Decision analytic models

As was previously discussed, economic evaluations require a framework that allows them to obtain the costs and outcomes being analysed. Such a framework can be given by randomised controlled trials (RCTs); however, RCTs have several limitations. Decision analytic models (DAMs) provide an alternative framework for economics evaluations.

A decision analytic model can be defined as a systematic approach to construct and structure decisions (Gray et al., 2011). This approach uses mathematical relationships to define consequences from alternative options being evaluated (Briggs et al., 2011). The likelihood of a consequence, which has both a cost and an outcome, is expressed as a probability; consequently, DAMs can give the expected costs and outcomes of decision options. Notably, DAMs can synthesise data from different sources (Petrou and Gray, 2011) and are able to incorporate and quantify uncertainties in a decision problem (Gray et al., 2011).

DAMs have been used extensively in medicine and pharmacology and their use has increased in recent years (Philips et al., 2006). While it is true that there are no reviews on the frequency of DAMs in dentistry, it is possible to deduce that this kind of study is scarce. This assertion is based on: (1) the fact that not all economic evaluations use DAMs as framework and (2) the relative scarcity of economic evaluations in dentistry (Mariño et al., 2013).

As an example of the use of DAMs in dentistry, Pennington et al. (2009) evaluated different restoration pathways following an initial treatment decision (root canal treatment or tooth extraction with replacement). Using a Markov model, they were able to simulate the costs and effects of different treatment alternatives until patients reached 100-year-olds or until they died. In another example, Schwendicke et al. (2015) evaluated the cost-effectiveness of mineral trioxideaggregate (MTA) and calcium hydroxide for direct pulp capping in Germany. Through a Markov model, they determined that MTA was more cost-effective (over a long-time horizon) because such material could avoid expensive retreatments.

Several authors have given suggestions about what to include or not in DAMs (Weinstein et al., 2003;Drummond et al., 2005;Briggs et al., 2011;Gray et al., 2011). There is no agreement related to what constitutes a ‘good model’ or how models should be formally assessed (Philips et al., 2006), although there have been efforts to reach a consensus on best practices. For this

reason, some institutions have started to formulate their own recommendations to perform these models.

For example, the Health Economic Evaluation Publication Guidelines Good Reporting Practices Task Force of the International Society for Pharmacoeconomics and Outcomes Research (ISPOR) published, in 2013, the Consolidated Health Economic Evaluation Reporting Standards (CHEERS). Such a consensus guideline merges existing opinions and provides recommendations to optimize the conduct and reporting of health economic evaluations, including model-based economic evaluations. In the Chilean context, the methodological guide for economic evaluations (MINSAL, 2013c) includes a chapter specifically dedicated to these mathematical models.

The present thesis considers the recommendations of these guidelines with an emphasis on the Chilean context.

5.4.1 Defining the decision problem

This part of the construction process of a DAM is related to the definition of the question to be analysed under conditions of uncertainty, also called defining the ‘decision problem’. This concept is like the specification of the study question for economic evaluations (Drummond et al., 2005). The definition of the question should reflect data availability and the perspective of the institution that will make the decision (or that is assumed to be making the decision). All alternative interventions and settings to be analysed must be clearly defined as well as the recipient population. It must include the time horizon to be evaluated and a clear definition of costs and outcomes. Finally, this section should specify the boundary of the model, meaning how far the model should go to capture all possible implications of an intervention (Drummond et al., 2005).

5.4.2 Structuring a decision model

Several authors (Weinstein et al., 2003;Barton et al., 2004;Petrou and Gray, 2011;Siebert et al., 2012) have proposed guidelines about the selection process of the structure of the models being used.

As an example, Gray et al. (2011) adapted an algorithm created by Barton et al. (2004) that also helps to define a possible decision model. This algorithm is based on sequential questions about what the model needs to represent.

First, they state that when an interaction (e.g. between individuals) is important, they recommend more complex models such as system dynamic models or discrete event simulations. A system dynamic approach models the state of a system in terms of changing, continuous variables over time and a discrete event simulations describes the progress of individuals, which pass through various processes that affect their characteristics and outcomes over time (Brennan et al., 2006).

Then, when the events are not recursive, they suggest decision tree models, otherwise, they recommend the use of Markov models. Finally, they propose the use of individual sampling models when the models require the representation of many health states.

Some characteristics of both disease and intervention being evaluated help to answer the questions formulated by Gray et al. (2011). For example, when the disease is infectious, it would be necessary to evaluate the interaction among individuals. Also, when the disease is chronic, it is likely that one intervention or event might be repeated during the lifetime; thus, individuals should require multiple interventions or movement between several health states should be evaluated.

At the end, the selection of the structure of the model must be analysed case-by-case because there is not agreement about what is the most appropriate model structure in a given case (Briggs et al., 2011). Although several types of models are available, only decision trees, Markov models, and a combination of both (the Markov cycle tree model) will be discussed in more detail in this chapter because, following the algorithm proposed by Gray et al. (2011), there is no interaction between children, and the application of FV needs to be repeated several times; thus, these are the relevant models.