Table 1.

Key characteristics of modelling techniques

Modelling technique	When to use	Strengths	Weaknesses	Key aspects of complexity accounted for in technique	Relevance to the mental health context
Agent-based modelling (ABM)	• Well-suited to individual-level problems and the interactions that generate emergent behaviour • Instances where capturing heterogeneity is critical, such as equity challenges • Infectious diseases, epidemics	• Individual-level simulation means this method excels at capturing patient heterogeneity, individual characteristics, changes in individual behaviour, and interactions with other agents	• Resource and time intensive to develop, program, and run	• Interaction between individuals, other parts of the system, and the environment • Dynamics • Non-linearity	• Transmission effects of mental health challenges among social networks • Ability to account for service capacity constraints • Ability to track individual patient medical history, behaviour, and treatment response over time
Discrete event simulation (DES)	• Operational research, tactical problems, and process-centred situations when events, the timing of events, and the influence of queuing process are of primary interest • Well-suited to logistical and service planning contexts due to analysis of queuing processes, such as emergency departments and intensive care units based on patient flow • Shorter time horizons more appropriate, like medical decisions	• Individual-level simulation means this method can capture heterogeneity in individual patient characteristics and these are traceable over time • Prior events can affect subsequent event rates • Disease progression can be represented as a continuous process • Great degree of flexibility in the functions and logic governing the flow of entities • Can be very detailed and handle great complexity • Designed to capture queuing processes and networks of queues	• Data intensive • Time and resource intensive to develop • Validation can be difficult	• Dynamic changes in the probability of events over time • Non-linearity • Feedback can be accounted for • Interaction with service providers	• Effectiveness and side-effects of psychiatric medicines, including past treatment history and progression • Service planning where waiting lists are particularly relevant • Ability to account for service capacity constraints
Markov cohort modelling	• Ideally suited for the analysis of health technologies (new medicines) for well-defined conditions and relatively homogenous populations	• Well-established best practices and history of wide adoption in health technology assessment due to relative simplicity due to the cohort approach and ubiquity of relevant software	• Memorylessness of the Markovian assumption (the transition to future states depends only on the present state, not preceding states), which ignores patient history and individual characteristics • Difficult to account for many aspects of complexity • Does not usually account for various constraints faced by healthcare delivery systems	• Limited dynamics, individual characteristics, patient history, and non-linearities can be accounted for by using ‘workarounds’ (as opposed to being an inherent part of the approach)	• Comparison of medicines or psychotherapies for diagnosed disorders, particularly in the context of health technology assessment
System dynamics modelling (SDM)	• Well-suited to strategic-level, top-down, and conceptual decisions where a systemwide perspective is required and learning about long-term system behaviour would be advantageous • Also useful for operational research and other contexts where service capacity constraints are important • Less useful for detailed resource allocation problems • Epidemics, disease prevention, developing a new service, and forecasting the demand for services are examples where SDM would be useful • Useful for formalising a mental model of a problem and defining the relations between a system’s structure and its behaviour	• Modelling structure of stocks and flows clearly captures feedback loops, interactions between different parts of the system, and dynamic changes over time • The development of causal loop diagrams, also known as influence diagrams, are useful exercises in and of themselves to aid understanding of the problem, the system in which it occurs, and relationships between parts of the system • Participatory systems modelling exercises can be learning experiences about the system in and of themselves, including the influence of the system on health outcomes • Allows optimisation analysis • Generally faster to run than ABM or DES models • Able to model large, complex systems • Range of qualitative and quantitative output can be produced	• Judgement required to draw boundary around parts of the system that will be included • Large amount of data required to populate model • Larger models can be too complex for stakeholders to fully understand • Higher level of aggregation than other dynamic approaches, thereby failing to account for individual characteristics • More homogenous populations compared with other dynamic methods • Resource intensive to develop, both for the participatory systems modelling and technical programming components • Easier to validate	• Incorporates most characteristics such as feedback loops, non-linearity, interaction, dynamics, emergent behaviour as a fundamental model structure • Optimisation analysis extends the ability of SDM to allow the identification of a set of parameter settings and/or combination of interventions that maximises health outcomes, cost reductions, or net monetary benefit	• Ability to quickly test multiple scenarios of interventions alone or in combination, with or without service capacity changes • Interaction between demand and supply for mental health services, and the influence of service capacity constraints on intervention cost-effectiveness • Ability to assist with high-level decision making and strategic resource allocation for mental health interventions

Clear lines are drawn here between modelling techniques to aid conceptualisation and to explore differences. In practice, these lines may be blurred, with simulation models drawing on multiple techniques, and methods that can be used to overcome limitations of a technique. For example, individual microsimulation can be conducted within a Markov model and memorylessness assumption can be overcome by using ‘trackers’ that account for patient history over time

We also recognise that many other modelling techniques and their variations exist and, here, restrict our analysis to four options for tractability