Conformance analysis for comorbid patients in Answer Set Programming

Journal of Biomedical Informatics 103 (2020) 103377

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Conformance analysis for comorbid patients in Answer Set Programming Luca Piovesan , Paolo Terenziani, Daniele Theseider Dupré ⁎

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DISIT, Institute of Computer Science, Università del Piemonte Orientale, Alessandria, Italy

ARTICLE INFO

ABSTRACT

Keywords: Computer-interpretable clinical guidelines Comorbidities Conformance analysis Answer set programming

The treatment of comorbid patients is a hot problem in Medical Informatics, since the plain application of multiple Computer-Interpretable Guidelines (CIGs) can lead to interactions that are potentially dangerous for the patients. The specialized literature has mostly focused on the “a priori” or “execution-time” analysis of the interactions between multiple Computer-Interpretable Guidelines (CIGs), and/or CIG “merge”. In this paper, we face a complementary problem, namely, the a posteriori analysis of the treatment of comorbid patients. Given the CIGs, the history of the status of the patient, and the log of the clinical actions executed on her, we try to explain the actions executed on the patient (i.e., the log) in terms of the actions recommended by the CIGs, of their potential interactions, and of the possible ways of managing each such interaction, pointing out (i) deviations from CIG recommendations not explained in terms of interaction management (if any) and (ii) unmanaged interactions (if any). Our approach is based on Answer Set Programming, and, to face realistic problems, devotes specific attention to the temporal dimension.

1. Introduction In the last decades, the need to improve the quality and the standardization of healthcare, while optimizing costs, has led to the development of clinical practice guidelines (CPGs). CPGs provide evidence-based (mostly derived from clinical trials) recommendations to treat patients, and thousands of them have been developed. For example, the Guideline International Network (http://www.g-i-n.net) groups 106 organisations in 54 countries, and provides a library of more than 6500 CPGs. Most CPGs in the medical literature are in textual form; however, starting from the 1990s, several domain independent computer-based approaches to acquire, represent and possibly execute Computer-Interpretable Guidelines (CIGs; where a CIG is a computer-based version of a textual CPG) have been developed in the medical informatics literature (see, e.g., the book [32] and the survey [18]). By definition, CPGs (and CIGs) are dedicated to the management of patients affected by specific clinical circumstances, that is, by specific pathologies. However, for many reasons, including also the aging of population, and the increase of chronic pathologies, a large percentage of patients is nowadays affected by more than one pathology (comorbid patients). The treatment of comorbid patients is one of the main challenges for current healthcare systems. The main problem in the treatment of such patients is that simply applying the recommendations of the CIGs (one CIG for each specific disease that affects the patient) does

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not work, since the actions (and, in particular, drug administrations) in different CIGs may interact with each other, and such interactions may have critical effects on the patient. Although some CIGs covering the most frequent co-occurring diseases might be devised, the approach of considering all the possible combinations of diseases is not only difficult, but also impractical, so that “there is a need for formal methods that would allow combining several disease-specific clinical practice guidelines in order to customize them to a patient” [17]. The process of: (i) knowledge-based identification of possible interactions between CIGs; (ii) providing patient-specific “merges” of CIGs properly managing interactions in order to avoid dangerous consequences is very complex, so that in the last decade several approaches in Medical Informatics have tried to provide physicians with useful computer-based supports to manage comorbid patients. Specifically, depending on the approach, such issues have been considered from two different viewpoints: a. in an “a priori” analysis of CIGs (e.g., to consider potential interactions between CIG actions, independently of the specific patients, and/or to “merge” two or more CIGs); b. in an “execution-time” analysis, to support the application of multiple CIGs to a specific patient.

Corresponding author. E-mail addresses: [email protected] (L. Piovesan), [email protected] (P. Terenziani), [email protected] (D. Theseider Dupré).

https://doi.org/10.1016/j.jbi.2020.103377 Received 2 August 2019; Received in revised form 7 January 2020; Accepted 10 January 2020 Available online 27 January 2020 1532-0464/ © 2020 Elsevier Inc. All rights reserved.

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In the last years, we have contributed to such a challenging area of research by extending the GLARE (Guideline Acquisition, Representation and Execution) approach [33] to support physicians in the management of comorbidities, proposing an integrated approach taking into account both aspects (i) and (ii), mostly in the context of “execution-time” support [22]. More specifically, in our previous work, we have provided methods for:

of) time; the timing of actions should respect temporal constraints in the CIGs, and interactions occur (or do not occur) in time. This makes conformance analysis and explanation more complex but richer: for instance, the CIG constraints may be violated in order to temporally avoid undesired interactions. Notably, the goal of our “conformance analysis and explanation” approach is not to provide an evaluation of whether the treatment of a patient was appropriate or not, but to try to explain the actions executed on the patients (i.e., the log) in terms of the actions recommended by the CIGs, of their potential interactions (according to the approach in [1]), and of the possible ways of managing each such interaction (defined in [20]), pointing out (i) deviations from CIG recommendations not explained in terms of interaction management (if any) and (ii) unmanaged interactions (if any). We thus propose to expert physicians a rich and detailed starting point to interpret the treatments described by the logs. Such an a posteriori analysis may be important for different tasks. Execution time support would indeed be of great value for physicians, but in several contexts, including the Italian healthcare system, even the systematic adoption of CIGs by hospitals and healthcare organizations has not been achieved yet, and it could only be obtained through a major change in the current healthcare national policy. In such a context, physicians cannot exploit the support of computer-based approaches to manage (comorbid – but also non-comorbid) patients. However, clinical records may easily store both the evolution of the state of the patients and a log of the actions that have been performed on her, so that an a posteriori conformance analysis is still concretely possible. Additionally, also in contexts in which execution-time support to the execution of CIGs and to the treatment of comorbid patients is concretely available, the last decision about the treatment of patients is always left to physicians (who are free to deviate from the suggestions of the support tools), so that an a posteriori analysis of conformance can provide additional important insights into the processes actually executed on the patients. For example, the a posteriori conformance analysis and explanation provided by our approach may achieve a crucial role at the patient discharge stage, which usually involves the documentation of the patient care process, typically relying on a computer with access to the information system, including the patient’s Electronic Health Record. Patient discharge may therefore be the part of the process where a support tool based on CIGs may be used for a posteriori analysis [24]. Specifically, a tool based on the work described in this paper, which is capable of justifying, in terms of interaction management, deviations from a strict application of guidelines, may support the physician in describing the actual treatment with reference to the guidelines, reducing her effort in justifying deviations. Additionally, and very importantly, the a posteriori conformance analysis and explanation provided by our approach (like most work on conformance analysis for processes, also in non-medical domains) can provide domain experts with a valuable starting point for a combined evaluation of the quality of the treatment (actual execution, in general), and the completeness of knowledge (the guidelines themselves and knowledge about interactions) [8]. Remaining (i.e., non-explained) discrepancies may in fact mean a low quality execution (e.g., the physicians are not up-to-date with computerized medical knowledge), or one that is above the quality of guidelines (e.g., physicians may apply recent results not yet included in the available CIGs). Finally, given its capability of providing explicit explanations, our approach could also be applied in medical education, to show and explain how specific patients have been managed. In this paper, we propose a general approach to cope with the above issues, that is mapped to Answer Set Programming (ASP), which, as shown in [30] for the case of a single CIG, is quite useful to analyse conformance, since, on the one hand, it supports the non-monotonic forms of reasoning naturally used by physicians in this context and, on the other hand, it naturally supports the search for alternative

• knowledge-based detection of interactions between actions [1]; • mixed-initiative management of detected interactions [20]; • merging the CIGs into a unique treatment for a given patient [21]. Of course, execution-time support to detect CIG interactions and to suggest physicians proper recommendations (resulting from the management of the interactions and the “merge” of the CIGs) is a primary and vital goal. However, in this paper, we suggest that the comorbidity problem could also be beneficially analysed from a different and complementary perspective: the a posteriori analysis. Given:

• the evolution of the state of a comorbid patient (as stored in a clinical record); • a log of the actions that have been performed on the patient; • the CIGs that have been executed on the patient, the aim of our approach is to analyse a posteriori the treatment that has been applied to the patient. Notably, however, in the context of comorbid patients, a “standard” conformance analysis would not suffice at all. In many contexts in which there is a model for the expected execution of procedures, like, for instance, in Business Process Management, conformance analysis aims at identifying possible discrepancies from the “ideal” process (the one described in the process model) and the “real” one (the one recorded in the log). Such discrepancies are either interpreted as negative deviations from a golden standard or they motivate improving the model in order to cover them [34]. Such a “standard” analysis would not suffice in the case of comorbid patients, where the problem is much more complex. In the case of comorbid patients, more than one “golden” process model (i.e., more than one CIG) is involved, and such models may conflict with each other, since the full adherence to two or more CIGs may lead to the execution of actions whose effects may dangerously interact with each other, or the execution of one may dangerously interact with the patient state. As a consequence, a full conformance to CIGs recommendations is not necessarily a guarantee of quality. In such cases, deviations to avoid interactions are usually the best choice. But we neither deal with the second case of standard conformance analyisis: we do not want to use the actual executions to modify the CIGs, because (i) such deviations are dependent on the specific execution on a specific patient and (ii) making explicit all such executions would be impractical, leading to CIGs that are too complex to be readable and useful. As a consequence, we strongly believe that in the a posteriori analysis of the treatment of comorbid patients, conformance analysis and knowledge-based explanation are two tasks to be performed together:

• in the case of non-conformance to CIGs recommendations, we try to explain deviations in terms of ways to manage CIG interactions; • in the case of conformance, we still check whether such a conformance has led (or could have led) to interactions (such a situation has to be pointed out, as well as non-conformances).

Notably, since different modalities are used by physicians in order to manage interactions (see, e.g., [20]), alternative explanations must be supported by our approach. Additionally, to make our approach more precise in the analysis of non-conformances due to possible interactions, we take into account the temporal dimension. Indeed, patient data hold at specific (intervals 2

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explanations. In the following, we first describe (Section 2) the state of the art in AI support for comorbidities management and in conformance verification for CIGs. Then, in Section 3, we present in more detail the data/knowledge sources used in our analysis. Sections 4 and 5 are the core of the paper: we first introduce (Section 4) our general approach to perform conformance analysis for concurrently executed CIGs, then (Section 5) we describe in detail how the framework is developed in ASP. In order to evaluate our approach, in Section 6 we apply it to a case study taken from the literature [35], considering a realistic scenario involving a patient suffering from three diseases and in which the execution log has been defined taking into account the recommendations of an expert physician. In Section 7 we decribe some limitations of our approach and point out possible future work. Finally, in Section 8, we summarize our contributions.

concurrently execute CIGs. CIGs and merging criteria are represented in an OWL ontology (in the form of concepts and semantic web rules). Given such a knowledge, an Execution Engine merges CIGs according to the merging criteria. Then, an existing semantic-web based execution engine is adopted to execute the merged treatments. The approach in [11], also based on an ontological representation of CIGs and on an integration semantics, mainly focuses on the run-time (execution-time) integration of CIGs. Indeed, as the authors state, many aspects of the treatment of comorbid patients often change dynamically over time, in ways that cannot be foreseen and that must be considered at the execution time. Riaño et al. [25] proposes a model-based approach in which CIGs are modeled as directed graphs composed by decisions and actions, and a set of operators are defined by expert physicians to merge decisions or actions of the same type. Finally, two works [39,15] present ASP-based approaches in which, similarly to [35], user-defined mitigating operators are applied to the CIGs to mitigate conflicts. Some approaches in the literature cope with the problem of conformance analysis of event logs with the respective process models [34]. The approach in [26] proposes some metrics to evaluate the fitness between the log and the model (i.e., how much the observed process complies with the control flow specified by the process model) and the appropriateness of the model with respect to the log (i.e., how well the model describes the observed process). A limited number of approaches have dealt with verifying conformance of a log of actions with recommendations in a CIG. In [9], differences between actual actions and CIG prescriptions are detected and analyzed, e.g., by comparing, for non-compliant actions, actual findings with findings that support the action according to the CIG. [3] focuses on the interaction between a CIG and the basic medical knowledge (i.e., “different forms of medical knowledge that physicians have acquired during their studies and clinical practice” [30]; BMK) in the light of the conformance analysis problem. The work in [30] also focuses on the interaction between BMK and a CIGs, using ASP, aiming at providing a justification for non-conformances.

2. Related work In the current literature, no approach has been devoted to the conformance analysis of CIGs for comorbid patients, except for [23], that represents a short and preliminary version of the work in this paper. On the other hand, the problems of (1) supporting the management of comorbid patients and of (2) performing conformance analysis for single CIGs have been faced by several separate approaches. In this section, we separately consider the state of the art for the two issues, only focusing on the work that is more closely related to ours. In the last years, several AI approaches have been developed for supporting the treatment of comorbid patients (see the survey [6]). For the knowledge-based identification of interactions between CIGs, the approaches most closely related to our one are the ones in [38,13]. The approach in [38] provides a semantic-based framework for analyzing the combination of recommendations from several guidelines. The knowledge needed to analyze interactions is modeled in a conceptual model, describing CIGs, actions, their effects and goals. A set of first order logic rules is provided, working on the conceptual model, to recognize different types of interactions. For instance, alternatives, contradictions and repetitions of actions can be detected. The work in [13] presents a goal-based method that utilizes knowledge of drug physiological effects and therapeutic usage to combine knowledge from CIGs. [13] is based on PROforma, and exploits standards such as the Fast Healthcare Interoperability Resources (FHIR) patient data model and SNOMED-CT. It is characterized by a MVC (model-view-controller) architecture, in which the controller has the role of providing support to the execution of different CIGs, detecting (using an ontology) possible interactions between goals and actions, and mitigating them. Similarly to the interaction detection tool of GLARE (see, e.g., [1] and Section 3.4), the approach in [13] is semi-automatic (i.e., an interaction with user physicians is possible). Several approaches have been devoted to the generation of integrated CIGs or treatments. The work in [27] uses an agent-based approach and hierarchical planning. Basically, in [27], each agent represents an expert in the treatment of a specific disease. The integrated treatment is the result of the coordination of all the agents coping with a specific patient. The approach in [36] is based on constraint logic programming to obtain a treatment for a comorbid patient. The original CIGs coping with specific diseases, the definitions of the possible interactions occurring between them and of their managements (called revision operators) and patient data are modeled in logic programming and taken as input by a mitigating algorithm, that returns as output a possible treatment for the comorbidity. In [36], the number of CIGs is limited to two, no parallel or hierarchical actions are allowed and the temporal aspects are not considered. The work in [35] basically extends the previous one, coping with the limitations above. Finally, the work in [16] simplifies the two previous approaches, presenting a planningbased approach in which the mitigation process is made using a PDDL planner. Jafarpour and Abidi [12] use a semantic-web framework to

3. Data and knowledge models In this section, we introduce the input elements of our approach. First, we describe the formalism we adopted for the CIGs (Section 3.1). Then, we describe how execution log and patient data are represented (Section 3.2). Finally, in Section 3.3, we introduce the knowledge model used to explain non-conformance. 3.1. CIG model As concerns the CIG model, our approach is general enough to be applied to different CIG formalisms. Basically, our approach was developed to work with a formalism adopting the Task Network Model (TNM) representation (see, e.g., the PROforma [31] and Asbru [28] approaches, and the survey [18]) and such that all the actions in the CIGs can be mapped into our ontological model (see Section 3.3). Moreover, we cope with temporal constraints, repetitions, alternative paths, hierarchical actions and a specific set of action types described below. Although the approach in this paper is based on such representation features, we are confident that our approach is general enough to consider additional ones. For the sake of concreteness, we ground our approach on GLARE ([33]), which supports the above features. GLARE (GuideLine Acquisition Representation and Execution) is a domain-independent system for the acquisition and execution of CIGs, developed since 1997, in a collaboration between the University of Eastern Piedmont, Italy, and the Azienda Ospedaliera San Giovanni Battista, Italy (one of the largest hospitals in the country). GLARE adopts a TNM representation: a CIG is represented as a hierarchical graph, where nodes are the actions to be executed, and arcs are the control relations linking them. GLARE supports the distinction between atomic (simple steps in a CIG) and 3

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composite actions (plans), where composite actions can be defined in terms of their components (i.e., other actions and control relations between them). In GLARE, four types of atomic actions are available:

arcs, where [m , M ] represents the fact that the delay between the two actions must be at least m and at most M basic time units (with the special value inf that represents an infinite duration). By default, GLARE adopts days as basic time unit, and in our examples we adopt days too. However, different time units can be adopted. Furthermore, where not explicitly declared, we intend a delay in [0, 1] (i.e., between 0 and 1 time unit - days in our examples). For durative actions (i.e., actions with a duration greater than one time unit), we represent with [m , M ] the minimum (m) and maximum (M) possible duration. The value inf represents a duration that lasts throughout the patient’s life. In Fig. 1, we show an example of CIG for the treatment of chronic kidney disease (CKD), taken from [35] and modeled through METAGLARE. The CIG for CKD starts with a diagnostic decision that analyzes the EGFR (EGFR?; estimated glomerular filtration rate). The result can be LT60 (EGFR < 60 ) or GE60 (EGFR 60 ). In the latter case (EGFR 60 ; right part of Fig. 1), patients are treated with both (action x4 is a xorJoinAndSplit) acetylsalicylic acid (aspirin; composite action asp_ckd) and an angiotensin-converting enzyme inhibitor (composite action acei_ckd). Notice that both composite actions asp_ckd and acei_ckd contain a plan (not shown at the higher-level representation of the CIG) prescribing individual administrations of the respective drugs, following their posologies. Moreover, they have an infinite duration: they must continue for all the patient’s life. Finally, a proper lifestyle management (ls_ckd_mgmnt) and a cardiovascular risk management (cv_risk_ckd) are started eight weeks (56 days) after the beginning of the pharmacological therapy. On the other hand, patients with low EGFR (EGFR < 60 ) are evaluated for anemia (ANEMIA diagnostic decision). Patients suffering from anemia (ANEMIA_PRESENT) are further evaluated for the ferritin level (FERRITIN), and the ones with a low ferritin level (FERRITIN < 100 ) are treated with ferrous salt (fe_salt_ckd composite action) for eight weeks. Then, both patients with a low ferritin level and patients with a normal level (action x9 is a xorJoinAndSplit action) start the treatment with an erythropoiesis-stimulating agent (esa_ckd). Moreover, metabolism abnormalities are evaluated: if present, patients are treated with phosphate binders (pb_ckd), and in both cases (abnormalities present or absent), the CKD lifestyle management and the cardiovascular risk management are started.

• work actions, i.e. actions that describe a procedure which must be executed; • pharmacological actions are a specific sub-type of work actions, •

•

specifying a drug (or drug category) to be administered to the patient, and the posology; decision actions, used to model the selection among different alternatives. GLARE supports the distinction between: (i) diagnostic decisions, to assess the state of patients on the base of their findings; (ii) therapeutic decisions, used to represent the choice between paths in a CIG, where each path represents a particular therapeutic process. The choice can be made by evaluating a fixed set of parameters (effectiveness, cost, side-effects, compliance and duration); query actions, i.e. requests of information (typically patient’s parameters), that can be obtained from the outside world (physicians, databases, patient visits or laboratory tests);

To be easily distinguished, in GLARE actions are graphical represented with different shapes: work and pharmacological actions are represented with blue circles, decisions with yellow diamonds, queries with green quadrangles, and composite actions with red hexagons. Notably, each action in the CIGs is linked to its type in the ontological model of GLARE (see Section 3.3), which contains the description of its effects, intentions, and the possible interactions with other elements (e.g., other actions or patient conditions). Actions in a CIG are connected by control arcs, representing the flow of actions (e.g., which actions can be executed next), and can be annotated by temporal constraints, expressed in the formalism in [2]. Starting from 2014, GLARE has been extended in META-GLARE ([4]). META-GLARE is a “meta” system, in that it takes in input a CIG representation formalism, and automatically generates a CIG system to acquire and execute CIGs expressed in the input formalism. In order to provide a CIG representation as close as possible to the one provided by Wilk et al. for the benchmark example in [35], in this paper, we exploited META-GLARE to add two additional constructs not representing medical actions1: “andJoinAndSplit” and “xorJoinAndSplit” gateways. Both gateways represent the join of several parallel paths (in case two or more arcs enter in the gateways) and the split of the CIG into two or more parallel paths to be all executed concurrently. Their execution has no duration, and after it all the actions following the gateways (considering the control arcs, and the temporal delays) become executable. The two gateways differ in the way joins are handled:

3.2. Execution log and patient data In our approach, the execution log is represented by a set of entries (e.g., see Table 1). Each entry is a triple, with a unique key (ID), the description of the event and the time in which such event happened. In our model time is discrete and days are the basic time unit. The description of each event consists of the type of the action involved, plus a specification of the type of the event. Events can be of three types:

• an “andJoinAndSplit” gateway is executed immediately after that all •

the actions preceding it in the CIG (considering the control arcs, and the temporal delays) end; a “xorJoinAndSplit” gateway is executed immediately after that the first action preceding it in the CIG (considering the control arcs, and the temporal delays) ends;

• starting/ending points of a CIG (e.g., entry with ID = 10 in Table 1) • starting/ending/aborting points of an action, which can temporally •

Gateways are graphically represented through small black (for “andJoinAndSplit”) or gray hexagons (for “xorJoinAndSplit”). Temporal delays between actions, where specified, are shown along

coincide for punctual actions, such as decisions (e.g., entry with ID = 11 in Table 1). outcomes of decisions (e.g., entry with ID = 12 in Table 1).

Since gateways are not medical actions, but only constructs to manage parallelism, the log does not contain entries related to them. We assume that, as soon as a gateway becomes the next action to be executed, it is “executed” immediately. For composite actions, the execution log contains both entries for the starting and ending of the composite action, and entries for the start and end times of their components. Repetitions (e.g., the daily administration of a drug) are treated as a special case of composite actions, in which the components are all instances of the same action. In the case study in Section 6, for the sake of simplicity and for homogeneity with [35], repeated actions are treated as a single macro-action, and the log contains only their start and end points (and not the ones for the atomic

1 In actionable graphs, the representation formalism used by Wilk et al., gateways are used in order to model parallelism between actions. It is worth stressing that also GLARE supports parallelism, but using different control structures (see [33]). However, the clinical case study presented in this paper (see Section 6 and [35]) was originally introduced using the “actionable graph” formalism, and the use of the GLARE representation of parallelism would have produced CIGs structurally different from the ones in [35]. Therefore, to improve the comparison between this work and the one in [35], we introduced gateways in our formalism.

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heart _rate, irregular , 90, 98, 105, 115 represents the fact that the patient experienced an irregular heart rate certainly between day 98 and day 105 and possibly between days 90 and 98 and between days 105 and 115. 3.3. Ontological model To perform conformance analysis and explanation, a representation of the medical knowledge involved in interactions is needed. To this end, we take advantage of the model defined in ([1,22]). Such an approach includes an OWL ontological model representing CIG actions, their effects and their intentions (i.e., the goals of the actions within a specific CIG), and the interactions between such elements. Effects and intentions are expressed as variations of patient’s status, which represents a change in the patient status. Each variation (e.g., the “Anticoagulant” one) relates to exactly one attribute (“blood coagulation status”), describing the patient’s status, and to exactly one modality of the variation (“decrease”). The ontological model, besides describing the actions, provides a representation of the possible interactions. In particular, four classes of interactions exist: Variation interactions represent interactions between the effects of two actions; Intention interactions are the ones involving at least an intention of an action; Drug interactions involve the drugs prescribed by pharmacological actions and Status interactions are the ones between an effect of an action and the status of a patient. As detailed in the hierarchy proposed in [20], Intention interactions are a particular case of Variation interactions, and interactions can be caused by other interactions. Each interaction can have a type, which can be “Concordant” if the interaction strengthens one (or more) of the involved elements, or “Discordant” if it weakens one of the elements. Elements that do not interact are defined as “Independent”. Further refinements are possible, for instance “Opposite” (refining the type “Discordant”) is used for (variation) interactions in which elements are focused on the same attribute, with different modalities (increase/decrease). Techniques to automatically infer such interactions are provided (see Section 3.4). However, for the sake of completeness, some of them can be manually inserted in the knowledge base (e.g., by loading them from external repositories). If compared to the medical literature, our interaction ontology presents several aspects overlapping the medical classifications. For instance, the distinction between drug-drug (Drug interactions) and drug-disease (Status interactions) interactions is adopted by many medical interaction repositories (see, e.g., https://www.drugs.com/ drug-interactions2, which also considers drug-food interaction – not useful in our context). On the other hand, also the “Independent”, “Discordant” and “Concordant” interaction types can be found in medical literature. Consider, for instance, the distinction between additive, antagonistic and synergistic interactions in [37]. Other medical classifications, however, are more knowledge-based (see, e.g., [10], focusing on the distinction between contraindicated, provisionally contraindicated, conditional, minimal risk and no interactions) and our approach does not cover them. On the other hand, if considering the medical informatics literature, other approaches provide interaction classifications. For instance, the approach in [38] distinguishes between Divergent Causations, Repetition, Alternative, Repairable, Contradiction, Side-Effect, Compliance, Safety interactions. Such a classification is mostly complementary to our one. In Fig. 2 we show part of our ontological model representing the actions “Warfarin therapy for AFib” and “Aspirin therapy for CKD”, their effects/intentions and an interaction between them. In [1], the ontological model described above was extended to cope with temporal information (not shown in the figure, for the sake of

Fig. 1. META-GLARE representation of the CKD CIG. EGFR = eGFR level, LT60 = <60, GE60 = 60, ANEMIA = anemia, FERRITIN = ferritin level, LT100 = <100, GE100 = 100, METABOL ABNORM = metabolism abnormalities, fe_salt_ckd = ferrous salt, esa_ckd = erythropoiesis-stimulating agent, pb_ckd = phosphate binders, ls_ckd_mgmnt = lifestyle management, cv_risk_ckd = cardio-vascular risk management, asp_ckd = aspirin, acei_ckd = angiotensin-converting enzyme inhibitor. Table 1 Example of part of an execution log for the CKD CIG. ID

Event

Time

10 11 12 13 14 15 16 17 20

(CKD, cig_started) (EGFR?, started) (EGFR?, result = GE60) (EGFR?, ended) (asp, started, dosage:d1) (acei, started, dosage:d3) (ls_ckd, started) (cv_risk, started) (asp, ended)

105 105 105 105 106 106 133 133 360

actions composing them). A single execution log contains all the entries related to all the executed CIGs for a specific patient. As concerns patient data, we use a model that supports temporal indeterminacy. Data are represented as tuples attribute , value, IS , DS , DE , IE . The non-temporal attributes attribute and value represent, respectively, a patient’s status attribute (e.g., “heart_rate”) and its value, that can be either quantitative or qualitative (e.g., “irregular”). The remaining attributes represent the temporal validity of the datum. Intuitively speaking, the interval [DS , DE ] (where D stands for determinate time) represents the time interval in which the datum is certainly true, while the interval [IS , IE ] (where I stands for indeterminate time) represents the time interval in which the datum is [IS , IE ]). For instance, the tuple possibly true (with [DS , DE ]

2 Gathering medical information provided by Wolters Kluwer Health, American Society of Health-System Pharmacists, Cerner Multum and IBM Watson Micromedex.

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The above interaction detection is, however, abstract if not paired with a temporal analysis. Indeed, the detected interactions highlight the fact that the involved actions can potentially interact. However, actions actually interact only if their effects, intentions or drug administrations overlap in time. For such a reason, the approach [1], which is based on an extension of the STP (Simple Temporal Problem) framework [5], provides a set of facilities to analyze interactions also considering time. In particular, given two actions, their execution times and the temporal information provided in the ontological model, the approach in [1] exploits temporal reasoning techniques to detect whether:

• the two actions could hypothetically interact, but they actually do not • •

Fig. 2. Part of the ontological model representing the warfarin treatment for atrial fibrillation and the aspirin treatment for chronic kidney disease (solid lines), and the interactions inferred between such elements (dashed lines).

For the work in this paper, we slightly extended such an analysis: the approach [1] copes with the temporal indeterminacy deriving from delays, that may be partially unknown, between the execution of actions and the arising of their effects. In this paper, we also consider indeterminacy about execution times of actions scheduled in the future (see the predicate possiblyInteractRelevant in Section 5).

simplicity). Basically, temporal constraints have been added, representing for effects (property “hasEffect”) the delays between the starting/ending of an action and the starting/ending of its effects (or, alternatively, the duration of the effects), and for intentions (property “aimsTo”) the time in which they should occur within the CIG execution. Since this kind of information tends to be temporally indeterminate (i.e., one cannot predict the exact delay between the starting of an action and the occurrence of its effects) a representation of temporal indeterminacy similar to the one presented in Section 3.2 was adopted. The model allows, for instance, to represent the fact that the anticoagulant effect of action “Warfarin therapy for AFib” starts within the first week after the starting of the therapy (i.e., between 0 and 7 days after the first administration) and ends within the two weeks after the ending of the therapy.

4. A general approach to conformance analysis and explanation In this section we describe our approach for conformance analysis. We first recall (Section 4.1) the modalities that have been identified in [20] for managing interactions. We then describe the execution model of individual actions in CIGs (Section 4.2) and how potential interactions in their execution are defined. Then, (Section 4.3) we highlight the general conformance analysis and explanation process. In the following we refer both to the case of interactions between actions in different CIGs and to the case of interaction between a CIG action and the patient status.

3.4. Knowledge-based interaction detection

4.1. Management modalities

In previous work (see, e.g., [22]) GLARE was provided with a set of reasoner modules to support the management of comorbidities. In this work, we take advantage of the modules devoted to the knowledgebased detection and to the temporal analysis of interactions. In GLARE, knowledge-based detection of interactions is performed by rule-based OWL reasoning [19]. Given two actions, the reasoner exploits the ontological model described in Section 3.3 to infer all the possible interactions between the effects, the intentions and the drugs related to the two actions. For instance, for the two actions “Warfarin therapy for AFib” and “Aspirin therapy for CKD”, the reasoner first retrieves, from the ontological model, all the effects/intentions/drugs associated to such actions. Among them, the variations “Anticoagulant” and “Prevent cardiovascular diseases” are found. Due to the causal relationship between them, the interaction “Pcd-Anticoag Interaction” is automatically asserted by the reasoner. For instance, the following SWRL rule3 is exploited to infer the type, (i.e., “Concordant”), the changed variation (“Prevent cardiovascular diseases”) and the modality of the interaction (“Increase”).

3

interact considering their times of execution (in case the interacting effects/intentions/drug administrations do not overlap in time); the two actions can potentially interact considering their execution times (in case the interacting effects/intentions/drug administrations could probably overlap - considering temporal indeterminacy); the two actions certainly interact (in case the interacting effects/ intentions/drug administration certainly overlap in time).

In the medical practice, physicians adopt different methodologies to manage interactions (e.g., avoid undesired interactions) between (the intentions, the effects and the drugs of) CIG actions and between CIG actions and patient status. In [20], considering the medical literature, a set of modalities to achieve such a goal has been identified4. Notably, such options are not mutually exclusive: indeed, usually in clinical practice many options are possible, and the physicians have to choose between them. The replanning and the temporal avoidance modalities aim at avoiding an interaction. Replanning. One of the interacting actions (or the single action interacting with the patient state) is substituted by a new plan (set of actions), achieving the same intention, or a similar one, but avoiding the interaction. 4 It is worth stressing that, even if the set of modalities described in this paper has been found exhaustive enough to cope with different use cases, defining a complete set is difficult. Indeed, other modalities could be defined, for instance, considering additional knowledge and/or phenomena. In such a case, to extend our approach to cope with the new modalities, only the addition of new ASP rules explaining the modalities and of the additional knowledge (if any) in the ontological model are needed.

https://www.w3.org/Submission/SWRL/ 6

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Temporal avoidance. Interactions can be temporally avoided. In order to do so, interacting actions (or the interacting action) can be executed at times such that the interaction cannot actually occur (since their effects cannot overlap in time). Medical practice indicates that not all undesired interactions strictly need to be avoided. In some cases, CIGs can be adjusted to manage the situations in which the interactions arise. We support three main management options to this purpose: dosage adjustment (for drug interactions), effect monitoring, and interaction mitigation. Dosage adjustment. Interactions can be mitigated through a variation of dosage with respect to the ones recommended in the CIGs. Interaction mitigation. In some cases, the undesired effects of interactions can be mitigated through the introduction of “mitigating” actions, with effects discordant or opposite with respect to the changes caused by the interaction. Mitigating actions are deviations with respect to the two CIGs. Effect monitoring. In some cases, interactions are not handled beforehand. Rather, physicians decide to monitor the possible undesired effects of an interaction. An actual management is applied afterwards, only in case monitoring shows that it is needed. Effect monitoring implies the addition of one or more monitoring actions focusing on the effects of the interaction, and of decisions to evaluate them. In case the interaction cannot be tolerated, another management must be applied. However, since the interacting actions are under execution or ended, the application of the managements is slightly different from their description above. For instance, when applying a replanning after an effect monitoring, one needs to first interrupt and then replace one of the interacting actions instead of simply replacing it before its execution. Not all interactions between CIGs are negative or undesired. This is the case when two actions in the two CIGs pursue the same or similar intentions, or enforce each other. In such a case, intention alignment or interaction alignment can be applied by physicians. Intention alignment. In the case of intention alignment, the physician may want to “merge” two actions of two different CIGs into a single one, possibly respecting the temporal constraints of both CIGs, or to substitute them with a new action, which pursues the same (or similar) intentions of the two actions. Interaction alignment. In some cases an interaction enforces the intention(s) of one of the interacting actions (e.g., because the actions reach the same intentions through different physiological mechanisms). In such cases, to increase the efficacy of the treatment, the interaction can be forced by maintaining the interacting actions and by executing them in times such that the interaction occurs. Besides the above modalities, the safe alternative modality has been identified in [20]. Such a modality is relevant in decision support, but detecting it is less useful in an a posteriori analysis (see however the discussion in Section 7). Safe alternative. Such modality consists in the avoidance of an interaction through the choice of alternative paths in the CIGs, when alternative therapeutic actions or paths of actions are specified.

Fig. 3. States for an action.

when the control flow indicates that a could be the next action to start. The execution window at time t for a scheduled or candidate action a is the uncertain time interval, determined at time t given the temporal constraints in the CIG and the actual time of previous events, when a could be in execution. A candidate action a becomes active when it starts6. An active action either becomes completed or aborted, in case some failure arises during its execution. By uncertain time interval we mean an interval whose start and end are in turn intervals [s , s ], [e, e ] meaning that the interval could start at some time in [s , s ] and end at some time in [e , e ]. The definition is informal given that the semantics of the actual control flow constructs in the CIG contributes to determining the candidate actions at a given time. A candidate action is not necessarily ready to start, given the temporal constraints on it. It is worth noticing that the states defined above partially overlap the ones defined in Asbru [28] for plans: active, completed and aborted have a counterpart in Asbru. On the other hand, candidate and scheduled cannot be mapped into Asbru states. The following additional definitions are used in conformance analysis, in order to detect whether the management of an interaction can be used to explain deviations from the strict execution of the CIGs. Definition 2. A Reference Time (RT) is a time when, according to the log, an action in a CIG changes its state, or a time such that a new value for a patient status attribute is detected. Intuitively, a RT is a “qualitatively relevant” time in the execution of a CIG on a patient, i.e., a time when something happens or changes. In order for an action (a current or future action, or a past one whose effects are ongoing) to be considered as a possibly interacting action, we have to know when its effects may hold. Knowledge about the effects of the actions and the temporal constraints between actions and effects are part of the general methodology devised in [1] for temporal detection of interactions (see Section 3). Definition 3. The existence window of an effect e of an action a at a reference time RT is the time interval in which e may hold, given the known or predicted execution time of a at RT, and ontological knowledge. Definition 4. The relevant actions at a reference time RT are:

• the actions that are scheduled, candidate or active at RT; • the actions that are completed at RT that have an effect whose ex-

4.2. Execution model and interactions

istence window at RT includes RT.

In Section 3.1 we have described how the control flow of a CIG is specified. A CIG may include temporal constraints between actions. An action can be reached because it is the successor of an action which has terminated, or because it is after a gateway (andJoinAndSplit, or xorJoinAndSplit) which has been activated. We introduce the following possible states for an action (see Fig. 3):

Definition 5. A relevant interaction at a reference time RT is either: 1. a possible interaction (according to [1]) between two relevant actions at RT from different CIGs, where at least one of them is not completed; 2. a possible interaction (according to [20]) between a non-completed relevant action at RT and patient state at RT.

Definition 1. An action a becomes scheduled when the control flow indicates that a will be executed5. An action a becomes candidate

6 In the execution model in [30], preconditions for actions are also considered, and an action should start (become active) at a time such that all preconditions, with their temporal constraints, enable the action, if such a time exists; otherwise the action is discarded.

5

Then, all and only the actions from the current points of execution — such points may be more than one in case of parallelism — to the next decision point are scheduled actions. 7

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In the first case, the two actions have interacting effects; in the latter, an effect of the action interacts with the patient state. Observe that a possible interaction at RT may involve the future wrt RT, taking into account the possibile indeterminacy, at RT, of the actual execution time of the actions (in case they have not started, or not completed), and the temporal indeterminacy of the effects wrt the time of actions. That is, the effects which actually interact would occur in the future, wrt RT, and there is a possible interaction if their possible time span may overlap. In case 2, an action effect in the future interacts with a state that holds at RT and is hypothesized to persist until the action effect arises. Note that in this paper we do not consider, for the sake of simplicity, interactions between more than two actions, or between multiple actions and patient state, and we restrict our consideration to actions from different CIGs, assuming that interactions internal to a CIG are explicitly considered in the CIG itself (see however the discussion in Section 7).

account the log up to RT, i.e., the information the physicians had at that time. Notably (see Definition 1) the detection of possible interaction at a given RT must consider the fact that scheduled actions can be executed at any time compatible with the temporal constraints in the CIG8. (B) Reasoning on interaction management. For each relevant interaction, let RT be the corresponding reference time. Alternative management modalities for the interaction are hypothesized; for each of them, this implies that the log after RT is checked with respect to the execution of the CIGs as modified by the interaction management. In case multiple interactions are detected, the combination of hypothesized management modalities (one for each interaction) is taken into account. In this way, non-conformances to a “blind” execution of the CIGs can be explained in terms of interaction management. A “no management” modality is also considered, corresponding to the hypothesis that in the actual execution the interaction has not been detected, or in any case has not led to changing anything in the CIG execution. Fig. 4 summarizes the above idea, distinguishing between actionaction vs action-state interactions. Please notice that, while the approach in [20] provides a richer hierarchy of interactions (variation, intention, drug and status interactions), hereinafter without loss of generality we adopt a simplification. Indeed, besides the fact that intention interactions are a particular case of variation interaction, also drug interactions can be brought back to variation interactions. Drug interactions are, in our model, always related to at least a variation interaction9 and, for the sake of conformance analysis, coping with the variation interaction also covers the related drug interaction. This fact allows us to cope with variation, intention, and drug interactions in a homogeneous way (as action-action interactions), while status interactions (i.e., action-status interactions) deserve different managements. (C) Evaluation of the hypothesesis also crucial. The hypotheses that lead to a minimum number of non-explained discrepancies (possibly, zero) with the log are considered. If in one such hypothesis contains the “no management” modality for a relevant interaction, this is pointed out as a potential interaction that has not been managed. If it contains one of the “actual management” modalities, it is also pointed out, since it helps interpreting what could otherwise be considered as a non-conformance. The remaining discrepancies (if any) in the solution are pointed out as non-explained non-conformances. As regards the management of the combinatorial space of hypotheses, ASP (see Section 5) allows for specifying (A), (B) and (C) in a declarative way, even though the solver does not exhaustively build the space of hypoteses before evaluating them. In the following we describe for each management modality the necessary conditions for hypothesizing it, and how the modality can be used to explain the actions in the log in cases which would represent non-conformances with respect to a strict CIG execution. Replanning. Such an option explains cases in which an action in a

4.3. Conformance analysis & explanation process Conformance analysis for a single CIG should check whether the trace of actions in the log can be seen as an execution of the CIG, or whether there have been deviations. The analysis should point out, for example, whether an action was executed when it was not candidate (including the case of an action which is not part of the CIG), or it was executed late with respect to temporal constraints. This is the basic form of temporal conformance analysis in [30] (where general medical knowledge in the form of rules is also considered, in order to allow for a non-strict application of the CIG, but without relying on interaction modeling). The case of multiple CIGs basically requires checking whether the log of actions can be seen as the “blind” parallel execution of the CIGs. This would however consider as (unjustified) deviations the modifications to the strict application of CIGs that may have been applied in order to deal with interactions. Therefore, the core issue here is to identify how the managements of the possible interactions can explain the deviations from the blind parallel execution of the CIGs. This is a challenging task, since (i) each interaction can be managed through different management modalities, and (ii) in the (general) case of multiple possible interactions, the combination of the management modalities (one modality for each interaction) must be considered. As a consequence, even if the input log is precise, one needs to take into account a combinatorial space, to identify the combination(s) of hypotheses, in terms of instances of management modalities, that better explain(s) the log. This involves the need to reason also about CIG actions that could have been executed (in a “blind” parallel execution), and about their possible execution times7. Notably, in real-world scenarios, an explanation perfectly matching the log may not exist. The three core tasks of our approach are the detection of possible interactions, reasoning on interaction management, and the evaluation of the hypotheses. (A) Detection. Possible interactions are detected according to Definition 5 (and then to [1]), for relevant times RT, taking into

8 To avoid redundancy, and then for the sake of efficiency, the detection of a possible interaction between a single pair (a1, a2) of actions can be limited to the earliest RT for which (a1, a2) constitute a relevant interaction. At RT they may, e.g., be both scheduled with some uncertainty related to their actual execution time, also due to the uncertain execution time of other scheduled actions at RT (e.g., a3 ) that precede them in the CIG. At a later RT’, (a1, a2) might still constitute a relevant interaction: but there is an equal or smaller uncertainty on their execution time, given that they may have started, one of them may have completed, or they may still be scheduled, but the uncertainty on their timing may be smaller, because a previous action - like a3 above - has been executed in the meanwhile, so that its timing is now certain. 9 Notably, some drug interactions involve chemical processes which are not directly modeled in terms of variations of the patient status. However, such cases can be easily coped with in our approach by introducing attributes “drug A presence” and “drug B presence”, and asserting that the drug interaction between A and B is caused by the (variation) interaction between the increasing of “drug A presence” and of “drug B presence”.

7 For instance, suppose that we consider the log of a comorbid patient treated with CIG1 and CIG2. We have in the log the beginning of action A’, at time t’. But suppose that A’ is neither recommended by CIG1, nor by CIG2. This fact could be explained by the fact that, “around” time t’, CIG1 would have recommended action A1 (to be executed within a given range of time), and CIG2 action A2 (to be executed within a given range of time). Suppose also that one of the effects of A1 and A2 are contrasting, and that their effects may overlap in time. And suppose that A’ is an action which can reach the same goals of A1, but without having the same effect (the one that contrasts an effect of A2). This fact could explain the presence of A’ in the log (and the absence of A1). However, to identify such an explanation of the log, we have to resort to the “actions that should have been executed” (in the “blind” execution of CIG1 and CIG2).

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Fig. 4. The possible interaction between two actions relevant for a reference time RT, or between an action and the patient state, may be used to explain the rest of the log.

CIG is not executed (while it should have been, given the conditions and constraints in the CIG), and one or more actions, not present in the CIGs, are executed (they are present in the log). Ontological knowledge is used to check whether the actions in the log but not in the CIGs reach the same intentions as the “substituted” action. Temporal avoidance. Such a modality can be used in order to explain cases of non-conformance due to the violation of some of the temporal constraints in one or more CIGs. To do it, our approach checks whether the relevant interaction at RT, which is possible in case actions are executed according to the CIG constraints, is instead not possible given the execution times in the log. Dosage adjustment. This management modality can be used as an explanation if for at least one of the interacting actions, the dosage in the log is different from the one in the CIG; the ontology is used to check whether the modality of the dosage variation is the proper one for mitigating the relevant interaction.

Interaction mitigation. An action, not included in the CIGs, can be explained by the interaction mitigation modality if, according to the ontological knowledge, it mitigates the effects of the relevant interaction. Effect monitoring. The effect monitoring modality explains situations in which (i) interacting actions present in the CIGs are indeed executed, but (ii) they are followed by a monitoring action (not present in the original CIGs) and a decision action (not present in the original CIG) to evaluate the state of the patient and decide whether to continue the current therapy or not. In the latter case, the log must contain another management or the CIG must be suspended. Intention alignment. This modality can be used to explain the fact that one action has been removed or shortened, in case an action in the other CIG already achieves its intention. It can also be used to explain the occurrence in the log of an action which is not present in any of the two CIGs, instead of two CIG actions. In all case, ontological knowledge 9

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is used to check whether the actual action(s) achieve the intentions of the original ones. Interaction alignment. This modality can explain the presence of an interaction that enforces the intention(s) of one of the interacting actions.

into the ASP representation is trivial and it can be made automatically. For the sake of brevity, the translating algorithms are omitted. It is worth stressing, however, that for efficiency reasons not all the ontological knowledge is exported into the ASP representation. Only the elements related to the actions in the CIGs and in the execution log are exported.

5. ASP representation

5.3. Managing the execution model in ASP

Answer Set Programming (ASP) (see [7]) provides an efficient framework for solving search problems based on a declarative representation. In particular, alternative choices can be evaluated according to their implications, based on rules defined in the representation. The conformance analysis framework in this paper is represented in ASP, like the ones in [29,30]. Similarly to that previous work, an explanation should be searched with no unjustified deviation from CIG execution, or a minimum number of such deviations; in the work in this paper, however, the explanations can be in terms of the application of some interaction management modalities.

The basic idea of conformance analysis is trying to match the log with a possible execution of a process model. In the comorbidity context, the basic process model (i.e., without considering interactions) is given by the set of CIGs being executed on a patient, and the execution model of individual actions discussed in Section 4.2. Similarly to [30], both the CIG(s) control flow and the execution model of individual actions can be modeled in ASP (in the fourth part of Table 2, we show the main predicates used for the execution model). For example, an action can be inferred to have started as part of the execution of a CIG at some reference time RT, if it is recorded in the log that an action of the same type started at RT and it is inferred that the action is candidate at RT for the CIG. How this is actually inferred depends on the control flow; for the simple case where an action A2 is the successor of another action A1, the action A2 becomes candidate when A1 ends, and remains candidate until it is inferred to have started. As a simple example, through the following rule:

5.1. ASP in a nutshell We explain here the meaning of some ASP rules and the ways they are used in problem solving. A basic ASP rule has the form: and is used to infer p if p1…pn can be inferred. All of p, p1…pn can be atomic formulae containing variables, which are instantiated to variable-free atomic formulae in a grounding phase before the solving phase, using constants appearing in the program. For modeling and solving combinatorial problems, or, in general, for allowing the ASP solver to consider different scenarios, choice rules are used. An example choice rule is:

an action A2, that is not an “andJoinAndSplit”, starts to be candidate for the CIG Src at a time S, that is the time in which the action A1 preceding A2 in Src, that is not a decision, ends. The cases of “andJoinAndSplit” and of decisions require different rules, since a join becomes candidate only when all the preceding actions ended, and an action following a decision becomes candidate only if the path containing A2 is chosen as the result of the decision. The case where an action A is candidate for more than one CIG requires special attention. In such a case, a single instance of A in the execution log cannot be interpreted as the execution of A for both CIGs, except in the case in which the single action in the log is interpreted as the result of the application of an intention alignment between the two actions in the two CIGs. For such a reason, each log entry can be associated, by the ASP solver, only to (at maximum) one action in the CIGs. The choice of the CIG action to associate is made by the ASP solver, depending on the association that involves the minimum number of discrepancies. As in the approach in [30], we adopt a set of annotation rules to detect (non-explained) discrepancies between the recommendations in the CIGs and the entries in the execution log. Basically, in each annotation rule an instance of predicate info is implied, describing the detected discrepancy. For instance, the following rule:

Given such a rule, if s can be inferred in a scenario (a candidate “answer set”), the scenario is split in 3 different ones, where exactly one of p, q, r holds. In general, numbers m, n (with 0 m n) can be used in place of the 1’s: meaning that, if s can be inferred, the scenario is split in all the possible scenarios in which at least m and at maximum n elements among p, q, r hold. The case where n = 0 is a way to express negation (i.e., none of p, q, r holds). Integrity constraints of the form: can be used to reject scenarios in which p1…pn hold. Optimization statements can also be used, for example to select, among all answer sets, the ones with a minimum number of atomic formulae of a given form. As we shall see in the following, in the work described in this paper choice rules are used to consider alternative management modalities in case an interaction is detected, integrity constraints are used to prune hypotheses about management modalities, according to what the modality actually means, and optimization is used to select scenarios with a minimum number of (non-justified) discrepancies with respect to the log.

identifies the case in which an action A, candidate in the time interval [Tca,TcaEnd], has not been started at the end of such a time interval. To ensure that the non-execution of A was actually a discrepancy, the rule also checks that A was not blocked. Obviously, the rule does not apply to gateways.

5.2. Knowledge and data The first step to encode our framework in ASP is providing the representation of data and knowledge in input. The first three parts of Table 2 describe the predicates we used in ASP. In particular, the first part of the table shows the predicates adopted to model the CIGs and the actions belonging to them. The second part of the table shows the predicates representing the ontological knowledge. The third part describes the predicates for the execution log and the patient’s status. Given the input elements, as described in Section 3, their translation

5.4. Explanation based on interactions 5.4.1. Action-action interactions The core of the ASP representation for the explanation approach for action-action interactions is in choice rules for alternative management 10

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Table 2 Main ASP predicates adopted to model CIGs, patients’ data, execution logs, ontological knowledge and the execution model. Predicate

Description

Predicates modeling CIGs action (C , A , Aglaretype )

Action A belongs to CIG C, and it has the GLARE action type Aglaretype (e.g.,

repetition (A) succ (C , A1 , A2 ) prescribeddosage (C , A , Dos) wf _tc (C , A1 , S1, A2 , S2, m , M ) Predicates modeling ontological knowledge isA (A , Atype )

aimsTo (C , A, I , Is , Ie ) hasEffect (Atype , V , Vis , Vds , Vde, Vie ) focusOn (El, Elattr ) causes (V1, V2) interaction (I ) hasElement (I , El) hasType (I , Itype )

changes (I , Ichanged )

hasModality (El, Elmod) Predicates modeling execution log and patients’ data started (Atype , T , ID )

completed (Atype , T , ID ) administereddosage (Atype , Dos, ID)

status (Attr , V , Vis, Vds, Vde, Vie ) Predicates used for the execution model candidateStart (C , A , S ) candidateWindow (C , A, S1, S2) block (A , S ) relevant (C , A , S ) info (Type , P1, …, Pn)

workAction, decisionAction, pharmacologicalAction , …; see Section 3.1). Composite action A contains one (or more) repeated action. In C , A1 precedes A2 . Action A in CIG C is recommended with dosage Dos.

with S1, S2 {started, completed} . The delay, in CIG C, between the starting/ending point of A1 and the starting/ending point of A2 must be at least of m and at most of M time units. Action A, in the ontological knowledge, has type Atype (e.g., ACE inhibitor administration, Calcium channel blocker

administration, …). Action A, belonging to C, aims to achieve the intention I between the time Is and Ie . Actions of type Atype can have the variation V as effect, starting between Vis and Vds time units after the starting of the

actions and ending between Vde and Vie time units after the ending of the actions. If El is a query action, El investigates the attribute Elattr . If El is a variation, El has effect on the patient attribute Elattr . Variation (intention or effect) V1 causes variation (intention or effect) V2 . I is an interaction in the ontological knowledge. Element El participates in the interaction I. The interaction I has type Itype (e.g., concordant). The interaction I has effect on the attribute (e.g., blood _pressure ) or the variation (e.g., prevent_cardiovascular_disease) Ichanged . If El is a variation, El changes the attribute indicated by focusOn (El, _) following the modality Elmod . If El is an interaction, El changes the attribute/variation indicated by changes (El, _) following the modality Elmod .

An action of type Atype started at time T. ID is the identifier of the log entry describing the event. An action of type Atype ended at time T. ID is the identifier of the log entry describing the event.

For the action of type Atype has been administered with dosage Dos. ID is the identifier of the log entry describing the event. The attribute Attr, describing patient’s status, has value V. Such a fact has validity starting between Vis and Vds and ending between Vde and Vie .

Action A in CIG C became candidate (accordingly to Definition 1) at time S. Action A in CIG C was candidate (accordingly to Definition 1) between time S1 and time S2 . Action A at time S was removed from the control flow of the respective CIG. Action A of CIG C was relevant at time S. A non-explained discrepancy of type Type has been detected. P1, …, Pn are a variable number of parameters describing the discrepancy.

modalities. The following rule deals with interactions between two actions:

effects of actions A and B, and they may potentially interact; in possiblyInteractRelevant we check that they may actually overlap in time, considering temporal indeterminacy of the execution time of actions, which have not necessarily started, and of effects with respect to the actions. The different management modalities imply some alteration of the execution of the CIGs, except for the “no management” one: in case both interacting actions are actually executed (or the action interacting with patient state is executed), in the answer set where the “no management” option has been chosen, an instance of info is generated as a warning: there may be no deviation from the CIG, but, presumably, there should have been some, in order to deal with the potential interaction. We describe in the following the implications of the management modalities. Replanning. In this case, for one of the interacting actions A, given that in the guideline Cg it has the intention IntA, another action C is chosen as substitute for A, which is different from both interacting actions, and which achieves (possibly indirectly) IntA:

When the rule applies, it allows the ASP solver to consider a candidate answer set for each management modality: one of the facts management(..) becomes true, arguments A and B are the interacting actions, VarA and VarB are the variations involved in the interaction. The premise of the rule detects relevant interactions as from the first case in Definition 5, i.e., it applies at a reference time S if:

• the actions are relevant: the definition of relevant corresponds to • •

Definition 4 and identifies the actions that should be considered for potential interactions, including the ones that at time S are scheduled; they are not both completed; they possibly interact, given the state of the execution at S and the temporal constraints in the CIGs. This is verified with possiblyInteractRelevant, which is defined based on the knowledge about effects and actions exported by the knowledge server in Fig. 4, and temporal reasoning implemented in ASP. From the knowledge server we export the fact that VarA and VarB are

Further rules impose that A cannot have started and avoid that the effect IntA is achieved by C (given its start and end time) in an interval 11

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that does not cover the one for which A is intended to achieve IntA. Additional rules impose that in the control flow of Cg the substitute C has the same predecessor and successor as A, while A is blocked (a blocked action cannot start). Temporal avoidance. This case means that actions are executed at a time such that they do not interact; therefore we exclude as follows the case that this management is hypothesized and the actions are executed at times such that they possibly interact:

Intention alignment. This management modality actually corresponds to different submodalites, and an ASP rule is used to consider them in different scenarios. The submodalities we consider are (i) the removal of one of the interacting actions (removeduplicate), (ii) the shortening of one of the two actions (shortenduplicate) and (iii) the removal of both the interacting actions, and their replacement with an action achieving all their intentions (removeboth). The first case (i), where an action is removed, is represented by the choice of removeduplicate(Cg1,A,Cg2,B), meaning that A was removed from Cg1 because B in Cg2 suffices. The following rule:

in fact, possiblyInteract checks for a potential interaction based on the actual time of execution of the actions taken from the log. This is different from possiblyInteractRelevant which is based on the possible execution time of actions, limiting reasoning to the information that is available at the RT for which the interaction is detected; i.e., the indeterminate time provided by the temporal constraints in the CIGs. Additionally, the detection of the violation of temporal constraints for the execution of A and B is disabled, as well as for the constraints that relate subsequent actions to previous actions, to avoid cascade discrepancies that can be explained by the current management (since delaying A and/or B may imply delaying subsequent actions). Dosage adjustment. In this case, the dosage for one of the interacting actions is assumed to be changed:

excludes this hypothesis if at least an intention I of A is not achieved as an effect of action B, considering also the temporal interval [Is,Ie] of I. The second case (ii) is where one of the two actions is shortened. In such a case, we distinguish between two different sub-cases: (ii.a) actions A and B are of the same type and (ii.b) actions A and B are of different types. Basically, in sub-case (ii.a), one of the two actions has been shortened (by ending earlier or starting later) to avoid overlap. This sub-case can be recognized by the following rules:

and the following rule requires that the dosage is increased if the interaction was discordant (a similar one requires that the dosage is reduced if the interaction was concordant):

checking that A lasted less than its minimum duration, and that B started the time unit after the ending of A (shortenEnd) or B ended the time unit before the starting of A (postponedStart). The rules to recognize sub-case (ii.b) and case (iii), which are similar to (/combinations of) the previous ones, are omitted for the sake of brevity. Interaction alignment. In this management, an interaction is justified if it involves an intention of one of the interacting actions, with increase modality. Therefore, the following rule excludes the management if it is not the case that an intention I, of action A, is an element of interaction Int, that increases I.

Interaction mitigation. The interaction mitigation management justifies the presence of a “mitigating” action, which is discordant with the effect of the interaction.

Effect monitoring. In this case, the interaction has effect on a patient attribute Attr. The following rule:

5.4.2. Action-status interactions The description above deals with case 1 of Definition 5. The choice rule for the second case, i.e., an interaction of an action with the patient state is:

justifies the presence, in the execution log, of a query action Q focusing on the value of Attr and of a decision action D evaluating Attr. Other rules check that (if an instance of queryanddecide has been inferred) Q and D have been executed in a span of time in which the interaction can occur, and that D follows Q. In this case, both actions A and B are not repetitions. The rules to manage repetitions are similar and justify multiple occurrences, in time, of Q and D. In case the decision, based on the query results, states that the interaction cannot be tolerated, some other management has to be applied. A choice rule is used for this, similar to the basic one for generating alternative managements:

There are actually be two subcases for case 2 of Definition 5: (i) an action a becomes relevant at RT and it interacts with patient state at RT (detection of possible interactions considers that the state may persist in the next future, when the effects of a will hold); (ii) an action a was relevant before RT, it was not possibly interacting with the patient state, but the state changed, so that at RT there is a possible interaction.

As anticipated in Section 4.1, variants for a subset of the modalities are considered. In the rule we see the modality for “ongoing action replanning” (oa_replanning). Its implications are different from the ones of “basic” replanning: rather than cancelling action A (replaced by some C), in this case the execution of A should be interrupted and replaced by some C.

In subcase (ii), action a may be ongoing. The names of the management modalities in the choice rule above are the same names used for case 1; however, the management predicate is a different one (in ASP a different arity, 6 in this case and 7 in 12

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the previous case, suffices for predicates to be considered different) and the implications of instances of this 6-ary management are the appropriate ones for case 2. Given that action a (i.e., A in the rule) may be ongoing, this is checked, and in that case the implications of the modality are analogous to the ones for the second phase of effect monitoring, where the fact that actions are ongoing is taken into account (see, e.g., the “ongoing action replanning” modality). 5.5. Solving and optimization of the ASP problem In our experimentation, we used the Clingo10 solver. Besides grounding and solving facilities, Clingo allows the definition of a cost function to search for solutions that maximize or minimize some parameters. As anticipated before, we used this feature to minimize the number of non-justified discrepancies (i.e., instances of info) between the elements in the log and the recommendations in the CIGs and the number of unmanaged interactions11 (i.e., no_management modality). Given that different hypotheses about the management of interactions can be considered by the solver, due to the choice rules described in Section 5.4, the result is to minimize the discrepancies that cannot be justified by the management of any interaction. 6. Clinical case study In order to demonstrate our approach, we apply it on a case study taken from the literature [35]: a 50 years old comorbid patient suffering from chronic kidney disease (CKD), hypertension (HTN) and atrial fibrillation (AFib). While the CIG for CKD has already been described in SubSection 3.1, Figs. 5 and 6 show the GLARE representation of the HTN and AFib CIGs, respectively. Such a case study describes a realistic scenario, since patients suffering from CKD (i.e., “an abnormality of kidney structure or function that is present for longer than 3 months” ([14])) frequently suffer also from HTN and from some form of cardiovascular disease, such as AFib. Moreover, the case has been built considering a realistic patient and actual CIGs, and the execution log has been defined taking into account the recommendations of an expert physician. The case study concerns a patient initially suffering only from HTN. Fifteen weeks after the beginning of the treatment for HTN, the patient was diagnosed also for AFib and CKD, and consequently she started the respective treatments. Thus, for the sake of simplicity, we set as the starting point of our description the starting day of the HTN CIG. All the other times are relative to such a starting point. We set, as ending point of our analysis, the day 360. Since some actions in the three CIGs must continue for the entire patient’s life (consider, for instance, ls_htn in the HTN CIG), we limited the examination of their duration to the day 360. In the lower part of Fig. 7, we provide a graphical representation of the execution log for the actions in the three CIGs, as it was actually performed in the case study. Durative actions are shown as horizontal lines, while punctual ones (e.g., decisions) are represented as vertical segments. For decisions, we shown their outcomes (e.g., AGE = LT55 means that the outcome of decision AGE? was LT55). Moreover, we also show the patient status attributes and their values, if relevant to the analysis, in the span of time when they are known (e.g., the fact that the

Fig. 5. META-GLARE representation of the HTN CIG. AGE = age of the patient, LT55 = <55 years, GE55 = 55 years, BP1_CTRL, BP2_CTRL, BP3_CTRL = controlled blood pressure, acei_htn1, acei_htn2, acei_htn3 = ACE inhibitor, ccb_htn1, ccb_htn2, ccb_htn3 = calcium channel blocker, diur_htn3 = diuretics, htn_consult = specialist consult for HTN, ls_htn_mgmnt = lifestyle management for HTN.

renal function of the patient is low is true along all the treatment for CKD). Finally, in the upper part of the figure, we show the original actions recommended by the three CIGs and their recommended times, concerning the patient at hand. A textual description of the case study can be found in Appendix A. Comparing the recommendations in the CIGs with the execution log, one can identify a set of discrepancies. In order to facilitate the comprehension of the case study, in the following we list them. Notice that such discrepancies are automatically detected by our approach, so they do not have to be provided as input12.

10

12

https://potassco.org/ A brief comment is needed. Such an optimization, favoring solutions in which interactions have been managed with respect to solutions in which they have not, may “optimistically” interpret the physicians’ decisions. Indeed, in some cases, given an interaction, an execution log can be interpreted both as (i) the result of the application of a temporal avoidance or an interaction alignment, and as (ii) an execution of the CIGs in which the interaction has not been managed. In such cases, even though both interpretations are possible, the solution that is returned is the one hypothesizing that the management has been applied.

It is worth observing that in a normal use of our approach, the tasks of explanation and of detection of discrepancies are executed together. As a consequence, only those discrepancies that cannot be explained are actually “detected” and reported in the output (predicate info). For discrepancies that can be explained, the output contains their explanations. This is also the reason because Fig. 8 in the following does not contain info predicates. However, in our implementation, disabling the explanation part is also possible. In such a case, all the discrepancies between the log and the CIGs are detected and their descriptions are reported in the output. The listing D1-D5 can be obtained in such a way.

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•

•

Fig. 6. META-GLARE representation of the AFib CIG. AFIB DUR = duration of atrial fibrillation, LT48H = < 48 h, GE48H = 48 h, CHA2DS2_VASC = CHA2DS2-VASc score, LT1 = <1, GE1 = 1, nsbb_afib = non-selective beta blocker, flec_afib = flecainide, ccb_afib = calcium channel blocker, acei_afib = ACE inhibitor, asp_afib = aspirin, warf_afib = warfarin).

D1 CKD recommends aspirin (action asp_ckd) starting at time 105. However, the treatment is not present in the execution log. D2 AFib recommends non-selective beta blockers (action nsbb_afib) starting at time 105. However, the treatment is not present in the execution log. D3 The execution log contains a treatment with selective beta blockers (action sbb), starting at time 105. However, no CIG recommends it. D4 AFib prescribes a treatment with ACE inhibitors (acei_afib), starting four weeks after the AFIB_DUR? decision (approximately, after day 132) with infinite duration. CKD prescribes a treatment with the same drug (acei_ckd), starting at day 105 and with infinite duration. Finally, also HTN prescribes ACE inhibitors (acei_htn2, starting at time 84, lasting 12 weeks). However, the execution log contains an ACE inhibitors treatment starting at time 84 and lasting 12 weeks, and an ACE inhibitors treatment starting at time 168 with an infinite duration. D5 AFib prescribes calcium channel blockers (ccb_afib), starting approximately at time 132. However, in the execution log such a treatment starts at time 168.

•

•

In the right part of Fig. 7 we have marked the related elements with the discrepancy number. To evaluate the conformance of the actual execution log to the CIGs, we apply our approach. First, we generate the ASP representation of the elements above, as described in Section 5. Then, we look for a possible solution for it. In Fig. 8, we show part of the optimal solution found by the solver for our case study. We only show the instances of predicates identifying potential discrepancies that cannot been explained (predicate info) and of predicates that justify discrepancies through the application of some management options, besides the cost of the solution itself. As it can be noticed from line 20, the given solution has cost 0 (and, in fact, no instance of info). Therefore, in such a solution, all the discrepancies have been explained as the result of the application of some managements. In particular, the solution hypothesizes that the following managements have been applied to the original CIGs:

that the interaction was managed by applying a “duplicate removal” management (line 2). Since all the intentions of asp_ckd can be reached by warf_afib, also considering their temporal extension, it is possible to justify the absence, in the execution log, of asp_ckd (second literal of the predicate removeduplicate of line 3). Consequently, D1 can be justified. a status-action interaction between the action nsbb_afib, prescribed by AFib (with the intention of control the heart rate) and the low renal function of the patient has been detected (line 4). Indeed, non-selective beta blockers can cause, as effect, the decreasing of the glomerular filtration rate (GFR; an indicator for the renal function, which is already low). Such an interaction can be managed (line 5) by a “replanning” management. Indeed, nsbb_afib can be omitted (D2) and replaced in the execution by another action, contained in the execution log but not recommended by any CIG, with effects that are concordant with the intentions of nsbb_afib. The solver identifies sbb (third literal of the substitute predicate of line 6) as such an action (D3). an interaction (line 7) has been detected between acei_afib and acei_ckd, prescribed by CKD. Indeed, both CIGs prescribe the same treatment with ACE inhibitors. Since the recommendation of acei_ckd temporally includes the recommendation of acei_afib, the interaction can be managed through a “duplicate removal” management (line 8), justifying the removal of the acei_afib action (line 9). Moreover, another similar interaction is detected between acei_ckd and acei_htn2, prescribed by HTN (line 10). The interaction can be managed through a “duplicate removal” management (line 11), justifying the shortening of acei_ckd (line 12) by postponing its starting point to time 168 (line 13). The application of both managements above justifies D4. an interaction is detected between ccb_htn2 and ccb_afib (line 14). Indeed, both CIGs recommend the same treatment with calcium channel blockers, and such treatments have a temporal overlap between the starting point of ccb_afib and the ending point of ccb_htn2. To avoid such an interaction, the solver hypothesizes that a “duplicate removal” management has been applied (line 15) to the two CIGs, shortening one of the two actions to avoid the overlap (line 16). In particular, the starting point of ccb_afib has been postponed (line 17), to start the treatment the day after the ending of ccb_htn2. Such a management explains D5. an interaction is detected between ccb_afib and acei_ckd (line 18). Indeed, both the actions have the effect of decreasing the heart rate. Such an interaction can be considered as desired and it can be justified by the application of an “interaction alignment” management (line 19). This management does not explain any deviation. However, it justifies the presence of the interaction.

7. Limitations and future work The work in this paper addresses a new and complex challenge, namely a posteriori conformance analysis and explanation, concerning the treatment of comorbid patients. Given the complexity of the problem, some phenomena have to be faced yet, and this is the purpose of our future work. In the current approach, we only consider binary interactions, i.e., interactions between two actions, or interactions between an action and a state. Of course, such an approach is trivially scalable to n-ary interaction that can be decomposed into (subsets of) binary ones. However, the medical literature also presents cases of n-ary non-decomposable interactions. For such cases, an extension of our current approach is needed. Indeed, as regards the knowledge representation formalism, we already support the modeling of n-ary (non-decomposable) interactions [19]. Based on such a representation, our detection algorithm can easily retrieve n-ary interactions [19]. On the other hand, the definition of management modalities, as described in this paper, only operates on binary cases. In some cases, the extension to nary cases is quite easy. For example, n-ary replanning management

• an interaction between asp_ckd and warf_afib has been detected

(line 1). Indeed, both drugs have an anticoagulant effect. In CKD, aspirin is recommended with the intention of preventing cardiovascular diseases. However, also warfarin (recommended for AFib) reaches such an intention. Therefore, our approach hypothesizes 14

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Fig. 7. Comparison between the recommendations provided by the three CIGs (upper part of the figure) and the actual execution log for the case study (lower part of the figure). The middle part of the figure shows the patient status (limited to the useful attributes), the outcome of the decisions and their times of execution.

Fig. 8. Optimal solution for the case study. Only the instances of predicates useful for conformance analysis and explanation are shown.

modality operates like the binary one, since the substitution of one on the n interacting actions can be achieved as in the binary case. However, a systematic analysis of all the possible managements is needed. In our current approach, we aim at recognizing and explaining the CIG paths corresponding to the log. However, in the case of comorbid patients, explanations could be even richer. In principle, it could be

hypothesized that, at the time of some decision, some potentially applicable CIG paths have been disregarded to avoid possible interactions. Indeed, the choice of paths avoiding interactions is a quite common medical practice, and in our previous work we have modeled it through the safe alternative management modality (see also [20] and Section 4.1). Notably, in the work in this paper, we do not even try to detect 15

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whether some interaction (which has motivated some deviation from the CIGs) could have been avoided through the application of the safe alternative option (i.e., by selecting, a priori, different paths from the CIGs). Such an analysis would be quite complex, and, in the clinical practice, it is not realistic to expect that physicians consider all the possible future consequences of their therapeutic choices, exploring in the CIGs all the paths stemming from each decision, and analyzing all possible interactions between them. On the other hand, the analysis would have the advantage of highlighting the ability of physicians to foresee and avoid “a priori” possible dangerous situations for their patients. Therefore, such an analysis could be important in cases the explanatory capabilities of our approach are used in medical training. Our approach is flexible, in the sense that we take into account a large space of hypotheses, but it is “crisp”, in the sense that conditions and constraints are either verified or not. For instance, in our current approach, only exact match is considered, so that either a modality is consistent with the log or not. Additionally we do not consider the probabilities of effects, and of interactions. Moving towards a “non-crisp” approach is a major challenge, that we will take into account in our future work. Finally, we plan to experiment the approach also considering realistic logs containing also imprecise (and possibly missing) data, through a mixed-initiative approach.

a context in which interactions are possible). Additionally, a central point of the current approach is the analysis of interactions between CIGs, while interactions (not even between the CIG and the actions suggested by the basic medical knowledge) are not taken into account in [30]. As a consequence, the overall process of detecting and analysing non-conformances, as outlined in Fig. 4, is completely different from the conformance analysis carried on in [30]. A more complete approach can however be obtained also considering general medical knowledge for dealing with relatively minor health problems whose treatment does not deserve developing a proper CIG, but can nevertheless be modeled in the same formal language as CIGs and possibly executed concurrently with the CIG actions. For this reason we plan, as a future work, to integrate the approach of this paper with the one in [30] to provide a more comprehensive framework. A preliminary version of this work has been presented in [23]. This paper extends it in several ways. While in [23] only the basic ideas have been introduced, in this paper we provide a comprehensive and more complete technical description of our work. In particular, Section 4 provides a detailed description of the approach, including formal definitions. Moreover, we introduced, as possible explanations for deviations, the “interaction alignment” and the management of interactions between the status of the patient and the effects of prescribed actions. We also describe in more detail how the approach is realized in ASP, dealing with all management modalities that we considered. Finally, we provide an evaluation of our framework with the detailed description of a case study from the literature, with the CIG models that have been used, and the description of the results that are obtained by the ASP solver.

8. Conclusions The treatment of comorbid patients is one of the main challenges of modern health care, and many CIG appproaches to manage them have been proposed in the last years. However, while such approaches propose a wide range of solutions to the “a priori” and/or “execution time” detection and/or management of CIG interactions, and to CIG “merge”, no approach in the literature (to the best of our knowledge) has focused on the a posteriori analysis of the treatment of comorbid patients. Such a conformance analysis of processes can be quite important not just in a medical context but also, e.g., in business contexts (see [34], Chapter 7: e.g. the software supporting business activities may encode general “best practices” that are not specific enough for the company). However, in the case of comorbidities, a “standard” conformance analysis, simply pointing out the discrepancies between the process predicted by the CIGs and the “’real” process in the log, would not suffice. Indeed, deviations from the CIGs may be motivated by the need to avoid dangerous interactions. Therefore, we provide an homogeneous and innovative approach, in which conformance analysis and explanation are intrinsically related. We try to explain non-conformances (discrepancies) in terms of ways to avoid interactions (alternative explanations are therefore supported), and, even in case of conformance, we check whether interactions have (or could have) occurred. Notably, the goal of our “conformance analysis and explanation” approach is not to provide an evaluation of whether the treatment of a patient was appropriate or not; rather, our explanations provide expert physicians with a starting point to interpret the treatments described by the logs. As discussed in Section 1, our analysis provides insights into the processes actually executed on the patients, which can be exploited, e.g., for explaining treatments in patients’ discharge documentation, for education, or to provide domain experts with a valuable starting point for a combined evaluation of the quality of the treatments, and the completeness of knowledge (the guidelines themselves and knowledge about interactions) [8]. Our approach is based on Answer Set Programming, and, to face realistic problems, devotes specific attention to the temporal dimension. While in this paper we exploit the model of CIG action execution developed in [30], the rest of the approach is different. First of all, in [30] only one CIG is considered, and non-conformance can be explained on the basis of a “general” basic medical knowledge, which may trigger new actions in case problems not considered in the original CIG arise in the patient. In this paper two or more CIGs are considered, and more specific rules (the modalities) are used to explain non-conformances (in

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This research was partially supported by the Università del Piemonte Orientale. We thank the anonymous reviewers for their insightful and constructive comments, which have greatly helped us to improve the quality of the paper. Appendix A. Description of the case study In this appendix, we provide a textual description of the case study. To improve the readability of the description, we divide it following time points and we group the actions related to specific CIGs. In case actions in the log cannot be associated to recommendations in any CIG, we indicate them with “(NO-CIG)”. Time 0: HTN. As shown by the execution log in Fig. 7, the treatment for HTN started at time 0 with the decision AGE?, which is the first action of the HTN CIG (shown in Fig. 5). The outcome of AGE? was LT55 (lower than 55 years old), therefore ACE inhibitors (action acei_htn1) was prescribed, for a duration of 12 weeks (84 days), starting at day 0. Time 84: HTN. After the end of acei_htn1, the blood pressure was evaluated at day 84 (action BP1_CTRL). The result of such an evaluation was NO (i.e., blood pressure was not controlled by the treatment), therefore the treatments with ACE inhibitors (acei_htn2) and calcium channel blockers (ccb_htn2) were started, with an expected duration of 12 weeks. Time 105: CKD. At day 105, the patient was diagnosed for CKD and AFib. CKD implies a (chronic) decreased renal function of the patient, therefore the patient status was updated with this new entry. As regards the CKD CIG, eGFR level was evaluated (decision EGFR?), with result GE60 (greater or equal to 60). As a consequence (see Fig. 1), treatments with aspirin (asp_ckd) and ACE inhibitors (acei_ckd) should have started at time 105. However, considering the log, none of them started 16

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at that time. Cardiovascular risk management (cv_risk_ckd) and lifestyle management (ls_ckd_mgmnt) were planned to start after 8 weeks, at time 160. AFib. Also the AFib CIG (Fig. 6) started at time 105. However, the treatment with non-selective beta blockers (nsbb_afib), recommended by the CIG, did not start. On the other hand, the duration of the AFib episode (decision AFIB_DUR?) was evaluated with result GE48H (longer or equal to 48 h). Therefore, treatments with ACE inhibitors (acei_afib) and calcium channel blockers (ccb_afib) were planned to start after four weeks (at day 132). Also the CHA2DS2-VASc score was calculated at time 105, with result GE1 (greater or equal to 1). As recommended by the CIG, warfarin treatment (warf_afib) was started. (NO-CIG). Not prescribed by any CIG, at time 105 a treatment with selective beta blockers (sbb) started, as reported in the log. Time 132: AFib. At time 132, actions acei_afib and ccb_afib were planned to start. However, they did not started, considering the log. Time 160: CKD. At time 160, as prescribed by CKD, cv_risk_ckd and ls_ckd_mgmnt started. Time 168: HTN. At day 168, after the end of acei_htn2 and ccb_htn2, blood pressure was evaluated again (action BP2_CTRL). This time, the result of such an evaluation was YES (i.e., blood pressure was controlled by the treatment). As a consequence, the lifestyle management for HTN (ls_htn_mgmnt) was started, with an expected infinite duration. (NO-CIG). At day 168, not explicitly recommended by any CIG, a treatment with ACE inhibitors an a treatment with calcium channel blockers started.

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