Advantages and disadvantages of discrete-event simulation for health economic analyses

KEYWORDS:

• Simulation
• modeling
• discrete event
• health technology assessment
• health economic analyses

Health technology assessments (HTA) are carried out to inform decision-makers of the possible consequences of agreeing to pay for a particular medication or other intervention. To carry out these analyses, it is nearly always necessary to construct a model that provides a framework for incorporating evidence from multiple sources together with assumptions that reflect the best understanding of the decision problem to be informed [1]. This model allows the analyst to compute the time spent in various conditions as well as counting the expected events and their timing. By assigning corresponding values to these, all the necessary elements for a health economic analysis are obtained.

Today, the ‘Markov’ model, which considers the states that the population can be in and the transitions among them, is most commonly used in our field [2]. An alternative approach is provided by structuring the problem around the events that can happen. This technique – discrete event simulation (DES) – was developed in operations research to model systems where entities compete for limited resources, forming queues as needed [3]. DES has been adapted for HTA, by redefining the events as clinically relevant occurrences and interpreting the entities as people, with individual attributes that reflect characteristics that determine their course [4]. Somewhat paradoxically, the majority of DES for HTA also assume that the capacities of resources are infinite (i.e. that all costs accrue immediately when a resource is required), thus eliminating queues [5].

A DES can address a wide variety of HTA problems because the event basis is much more flexible and natural than using states. For example, a clinical occurrence like a myocardial infarction (MI) is easily represented as an event, whereas being limited to states one has to use an awkward pair: pre-MI and post-MI. Moreover, the MI’s cost or impact on quality of life are assigned at the time of the event rather than forcing them into one of the states.

The event representation does not require abandoning states. Entity attributes can be used to reflect the states the entity is in, allowing these to change over time, as appropriate. At the MI event, the entity’s cardiovascular attribute can change from ‘healthy’ to ‘recent MI.’ These DES ‘states’ are more flexible than those in Markov models because many can coexist without having to create compound states. The entity’s heart failure attribute could also change at the MI event to indicate a diminished cardiac function; a mood attribute could change to ‘depression;’ and so on.

In many situations, the occurrence of other events depends on the time spent in a given state (e.g. mortality dropping precipitously as time since MI increases [6]). This is straightforward to handle in a DES since the time in the state can be tracked in an attribute and any related items updated appropriately, without resorting to ‘tunnel states.’ Indeed, anything that needs to be remembered because it may affect the downstream course (e.g. the level of response to induction treatment, prior experience with similar treatments, etc.) can be recorded, as needed, and used in the corresponding calculations at the appropriate time.

The event specification and attributes also facilitate handling complex logic [7]. For example, in many therapeutic areas, it is necessary to consider switching from one treatment to another, either due to side effects, lack of efficacy, or loss of effect [8]. The logic for determining when to switch, and what to switch to, can involve examining various aspects (e.g. renal function), accounting for time on treatment, considering previous experience, and so on. In DES, this is handled at the event leading to a treatment switch (e.g. disease recurrence) by implementing the change algorithm.

The DES approach provides for a much more compact representation of the model, whatever the degree of complexity, avoiding the problem of state explosion [9]. More importantly, this algorithmic structuring makes it easier to convey the model to non-experts and it accords well with clinical thinking.

Another advantage of DES is that competing risks can be applied properly [10]. In most situations, people face several hazards simultaneously: the disease might recur, they might die of unrelated causes, they can suffer a complication, etc. By translating these risks into the corresponding times until each event happens, a DES allows them to manifest correctly, without having to impose hierarchies or randomly assort the risks, as is necessary in Markov models [11]. This handling of time as continuous also improves the precision of estimates because events can occur whenever appropriate. Furthermore, this removes the need for half-cycle corrections. The time-to-event approach is also much more efficient than periodic checking since in most cycles nothing is happening to many people.

A difficult challenge for HTA models is the ubiquitous heterogeneity of the population regarding determinants of what happens [10]. People differ in demographics, biologic risk factors, physiologic function, and more. Taking this properly into account requires conditioning the probabilities on those determinants, and this is impossible when modeling at the cohort level [9]. As DES models individuals, it deals well with heterogeneity.

DES can extend beyond the bounds of HTA to create models of planned clinical trials and help optimize their design [12] and even to create intervention comparisons that have not yet been studied in any trial [13]. Of course, its original purpose can also be leveraged to model settings of care [14] or even to implement constrained resources in an HTA to more accurately represent problems [15].

Perhaps the largest disadvantage of using DES for HTA is that the technique was not intended for this purpose. It was designed to model industrial systems, typically with actual physical structures, and the concepts have been developed accordingly. Its use for HTA involves make the most of these tools by adapting them to different purposes. While this can work, the technique is not tailored to the problems encountered in HTA; many of its elements are superfluous (e.g. explicit resources, queues, even entities) and others are heavily modified (e.g. events are clinical occurrences rather than places where the system variables change). A bespoke technique, expressly designed to fit the needs of HTA might be easier to understand and use, and thus, better able to achieve wider acceptance more quickly.

Most of the disadvantages of DES for HTA are counterparts of its advantages. Although the technique permits framing the model to the depth required to adequately address the decision problem, this may lead to a more complex structure and the need for additional controlling equations. The increased complexity and level of detail, even if appropriate to the problem, may appear to reduce transparency and make it more difficult for reviewers to grasp the model and verify that it is a reasonable representation and correctly implemented [16].

The ability to handle more complex structures and to implement all necessary components of a problem also tends to increase the data requirements. Each equation must be estimated and its elements populated, ideally with data from relevant actual populations. Access to individual-level information becomes highly desirable but this is still a major challenge in our field [17]. The data demands become even more acute when one considers that some of them should be reserved for validation of the model’s predictions [18]. It also requires deeper understanding of standard distributions, their quantile forms, and the statistical methods for estimating them (see Chapter 6 in [3]). A competent biostatistician becomes a key member of the modeling team.

In order to properly address heterogeneity and the diverse course of illness, a DES uses random numbers to implement selection from distributions. Although this is not unique to DES, this stochastic approach can be disconcerting to some because the results change slightly every time the model is run [19]. By the same token, stochastic analysis requires that the model be executed many times to assemble a set of possible results from which an average can be estimated. This takes longer than a deterministic analysis and can significantly increase run times, particularly in complex simulations [20]. Time-consuming runs are not just annoying; they can constrain uncertainty analyses and reduce modelers’ motivation to explore sensitivity.

The use of entities to represent people together with their corresponding attributes is one of the most enriching features of DES, but it may mislead some into thinking one is simulating actual individuals and, thus, to the erroneous corollary that DES can produce customized predictions for real patients. This is not the case – DES is still estimating the effects in a population, not for any particular person. The entities are just the means used in DES to trigger the events and, although they reflect profiles of determinant values that may exist in a population, they do not carry the vast amount of known and unknown information that would be needed to represent a specific individual. Application of population-level predictions to a given patient is fraught with the well-known perils of employing a mean in this way.

Decision-makers in our field have shown a strong predilection for models implemented in spreadsheets such as MS Excel^®. While it is possible to construct a DES using spreadsheets [21], it is exceedingly difficult to do so because calculations in this type of software do not accord well with the sequential nature of DES. Thus, most DES are programmed using specialized software that can handle the clock, properly schedule events and find the next one to occur, allow for dynamic entity creation, assignment of attribute values and movement, process events at the appropriate time, and even implement animation of the model structure to facilitate visualization, understanding and debugging. These DES software (see, for example, chapter 10 in [3]) tend to be expensive and, of course, require learning the appropriate syntax and approach to structuring a DES peculiar to each one. This, in turn, increases training requirements and can prove a barrier to review groups who cannot be expected to know every piece of software that might be used. Fortunately, this obstacle can be overcome by using a newly developed modeling approach – DICE simulation [22] – which readily supports implementation of DES in a spreadsheet (as well as Markov models and even hybrids).

In summary, DES is a very flexible technique that can be adapted to structure the models required to inform HTA. It provides a larger toolbox than the standard Markov approach and enables the construction of models at a depth appropriate to the problem [23]. Its disadvantages are few and easily mitigated, bringing our field closer to fulfilling the requirements for solid models that decision-makers can trust [24].

Declaration of interest

The authors have no relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert testimony, grants or patents received or pending, or royalties.