and collectively exhaustive; cycle length must be short enough to capture the fastest important event. Every structure imposes simplifications — the Markov memoryless assumption is the classic example — so list them where a reviewer can see them and show that the ones that matter have been tested or relaxed.

5. Source every parameter deliberately and grade its evidence. Transition probabilities, costs, and quality-of-life weights should each trace to a stated source, with the strongest evidence used for the parameters that drive the result. Be explicit where a systematic review, a single study, a registry, or an expert judgement is doing the work, and prefer relative effects from randomized evidence combined with baseline risks from local observational data — mixing sources is legitimate, hiding the mix is not.

6. Model the comparators the decision actually faces, at real-world doses and prices. A cost-effective result against placebo or against an outdated standard is close to meaningless if clinicians actually choose between three current options. Include all relevant comparators, use the prices and adherence patterns that will obtain in practice, and be honest when a head-to-head comparison rests on an indirect or network comparison rather than direct trial evidence.

7. Extrapolate beyond the trial with declared, tested survival assumptions. Where the model projects effect past the observed data — almost always — the choice of extrapolation (which survival curve, whether treatment effect persists, wanes, or stops) can dominate the answer. Fit alternative parametric curves, show them against the observed data and external evidence, and present the range rather than smuggling in the most optimistic fit as a point estimate.

8. Characterize uncertainty probabilistically, not just one parameter at a time. Deterministic one-way analysis and tornado diagrams show which inputs matter, but only probabilistic sensitivity analysis, propagating all uncertainty together through Monte Carlo simulation, yields the probability that a decision is right. Report the cost-effectiveness acceptability curve alongside the point estimate; a favourable ratio with a 55% probability of cost-effectiveness is a different decision from the same ratio at 95%.

9. Separate the kinds of uncertainty and treat each on its own terms. Parameter uncertainty (we do not know the true value) is handled by probabilistic analysis; structural uncertainty (we are unsure the model is built right) needs scenario analysis across alternative structures; heterogeneity (the answer genuinely differs by subgroup) needs subgroup results, not an average that fits no one. Conflating them — for instance, hiding a structural doubt inside a wide parameter distribution — misrepresents what is actually unknown.

10. Validate at every level, and write the validation down. Check face validity with clinicians who did not build the model; verify the code with independent testing and extreme-value checks; cross-validate against published models of the same disease and explain divergences; and, where any external outcome data exist, test the model's predictions against them. A model presented for a funding decision without a validation account should not be trusted, however sophisticated it looks.

11. Make the model transparent and reproducible enough for an adversary to rebuild. Document structure, every input with its source, and every assumption, so a sceptical reviewer could in principle reconstruct the result. Transparency is not a courtesy; it is the mechanism by which optimistic errors are caught before public money moves, which is why HTA bodies increasingly demand executable models and full parameter tables rather than a summary ratio.

12. Quantify whether more research is worth buying before you commit. When uncertainty is wide and the sums large, value-of-information analysis estimates the expected value of resolving that uncertainty — sometimes justifying an "approve with research" or "only in research" decision rather than a simple yes or no. It reframes a stalemate ("the evidence is immature") into an economic question ("is a trial worth its cost, given the decision at stake?").

Questions to discuss with your team

1. Does this decision genuinely need a model, and if so, what is the model doing that the trial cannot? The instinct in many organizations is to reach for a model reflexively, or to distrust models wholesale as "made-up numbers" — both are wrong. The productive question is what specific gap the model bridges: extrapolating a two-year trial to a lifetime, comparing against a treatment never trialled head-to-head, or transporting evidence from one health system to yours. Naming the gap disciplines the model, because it tells you which part of the structure carries the decision and therefore deserves the most scrutiny and the strongest data. It also tells you when a model is not warranted — where a good within-trial analysis already matches the decision, an elaborate model adds assumptions without adding truth. An honest answer states the single most important thing the model is extrapolating and how much of the result rides on that extrapolation.

2. Which one or two assumptions, if wrong, would flip our conclusion — and how confident are we in exactly those? Every model has a handful of load-bearing assumptions and a long tail of inputs that barely matter; the danger is spending scrutiny evenly instead of on the joints that carry the weight. A tornado diagram or one-way sensitivity analysis identifies the drivers mechanically, but the team conversation is about evidence quality on precisely those drivers: is the pivotal transition probability from a strong meta-analysis or one small study, is the survival extrapolation anchored to external data or a hopeful curve fit? The uncomfortable pattern is a confident headline ratio resting on a parameter for which the evidence is thin. An honest answer does not claim the model is robust in general; it names the specific assumptions the decision hangs on and grades the evidence behind each, then decides whether that is enough to act on or a reason to gather more.

3. Who built this model, whose case does it help, and would an independent rebuild reach the same answer? Many models placed in front of payers are built by, or funded by, a party with a direct interest in the result — a manufacturer seeking reimbursement, a service seeking investment. That does not make them wrong, but it makes independent scrutiny non-negotiable, and it raises specific questions: were comparators chosen to flatter, was the most optimistic extrapolation selected, is the model transparent enough to be interrogated at all? The tension is that the people with the data and the modelling capacity are often the interested party, so the answer is rarely to reject their model outright but to demand transparency, run your own sensitivity analyses on their model, and cross-validate against independent work. An honest answer is candid about provenance and conflict, and treats a model that cannot be opened and re-run as a red flag rather than a proprietary detail to be waved through.

4. Has the disease chosen our model structure, or has convenience chosen it for us? The structure — decision tree, Markov cohort, microsimulation, discrete-event simulation — should follow from the clinical problem: how the condition unfolds, whether events recur, whether patient history or shared, constrained resources matter. The failure pattern is a structure adopted because it is familiar, because a vendor already owns one, or because it is quick to build, and then bent to fit a disease it does not suit. The team conversation is concrete: does the condition recur or persist in a way a decision tree cannot capture; does the Markov memoryless assumption flatten a risk that genuinely depends on history; do patients compete for beds or theatres in a way a cohort model ignores? Each structure buys clarity at the price of specific simplifications, so the productive question is not "is this the best model" but "which simplifications has this structure forced on us, and does any of them touch the part of the disease the decision turns on?" An honest answer names the structural assumptions the choice imposes and shows the ones that matter have been tested, rather than defending the structure because it is already built.

5. Which kind of uncertainty are we actually facing here, and are we treating each on its own terms? It is easy to collapse "we're not sure" into a single wide error bar, but the field distinguishes three quite different things: parameter uncertainty (we do not know the true value of an input), structural uncertainty (we are unsure the model is built the right way), and heterogeneity (the answer genuinely differs between subgroups). Each demands a different response — probabilistic analysis for parameters, scenario analysis across alternative structures for the second, subgroup results rather than an average for the third — and conflating them misrepresents what is unknown. The classic sleight of hand is hiding a structural doubt inside a fat parameter distribution, so the headline still reports a single reassuring probability of cost-effectiveness. The team should ask which of the three is really driving the doubt on this decision, and whether the analysis in front of them addresses that kind or merely the most convenient kind. An honest answer separates the three explicitly and admits where a doubt is structural — the hardest kind to quantify and the easiest to bury.

6. Given what we still do not know, should we decide now or pay to learn more first? When uncertainty is wide and the sum committed is large, "yes" and "no" are not the only options: an "approve with research" or "only in research" decision keeps the door open while the evidence matures. Value-of-information analysis turns the stalemate — "the evidence is immature" — into an economic question: what would it be worth to resolve the uncertainty before deciding, and does that exceed the plausible cost of the study that would resolve it? The tension is real, because delay has its own cost in health forgone by patients who wait, and because a manufacturer or service has every incentive to bank an early yes rather than commit to generating data. The team should weigh where the residual uncertainty is concentrated, whether a feasible study could actually narrow it in a useful timeframe, and what a conditional arrangement would require of the interested party. An honest answer treats "decide now versus buy more evidence" as a quantifiable choice rather than a matter of nerve, and is willing to recommend a conditional yes when the value of learning justifies it.

In practice: a health economics example

The National Health Insurance Fund of the fictional social-insurance country of Solenne is deciding whether to reimburse a new oral therapy for chronic heart failure. The manufacturer's submission reports a favourable incremental cost-effectiveness ratio, comfortably below the Fund's stated threshold. The pivotal evidence is a single randomized controlled trial: 18 months of follow-up, showing the drug reduces hospitalizations for heart failure and modestly improves survival against standard care. The Fund's assessment committee asks its economics team to appraise the model behind the number, not just the number.

The team first confirms that a model is unavoidable. Heart failure is lifelong; the trial ran 18 months; the decision concerns costs and benefits over patients' remaining lifetimes. A within-trial analysis would answer the wrong question. The manufacturer has, correctly, built a Markov cohort model with states for stable disease, hospitalized, and death, cycling monthly to capture frequent admissions. So far the structure fits the disease. The team's scrutiny then turns to the joints that carry the result.

Two assumptions dominate. The first is survival extrapolation: beyond 18 months the model projects a mortality benefit that persists undiminished for life, using the parametric curve with the most optimistic long-run fit. When the team refits alternative curves and tests a scenario in which the treatment effect wanes after five years — consistent with external registry evidence on similar drugs — the lifetime QALY gain shrinks and the ratio rises above the threshold. The second is the comparator: the model compares against an older standard of care, but Solenne's guidelines now recommend a newer combination that the trial did not include, reachable only through an indirect comparison with wide uncertainty. The team also notes the Markov memoryless assumption flattens the higher re-admission risk of patients recently hospitalized, which they address with a short tunnel state.

The team re-runs the model probabilistically, propagating all parameter uncertainty through Monte Carlo simulation. The cost-effectiveness acceptability curve shows roughly a 50% probability of cost-effectiveness at the Fund's threshold — a coin toss, not the confident case the point estimate implied. Because the decision is large and the uncertainty concentrated in the survival extrapolation, they run a value-of-information analysis: the expected value of resolving that uncertainty exceeds the plausible cost of a longer follow-up study. The committee's recommendation is neither a flat yes nor a flat no. It reimburses the therapy under a managed-entry arrangement with a confidential discount that improves the ratio, conditional on the manufacturer supplying extended survival data within three years — an "approve with research" decision that the modelling, not intuition, made defensible. The pricing mechanics of that arrangement belong to Chapter 2.4 — Pharmacoeconomics.

Four sector lenses

Startup

A digital health or device start-up usually builds its first model to raise money or to enter an HTA process it has never faced, often with sparse evidence — a small single-arm study, surrogate endpoints, strong founder conviction. The temptation is a model engineered to clear the threshold, with a short horizon that hides late costs and an optimistic extrapolation presented as fact. The wiser path is an early, deliberately conservative model that surfaces which evidence gap most threatens the value case, so scarce trial money is spent closing exactly that gap. A transparent model that honestly shows wide uncertainty is more fundable and more credible to a payer than a polished one that no reviewer can open.

Small business

A small but established provider, practice, or supplier — a specialist clinic, a diagnostics firm, a device distributor with a settled product — usually meets modelling not to raise capital but to answer a real purchasing or reimbursement question: will a payer fund this, is a service line worth continuing, does an equipment upgrade pay for itself? Unlike a start-up, it has actual operating data — real costs, throughput, local outcomes — but rarely an in-house health economist, so the practical risk is either outsourcing the model to the vendor whose product is under evaluation, or building a spreadsheet that never tests its own assumptions. The sensible course is a modest, transparent model that leans on its own real-world data for the inputs it can source locally and borrows published estimates, honestly graded, for the rest, with a simple sensitivity analysis on the two or three parameters that move the answer. Its credibility rests less on sophistication than on being open about where the numbers come from and being able to re-run the case when a price or a payer's threshold shifts.

Enterprise

A large manufacturer, hospital group, or insurer runs modelling as an industrial capability: reusable model platforms, standard parameter libraries, and dedicated health-economics and outcomes-research teams who prepare submissions for many jurisdictions at once. The strength is rigour, reproducibility, and the ability to adapt one global model to each country's methods guide; the risk is that scale and self-interest combine to produce sophisticated models optimized to persuade, with structural choices that quietly favour the sponsor. Enterprise credibility depends on governance that separates the modellers from the commercial pressure, on submitting fully executable and transparent models, and on inviting rather than resisting independent replication.

Government

A national payer, HTA body, or ministry is the consumer and referee of models more often than the builder, and its discipline is critical review at scale: a published methods guide that constrains horizon, perspective, discounting, and uncertainty reporting, and the capacity to re-run and challenge a sponsor's model rather than accept its headline. Bodies such as NICE, IQWiG, PBAC, CDA-AMC, and ICER exist to impose exactly this discipline, and increasingly they build or commission independent models to cross-validate industry submissions. Government also carries the decisions modelling makes possible but cannot make alone — approve, reject, or approve-with-research — and the accountability for the opportunity cost that every yes imposes on patients who never see the committee.

Common failure modes

• Building a model when a trial already answers the question. Adding assumptions where good within-trial evidence matches the decision, importing bias for no gain. Fix: choose trial-based versus model-based deliberately, and model only the gap the trial cannot cover.

• Truncating the time horizon. Ending the model before late benefits or costs accrue, flattering upfront-cost interventions such as prevention. Fix: run the horizon until no meaningful differences remain — a lifetime for lifelong conditions — and justify it against natural history.

• Optimistic extrapolation smuggled in as a point estimate. Choosing the survival curve or effect-persistence assumption that most flatters the result and presenting it as the base case. Fix: fit alternatives, test effect waning, show the range against external data.

• Reporting a point estimate with no uncertainty. A single ratio implying false precision. Fix: always run probabilistic sensitivity analysis and report the acceptability curve alongside the point estimate.

• Confusing the types of uncertainty. Hiding a structural doubt inside a wide parameter distribution, or averaging over real heterogeneity. Fix: handle parameter uncertainty probabilistically, structural uncertainty by scenario, and heterogeneity by subgroup.

• Weak or absent comparators. Showing cost-effectiveness against placebo or an outdated standard when clinicians choose among current options. Fix: include all relevant comparators at real prices and adherence, and be honest about indirect comparisons.

• The black-box model. A result that cannot be opened, re-run, or reproduced, especially from an interested party. Fix: demand executable models, full parameter tables, and a written validation account before any decision.

• Skipping validation. Trusting a sophisticated-looking model with no face, internal, cross, or external checks. Fix: validate at every level and document it; treat an unvalidated model as unproven.

Maturity model

Checklist

• State explicitly whether the evaluation is trial-based, model-based, or both, and why.
• Justify the model type (tree, Markov, microsimulation, discrete-event) against the decision problem and disease.
• Set the time horizon long enough that no further meaningful cost or health differences accrue, and justify it.
• List every structural assumption, including the Markov memoryless assumption where relevant, and test the ones that matter.
• Trace every parameter to a stated source and grade the evidence behind the drivers of the result.
• Include all relevant real-world comparators at realistic prices and adherence.
• Show alternative extrapolation assumptions and their effect on the conclusion, not just the base case.
• Run probabilistic sensitivity analysis and report a cost-effectiveness acceptability curve alongside the point estimate.
• Separate parameter, structural, and heterogeneity uncertainty and address each appropriately.
• Validate the model (face, internal, cross, and where possible external) and write the validation account down.
• Ensure the model is transparent and reproducible enough for an independent reviewer to rebuild.
• Where uncertainty is wide and the decision large, run a value-of-information analysis to weigh commissioning more research.

Key sources

• Andrew Briggs, Mark Sculpher & Karl Claxton, Decision Modelling for Health Economic Evaluation (Oxford University Press) — the standard framework for decision-analytic modelling in health economics.
• Alastair Gray, Philip Clarke, Jane Wolstenholme & Sarah Wordsworth, Applied Methods of Cost-Effectiveness Analysis in Health Care (Oxford University Press) — applied model-building and cost-effectiveness methods.
• Henry Glick, Jalpa Doshi, Seema Sonnad & Daniel Polsky, Economic Evaluation in Clinical Trials (Oxford University Press) — trial-based evaluation and within-trial versus model-based choice.
• ISPOR–SMDM Modelling Good Research Practices Task Force reports — good-practice guidance on conceptualising models, decision trees, Markov models, microsimulation, discrete-event simulation, and model transparency and validation.
• NICE health technology evaluations manual (PMG36) — methods requirements for models submitted to a national HTA body — https://www.nice.org.uk/process/pmg36
• Economics Network, Health Economics for Teachers — modelling module — https://economicsnetwork.ac.uk/health/teachers

References

1. Decision analysis — Wikipedia — https://en.wikipedia.org/wiki/Decision_analysis
2. Decision tree — Wikipedia — https://en.wikipedia.org/wiki/Decision_tree
3. Markov chain — Wikipedia — https://en.wikipedia.org/wiki/Markov_chain
4. Microsimulation — Wikipedia — https://en.wikipedia.org/wiki/Microsimulation
5. Discrete-event simulation — Wikipedia — https://en.wikipedia.org/wiki/Discrete-event_simulation
6. Sensitivity analysis — Wikipedia — https://en.wikipedia.org/wiki/Sensitivity_analysis
7. Monte Carlo method — Wikipedia — https://en.wikipedia.org/wiki/Monte_Carlo_method
8. Value of information — Wikipedia — https://en.wikipedia.org/wiki/Value_of_information
9. Statistical model validation — Wikipedia — https://en.wikipedia.org/wiki/Statistical_model_validation
10. Health technology assessment — Wikipedia — https://en.wikipedia.org/wiki/Health_technology_assessment
11. Randomized controlled trial — Wikipedia — https://en.wikipedia.org/wiki/Randomized_controlled_trial
12. Andrew Briggs, Mark Sculpher & Karl Claxton, Decision Modelling for Health Economic Evaluation — Oxford University Press, 2006.
13. Alastair Gray, Philip Clarke, Jane Wolstenholme & Sarah Wordsworth, Applied Methods of Cost-Effectiveness Analysis in Health Care — Oxford University Press, 2011.
14. NICE health technology evaluations manual (PMG36) — National Institute for Health and Care Excellence — https://www.nice.org.uk/process/pmg36
15. Economics Network — Health Economics for Teachers — https://economicsnetwork.ac.uk/health/teachers