Agent-Based Model

Agent-Based Models in Health Economic Evaluation

In an agent-based model each person, clinician or organisation is simulated as a separate agent with its own attributes and decision rules, and population results such as case counts, costs and QALYs are totalled after the agents have interacted and changed one another's risks. Health economists use the approach when those interactions change the answer to a decision problem, most often in infectious disease, where screening or vaccinating one person alters the risk faced by others, and in health behaviour and service delivery. The model outputs feed cost-effectiveness analysis, while structure and validation differ from those of other model types. Microsimulation, discrete event simulation, the dynamic transmission model and the system dynamics model have their own pages.

Agents, environment and rules

The ISPOR Simulation Modeling Emerging Good Practices Task Force (Marshall and colleagues, 2015) describes agents as autonomous, interacting objects that sense their environment and act on defined decision rules, and may pursue goals and learn. Chhatwal and He add that agent behaviour is not set by a global controller. In a disease model the agents are people whose attributes, such as age, sex, risk behaviour and disease status, change over time, and the environment is a place such as a hospital, school or neighbourhood. A network defines who can meet, and so infect, whom.

A general notation, given below, shows what each update can depend on.

$$X_i(t+1)=F\left(X_i(t),\,N_i(t),\,E(t),\,A(t),\,U_i(t)\right)$$

where $X_i(t)$ is the state of agent $i$ at time $t$, $N_i(t)$ is the set of agents in contact with agent $i$, $E(t)$ is the state of the environment, $A(t)$ is the intervention or policy in force, $U_i(t)$ is a random input and $F$ is the rule set written for the application. Chhatwal and He note that within each cycle the agents update in a set order, so the sequence of events inside a cycle is part of the model specification.

Emergence and indirect effects

Marshall and colleagues name agency, dynamics and structure as the three core concepts of the method, with structure emerging from agent interaction. Unlike isolated Markov cohorts, individuals in a nonlinear system must be simulated in a population context. Chhatwal and He give an example in which individual decisions to vaccinate, or to stay at home when sick, affect the peak of an influenza epidemic.

For economic evaluation the practical consequence is indirect benefit. Chhatwal and He point out that state-transition models and discrete event simulation typically do not capture direct interaction between individuals, such as transmission of infection (entities in discrete event simulation interact mainly by competing for limited resources, a queue logic agent-based models can also implement), so they can underestimate the value of interventions such as human papillomavirus vaccination, which reduces transmission, or HIV treatment, which also reduces onward spread. Effects on people who never receive the intervention are an externality (see vaccination externalities).

Time, open populations and randomness

Time in an agent-based model can advance in fixed cycles, as in a state-transition model, or jump to the next scheduled event, as in discrete event simulation. Chhatwal and He report that fixed steps are often more convenient, because event scheduling makes interactions harder to implement, and that cycles may need a half-cycle correction. Agent-based models can also represent open populations with births and migration, which Markov models generally do not.

Agent-based models are usually stochastic. Chhatwal and He explain that first-order uncertainty, the random variation between simulated histories, is typically higher than in state-transition or discrete event models, because chance acts both within agents and in their interactions, so more Monte Carlo runs are needed; the number needed depends on structure, number of parameters and time horizon, and can be judged qualitatively or from the variance in outcomes. Common random numbers are harder to apply because interaction can change the sequence of events between strategies. One solution they describe is to give each agent its own random seed.

Worked example of how fewer contacts compound through transmission

All numbers here are illustrative. A susceptible agent has three independent contacts with infectious agents in a day, each with a transmission probability of 0.10. The probability of at least one transmission that day is as follows.

$$P = 1-(1-p)^{k} = 1-(1-0.10)^{3} = 1-0.729 = 0.271$$

where $P$ is the daily probability of infection, $p = 0.10$ is the per-contact transmission probability and $k = 3$ is the number of contacts. A programme that cuts contacts to two a day gives 1 − 0.81 = 0.19.

An infected agent who is infectious for 5 days and meets 3 different susceptible people a day causes 5 × 3 × 0.10 = 1.5 expected onward infections; with two contacts a day the figure is 5 × 2 × 0.10 = 1.0, a direct reduction of one third. Followed as a simple chain from one index case, the next three generations contain 1.5 + 2.25 + 3.375 = 7.125 infections without the programme and 1 + 1 + 1 = 3 with it, a fall of 58% (4.125 out of 7.125). Counting only the 0.5 infections averted in the first generation would capture about an eighth of the 4.125 averted over three generations. The chain assumes every contact is susceptible, so it overstates growth; an agent-based simulation would deplete susceptible agents, cluster contacts in networks and let behaviour respond to prevalence. The population-level counterpart is the basic reproduction number.

From simulated agents to costs and QALYs

Marshall and colleagues list agent-based model outputs including QALYs, mortality, costs, resource use and bed occupancy. The model is run separately for each strategy. It records events and person-time, attaches unit costs and utility weights, discounts, and averages across runs, as shown below.

$$\Delta C=\mathbb{E}[C_{\text{int}}]-\mathbb{E}[C_{\text{comp}}], \qquad \Delta Q=\mathbb{E}[Q_{\text{int}}]-\mathbb{E}[Q_{\text{comp}}]$$

where $\Delta C$ and $\Delta Q$ are the incremental cost and QALYs, $\mathbb{E}$ denotes the mean over simulation runs, and the subscripts denote the intervention and the comparator. The increments feed the ICER.

Chhatwal and He's case study shows how interaction can move the result. They simulated 5,000 people with a hypothetical infectious chronic disease and compared screening 1% of the population each year with no screening, using 5,000 runs per scenario. The ICER of screening ranged from USD 23,091 to USD 60,352 per QALY depending on the contact radius, and infections and deaths averted rose nonlinearly with that radius, a pattern the authors note a state-transition model could not have predicted.

Chhatwal and He describe probabilistic sensitivity analysis in agent-based models as computationally challenging and sometimes impractical, because it combines first-order and second-order uncertainty; Latin hypercube sampling and Gaussian process emulation can reduce the burden. The NICE technology appraisal manual (PMG36, section 4.7.20) asks that model structures limiting the feasibility of probabilistic analysis be specified and justified, and that the choice of structure should not result in failure to characterise uncertainty.

How the method compares with other model types

The ISPOR-SMDM conceptualisation report (Roberts and colleagues, 2012) recommends dynamic transmission, discrete event or agent-based models when individuals interact, and discrete event or agent-based models when the problem involves geography or spatial proximity. The ISPOR-SMDM dynamic transmission report (Pitman and colleagues, 2012) adds that deterministic compartmental models suit average epidemic behaviour in large populations, while stochastic agent-based approaches may be preferred when chance effects, behaviour and disease interaction, or nonrandom mixing matter.

The rows follow Chhatwal and He, who add that compartmental models allow analytical insight that agent-based models do not. Terms overlap. Marshall and colleagues treat microsimulation and agent-based modelling as two traditions of individual-based modelling and use the agent-based label for both.

Applications in infectious disease, behaviour and service delivery

Tracy and colleagues report that in public health the method was historically applied almost exclusively to infectious disease transmission and control, where individual interactions give rise to population patterns of incidence. They also describe models of smoking, alcohol, physical inactivity and diet, with obesity and its correlates the most frequent subject of non-communicable disease applications, and tobacco control models that can identify potential unintended consequences. Marshall and colleagues cite health care delivery uses such as the diffusion of new drugs through patient, physician and pharmacist interactions.

Calibration, validation and transparency

Chhatwal and He define calibration as adjusting model inputs until outputs match the observed system; they expect it to be needed more often than in other approaches, for example to estimate an unobserved transmission rate from known incidence. For model validation, the ISPOR-SMDM report by Eddy and colleagues (2012) lists face validity, verification, cross validation, external validation and predictive validation, and Tracy and colleagues point out that validation data should ideally be independent of the data used to build and calibrate the model.

Pitman and colleagues recommend that agent-based models describe the rules governing the agents, input values, initial conditions and all submodels, including movement and mixing. The ODD protocol (Overview, Design concepts, Details), updated by Grimm and colleagues in 2020, gives a seven-element structure designed to make such descriptions easier to write and read and the models easier to replicate. Chapter 4 of the NICE manual (PMG36) does not name agent-based models, but its general requirements apply. Section 4.6.3 says the chosen type of model should be justified for each new decision problem, section 4.6.4 asks for quality assurance and validation results, and section 4.6.1 asks for sensitivity analyses where alternative plausible assumptions exist, a structural uncertainty question for rules about contact and behaviour.

Where agent-based models are misread or misused

Chhatwal and He state that agent-based models can be more challenging to construct and need large computing power, and that they do not replace state-transition, discrete event or compartmental models, which solve many problems efficiently. Bonabeau notes that the right level of detail remains an art more than a science, and that human agents bring soft factors that are hard to quantify, calibrate and sometimes justify. Several misreadings recur.

1. Individual-level means agent-based. Individuals simulated without interaction or adaptation form a microsimulation, whatever the label.
2. More detail means more validity. Each added rule brings parameters that need data and testing.
3. A good fit proves the mechanism. Different contact and transmission rules can reproduce the same incidence, so fit alone does not validate them.

Sources

• Bonabeau E. Agent-based modeling: methods and techniques for simulating human systems. Proceedings of the National Academy of Sciences of the USA. 2002;99(Suppl 3):7280-7287. https://doi.org/10.1073/pnas.082080899
• Chhatwal J, He T. Economic evaluations with agent-based modelling: an introduction. PharmacoEconomics. 2015;33(5):423-433. https://doi.org/10.1007/s40273-015-0254-2
• Eddy DM, Hollingworth W, Caro JJ, Tsevat J, McDonald KM, Wong JB. Model transparency and validation: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-7. Value in Health. 2012;15(6):843-850. https://doi.org/10.1016/j.jval.2012.04.012
• Grimm V, Railsback SF, Vincenot CE, Berger U, Gallagher C, DeAngelis DL, et al. The ODD protocol for describing agent-based and other simulation models: a second update to improve clarity, replication, and structural realism. Journal of Artificial Societies and Social Simulation. 2020;23(2):7. https://doi.org/10.18564/jasss.4259
• Marshall DA, Burgos-Liz L, IJzerman MJ, Osgood ND, Padula WV, Higashi MK, et al. Applying dynamic simulation modeling methods in health care delivery research: the SIMULATE checklist. Report of the ISPOR Simulation Modeling Emerging Good Practices Task Force. Value in Health. 2015;18(1):5-16. https://doi.org/10.1016/j.jval.2014.12.001
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). London: NICE; 2022, last updated 13 October 2026. Sections 4.6.1, 4.6.3, 4.6.4 and 4.7.20.
• Pitman R, Fisman D, Zaric GS, Postma M, Kretzschmar M, Edmunds J, Brisson M. Dynamic transmission modeling: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-5. Value in Health. 2012;15(6):828-834. https://doi.org/10.1016/j.jval.2012.06.011
• Roberts M, Russell LB, Paltiel AD, Chambers M, McEwan P, Krahn M. Conceptualizing a model: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-2. Value in Health. 2012;15(6):804-811. https://doi.org/10.1016/j.jval.2012.06.016
• Tracy M, Cerdá M, Keyes KM. Agent-based modeling in public health: current applications and future directions. Annual Review of Public Health. 2018;39:77-94. https://doi.org/10.1146/annurev-publhealth-040617-014317