Table 1 Description of modelling approaches employed in health economic evaluation

Decision tree

Decision trees embody the central paradigm of decision analysis. Events in the tree are typically arranged in temporal order from left to right. Decisions are broken down into three components:

(i) Decision node decision point between competing strategies

(ii) Chance node consequence to a given decision. Typically indicates point where two or more alternative chance events for a patient are possible. May contain sequential chance events

(iii) Terminal node Terminal branch, representing the value of a particular strategy

Branches connect the nodes and represent the pathways through the tree. At each chance node, the probabilities of each consequence will determine the proportion of patients progressing down each unique path

Consequences such as costs and effects of events and decisions may be attributed at each chance node of the tree or accumulated at the terminal nodes. The expected effect and/or costs associated with each treatment option or branch is estimated by ‘rolling’ back the tree whereby a weighted average of the value of all branches emanating from a decision node is calculated

Markov cohort model

Markov cohort models describe the transition of patients as they move through health states over time. Health states are mutually exclusive events, representing the entirety of the disease process and patients are assumed to be in one of a finite number of health states (known as the unitary state requirement). Patients within the same health state are assumed homogeneous

Movement between health states are governed by transition probabilities that occur only once per Markov cycle (i.e. a defined time period). The transition probabilities depend only on the starting state and not on any of the previous health states (i.e. memoryless assumption)

The model is run over many cycles to build a profile of how many patients are in each state of the model over time

Estimates of costs and health outcomes are attached to the states within the model. Cycle sum are calculated as the weighted average of the proportion of a cohort in a health state multiplied by the value for that particular health state, summing across all health states. Expected costs and QALYs are then calculated by summing all cycle sums over the model’s time horizon

Markov microsimulation

Markov microsimulation simulates individual patients over time. As individuals are modelled separately, microsimulation can store information as to what has happened to the individual (i.e. memory). Similarly, as individuals are modelled, there is no need to assume homogeneity between patients. The unitary state requirement remains as patients can only be in one of a finite number of health states during each cycle. Transitions govern patient prognosis and are calculated by model parameters that reflect actual event/transition rates and may be conditional on previous and current risk factors and historical outcomes. Transitions occur only once per cycle

Consequences such as costs and effects of events are attributed to health states and are summed over each cycle. Each patient has their own respective costs and outcome following a run through the model and the expected costs and QALYs can be calculated as the average from a large number of patients that have gone through the model

Discrete event simulation

Discrete event simulation describes the flow of entities through the treatment system. Entities are objects, such as individuals, that may interact indirectly with other entities within the system when waiting for resources to become available. Entities may be given attributes, such as characteristics or memory, which may influence their route through the simulation and/or the length of time between events. Another important concept is resources, representing an object that provides service to a dynamic entity

Life (and disease) histories of individuals are simulated one-by-one or simultaneously. If simulated simultaneously, one can model entity interactions or resource competition, thereby, explicitly embedding the effects of queues

Consequences such as costs and effects can be attached to events, resource use or time with a particular condition

Agent-based model

This approach focuses on the agent. Agents are aware of their state and follow decision rules on how to communicate and interact with other agents or their environment. Agents are flexible as they may adapt over time, learn from experience and/or exist within a hierarchical structure. From simple rules governing individual actions and communication, complex behaviour may emerge

As agents exist within a network, social network analysis may be used to examine interventions that impact inter-agent relationships and communication. It further provides a means for spatial considerations and can examine interventions that have a geographic impact

Consequences such as costs and effects can be attributed to the events or patient attributes

System dynamics model

The causal loop diagram provides a qualitative visualization of a system’s structure. Its basic building block is the feedback loop, describing change at one point within a system that triggers a cascading series of changes that ripple through and eventually returns in some form to either reinforce or push back against that original change. Complex behaviour may emerge from the interaction of multiple feedback loops

The system dynamics model is quantified by stock and flow diagrams. As per its name, these diagrams consist of two main variable types: stocks (also referred to as levels or state or accumulations) and flows (i.e. rates at which stocks are either drained or replenished). Movement between stocks is defined by the rate of flow and, together, a system’s behaviour may be described through a set of differential equations

Costs and outcomes may be attributed to the time-in-stocks or movements between stocks that are continuously updated

Compartmental model

Compartmental models are historically used to model the epidemiology of infectious disease. The population is divided into various compartments, representing their average state. Individuals within a single compartment are considered homogeneous. Most commonly, it contains compartments of the population whom are at different stages of the illness (e.g. susceptible, exposed, infectious, recovered).