A tutorial on discrete-event simulation for health policy design and decision making: Optimizing pediatric ultrasound screening for hip dysplasia as an illustration
Introduction
Simulation is any activity where an actual or proposed system is replaced by a functioning model that approximates the same cause and effect relationship of the “real” system. It is a tool of investigation that is most appropriately used when for reasons of cost, ethics or feasibility real-world trials and experiments cannot be conducted [1]. We use simulation best to generate evidence and support for decisions and policy making or to generate understanding of processes when actual experimentation is not possible. The most common types of computer simulation models used to inform health care decision making have been decision trees and Markov models [2].
Discrete-event simulation (DES) traces its origins to the field of operations research where it had been primarily used in industrial planning [5]. As the method has evolved it has been applied to a more and more diverse settings and has recently made inroads into healthcare. For example cardiovascular diseases [3], [4], screening [6], [7], [8], public health and policy [9], [10], cost effectiveness studies [11], [12], [13], [14], pediatrics [16], [17] and epidemiology [15]. DES differs from trees and Markov's in several ways. Most importantly it is one of the few methods that allow entities within a system, e.g., patients to interact and compete with each other. For example, two or more end-stage liver patients may compete for a donor liver when one becomes available [18]. In addition, unlike most Markov models, the timing of each interaction can be independent of fixed length Markov cycles and completely stochastic. Each interaction between entities can create a change in the state of the system. DES is a method best used when a decision strategy or the system being modeled involves competition for resources, the timing of events is not known a priori and when examining the interdependence between events or the flow of information or entities (e.g., patients) is important.
While DES is beginning to be used for health care decision and policy making [17], [19], [20], [21] when and how to apply DES, as opposed to other methods, is not well known to the healthcare community. This article describes a clinical example and explains where and why DES is used and walks through the steps from problem conception to working model to analysis. In this process we will look closely at the components of a DES model and how they are assembled for use in health care policy making.
We will proceed in 4 steps: first, the conceptual model and problem narrative, second the framing of the question, third, building the actual DES model and fourth statistical analysis appropriate to DES. Throughout this paper we will describe and illustrate each step with examples based on our ongoing study on the implementation possibilities of ultrasound screening for developmental dysplasia of the hip (DDH) in the Netherlands.
Section snippets
Step 1: conceptual model and problem narrative
A common first step in building a DES model is to create a problem narrative or conceptual model. The process of creating a narrative description of the problem lets the problem stakeholders and decision makers provide direct input into the model and (structurally) validate what the modeler proposes to build. It is important in this collaborative process to incorporate sufficient detail to satisfy the needs of the modeler (e.g., number of resources in the system, probability of certain events,
Step 2: framing the question
Framing takes the conceptual model of the system and articulates the questions the model needs to address in a meaningful and answerable way. When framing a question using simulation models, one must keep foremost in mind two things. First, pay attention to what is important to the stakeholders. This is in part understood in the process of creating the project narrative. A model generates the kind of output for which it is designed. Second, define relevant outcome measures. The outcome measures
M/M/1 – the paradigmatic model
The simplest, most constrained and most paradigmatic model for DES is the M/M/1 or single server model. This model represents a system with a single source of arriving entities and a single resource/server for which these entities compete. Both the arrival rate of entities and the time it takes to process these entities are Markovian, i.e., independent and without memory [25], [26]. A very simple example is a bank teller with arriving customers. While most DES become rapidly more complex as the
Step 4: statistical analysis/experimentation
A primary purpose for building a simulation model is to use it to experiment and compare alternative scenarios. This allows identifying the optimal scenario as judged by some output criteria. The statistical tests used to compare scenarios are determined by the types of outcome measures used. In DES the most common output types are observational and time-weighted. Observational outputs are equally weighted observations usually related to the entities history. Examples are counts, waiting times,
Conclusion
In this paper we introduced DES and a real-world example as a vehicle to describe how to construct and analyze a DES model. One first starts with a narrative or conceptual model with the aide of the problem stakeholders. This in turn facilitates the framing of the problem in a relevant and answerable way with the tools and resources available. As in the example problem, DES is most readily applicable when the problem or the system being studied involves competition for resources, where the
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On behalf of the Soundchec 2 study group.