## 2 Materials and Methods
### Metrics for the Evaluation of PROforma Models
Notice that the use of plans is related to modularity, which is a key principle to deal with complex processes and usually it facilitates the understandability of complex models [31]. However, the decomposition of a process into plans depends on the knowledge engineer criteria, and as [PERSON] et al. [31] argued, there is no objective benchmark on how to use it. Moreover, it seems that when the process logic is fragmented across several sub-plans, decomposition might become a drawback instead of a benefit. For that reason, we have defined new metrics to study their effect in the understandability and modifiability aspects of the model. Therefore, considering the differences between PROforma models and BPMN models described in the preceding paragraphs, we have redefined the initial set of metrics as follows:  
* We have not considered the cyclicity metric, since we have ruled out the possibility of arbitrary cycles (see above). * We have referred to connectors instead of to gateways in the following metrics: average connector degree (Section 2.2.2), maximum connector degree (Section 2.2.2), and connector mismatch (Section 2.2.4). In the calculation of the token split metric (Section 2.2.5), we have also simplified the join connectors, having a single type instead of distinguishing between AND, OR, and XOR joins. * We have not considered the behavior of the different split nodes. For that reason, we have ruled out the gateway heterogeneity metric that measures the type entropy of the gateways. Besides, the metrics connector mismatch and control flow complexity (Section 2.2.4) have been redefined considering that all the split connector nodes have the same behavior. Moreover, we have also defined new metrics in order to consider the specific characteristics of PROforma. First, in order to capture the impact of decisions in the complexity of the model, we have formulated the following new metrics: number of decisions, density of decisions, and number of preconditions. Second, the use of plans in the clinical processes modeled with PROforma has several implications regarding the metrics and also brings about the definition of new metrics:  
* Whenever there is more than one start task (i.e., tasks without any incoming scheduling constraint) and/or more than one end task (i.e., tasks without any outgoing scheduling constraint) in a plan, we have considered an implicit parallel split and/or join within the plan. Accordingly, dummy components (tasks and scheduling constraints) have been incorporated to account for these implicit splits and/or joints. * We have defined some metrics in order to determine the effect of plans and their size in the quality of the model: number of plans, density of plans, average size of a plan, plans with a single task, and plans with a size above the average. * For each metric, we have defined an aggregation method of the values obtained for every graph that is part of the model (see Section 2.2.6). These metrics provide a more comprehensive characterization of the entire model. The complete collection of metrics for PROforma models is described below, providing a formula for those metrics that do not correspond to a single observable value. We have subdivided the set of metrics into the following six categories: size, density, partitionability, connector interplay, concurrency, and aggregation. The elements within a PROforma plan have been represented as a directed graph (\(G\)) where tasks are nodes and scheduling constraints are arcs. We have used the following notation:  
* \(N\): set of nodes--actions, inquiries, decisions, and plans--(see Figure 1 for examples of each one of these elements),
* \(A\): set of arcs, i.e., scheduling constraints between a pair of tasks,
* \(P\): set of plans, i.e., nodes that correspond to PROforma plans,
* \(CT\): set of all connector tasks, i.e., nodes with more than one incoming arc and nodes with more than one outgoing arc,
* \(NCT\): set of all non-connector tasks (\(NCT=N-CT\)). * \(SCT\): set of split connector tasks.