Rule extraction for process mining based on machine learning techniques

Rule extraction for process mining based on machine learning techniques Tom´ as Benavides- ´ Alvareza,∗ aCentro Singular de Investigaci´on en Tecnolox´ıas Intelixentes (CiTIUS), Universidade de Santiago de Compostela, Santiago de Compostela, Spain Abstract Process mining is a discipline that has been gaining importance by offering a set of techniques that allow extracting knowledge from the event logs in which the information generated in the execution of processes is stored. One of the main objectives in process mining is to understand what has happened during the execution of a process. Typically, this goal is achieved by manually exploring the actual model, describing the behaviour of the process and temporal and frequency analytics on its variants and business indicators. In this paper, an innovative approach based on decision trees is presented that allows the automatic classification of certain behaviours that occur during a process based on the information generated during its executions and the variables associated with them, so that process stakeholders can have a better understanding of what is going on and thus improve decision making. This technique has been validated on a medical process, the Aortic Stenosis Integrated Care Process (AS ICP) implemented in the Cardiology Department of the University Hospital of Santiago de Compostela. On this process, the waiting times of patients have been tackled in order to extract those patient profiles susceptible to delays or to be prioritised. Keywords: Process mining, Healthcare processes, Declarative processes, Decision trees 1. Introduction The large amount of information generated individually by people in their daily lives is currently one of the main assets of many companies and organisations, which seek to extract knowledge from it in order to improve the results they obtain from their activity. Business processes consist of a collection of activities or tasks that, following a certain sequence, provide a product or a service to their customers or users [1]. These business processes are present in many aspects of our daily lives, one example being healthcare organisations. Typical processes in this sector, known as healthcare processes, consist of a series of activities focused on the detection, treatment or prevention of a disease, in which patient information is also collected to guide decision-making throughout the process. Concern for improving this type of processes and making them more efficient has led to an approach to process mining, a very recent discipline that bridges the gap between data mining and traditional business process management [2]. To this end, it offers a range of techniques that allow knowledge to be extracted from the event logs in which the information generated by information systems during the execution of processes is stored [3]. With these techniques, the real behaviour of the processes can be discovered, using this information for the detection and correction of performance problems, i.e. bottlenecks, which would otherwise be practically impossible to address. ∗Work supervised by Manuel Lama and Manuel Mucientes Email addresses: [email protected] (Tom´ as Benavides- ´ Alvarez), [email protected] (Manuel Lama), [email protected] (Manuel Mucientes) In the medical field, waiting times are a recurrent problem that has been tried to be solved by different means [4], as it is one of the main reasons for dissatisfaction and directly harms patients by postponing the benefits of the application of their treatments [5]. An example of this type of process could be the preparation and execution of a surgery, where, following traditional methodologies, a detailed manual analysis would be necessary to detect and optimise delays affecting patients, which is costly and time consuming. Moreover, this analysis may be conditioned by the heterogeneity of opinions among those involved in the process (physiscians, managers, etc.), who tend to consider one ideal scenario out of the many possible ones, which may lead to discussions among stakeholders with discordant points of view. To solve these problems, an objective analysis by exploiting the data stored in the event logs is possible thanks to the techniques offered by process mining. This, in a medical process associated with a healthcare centre, can be a great opportunity to improve the management of patients, detecting those groups prone to delays or which patients tend to be prioritised. However, this is no easy task, as working with healthcare processes is complex in a way that cannot be compared to other business process organisations, creating a number of challenges that need to be addressed to achieve satisfactory results [6]. The main reason behind this is the heterogeneity of patients, diseases and treatments, in addition to the multidisciplinary nature of healthcare centres and the ad hoc decision making that takes place at the time. All this generates dynamic and complex processes in which deviations from the theoretical model are very common, even among patients with the same disease and the same treatment, something that does not occur in other domains in which the same sequence of activities always takes Preprint submitted to Journal of Biomedical Informatics February 6, 2024 place for each task. Another characteristic of the medical field is the transparency of decision making and the understandability of the models [7], which considerably limits the number of options and poses a challenge when designing and implementing a system based on artificial intelligence. To address all these problems that have just been introduced, this study presents an approach focused on the extraction of knowledge through decision trees, which will allow the extraction of those rules present in the event logs that store the information generated during the execution of the processes. For this, a declarative approach will be followed to model the relationships between activities in a clear and understandable way, taking into account not only the workflow perspective of the process, i.e. the relationships between activities, but also the temporal and data perspective of the process. This system will be validated on a real medical process, specifically on the Aortic Stenosis Integrated Care Process (AS ICP) implemented in the Cardiology Department of the University Hospital of Santiago de Compostela. This process covers the path followed by patients from the detection of the disease until their intervention, discharge and subsequent follow-up. On this basis, an attempt will be made to extract the profiles of patients who suffer a delay in their interventions or who are correctly prioritised, which will be defined by the variables used by the decision trees when classifying them. The following sections are structured as follows, Section 2 will introduce the current knowledge of the field to be addressed, with a special emphasis on declarative process modelling; Section 3will focus on describing the two main proposals related to the approach adopted in this paper, illustrating their similarities and differences; Section 4will present the methodology proposed to solve the problem, addressing its different phases; Section 5will describe the real process on which this proposal has been validated, the AS ICP implemented in the Cardiology Department of the University Hospital of Santiago de Compostela; the experimentation carried out and its results will be shown in Section 6; finally, Section 7will present the main conclusions reached during this process and some of the points for improvement that have been detected. 2. Background 2.1. Process mining Process mining is a relatively young discipline that began to gain importance in the first years of the 2010s, when the most relevant proposals in the field started to appear [3]. As already mentioned, this discipline allows extracting the knowledge that is stored in the event logs during the execution of processes. These logs store the different instances of a given process, which are called cases. Each case has a unique identifier that differentiates it from the others, and is formed by the sequence of activities that define it, the timestamps of its execution and, optionally, variables related to it, such as the resource in charge of carrying them out or their result. Even trace variables can be found, which are those related to the case and not to a specific activity, such as the final state of the case. To extract the knowledge stored in these event logs, process mining offers three main types of techniques illustrated in Figure 1: process discovery, process conformance and process enhancement [8]. Process discovery focuses on obtaining the model that describes the behaviour recorded during the execution of a process from its event log. In contrast, process conformance techniques aim to detect differences between the recorded behaviour and the theoretical model in order to detect possible deviations from the latter. Finally, process enhancement methods seek to improve the theoretical model with the information extracted from the logs, so that critical points that present performance problems, such as bottlenecks, can not only being detected, but also corrected. Figure 1: The three basic types of process mining: discovery, conformance and enhancement. [8] In the healthcare domain, process mining has been used in different case studies, with promising results. The new techniques offered by this paradigm make it possible to deal with the great complexity and variability of medical processes, making easier to understand them and providing an efficient analysis, which improves the quality of the services offered and their management. Among the possibilities offered by the application of process mining in this type of processes are a better identification of the real behaviour of the process, the extraction of suggestions for improvement, the analysis of performance to reduce waiting times, the prediction of patients based on previous cases or the identification of the rules that manage the course of the process [9]. 2.2. Declarative processes Focusing on process discovery, the techniques that have received the most attention are focused on generating a model that represents the explicit relationships between the activities in the process, known as procedural or imperative modelling [10]. This type of modelling provides good results when working with structured processes, i.e. processes in which there is little variability and the same chain of events is normally followed. However, when dealing with unstructured processes uncertainty and high variability increase the number of relation2 ships that can be established between activities, giving rise to models such as the one shown in Figure 2, known as spaghetti processes. Unlike structured processes, where variability is low and the same chain of events is usually followed, in these it is not possible to explicitly represent each of the relationships between activities, as this leads to incomprehensible processes such as the one seen, so other approaches are advisable. Figure 2: Spaghetti process describing the diagnosis and treatment of 2765 patients in a Dutch hospital. [11] To solve this, the DECLARE language appeared in 2007 [12], giving rise to the declarative paradigm, in which instead of explicitly representing all the possible relationships between each pair of activities, a set of restrictions that must be satisfied throughout the execution of the process are described. The models obtained with this type of techniques therefore offer a greater degree of flexibility, describing more clearly the relationships established between the activities of a process in which uncertainty is high, as would be a case study focused on the medical domain [13]. These constraints, which can be seen as rules to be complied with during the execution of the process, limit or prohibit certain behaviours rather than representing the explicitly allowed one. The difference between the two approaches is ilustrated in the example shown in Figure 3, where there are two activities Aand Bthat cannot occur simultaneously. Figure 3: Declarative vs Imperative approach. [12] This versatility offered by DECLARE is given by the Linear Temporal Logic (LTL) [14], which is the one that allows defining the constraints on which the language is based. This type of logic allows to represent formulae about the future of a path following a temporal approach, i.e. basing its conditions on the succession of events over time. Table 1shows the constraints offered by DECLARE, along with their formulation in LTL logic, which restrict the behaviour of a process without explicitly representing a relationship between two activities. At this point, it can be see that one of the problems detected in the unstructured processes typical of the medical domain has been solved. Despite this, the declarative models represented through DECLARE have a major limitation, which is that they only take into account the workflow of the process, that is, the succession of activities that take place in each of its executions, leaving aside all the remaining information that is stored in the event logs, such as the time or data perspective. In a problem such as the one at hand, in which a lot of clinical information about the patient, that is also relevant to decision-making and the course of events, is available, it is essential to take advantage of it to achieve good results. As a solution, MP-DECLARE [15] has emerged, an augmented version of DECLARE itself that offers a multiperspective view of the process, making it possible to obtain models in which all the information just mentioned is taken into account, as can be seen in Figure 4. Figure 4: Example of a declarative multi-perspective model. [16] With the emergence of this new paradigm, new tools such as RuM emerge [16], which allows, among other things, the discovery of declarative models from a multiperspective view. Even so, all these types of approaches present in the state of the art of the problem focus on discovering those restrictions whose support and confidence satisfy a certain threshold, giving a general vision of the behaviour of the process, as shown in Figure 4. On the other hand, in this case the aim is to use all this expressiveness offered by MP-DECLARE to describe the rules to be extracted, being this extraction guided by certain behaviours that occur in the process, such as delays. In this way, those rules that explain and describe them will be extracted so as to identify which correlations are present in those cases. 3. Related work As mentioned above, the approach presented here is based on a knowledge extraction system that uses decision trees for rule extraction. These rules show the correlation between a set of attributes of the process and a class that will depend on the analysis to be performed. In this way, those rules that describe certain behaviours that occur in the process will be extracted to provide its stakeholders with information that is useful for them when it comes to its understanding and improvement. In terms of process mining work focused on extracting correlations from event logs, two main approaches have been identified. The first is the one proposed by de Leoni et al. [17]. In it, a development framework is presented that proposes a general solution to analyse a process from multiple perspectives, such as control, data or temporal. This is very similar to the approach presented here, as it encompasses the multi-perspective view of 3 Constraint LTL Expression Description Existence a a must be executed at least once. Init a a should be the first activity executed. Last (a∧¬T)ashould be the last activity executed. Choice a∨b a or bmust be executed. Exclusive Choice (a∨b)∧ ¬(a∧b)aor bmust be executed, but never both. Responded Existence a→bSi aes ejecutada, btambi´ en debe ejecutarse. CoExistence (a→b)∧(b→a)aand bare both executed, or neither is. Response (a→b) Each time ais executed, bmust be executed subsequently. Precedence ¬bWa b can be executed only if ahas been executed before. Sucession (a→b)∧(¬bWa) Combination of Response and Precedence. Alternate Response (a→(¬aUb)) Each execution of amust be followed by an execution of b, with no further execution of ain between. Alternate Precedence (¬bWa)∧(b→(¬bWa)) Each execution of bmust be preceded by an execution of a, with no further execution of bin between. Alternate Sucession (a→(¬aUb)) ∧(¬bWa)∧(b→(¬bWa)) Combination of Alternate Response and Alternate Precedence. Chain Response (a→b) Each time ais executed, bmust be executed immediately thereafter. Chain Precedence (b→a)bcan only be executed immediately following a. Chain Sucession (a≡b) Combination of Chain Response and Chain Precedence. Not CoExistence ¬(a∧b)aand bare never both executed. Not Sucession (a→ ¬b a must not be followed by b, and bmust not be preceded by a. Not Chain Sucession (a≡¬b)aand bmust not be executed in succession. Table 1: DECLARE templates for the constraints taken into account in the approach along with their expression in LTL logic. the process discussed above. However, there is one major difference, which lies in the use of LTL logic and the constraints offered by DECLARE based on it. If the pipeline of the proposal is observed, it is not very different from the one that will be shown in the following section, being key the manipulation and enrichment of the initial event log. This preprocessing phase is in charge of adding the features to be taken into account in the knowledge extraction, which will be generated from the information stored in the log, and of adapting its format for further processing. Finally, with regard to the input characteristics of this approach, it has already been said that the main difference in favour of the proposal presented in this article is the presence of declarative constraints, which are key when working with unstructured processes. On the other hand, variables related to process conformance are also offered by de Leoni et al., allowing the discrimination of cases on the basis of their compliance with the theoretical model of the process, i.e. their expected behaviour, something that is beyond the scope of our proposal. The second approach is the one proposed by Leno et al. [18]. This proposal aims to address the discovery of declarative correlations by also including the perspective of the data. Therefore, it is similar to the solution of this article in the declarative approach when representing the behaviour of the process, although from a completely different focus. In this case, instead of extracting those rules that classify the cases of the process, the correlations between the attributes of the activities that satisfy a declarative constraint previously specified by the user are extracted. To do so, two different techniques are used, one based on clustering and the other based on trees, more specifically on redescription mining. As can be seen, although there are proposals with similar characteristics, none of them allows the discovery of rules from a multiperspective and declarative point of view in a guided way. The most similar is the one presented by de Leoni et al. [17], although it offers an imperative approach in which the relationships between activities are explicitly represented, so it is not suitable for environments with high variability such as the medical domain. This is the gap that the approach presented below aims to fill, providing an innovative and appropriate solution for the problem being addressed. 4. Methodology The solution proposed in this work is based on decision trees [19]. The use of this technique is mainly due to the ease it offers to extract intuitively the set of if-then rules that follow each other in its decision nodes, encouraging the explainability and interpretability of the results, which is of great interest in the medical field. In addition to this, a previous preprocessing of the data will be necessary to generate the information that will be used to train these trees. This will generate a large number of variables which, in problems with few instances, may negatively affect the training of a single tree. Therefore, to solve this problem, a feature selection process will be carried out using tree ensembles, specifically XGBoost [20], to improve the 4 Figure 5: Pipeline of the proposal, in which the phases of preprocessing, feature selection, decision tree training and rule extraction are identified. robustness of the variable selection that is already done by the decision trees. Figure 5shows the general pipeline of the proposal, where all these stages can be identified, which will be detailed below. 4.1. Preprocessing of the event log The preprocessing of the event log is one of the most important parts of making rule extraction possible. Unlike traditional datasets, where each row represents an instance of the problem, in event logs each row stores information about the specific execution of an activity belonging to a case. In this way, each case spans several rows, as can be seen in the original event log in Figure 5. In order to be able to process such datasets using traditional learning algorithms, the dimensionality of the event log must be reduced so that each execution of the process corresponds to a single row. During this process, not only must the dataset be resized, but the variables that provide the necessary information for the subsequent classification process must also be generated, including the class that will guide this process. In the case of the process workflow, which will be the only one that will always be present after preprocessing, reducing the dimension of each case to a single row raises a problem with the distribution over time of the different activities that make up each execution of the process. Unlike other techniques such as recurrent neural networks [21], decision trees cannot deal with an arbitrarily large number of variables that represent the succession of activities that have taken place throughout each of the cases. Through the specification offered by DECLARE, these explicit sequences that would be impossible to handle can be converted into a set of bounded variables that describe the different behaviours that occur in the process. To do this, what is done is to process each trace or case with a set of symbolic automata, which are defined from the expressions in LTL logic of each of the constraints offered by the language, already shown in Table 1. These automata, generated through the FLLOAT library [22], make it possible to detect the fulfilment of each of the constraints that have been specified for the sequence of activities that make up each instance, regardless of their length. In this way, instead of explicitly specifying each arc between activities, a series of boolean variables are generated that indicate, for each instance, whether or not a declarative restriction on one or two activities is fulfilled. An example could be that activity B is executed after the occurrence of activity A, whose automaton is illustrated in Figure 6. Additionally, variables related to the redundancy of the events will also be generated, which will indicate the number of times each of them has been executed, something that could be of importance for loop detection. In this case, as introduced in previous sections, the aim is to provide a multiperspective approach that looks beyond the workflow of the process, taking advantage of the temporal and data information stored in the event logs. To this end, during preprocessing, in addition to generating the above variables, also the following will be produced. •Time. The duration of the activities or the time elapsed between each particular pair of activities is very useful information when discriminating one process execution from another. Here, both these two values and the time elapsed between the start or end of the execution and the completion of each task are considered. Regarding these time variables, it must be taken into account that it is possible that there is more than one value for each of them, since the 5 repetition of activities is not uncommon in processes. To solve this, aggregation of the times has been considered, usually by choosing the maximum or minimum value of the variables. •Resources. Interactions between different members of an organisation can be of great relevance when analysing the performance of a process. Synergies when collaborating between two colleagues or the clash of two completely different methodologies can make a big difference in the final result. With the resource perspective, information is stored on which resource or resources perform which activity throughout the process, in order to detect performance problems related to the specific execution of an activity by one resource or poor coordination between two of them. •Attributes. In event logs, as mentioned above, two types of attributes are distinguished: trace attributes and event attributes. The former apply to the whole case, while the latter are related to the execution of a specific activity and would have no meaning without it. Thus, variables related to both will be generated, containing for the second scenario also information about the event with which the attribute is associated. This perspective will be very useful, especially in the domain to which this approach is applied, since attributes are fundamental for decision making in the medical field. Figure 6: Symbolic automata generated by FLLOAT for the template Response(A, B). This constraint implies that if activity Aoccurs, activity Bmust occur afterwards. These would be the parameters considered by the proposal, which offer a multiperspective view covering all levels of the process for a detailed and customised analysis. While the workflow is always taken into account, the other aspects are optional and will depend on the problem to be addressed. On the other hand, given the high complexity of some processes, it should be noted that the number of variables can be very high and can exponentially increase, especially in terms of declarative constraints. This is due to the three types of interactions that can be seen between the activities involved. •Simples. Constraints formed by a single activity, such as Existence(A), i.e. activity Aoccurs in the process. In this case, only one activity is involved in the constraint, so we would have a maximum of nvariations, where nis the total number of different activities in the process. •Combinations. Constraints composed of two activities where the order does not matter, such as the Choice(A, B) constraint, i.e. activities Aor Boccur in the process. Here, the maximum number of variants of the same constraint would be limited by the formula Cp n= n k!=n! (n−p)! p! where nis equal to the number of different activities in the process and pis equal to 2. •Variations. Constraints composed of two activities where order matters, such as the Response(A, B) constraint previously seen, which would have a different meaning from Response(B, A). For this type of constraint, the maximum number of variants would be limited by Vp n=n! (n−p)! where again nis equal to the number of activities in the process and pis equal to 2. As can be seen, as the number of unique activities of a process increases, so does its complexity, and with it the number of variables generated in the preprocessing, which can explode. 4.2. Selection of features The preprocessing phase that has just been introduced entails the generation of a large number of variables that grows with the complexity of the process to be treated. This is added to the scarcity of data inherent to process mining, which studies very specific cases such as the one under discussion. Additionally, it should be taken into account that some of the declarative constraints considered, which constitute the majority of the variables in the problem, represent very similar behaviours. An example can be seen with the variables Response(A, B) and ChainResponse(A, B), where the only difference is that the latter implies that activity Bmust occur immediately following activity A, if Aoccurs, rather than at any time thereafter. In some processes, the variables could be identical, since the behaviour expressed by the latter is contained in that of the former, and the same is true for other sets of constraints. Because of this, a variable selection process is needed to reduce the dimensionality of the problem so that it is addressable in the rule extraction process. For this purpose, XGBoost [20], one of the most widely used and effective methods in the field of machine learning, has been chosen. This algorithm is based on ensemble methods, which rely on the combination of models to obtain results of higher quality and robustness than those achieved by a single model. Within ensembles, this is a boosting method, characterised by 6 the sequential combination of models so that, in each iteration, the new model focuses on the most complicated data, i.e. those where classification has failed. For all these reasons, this algorithm has been used to implement an embedded feature selection method. This type of method is based on including the selection of variables in the learning process itself, for which XGBoost will be applied to the dataset obtained after preprocessing and, subsequently, the information on the importance of the attributes used will be extracted. In this learning process, some of the main features offered by the algorithm will be used, such as column and row subsampling, also used by random forests [23], which is another of the main methods used for the embedded selection of variables. Furthermore, small trees will be used, offering low variance and high bias, since it will be the sequential combination of the models in the ensemble that will reduce the latter. Once the models have been trained, the information related to the feature importance of each of the attributes that have been used for their creation can be extracted. For this purpose, XGBoost offers several evaluation criteria. Of these options, it will be used the average information gain offered by the attribute in each of the splits in which it participates, i.e., how much the purity of a tree node improves when its instances are split by that attribute. This is the most balanced criterion and the one that best suits our purpose, favouring those attributes that most correlate with the target used to guide the classification. In contrast, other criteria, such as the number of times a feature is used to split the data across trees, may favour certain types of attributes over others, such as numerical attributes over binary ones, as this can only occur once per branch for the latter, while in the former can happen at different levels of the same branch. In this case, most attributes are boolean, i.e. they store a true or false value, so using such methods could give biased results that do not favour the final classification process. With this criterion, the average gain values of each of the attributes used by the ensemble will be extracted, on which a normalisation process will be carried out to facilitate their comparison. Additionally, a filtering will be applied to the total number of attributes used by the trees based on the amount of information they represent, i.e., attributes that accumulate a user-specified percentage of the total information gain will be selected, sorted by importance. The final result will be a graph showing, in order of importance, the different attributes used during the learning of the algorithm along with the threshold that delimits which of these attributes will be selected for the training process of the final decision tree, from which the rules will be extracted. This information on its own may already be of great relevance to the stakeholders of the problem. However, there is no way of knowing from this information how the extracted features affect the process, i.e. whether they contribute to the delay or favour the agility of the assistance. Moreover, the combination of trees in the ensemble hinders explainability, making the extraction of rules from them very complex to analyse. Therefore, an additional stage is necessary in which the variables extracted in this step are used to train a single tree, from which a set of rules will be extracted to show the correlations of the attributes with the final output of the process to be explained. In this way, the information extracted from this phase will be complemented with knowledge that will allow measures to be taken to improve the process or help to better understand what is happening in it. 4.3. Generation of decision trees Decision trees are one of the best techniques for discovering key patterns when discriminating instances of a dataset based on a class, i.e. in supervised learning problems. Moreover, their simplicity and intuitiveness when it comes to interpreting their reasoning make them one of the main techniques in the exploratory analysis of data, as will be seen later in the rule extraction phase. In this case, regarding the input features of the model, those selected in the previous feature selection process will be used. These variables have been generated in the preprocessing phase, by which the initial event log is converted into a dataset with the input features of the problem to be analysed, taking into account the different perspectives of the process. Therefore, this will be the final phase that allows the extraction of knowledge from the event log being worked on. To this end, this process will be guided by the assignment of classes that has been carried out previously, so that the final result will be the rules that show which combinations of variables correlate with each one of them. To implement this solution, it has been chosen the implementation of the CART algorithm [24] offered by the Weka tool [25], one of the main open source machine learning and data mining software developed by the University of Waikato. This algorithm is characterised by offering a binary decision tree in which each decision node is divided into two different branches based on a condition, following a greedy approach known as recursive binary splitting. To do this, at each of these nodes, a certain cost function is evaluated on the different values of each one of the attributes that make up the dataset, selecting the splitting that offers the lowest cost. As cost function, this algorithm uses the Gini index or Gini impurity. This criterion measures how often a randomly chosen element of a set would be incorrectly labelled if it were labelled according to the distribution of labels in the set, i.e. it gives an insight into how pure a node is based on the instances it contains. The following equation is used for its calculation GI = c X i=0 Pi(1 −Pi)=1− c X i=0 P2 i where Pirefers to the proportion of instances of class iin the node under consideration, representing the probability that an instance of that class is randomly selected in the node. With this in mind, the best scenario in a binary case would be the one in which a node only contains instances of one class, GI =0, while the worst scenario would be that in which the classes are equally distributed, yielding a GI =0.5. Taking this into account, to evaluate a split in a decision node, what is done is to weight the Gini index of each of the nodes resulting from the split by the number of instances of the parent 7 node, which would give its Gini score GS =GIle f t ∗nle f t n+GIright ∗nright n where GIle f t and GIright correspond to the Gini index of the child nodes generated by the split and nle f t and nright to the number of instances of each of them. Thus, all the cut-offpoints for each of the attributes under consideration are tested in order to select the one with the lowest GS . This process is repeated iteratively until one of the stopping conditions specified in the form of hyperparameters to the algorithm is met, such as the maximum depth of the tree, the minimum number of examples that a leaf node must contain or the minimum number of examples that a decision node must have to be able to split again. In addition, there are other relevant characteristics for the operation of the algorithm that have been taken into account when selecting it, choosing those that best adapt to the nature of the data with which this kind of problems work. 4.3.1. Missing values Missing values are one of the main problems faced by machine learning algorithms. In this case, as far as declarative variables are concerned, they do not pose any problem, since there is always a true or false value depending on whether or not each constraint is met. On the other hand, when taking into account the variables related to the time and data perspective of the process, it may be the case that null values are present, especially in the first case. This is because, when generating the variables related to the temporal aspect of the process, it may be possible that an activity does not occur in a specific execution, which would make the variable in charge of storing its duration empty, as well as any other attribute in which this activity is involved, such as the time elapsed between it and another given activity. Because of this, for some variables in the dataset the presence of missing values can be a problem. To solve it, some method of imputation by the mean, or even replacing these values by zero, could be used. But in this particular problem, this would only introduce bias, since the fact that an activity has not been performed should not be confused with the fact that this activity has been completed in a given duration, be it zero or any other value considered. Another approach that can be adopted in this case, taking advantage of the characteristics of decision trees, is that of fractional instances, proposed by Quinland in another of the great decision tree algorithms, C4.5 [26]. This is the technique used by Weka in its implementation of CART, and is based on assigning a probability to each of the possible values of the attribute under consideration. For this, all the instances that present a valid value for the attribute on which the split is being performed are taken into account. From them, the probability that the attribute takes each of these values is extracted, and the instances with missing values are partitioned on the basis of these probabilities. Consider an example for a given node to be partitioned over the numerical attribute Tusing a threshold x. In this node, we have ten instances with valid values, of which six are less than xand four are greater, i.e., the probability that T≤xis 0.6, while the probability that T>xis 0.4. Taking this into account, if in this node there is an instance that has a null value for the attribute T, what will be done is to distribute a fractional instance with a weight of 0.6 for the corresponding branch with T≤x, and a fractional instance with a weight of 0.4 for the other branch. In this way, it will be these fractional instances that will be used when calculating the Gini index of each node and that will be taken into account in the following partitions. This method allows the missing values problem to be solved in an elegant manner, taking advantage of the characteristics of the decision trees, both for the learning and the prediction processes, although in this case it is the former that is of interest. Moreover, it is considered to be the most appropriate strategy considering the nature of the missing values used in this type of problem, so it was one of the main points in favour when selecting the algorithm. 4.3.2. Categorical values Another key issue when working with decision trees are categorical or nominal variables, which are related to qualitative characteristics of the data, offering a limited number of different values. The most common approach is to perform their discretisation using one hot encoding. With this, each variable is split into ndifferent variables, where nis the number of different values the original variable has. In this way, one of these new attributes will take the value 1 and the rest will take the value 0, indicating the value of that instance for the original variable. This is one of the possible approaches in decision trees. In fact, for a binary tree, it is not necessary to apply one hot encoding, as this discretisation will be done naturally by the algorithm when selecting the corresponding threshold for the variable when splitting. However, splitting the data based only on a specific value of a categorical attribute may not be optimal, since in the case that this categorical attribute has several different values that share the same correlation with the class that guides the learning process, several levels in the tree will be needed to represent it, which may even make it difficult to reach this conclusion. However, if instead of this approach, the possible subsets for this type of variables are considered, the sparsity of the trees obtained could be reduced and the quality of the models could be improved. Therefore, it has been decided to use this strategy, offered by the implementation under consideration, as it can be beneficial for the models and rules obtained when such variables are present. 4.4. Rule extraction Once the characteristics of the decision trees that will be used following the presented methodology have been introduced, it remains to explain how the extraction of rules from them will be performed. These decision trees will be formed by decision nodes and leave nodes. The former contain the variables used to discriminate the data based on the classification that guides the learning process, while the latter are the terminal nodes of each branch that represent the class assigned to the instances that 8 reach them. In this way, from the root node to each leaf node of the tree there is a path formed by a conjunction of decision nodes, which indicate the conditions that must occur in order to reach that terminal node. Each of these paths can be understood as a rule, so that a tree is nothing more than a set of decision rules, which have certain support and confidence values based on the instances they cover. •Support. It refers to the coverage of the rule, i.e. the percentage of instances to which the condition of a rule applies. •Confidence. It refers to the accuracy of the rule, i.e. how accurate the rule is in predicting the correct class for the instances to which the condition of the rule applies. Thanks to the use of decision trees, this process just introduced is extremely intuitive and trivial, as can be seen in the example shown in Figure 7. However, in order to make it even more systematic, support and confidence thresholds will be established, so that only those rules that satisfy these restrictions on the class of interest for the stakeholders of the process will be extracted. That is, only those rules will be extracted whose antecedent affects at least a pre-specified minimum number of cases, i.e. rules with a higher support than a given threshold, and whose consequent is also true for at least a given percentage of these cases, i.e. rules with a higher confidence than a give threshold. With this, the rule extraction process, which is a manual process, will become systematic. Finally, following these steps, a set of rules about the class or classes of interest will be obtained whose antecedents will be given by the variables that form the decision nodes, and whose consequent will be related to the class of the leaf node to which its succession leads. Figure 7: Example of the rule extraction process from a decision tree. 5. The Aortic Stenosis Integrated Care Process This proposal works on a medical process, as mentioned above, more specifically on the Aortic Stenosis Integrated Care Process (AS ICP) implemented in the Cardiology Department of the University Hospital of Santiago de Compostela. Aortic stenosis (AS) is a chronic progressive disease that affects the aortic valve, limiting blood flow from the left ventricle when this valve does not open properly. In fact, severe AS is the most prevalent valve disease in elderly patients [27], which is expected to worsen in the coming decades as the population ages. Mortality in this disease is strongly related to the development of symptoms, with a poor prognosis in the absence of intervention. However, the negative point when an intervention is indicated is that it is not performed immediately, but patients may suffer delays of even years [28]. During this waiting time, complications can occur that may hinder the prognosis, which is why the correct evaluation of the patient and the analysis of his or her conditions is key. The paradigm of care for patients with AS is a process involving different professionals who provide fragmented care at different times and places, with little continuity of care and a high risk of lack of coordination that can hinder patient management. In order to solve this, Integrated Care Processes (ICPs) have emerged, which seek to ensure the effectiveness of clinical actions through greater coordination and a guarantee of continuity in care [29]. In January 2018, the ICP for severe symptomatic AS was implemented in the Cardiology Department of the University Hospital of Santiago de Compostela, with the aim of managing the care of patients requiring intervention and guaranteeing the correct and coordinated functioning of each and every one of its stages [30]. 5.1. Definition of the process The AS ICP covers all diagnostic and therapeutic events, from the indication for intervention at the heart team meeting (formal inclusion in the process), to the return of the patient to normal activity after completion of the post-intervention rehabilitation (exit of the patient from the process). The following stages can be distinguished: •Stage 0. Stage prior to formal inclusion of the patient in the AS IPC, where the necessary tests will be requested and evaluated for presentation at the heart team meeting. The aim of this phase is to identify patients with severe AS who require intervention and to accelerate appropriate complementary tests to avoid delays and loss to follow-up. •Stage 1. From the decision to intervene at the heart team meeting (formal entry into the process) to the valve replacement procedure, including prehabilitation of the patient. The aim of this phase is to optimise the situation of the patient prior to the intervention, to speed up pending tests and the resolution of conditions, and to identify possible alerts or decompensation early on, so as to avoid unexpected events on the waiting list or loss of follow-up. •Stage 2. Valve replacement surgery, surgical or percutaneous. The aim of this stage is to guarantee a protocolised and homogeneous management of patients during their hospitalisation for the intervention. •Stage 3. Rehabilitation and follow-up after valve surgery. This facilitates the recovery of the patient after the operation and the return to normal life. To monitor the results of the AS ICP, a patient log is established in which the clinical information relevant to the process 9