Anne Bonfante
email: anne.bonfante@libertysurf.fr

Jean-Yves Marion
email: jean-yves.marion@loria.fr

On the defence notion ⋆

virology and art of war "Trojan horses", "logic bombs", "armoured viruses" and "cryptovirology" are terms recalling war gears. In fact, concepts of attack and defence drive the world of computer virology, which looks like a war universe in an information society. This war has several shapes, from invasions of a network by worms, to military and industrial espionage. . .

 for further information about the definitions and classifications of malware.

We could think at first sight that questions about computer security, and particularly about fights against computer viruses, are just a matter of highly trained security computer officers, and that a victory just depends on scientific and technical knowledge. But sometimes algorithmic and programming are not enough to catch the whole picture. Indeed, the study of malware strategies shows that they are close to the battle of the Horacii against the Curiacii. . .

A different point of view could then bring to computer virology a new prospect. This study is a part of a general investigation, which tries to understand viral strategies in order to anticipate attacks and improve defences, and to define the philosophical and political issues. Reading famous strategists and philosophers could give precious information about conscious-or unconscious viral practices, explicit-and implicit behaviour of the malware's writers, whatever kind of attacks they launch. For this, a case study is a good way to make the connection between the technical or scientific profiles of a virus and the kind of strategy used (the meaning of the word "strategy" is here conveyed by political and war philosophies). The case of the Whale virus can be extended to the Bradley concept, its epistemological model, which is meaningful.

The question of War, as well as the best way to do it and the politicaland human issues related to it, is very old in the history of philosophy, as we

can already find it in the Peloponnesian war [START_REF] Thucydide | The Peloponnesian war[END_REF], written by Thucydide, a Greek general and historian in 430 BC, or Plato's Republic [START_REF] Platon | The Republic[END_REF] (420-340 BC). Philosophy of war has always been an active theme of philosophy and was the main issue for some authors like Machiavelli (1469-1527), who wrote the Art of war [START_REF] Machiavel | The art of war[END_REF] in 1519.

Are the writers of malware Machiavelli's readers? This question sounds like a joke, but is legitimate, as we shall see. Indeed, the more dangerous viruses are the ones which seem to apply principles and to use strategies of the art of war, like Machiavelli's, or from other war theorists like Clausewitz [START_REF] Clausewitz | On war[END_REF].

Bradley defences

The Whale virus challenged Scotland Yard for about two weeks during the 1990's [START_REF] Filiol | Whale : le virus se rebiffe[END_REF]. This virus is a typical case study, because it has its own defensive weapons. From the Whale virus, a virus shape named Bradley was proposed by Filiol [START_REF] Filiol | Strong Cryptography Armoured Computer Viruses Forbidding Code Analysis: the Bradley Virus[END_REF]. This shape, which could also be considered as an epistemological model, will guide us in our study on virus defences. Indeed, it uses very complex notions coming from mathematics and computer science in order to defend and attack.

Bradley protection systems are first used to prevent the detection of the viruses by an antivirus software, and then to bypass the defences of the host system, which is under attack. We will study the two most interesting types of defence: the armoured code aspect and the virus's one because they are typical and relevant. It is worth to notice that the furtive aspect was a Whale feature.

An armoured code consists in protecting a code from an analysis, which can be static by disassembling, or dynamic, by monitoring executions.

Protecting a code against static analysis is a scientific challenge. The paper of Barak & al [START_REF] Barak | On the (Im)possibility of Obfuscating Programs[END_REF] on obfuscation is a good illustration of these difficulties. With the benefit of hindsight, all the protection methods used lean on the same approach. The code protection is performed by an obfuscator. In fact, the latter is a kind of compiler, which transforms a source programme s into a scrambled programme s ′ in such a way that:

1. The scrambled programme s ′ computes the same thing as the source programme s. (in other words, there are semantically equivalent). 2. The runtime of the scrambled programme s ′ is close to the one of s. (that is up to a polynomial). 3. The programme s ′ is unreadable as well for a human analyst as for a deobfuscation programme.

The third point corresponds to the obfuscation clause, which turns out to be difficult to formalize. Obfuscation consists in rewriting the code in order to make it less understandable. Cryptography plays a crucial role in this task. The interested reader may consult the recent paper of Beaucamps and Filiol [START_REF] Beaucamps | On the possibility of practically obfuscating programs: towards a unified perspective of code protection. TCV 2006 Special Issue[END_REF] about the practical obfuscation methods. Moreover, a virus may mutate when it duplicates with polymorphism or metamorphism techniques.

An obfuscator protects a programme in a way that we could call passive, unlike furtivity techniques. It aims to camouflage a code in order to slow the analysis of its adversaries down. Advantage for the attacker with this method: the guarantee of immunity for a while, because the time spent to camouflage is ever shorter than the one spent by the adversary to detect it. Thus, the attacker protects itself against antivirus software, which, on the one hand search for a signature of a known malware. On the other hand, it protects itself against the work of analysts, which are trying to understand the meaning of its code. This method used by virus looks like both a camouflage and a shield, which are designed to resist an attack as long as possible. It appears then to be a method of passive defence.

A Bradley virus also combines an active defence method: "furtivity". It consists in deceiving a host system, by modifying, for example, system interruptions. In the case of Whale, techniques of furtivity allow to detect a debugger. The defence becomes active, because a virus can trigger an action off, if it is aware that some agent is trying to analyse it. Furtivity then allows the prevention of behavioural analysis techniques used by antivirus. Moreover, the resistance of a virus to such an analysis allows the collection of information about the defence methods of the host system. Consequently, we may suppose that this fact is a piece of its attack plan and the reasons why the virus was launched. . . We must then look at the reasons for which a virus like Bradley integrates so many defence techniques.

Why does a virus defend itself?

The part of the virus code which purpose is to infiltrate a system and to deceive the antivirus can be considered as both an offensive weapon (it enters a fortress) and a defensive weapon (camouflage). A particularity of Whale, as well as the Bradley concept, is that its code contains advanced defensive functionalities, which go beyond the traditional ones used to enter a system. If a virus was a mere offensive weapon, why allowing such defence mechanisms then?

If we send troops to attack a place, and whatever the issues are, it seems normal to arm them and to give them some means to protect themselves. Such defensive means are necessary in order to protect troops and avoid casualties. However, in the context of a conflict in the information society, what does the attacker try to protect?

If the only goal is to get some information back, the loss of a virus is a part of the operation. Why are viruses protected then? We think that the host systems should address those questions in order to prepare its defence.

This brings us to a first hypothesis. The attacker is a Machiavelli's reader without knowing it. Indeed, one of the fundamental principles of the art of war is that we must have both offensive and defensive weaponries. A good defence is meaningless if it is not armed: the only guarantee of autonomy and independence is the ability to be in a defensive position as well as in an offensive one if necessary. Computer security questions should then necessarily consider the possibility to prepare and use offensive methods. However, state legislations, like the French one, do not allow attacks and force security officers to set only defensive methods with no possibility of counter-attack. The efficiency of the defence is also related to the questioning about this ban on possessing and training with its own (offensive) weapons. Machiavelli's readers know how important it is to keep control over one's own weapons because it is a sine qua non condition for security and independence.

The second hypothesis is that a virus provides a defence because it has some hostile intentions. If there are as sophisticated high-level defence mechanisms as the ones mentioned above, it means that the virus was made for a very important purpose. We could use this criterion in order to set a typology of viral attacks: the more elaborated the defence is, the more important the objective is.

Lastly, the third hypothesis is that we should call security policy views into question. If a virus based on the Bradley concept integrates such elaborated sequences of defence, it is because it probably expects a serious counter-attack. The defences are thus stronger than what they claim or than they are known to be (but it is maybe a trick: fooling the adversary while looking more vulnerable than you are in reality.)

Other hypotheses are conceivable, and some show that 'viral war' takes sometimes paradoxical or new shapes we should study in order to anticipate the future.

New time scales?

Information technology war implies to have to reconsider the scales of the conflicts, particularly the time scale, but also the one of the space. The time necessary to decipher and analyse a virus (remember the two weeks which were necessary to analyse Whale!) is a "long" time. It means that it corresponds to a human time-scale. On the other hand, if we consider that a viral attack symbolically represents a hostile operation, the length of the attack is very short (between a second and a minute). There are at least two levels of analysis to bring out in order to understand the defence question:

-The human scale. The conception of dangerous viruses is a long process because they integrate a lot of mathematics and a big knowledge in computer science. It is hard to capture a virus and difficult to analyse it. This is the case of Whale.

-The computer scale. A virus is inside a system, and must fight against an anti-virus. The fight lasts a few seconds, or minutes, programme versus programme.

We could think at first sight that a viral attack is a completely new kind of war, since it takes place in an entirely different way compared to traditional war. Can we use the term of war again, since there is nothing in common between a few-second strike and a real battle in the field?

A virus writer finds time to design a virus efficiently and cannot ignore that it will require a lot of time to decipher and analyse the virus, if it is captured. Therefore, this time was anticipated and should be considered as a genuine part of the attack. It can be used to create a diversion or to have more time (indeed, during the phase of analysis, the attacker can do something else). Then this type of virus corresponds more to a traditional war, and consequently sets conflicts back in a long time-scale and not in an instantaneous one. Isn't it the aim of the attacker? So don't we have to consider that a viral attack is just a weapon as another one, or just a part, of a global conflict? Such a viral attack is a way to set things back in a better-known field, which is more traditional, in a way more human: the field of men, logistics and "normal" time.

This shift of scale between viral attacks and traditional fights allows us to ask further questions. For example, look at the ratio between the 14 days of analysis, which is the time necessary to understand Whale, and 1 minute, which will be considered like a time-reference at the computer level. The ratio between these scales is around a million. The change of scale directly implies that when a viral attack is launched, it cannot be controlled at the human level anymore, because it is too fast. Admittedly, the use of a gun implies that its process is autonomous and does not depend on a human (when a gun is fired, the bullet is unavoidable. . . except in "Matrix"!). But in the case of a computer war, we should not consider a single virus, but a set of viruses against defences. Each of these agents communicates with the others, reacts to its environment and takes decisions, independently from any human interventions. Moreover, if the computer scale is very short, the conflict area could be the whole net [START_REF] Balepin | Superworms and Cryptovirology: a Deadly Combination[END_REF]! This change of the scales maybe implies that we should change our classical concepts of war analysis, as we traditionally find them in books of great authors like Clausewitz [START_REF] Clausewitz | On war[END_REF].

A central question: the losses

Cyberwar implies to reconsider a crucial notion of every armed conflict: the one of the casualties. Indeed, why does someone program an armoured virus? What is the attacker's objective? What may he lose, and which losses does he want to avoid?

In the setting of traditional war with different armed forces, the question of the casualties is one of the most important to make strategic and tactical choices. This question is coupled with an obvious moral issue. This issue is represented by the assessment of the inherent ratio in any operation: the (human-, technicalor practical) cost of an action must be related to the interest or to the benefit of this action. So, this assumes the responsibility of the military leaders and of the governments, particularly a moral responsibility, since casualties should be avoided. Taking a risk should then be justified with respect to the current issue, especially when human lives are concerned. The moral responsibility is more difficult to take, but it just exists in the case of real wars, because we can always know the number of deaths, without always really understanding the benefit of an operation. Cyberwar changes traditional war categories, since the moral and the casualty question as well as the question of the just cause, do not come up anymore.

Inversely, the heroic figure or the heroic action supposes that the loss of a life is there for a great collective benefit. The greater the sacrifice of the hero is, the more he takes risks; the more conscious he is that he will not survive to his action, the more heroic he is. We can ask if hackers identify to the issues of the hero, as we already mentioned, by overcoming all difficulties and responding to all challenges. Indeed, the point for a hacker is here to accomplish a technical exploit giving him the feeling of being a hero, even if his actions are reprehensible. Recent movies show that clearly: it is the heroic figure of Neo in Matrix.

It seems to us that we should understand the specificity of modern wars with respect to how they consider casualties. In the case of a virus, the loss of the latter is somehow immaterial, maybe anticipated, or even programmed by its designer. It means, first, that we do not consider losses as real ones (like events to avoid), or at least that it is a part of the strategy, especially as we can always replace a virus: losses are duplicable because a virus can be duplicated.

Another characteristic of computer-war is that it does not lean on economical and industrial resources, which are decisive factors in the case of a "real" war, even if they are not the only ones. In the case of a viral war, the attacker's strength is not directly related to economical-or industrial resources, but to a scientific and technical knowledge, which then becomes a possible cause of war, or at least reasons for a competition.

When an attacker "loses" a virus, the latter can be analysed. From then on, we may reproduce quite easily its design. However, there are some interests in avoiding the loss of a viral weapon in order to protect knowledge, in terms of cryptography for example. The attacker, as a war leader or a strategist, measures the interest of an action and determines the risk he runs. One of the clearest specificities of a modern or post-modern conflict is that the technical questions aim more and more at replacing the question of force. Violent confrontation is shifted to technical considerations.

Counter-attack and issues

The viral defence system often allows the attacker to stay anonymous, which prevents possible counter-attacks. But this fact changes the concept of war because the enemy is not identified. What is peculiar to war is to have an enemy, a known opponent. Once the enemy remains anonymous, confrontation does not correspond to the representation of war, but more to guerrilla warfare: the enemy is not conventional and cannot be spotted.

Furthermore, if the attacker tries to hide his strategy as long as possible, it means that the host system itself can be protected. Indeed, a virus is able to delude a defence in such a way that it can be in position to observe tools used for defence: a virus is able to be behind the line, and so is able to list all defensive tools. Therefore, this means that the virus code has a mechanism the function of which is to detect the tools used by the defence in order to analyse intruders, viruses and so on.

We could conclude for the time being that the strategy used by the virus in this case is a prospective one. Detecting the defence tools has a meaning only if another attack is planned in the near future. Consequently, we should analyse the aims of the virus from a temporal point of view. A viral attack can be an initial assault before another one, so we should not simply consider what represents a given attack at a given time.

Lastly, the issues of computer virology are directly related to other domains where computer networks are used as tools to exchange information. It is a way to say that the field of viral war is also economic and financial, and that it implies political positions, in particular questions about individual rights. Economic issues are not always perceptible behind some behaviour, which may have some moral justifications: for example, it is the case of Sony rootkit [START_REF]Sony Rootkit Case[END_REF]. The reason of the integration of computer virology was to protect author rights, and to protect the data contained in the disk. The reality was that this technology allowed to spy the user's data (it is of great interest from a commercial point of view. . . ). The ambiguity is in the fact that Sony was perfectly able to justify this functionality, which is usually used by malware, in order to protect author rights. This worry is legitimate, but nothing proves that the real purpose was this one. . . So, computer virology is the place of different kinds of wars, but the hostility logic often remains the same.

Evolutions and perspectives

Viral defence, as a large part of computer security, depends on the results of theoretical computer science. For the record, there are Cohen's results on viral detection undecidability: it is not possible to construct perfect anti-virus software. Other results depend on conjectures of the algorithmic complexity theory (like if P=PSPACE, then practically all cryptographic codes will be broken). It is interesting to see once more that we face a scale problem. Indeed, conjectures related to the algorithmic complexity theory imply that a given problem is computable but the runtime is beyond belief and is greater than the age of the universe! Science acts as a guarantor for defence soundness. If a defence depends on the algorithmic complexity theory, so it must take into account the time scales that we have mentioned previously. A viral defence may be conceived to resist an analysis at a human scale, and from then on can be considered as immune with respect to the computer time scale (where the time scale is about a minute). On the other hand, during a computer attack, and at a computer time scale, this heavy defence slows the virus execution down. So, the issue is to choose the right weaponry according to the targets that are aimed. This subject was widely discussed in many strategy books, as Machiavelli did in his Art of war.

As we saw it above, viral war integrates the necessity of a prospective strategy: on the one hand, because it could use the information the virus found, pursuing the elaboration of its attack's tactics according to the environment it is located in. In this sense, a virus is a modern weapon since it is adaptable: there are interactions between a virus and its environment. There is an epistemological and scientific dimension as soon as we think about a viral attack as a deployment of a large number of autonomous and cooperative agents. This direction recalls analogies with biological immune systems [START_REF] Editorial | Making connections[END_REF]. Another possibility is to consider the agents of a network with divergent interests like in the algorithmic game theory. The game theory, which tries to predict behaviours of a population in a given environment, could then be used to analyse political and sociological behaviours of agents running viral attacks, and also of the users who are concerned by those attacks.

To come back to the question of the interaction of a virus in its environment, we can say it is inseparable from a forecast. That is that a virus adapts to its environment in order to pursue an attack, or to send information back with the view to make another attack. This temporal forecast, even if it is implicit, is the sign that a viral arm cannot be understood, or analysed, without thinking of the one who possesses it. The attacker's intention (or the intention of the ones who order this action) is revealed by the question, which seems harmless at first glance: what is the purpose of a weapon? If, to be specific, it can be used to make another attack, or just to pursue the current one: this attack is a step. It also means that it is necessary for the ones who are fighting against viral attacks, not only to view an attack here and now, but always to think about the intentions that could be implied. To give another conclusion to this discussion, we should analyse a viral attack by what it implicitly discloses: the virus's method for the attack indicates what its writer knows, or what he thinks he knows about the target he aims. Anybody thinking he is a potential target should integrate into its security policy what he wants to show to the others, in such a way that he directs the kind of attack he can be the target of. The issue at stake here is to apply the good old strategy: a false lure, a false target, or a noticeable weakness, which transforms stratagems into an art of playing with representations and to trick enemies. We must always come back to this Machiavelli's principle: "Never believe that the enemy doesn't know what he does", always assume that you have to deal with a smart-, surely crafty enemy, whose intentions are not always visible. So, the security of a target should not only stem from the strength of a defence: the attackers will always succeed to penetrate by a way or another. We should also know how to use trickery, how to play with psychological effects and make our opponent believe that defences are different from what they really are. . .

Acknowledgement

We would like to thank first lieutenant de Marqueissac for her valuable help in improving the correctness of our English.

⋆ This work has been supported by project ARA Virus.


Rosy Tsopra
email: rosytsopra@gmail.com

Jean-Baptiste Lamy
email: jibalamy@free.fr

Karima Sedki
email: sedkikarima@yahoo.fr

Using preference learning for detecting inconsistencies in clinical practice guidelines: methods and application to antibiotherapy

Keywords: Preference learning, Antibiotherapy, Clinical practice guidelines, Inconsistencies in guidelines

Using preference learning for detecting inconsistencies in clinical practice guidelines: Methods and application to antibiotherapy

Rosy Tsopra, Jean-Baptiste Lamy, Karima Sedki

Introduction

In the 1990s, the concept of Evidence-Based Medicine was introduced and defined as "the integration of best research evidence with clinical expertise and patient values" [START_REF] Sackett | Evidencebased medicine: How to practice and teach EBM[END_REF]. This new paradigm led to the redaction and diffusion of Clinical Practice Guidelines (CPGs) by national health authorities [START_REF] Woolf | Clinical guidelines: potential benefits, limitations, and harms of clinical guidelines[END_REF]. CPGs are narrative documents providing recommendations stated by a group of experts according to a systematic review of the available clinical evidence. They aim at improving the quality of health care by providing standardized best practices for diagnosis and treatment. Their development is complex and requires time, rigor and multiple verification and validation steps to guarantee their quality [START_REF] Goud | A parallel guideline development and formalization strategy to improve the quality of clinical practice guidelines[END_REF][START_REF] Tierney | Computerizing guidelines to improve care and patient outcomes: the example of heart failure[END_REF][START_REF] Woolf | Developing evidence-based clinical practice guidelines: lessons learned by the US Preventive Services Task Force[END_REF][START_REF] Peleg | Support for guideline development through error classification and constraint checking[END_REF]. However, many problems are reported like incompleteness, contradiction, inconsistency, redundancy or ambiguity within CPGs [START_REF] Tierney | Computerizing guidelines to improve care and patient outcomes: the example of heart failure[END_REF]. This leads to a lack of confidence of physicians in CPGs [START_REF] Cabana | Why don't physicians clinical practice guidelines? A framework for improvement[END_REF], and thus a poor consideration of CPG recommendations in their daily routine clinical practice [START_REF] Mcglynn | The quality of health care delivered to adults in the United States[END_REF].

For verifying the quality of recommendations within CPGs, various methods were developed. The structure of CPGs can be verified by tools [START_REF] Shaneyfelt | Are guidelines following guidelines? The methodological quality of clinical practice guidelines in the peer-reviewed medical literature[END_REF][START_REF] Cluzeau | Development and application of a generic methodology to assess the quality of clinical guidelines, International journal for quality in health care[END_REF] such as AGREE instrument [START_REF]Development and validation of an international appraisal instrument for assessing the quality of clinical practice guidelines: the AGREE project[END_REF]. These tools focus on quality criteria, e.g. presentation of guidelines, or independence of experts [START_REF] Siering | Appraisal tools for clinical practice guidelines: a systematic review[END_REF]. However, these methods are limited to the verification of the structure of CPGs, and do not consider the consistency and medical pertinence of recommendations.

The consistency of recommendations can be verified by formal methods [START_REF] Teije | Improving medical protocols by formal methods[END_REF]. The recommendations are first represented using an explicit and non-ambiguous model in a formal language. Several Computed Interpretable Guidelines (CIG) were developed [START_REF] Peleg | Computer-interpretable clinical guidelines: A methodological review[END_REF].

They allow detecting ambiguity, incompleteness, inconsistency or redundancy within CPGs [START_REF] Peleg | Support for guideline development through error classification and constraint checking[END_REF][START_REF] Miller | Using semantic constraints to help verify the completeness of a computer-based clinical guideline for childhood immunization[END_REF][START_REF] Teije | Improving medical protocols by formal methods[END_REF][START_REF] Goud | A parallel guideline development and formalization strategy to improve the quality of clinical practice guidelines[END_REF][START_REF] Galopin | Using an ontological modeling to evaluate the consistency of clinical practice guidelines: application to the comparison of three guidelines on the management of adult hypertension[END_REF][START_REF] Duftschmid | Knowledge-based verification of clinical guidelines by detection of anomalies[END_REF]. For example, some authors [START_REF] Shiffman | Improving clinical guidelines with logic and decisiontable techniques: application to hepatitis immunization recommendations, Medical decision making : an international[END_REF][START_REF] Shiffman | Representation of clinical practice guidelines in conventional and augmented decision tables[END_REF] state that, if narrative guidelines are encoded into logical language ("if... then..." rules), then the generation of all possible variable combinations allows the detection of incompleteness (i.e. variable combinations not covered by CPGs) and inconsistencies (i.e. similar variable combinations leading to different conclusions). But these methods are time-consuming and dependent on the formal language. Moreover, these formal approaches don't verify the medical pertinence (e.g. they do not verify that the recommended drug treatments are not contraindicated for the patient).

Few approaches have been proposed for verifying the medical pertinence of recommendations. These approaches require the formalization of the medical knowledge involved (e.g. drug properties such as contraindications) and the identification of the medical principles underlying the recommendations of CPGs. However, formalizing the knowledge and the reasoning principles is a complex task [START_REF] Teije | Improving medical protocols by formal methods[END_REF]. For example, in oncology, a medical domain where multiple drugs are often prescribed, the adverse events can be limited by checking the known adverse effects [START_REF] Hammond | Formalisation of safety reasoning in protocols and hazard regulations[END_REF].

Recently, many approaches have been proposed for enriching recommendation by integrating additional information. These pieces of information concern particularly patient context (psycho-social, multi morbidity, etc.) and patient preferences [START_REF] Wilk | Using constraint logic programming for the verification of customized decision models for clinical guidelines[END_REF][START_REF] Wilk | Comprehensive mitigation framework for concurrent application of multiple clinical practice guidelines[END_REF][START_REF] Sacchi | From decision to shared-decision: Introducing patients' preferences into clinical decision analysis[END_REF][START_REF] Sedki | A Preference-based framework for medical decision making[END_REF][START_REF] Sacchi | From decision to shared-decision: Introducing patients' preferences into clinical decision analysis[END_REF][START_REF] Parimbelli | Use of Patient Generated Data from Social Media and Collaborative Filtering for Preferences Elicitation in Shared Decision Making[END_REF]. For example, in multi-criteria decision making, to recommend an appropriate manual wheelchair, user preferences that are often conflicting must be taken into account [START_REF] Delcroix | A Bayesian network for recurrent multi-criteria and multi-attribute decision problems: Choosing a manual wheelchair[END_REF]. Nevertheless, the manual construction of preferences remains complex and time-consuming. Thus, it is more appealing to learn preferences from data, because in general, data are easily collected or observed.

In this article, we propose a method for the semi-automatic detection of inconsistencies in guidelines using preference learning, and we apply this method to antibiotherapy in primary care. In primary care, CPGs recommend prescribing antibiotics empiri-

A set of instances X = {x i |i = 1 . . . n}. A set of labels L = {l k |k = 1 . . . m}. For each instance x i , a set of pairwise preferences of the form l k x i l j .

Find a ranking function that maps any x ∈ X to a ranking x ∈ L.

Instance ranking

A set of instances X = {x i |i = 1 . . . n}. A set of ordered labels L = {l k |k = 1 . . . m} such that: l 1 l 2 . . . l k . A label l k is associated with each instance x i .

Find a ranking function that allows to order a new set of instances according to their (unknown) preference degrees.

Object ranking

A set of objects X = {x i |i = 1 . . . n}.

A finite set of pairwise preferences x i x j .

Find a ranking function that assumes as input a set of objects and returns a permutation (ranking) of this set. cally, i.e. without knowing the causative bacteria and its susceptibility to the various antibiotics. The most likely bacteria are guessed from the infectious disease (e.g. cystitis is usually caused by E. coli). Then, CPGs recommend an antibiotic according to the various antibiotics features (e.g. susceptibility of the likely causative bacteria, side effects) and the patient profile (e.g. child or adult) [START_REF] Tsopra | An algorithm using twelve properties of antibiotics to find the recommended antibiotics, as in CPGs[END_REF][START_REF] Tsopra | Towards evidence-based CDSSs implementing the medical reasoning contained in CPGs: application to antibiotic prescription[END_REF].

In order to detect inconsistencies in these CPGs, we made the following hypotheses: 1) it is possible to learn a preference model from the recommendations and a knowledge base describing the domain; 2) a generic model can be defined for all infectious diseases and all patient profiles encountered in CPGs; and 3) this preference model can be used to detect inconsistencies in CPGs.

The rest of the paper is organized as follows. Section 2 gives background about preference learning, and describes the optimization algorithm we used and the antibiotherapy knowledge base we previously designed. Section 3 describes the preference learning. Section 4 describes the detection of inconsistencies and their validation by a medical expert. Section 5 discusses the methods and the results obtained, and finally, concludes.

Background

State of the art in preference learning

Preferences are basically acquired in two ways: i) by elicitation from the user (for instance through a sequence of queries/answers) or ii) by directly learning them from data. Preference elicitation is often time-consuming, especially if the number of alternatives/outcomes is large. Moreover, different elicitation techniques are likely to provide different results. It is then more appealing to learn preference from data which is easy to observe and collect. Preference learning is one of the research problems that have recently received considerable attention in disciplines such as artificial intelligence, machine learning, data mining, decision making and others. It aims to learn and construct a preference model from observed preference information. Once the preference model learned, it can be used for decision making for instance. Preference learning can be formalized within various settings, depending for example on the underlying preference model and the type of input provided to the learning system. We can distinguish three common problems in preference learning [START_REF] Frnkranz | Preference Learning, 1st Edition[END_REF]: i) learning from label preferences (also designed as label ranking in the literature because frequently, the predicted preference relation is required to form a total order), ii) learning from instance preferences (instance ranking) and iii) learning from object preferences (object ranking). Table 1 summarizes the different ranking problems.

In label preferences problem [START_REF] Hüllermeier | Label ranking by learning pairwise preferences[END_REF][START_REF] Vembu | Label ranking algorithms: A survey[END_REF], the training data contains a set of instances. A set of pairwise comparisons between labels is associated with each instance, expressing that one label is preferred over another for that instance. The objective is to use these pairwise preferences for predicting a ranking function that attributes for any instance a ranking (a total order in general) of all possible labels. Namely, the task is to rank the set of labels for a new instance (label ranking). Label ranking can be considered as a generalization of the supervised classification problem where an order over class labels is associated with an instance instead of only one class label. As an example of a label ranking problem, consider a set of labels L representing three types of activities: football, tennis and basket. The training data contains a set of students who have to give a list of pairwise preferences between activities (e.g. {(Adrien, [ f ootball tennis]), (Marie, [tennis f ootball]}). Thus, the aim is to compute a ranking over the labels for each instance. For example, the possible prediction of the learnt function for a student x is football basket tennis.

In the setting of learning from instance preferences problem [START_REF] Cohen | Learning to order things[END_REF], the input contains a set of ordered labels and a set of instances, each one associated with a label. The objective is to find a ranking function that allows ranking a given new set of instances. In case where there are two ordered labels, the problem of learning is often called bipartite ranking problem [START_REF] Clémençon | Ranking the best instances[END_REF]. In case where there are more than two ordered labels, the problem of learning is often called multipartite-ranking problem [START_REF] Bergeron | Multiple instance ranking[END_REF].

Concerning learning from objects [START_REF] Waegeman | A survey on roc-based ordinal regression learning[END_REF][START_REF] Joachims | Accurately interpreting clickthrough data as implicit feedback[END_REF], the objective is to learn a model that allows determining which object is preferred to another. The training data is given in the form of pairwise comparisons between objects. For this type of learning problems, there is no supervision since no class label is associated with an object and each object is not necessarily represented by a set of features or attributes. As an example, to rank query results of a search engine, user clicks on some of the links in the query result and not on others can be exploited to provide training information. Thus, selected pages are preferred over pages that are not clicked.

Two approaches can be distinguished for preference modeling and learning: quantitative and qualitative approaches. Quantitative preferences learning [START_REF] Dekel | Log-linear models for label ranking[END_REF][START_REF] Burges | Learning to rank using gradient descent[END_REF] consist mainly to learn a utility function on training data. This function assigns a utility degree (or a score) to each alternative (instance, object or label) following the learning problem. For learning problems that are based on qualitative approach [START_REF] Dembczynski | Learning of rule ensembles for multiple attribute ranking problems[END_REF][START_REF] Jiang | Mining preferences from superior and inferior examples[END_REF][START_REF] De Amo | Contextual preference mining for user profile construction[END_REF][START_REF] Chevaleyre | Learning ordinal preferences on multiattribute domains: The case of cp-nets[END_REF][START_REF] Boutilier | Cp-nets: A tool for representing and reasoning with conditional ceteris paribus preference statements[END_REF], the objective is to learn a binary preference relation that compares each pairs of alternatives.

When it comes to modeling utility functions, the task is rather more complicated since users may not be used with this formal-ism and the problem size could be very large. Utility functions (for example, the one a user is supposed to use while making decisions) can be inferred or estimated from past decisions. In [START_REF] Chajewska | Learning an agent's utility function by observing behavior[END_REF], this problem is solved by imposing constraints derived from the data over the set of all utility functions. One could go one step further by searching for the optimal utility function given the available constraints. Among first works dealing with deriving utility functions from data, one can mention [START_REF] Ng | Algorithms for inverse reinforcement learning[END_REF] where the authors aim at extracting reward functions given optimal behaviors in the context of Markov Decision Processes. The main issues dealt with the literature last years concern noise and data inconsistencies and uncertainty, large search spaces and taking into account data sequence, etc. In [START_REF] Ramirez | Automatic Derivation of Utility Functions for Monitoring Software Requirements[END_REF], the authors proposed an approach to learn utility functions allowing to monitor requirements of a dynamically adaptive system. The learned utility functions map at run time monitoring information to a value assessing how well a requirement is satisfied.

Once the preferred model is learned, there is need to measure its quality of prediction. For this, different performance measures can be used such as precision, recall, NDCG (Normalized Discounted Cumulative Gain), etc. In addition, preference learning methods require optimization algorithms. In this study, we will use the Artificial Feeding Birds (AFB) metaheuristics [START_REF] Lamy | Les oiseaux picorant artificiels : une nouvelle méta-heuristique inspirée du comportement des pigeons[END_REF][START_REF] Lamy | Advances in nature-inspired computing and applications[END_REF]. We developed this metaheuristics in previous works, and we describe it in the following section.

Artificial Feeding Birds (AFB) metaheuristics

Nature-inspired metaheuristics [START_REF] Lones | Metaheuristics in nature-inspired algorithms[END_REF][START_REF] Yang | Nature-inspired metaheuristic algorithms[END_REF] are an optimization approach, which often leads to simple, efficient and adaptable algorithms. In this work, we chose Artificial Feeding Birds (AFB) [START_REF] Lamy | Les oiseaux picorant artificiels : une nouvelle méta-heuristique inspirée du comportement des pigeons[END_REF][START_REF] Lamy | Advances in nature-inspired computing and applications[END_REF], a recent metaheuristic inspired by the behavior of pigeons.

AFB considers a population of artificial birds. The position of a bird corresponds to a candidate solution to the optimization problem. The optimization process aims at minimizing the cost() function, (i.e. finding x such as cost(x) is as low as possible). The value returned by the cost() function is associated with the presence of food: if the value of the cost() function for the new position of a bird is lower than his previous lowest value, the bird has found some food and he keeps his current position in memory.

In each iteration of the algorithm, each bird performs a move. Four possible moves are considered: (1) the bird walks to a close random position, (2) the bird flies to a completely random position, (3) the bird flies back to the best position he has encountered so far, and (4) the bird flies to join the position of another random bird. For a given bird, the next move is determined as follows: if the bird has flown in the previous cycle, he walks. If the bird has found a better solution in the previous cycle, he walks. Otherwise, the next move is chosen randomly, with different probabilities associated with each move. Two sizes of birds are considered, and the fourth move (join another bird) can only be performed by the largest birds (representing 25% of the population).

The optimization problem is defined by three functions: cost(), the function to minimize, f ly(), a function that returns a random position in the solution space, and walk(i), a function that modifies the current position of the bird i by performing a small random move.

The metaheuristic takes 5 parameters:

n = 20, the number of artificial birds, r = 0.75, the ratio of small birds in the total bird population, p 2 = 0.01, the probability that a bird chooses move 2, p 3 = 0.67, the probability that a bird chooses move 3, p 4 = 0.07, the probability that a bird chooses move 4. The parameter values given here are the ones we used; they correspond to the default values proposed in [START_REF] Lamy | Advances in nature-inspired computing and applications[END_REF]. The AFB algorithm is known to have a low sensitivity to parameter values, and these values were successfully used in very different optimization problems (non-linear global optimization on benchmark functions, neural network training, combinatorial optimization). The metaheuristics algorithm is given in Supplementary File 1.

Antibiotherapy knowledge base

In previous works [START_REF] Tsopra | An algorithm using twelve properties of antibiotics to find the recommended antibiotics, as in CPGs[END_REF][START_REF] Tsopra | Towards evidence-based CDSSs implementing the medical reasoning contained in CPGs: application to antibiotic prescription[END_REF], we designed an antibiotherapy knowledge base for helping physicians with empirical prescription of antibiotics. The knowledge base contains information related to 11 infectious diseases, the 50 antibiotics marketed for use in primary care in France, and 21 patient profiles.

Figure 1 shows the general model of the knowledge base. Infectious diseases are associated with the likely causative bacteria (one or several; several types of bacteria can cause the same disease). A patient profile is described by the age class and the presence or absence of pregnancy, allergy, and history of antibiotic treatment. A clinical situation corresponds to the intersection of an infectious disease and a patient profile. Finally, a given antibiotic prescribed for a given clinical situation is called a case in the knowledge base. It is the lowest granularity level in the knowledge base. Each case has an integer recommendation rank, which is 0 if the antibiotic is not recommended by French CPGs in the clinical situation, 1 if it is recommended as a first-line treatment, 2 if it is recommended as a second-line treatment, and so on (up to 4).

In addition, cases are characterized by 11 features (listed in Table 2). In the paper, each feature is identified by a short name, such as protocol. For a given feature, the value may depend on the antibiotic, the patient profile, the infectious disease and/or the likely causative bacteria. For example, no side e f depends only on the antibiotic, whereas no contraindication depends on the antibiotic and the patient profile (e.g. a given antibiotic may be contraindicated for children but not for adults). Each feature is Boolean (T rue if the feature holds for the case and False otherwise), with possible missing values (Unknown) when no data is available in the medical literature. For each feature, T rue corresponds to an advantage for the antibiotic, whereas False is a disadvantage.

The knowledge base was built and populated by a medical doctor (RT) through a 2 steps-process. In step 1, RT extracted the features of antibiotics and their dependence relationships [START_REF] Tsopra | An algorithm using twelve properties of antibiotics to find the recommended antibiotics, as in CPGs[END_REF][START_REF] Tsopra | Towards evidence-based CDSSs implementing the medical reasoning contained in CPGs: application to antibiotic prescription[END_REF], from the manual analysis of six CPGs related to urinary [START_REF] Afssaps | Guidelines -diagnostic et antibiothérapie des infections urinaires bactériennes communautaires du nourrisson et de l'enfant[END_REF][START_REF] Afssaps | Guidelines -diagnostic et antibiothérapie des infections urinaires bactériennes communautaires chez l'adulte[END_REF] and respiratory [START_REF] Ansm | Guidelines -Antibiothérapie par voie générale dans les infections respiratoires basses de l'adulte et de l'enfant -Recommandations et Argumentaires[END_REF][START_REF] Afssaps | Guidelines -antibiothérapie par voie générale dans les infections respiratoires basses de l'adulte[END_REF][START_REF] Afssaps | Guidelines -antibiothérapie par voie générale en pratique courante dans les infections respiratoires hautes de l'adulte et de l'enfant[END_REF][START_REF] Spilf Sfp | Guidelines -Antibiothérapie par voie générale en pratique courante dans les infections respiratoires hautes de l'adulte et de l'enfant[END_REF] Whether the antibiotic has an acceptable taste for the patient (e.g. Cefuroxime axetil has a bad taste and thus is not acceptable for children) X X of existing antibiotic knowledge base able to describe the features identified in step 1, only textual resources were used to populate the knowledge base. RT manually extracted the values for each feature (i.e. T rue, False, or Unknown) from seven French CPGs [START_REF] Afssaps | Guidelines -diagnostic et antibiothérapie des infections urinaires bactériennes communautaires du nourrisson et de l'enfant[END_REF][START_REF] Afssaps | Guidelines -diagnostic et antibiothérapie des infections urinaires bactériennes communautaires chez l'adulte[END_REF][START_REF] Ansm | Guidelines -Antibiothérapie par voie générale dans les infections respiratoires basses de l'adulte et de l'enfant -Recommandations et Argumentaires[END_REF][START_REF] Afssaps | Guidelines -antibiothérapie par voie générale dans les infections respiratoires basses de l'adulte[END_REF][START_REF] Afssaps | Guidelines -antibiothérapie par voie générale en pratique courante dans les infections respiratoires hautes de l'adulte et de l'enfant[END_REF][START_REF] Hcsp | Guidelines -rapport relatif à la conduite à tenir devant un ou plusieurs cas de coqueluche[END_REF][START_REF] Afssaps | Guidelines -mise au point traitement antibiotique probabiliste des urétrites et cervicites non compliquées[END_REF], two international CPGs [START_REF]Guidelines for the management of adult lower respiratory tract infections[END_REF][START_REF] Idsa | Guidelines -international clinical practice guidelines for the treatment of acute uncomplicated cystitis and pyelonephritis in women: A 2010 update by the infectious diseases society of america and the european society for microbiology and infectious diseases[END_REF], five antibiotic guidelines produced by national authorities [START_REF]Guidelines -fiches de transparence médicaments anti-infectieux en pathologies communautaires[END_REF][START_REF]Guidelines -livret médicaments et grossesse[END_REF][START_REF]Guidelines -spectre d'activité antimicrobienne[END_REF][START_REF] Has | Guidelines -stratégie d'antibiothérapie et prévention des résistances bactériennes en établissement de santé[END_REF][START_REF] Ansm | Guidelines -caractérisation des antibiotiques considérés comme critiques[END_REF], and one reference textbook on infectious diseases [START_REF] Spilf | ECN -PILLY[END_REF]. For example, for fosfocmycin trometamol in women cystitis, protocol = T rue was extracted from the following CPG excerpt [START_REF] Afssaps | Guidelines -diagnostic et antibiothérapie des infections urinaires bactériennes communautaires chez l'adulte[END_REF]: "Fosfomycin trometamol is recommended in women cystitis because it can be given in single dose". Each value was then blindly validated by two antibiotic specialists dur-ing a 5-round Delphi Process (14.7% of the values were modified).

Finally, the knowledge base has been formalized as an OWL 3. Building the preference model

Modeling the knowledge base

With regard to preference learning, we consider an instance to be a given antibiotic in a given clinical situation (i.e. what we called a case in the ontology, Figure 1). Building a preference model from the case features and the recommendations of CPGs is an instance learning problem (as described in section 2.1). In the knowledge base, there are 5 recommendation ranks: recommended as 1 st , 2 nd , 3 rd , 4 th line of treatment (R 1 , R 2 , R 3 , R 4 , respectively) or not recommended (NR), which correspond to 5 labels that are ordered (R 1

R 2 R 3 R 4 NR).
There are 102 cases labeled R 1 , 62 labeled R 2 , 30 labeled R 3 , 2 labeled R 4 and 3104 labeled NR. Since there are very few cases having the R 3 and R 4 labels, for facilitating the learning of preferences, we divide this multipartite-ranking problem in two bipartite ranking problems. In the first problem, we consider the two following labels: R 1 vs R 2 ∪ R 3 ∪ R 4 ∪ NR (i.e. all cases not recommended as first-line treatment are grouped together). In the second problem, the labels are: R 1 ∪R 2 ∪R 3 ∪R 4 vs NR (i.e. all cases recommended are grouped together whatever their recommendation rank). Thus, we will learn two different preference models, respectively named M 1 and M any , one for each problem. The two models will be learned following the same method, described below.

We model the antibiotic knowledge base as a case space X = {x 1 , ...x i , ..., x n } with x i = (x a i , x s i , x i,1 , ..., x i, j , ..., x i,p ) where x a i is the identifier of the antibiotic, x s i is the identifier of the clinical situation, and x i, j are the feature values, with x i, j ∈ {T rue = +1, False = -1, Unknown = 0}. n is the number of cases and p is the number of features (p = 11). We considered the 66 clinical situations for which at least one recommendation exists in CPGs, and the 50 antibiotics available on the market in primary care in France in 2014. Consequently, n = 66 × 50 = 3300.

In our formalization, we added x a i and x s i in cases, in order to permit having several cases with the same feature values in set X, provided that the antibiotic or the clinical situation differs. However, x a i and x s i are not considered as features for the purpose of learning. We also define S, a partition of X according to clinical situations: S = {S 1 , S 2 , ..., S k , ...} where S k is the set of all cases sharing a given clinical situation k: S k = {x ∈ X | x s i = k}. Finally, we represent the two labels as a set of two classes Y = {Y reco , Y not reco } which is a partition of the case space X. Y reco contains the cases recommended (in first line of treatment for M 1 , and in any line for M any ), and Y not reco contains the others. Therefore, Y reco is preferred to Y not reco (written Y reco Y not reco ).

2 AL: attribute language (including atomic negation, concept intersection, universal restriction, existential qualification limited to class Thing), C: complex negation, (D): use of datatypes [START_REF] Baader | The description logic handbook: theory, implementation and applications[END_REF]. Table 3 shows the structure of the knowledge base on a simplified example with only 5 antibiotics, 2 clinical situations, p = 3 features and n = 10 cases.

Feature

Determining necessary and preference features

We make the hypothesis that two categories of features exist: necessary features and preference features. Necessary features are mandatory for prescribing the antibiotic: if the feature does not hold for an antibiotic in a clinical situation, the antibiotic should not be prescribed and thus it is not recommended (necessary features can be viewed as constraints). On the contrary, preference features are not mandatory; however, an antibiotic having a preference feature is preferred to another antibiotic without the preference feature. For example, the absence of contraindications may be a necessary feature while the low rate of adverse effects may be a preference feature.

In order to learn which features are necessary, for each feature j (with 1 ≤ j ≤ p) we compute N j , the percentage of recommended cases for which the feature j is not necessary to recommend the antibiotic, i.e. feature j is not True but the antibiotic is nevertheless recommended in guidelines:

N j = {x i ∈ Y reco | x i, j 1} |Y reco | (1)
Table 4 shows the computed values for N j on the simplified example of Table 3. In an "ideal" error-less system, a necessary feature has N j = 0 (e.g. feature no contraindication in the example). In real life, there may be a few errors. Thus, we consider as necessary all features j having N j ≤ t ness , where t ness is a threshold that will be learned later. We define F ness and F pre f , the sets of necessary and preference features, respectively (each feature being identified by its index).

F ness = j ⊆ {1, 2, ..., p} | N j ≤ t ness (2)
F pre f = {1, 2, ..., p} \ F ness (3)
In the example (Table 4), the learning process leads to t ness = 10%. This means that no contraindication is a necessary feature, whereas protocol and no side e f are preference features.

Defining the utility function

For preference features, we define a utility function f : X → R that allows ordering cases according to their degree of preference, i.e. f (x i ) ≥ f (x j ) ⇒ x i x j . We define f as a linear combination of the preference features:

f (x i ) = j∈F pre f x i, j × w j (4)
The weights w j will be learned later. The utility function quantifies the utility of an antibiotic in a clinical situation. However, the utility is meaningless per se, and it can only be exploited relatively to the utility of other antibiotics. For example, an antibiotic with a low utility could be recommended if no better antibiotic exists in a given clinical situation. Moreover, the antibiotics recommended may not be limited to the one with the best utility: other antibiotics with a high utility, but slightly lower than the best one, might be considered as recommended too. Consequently, in a given clinical situation, we consider as recommended all antibiotics having a utility highest to the best utility found in this clinical situation minus t pre f , a second threshold that must be learned.

In the example, Table 4 shows the learned weights and thresholds. The resulting f (x i ) are given in the right part of Table 5. For example, for case x 4 , f (x 4 ) = False × 0.2 + T rue × 0.3 = 0.1 (we remind that False = -1 and T rue = 1).

Determining antibiotics recommended by the preference model

For each clinical situation S k ∈ S, the antibiotics recommended by the preference model can be determined in three steps. First, we compute S k cand , the set of candidate cases that can be prescribed with regards to necessary features:

S k cand = x i ∈ S k | j ∈ F ness , x i, j 1 (5)
If S k cand = ∅, no antibiotic is recommended by the preference model and the process stops here.

Second, we determine x best , the case ranked the highest by the utility function:

x best ∈ S k such as f (x best ) = max( f (x i ) | x i ∈ S k cand ) (6)
Third, we compute S k reco , the set of cases classified as recommended, and including all candidate cases from S k cand for which the utility function is higher than (or equal to) the best value found previously minus the threshold t pre f :

S k reco = x i ∈ S k cand | f (x i ) ≥ f (x best ) -t pre f (7)
In the example, the right part of Table 5 indicates which cases belong to S k cand and S k reco . The example has two clinical situations X and Y. There is a best utility value f (x best ) for each clinical situation (shown in bold in Table 5). Then, for each clinical situation, we determine recommended cases using formula 7. For example, in situation X, x 4 has the best utility, and is therefore recommended. x 3 has a lower utility than x 4 , but not lower than the utility x 4 minus t pre f = 0.5. Thus, x 3 is recommended too. On the contrary, x 2 has a utility lower than the utility x 4 minus t pre f = 0.5, and therefore is not recommended.

Optimizing weights and thresholds

In order to learn necessary features and preferences, we need to find the optimal values for the weights w 1 , ..., w p and the two thresholds t ness and t pre f .

The values of weights and thresholds were searched between 0 (the feature has no importance at all) and 1 (the feature has the maximal importance). The optimal weights and thresholds should minimize the total number of errors E, i.e. the number of recommended cases classified as non-recommended (false negatives) and the number of nonrecommended cases classified as recommended (false positive) by the preference model:

E = k z×|Y reco ∩ (S k \ S k reco )|+(2-z)×|Y not reco ∩ S k reco | (8)
where z is a coefficient that allows giving more importance to either type of errors (false negatives or false positives). By changing the value of z, it is possible to obtain different results in terms of precision and recall, and to produce the PR curve (precisionrecall).

This is an unconstrained global non-linear optimization problem with a solution space of p + 2 dimensions. We used the Artificial Feeding Birds (AFB) metaheuristics [START_REF] Lamy | Les oiseaux picorant artificiels : une nouvelle méta-heuristique inspirée du comportement des pigeons[END_REF][START_REF] Lamy | Advances in nature-inspired computing and applications[END_REF] for solving the problem. The system has been implemented in Python 3 and executed with PyPy 3, a Python interpreter that includes a JIT (Just-In-Time) compiler. The cases were extracted from the OWL ontology. We used two open source Python module: Owlready for ontology-oriented programming [START_REF] Lamy | Ontology-oriented programming in Python with automatic classification and high level constructs for biomedical ontologies[END_REF], and Metaheuris-tic_Optimizer for optimization with AFB.

Figure 2 shows the PR curve. For the rest of the analysis, we fixed z to 1 (i.e. both types of errors have the same weight). We performed 20 runs of the optimization program and we stopped it after 15,000 solutions were tested. We kept the best result found. For M 1 , we obtained E = 50 (14 false positives and 36 false negatives), leading to a sensitivity/recall of 64.7%, a precision of 82.5%, and a specificity of 99.6%. For M any , we obtained E = 82 (32 false positives and 50 false negatives), leading to a sensitivity/recall of 75.5%, a precision of 82.0%, and a specificity of 99.0% (corresponding to the dots on the PR curve). Table 6 shows the results of the learning process, for z = 1, for the two preference models M 1 and M any (i.e. considering only cases recommended as first-line treatment or as any line of treatment, see section 3.1). 4 necessary features are found in both models: naturally active, probably active, proved and no contraindication. The seven others are preference features. For determining the first-line treatments (R 1 with model M 1 ), the most important preference features are not precious, taste and no side e f . On the contrary, for determining treatments that are recommended in any ranks (R 1 ∪ R 2 ∪ R 3 ∪ R 4 with model M any ), the most important preference features are taste and protocol. Indeed, taste is more important than what we may expect, because many clinical situations involve children and children refuse to take drugs with a bad taste. Two features, e f f icacy level and spect, have no impact for determining the first-line treatments and a very low impact for determining the recommended treatments in any ranks.

Detection of inconsistencies in CPGs

Methods

The 106 errors obtained during preference learning can be seen as candidate inconsistencies in CPGs: for those cases, the recommendation of the CPGs does not match the result obtained using the preference model we built from the whole guideline recommendations. Therefore, our hypothesis is that there might be inconsistencies in the CPGs for those cases.

All these candidate inconsistencies were manually verified by a medical expert (RT). For each candidate, the inconsistency was confirmed if the medical expert retrieved arguments within CPGs in contradiction with the level of recommendation given in CPGs. If no contradictions were found within CPGs, then the medical expert searched for contradictions in the argumentation of other guidelines (e.g. previously published CPGs, CPGs from other countries). Then the medical expert categorized the inconsistencies into various groups.

An example of contradiction follows. The CPG [START_REF] Spilf | Guidelines -Diagnostic et antibiotherapie des infections urinaires bactériennes communautaires de l'adulte[END_REF] says "the proof of efficacy of fosfomycin in cystitis with risk of complication (including pregnancy) is not sufficient", but, surprisingly, the CPG nevertheless recommends fosfomycin for the treatment of cystitis in pregnant women.

Medical analysis of the candidate inconsistencies

Table 7 summarizes the various categories of candidate inconsistencies obtained from preference learning and the number of cases in each category. The expert validated 51.9% (55/106) of the candidates as inconsistencies in CPGs. The medical expert detected 29 contradictions related to the features probably active, 11 to proved, 9 to no contraindication, 4 to spect, and 2 related to a mix of several preference features.

Two categories of contradictions were distinguished:

(1) For 40 cases, CPGs recommend an antibiotic whereas there are arguments in the same or another CPG for not recommending this antibiotic. For example, the CPG [START_REF] Spilf Sfp | Guidelines -Antibiothérapie par voie générale en pratique courante dans les infections respiratoires hautes de l'adulte et de l'enfant[END_REF] recommends sulfamethoxazole/trimethoprim in child sinusitis, but the CPG also states "because of the evolution of frequency of acquired resistance, sulfamethoxazole/trimethoprim is not recommended in sinusitis". (2) For 15 cases, CPGs do not recommend a given antibiotic, whereas there are arguments in the same or another CPG for recommending this antibiotic in similar clinical situation. For example, in otitis with conjunctivitis, CPG [START_REF] Spilf Sfp | Guidelines -Antibiothérapie par voie générale en pratique courante dans les infections respiratoires hautes de l'adulte et de l'enfant[END_REF] do not recommend amoxicillin and prefers the combination of amoxicillin/clavulanic acid; this choice is justified as follows: "Amoxicillin/clavulanic acid should be preferred because of a strong suspicion of H. influenzae infection". On the contrary, in otitis without conjunctivitis, CPG [START_REF] Spilf Sfp | Guidelines -Antibiothérapie par voie générale en pratique courante dans les infections respiratoires hautes de l'adulte et de l'enfant[END_REF] recommends amoxicillin rather than the amoxicillin/clavulanic acid combination and justifies this choice as follows: "Amoxicillin should be preferred because (. . . ) it is active against H. influenzae strains".

Categories

The expert classified 16.0% (17/106) of the candidate inconsistencies as caused by flaws in the antibiotic knowledge base. Three categories of flaws were distinguished:

(1) For 9 cases, CPGs consider additional features that were missing in the knowledge base: bioavailability (i.e. antibiotic oral absorption), minimum inhibitory concentration (i.e. the lowest antibiotic concentration which prevents the growth of bacterium), and marketing authorization. For example, the preference model recommends levofloxacin in uncomplicated cystitis in women, but the argumentation of CPG [START_REF] Spilf | Guidelines -Diagnostic et antibiotherapie des infections urinaires bactériennes communautaires de l'adulte[END_REF] says " levofloxacin is not recommended because it does not have the marketing authorization" for this clinical situation in France.

(2) For 7 cases, the coding of features as Boolean is not precise enough. The two features involved are no side e f and not precious. For these cases, a more fine-grained gradation in at least three levels (e.g. none/moderate/high) is required. For example, the preference model recommends pristinamycin and telithromycin for pneumonia in children over the age of 12 years with betalactam allergy. Pristinamycin is recommended in CPG, but not telithromycin [START_REF] Ansm | Guidelines -Antibiothérapie par voie générale dans les infections respiratoires basses de l'adulte et de l'enfant -Recommandations et Argumentaires[END_REF]. The argumentation of guidelines says that both may cause side effects, but telithromycin is associated with side effects more serious than pristinamycin. This information is missing in the knowledge base because values are coded as Boolean.

(3) For 1 case, the antibiotic recommended by the preference model is not marketed any more. The antibiotic should be removed from the knowledge base.

The expert classified 15.1% (16/106) of the candidate inconsistencies as caused by flaws in the preference model. Two cate-gories of flaws were distinguished:

(1) For 7 cases, additional principles not considered in the model seemed to be used in CPGs. Two such principles were identified: (a) When several antibiotics are recommended, CPGs often propose antibiotics belonging to different therapeutic classes, because some patients have drug class allergy (e.g. penicillin allergy), and thus it is better to propose a wide variety of drug classes. (b) In a very few number of cases where no antibiotics have the necessary features, CPGs recommend some antibiotics without one of the necessary features (probably active).

(2) For 9 cases, the preference model seems different for children than from adult patient, whereas we hypothesized that a generic model exists for all patients and diseases (hypothesis #2 in introduction). More specifically, for these 9 cases, CPGs give more importance to side effects for children. For example: In adult sinusitis, CPGs recommends pristinamycin whereas in child, CPG [START_REF] Spilf Sfp | Guidelines -Antibiothérapie par voie générale en pratique courante dans les infections respiratoires hautes de l'adulte et de l'enfant[END_REF] says "pristinamycin is not recommended because of the risk of side effects". However, no side effect specific to children (e.g. developmental disorders) were mentioned.

Finally, 17.0% (18/106) of the candidate inconsistencies could not be categorized by the medical expert.

Discussion and conclusion

In this paper, we showed that strategies followed by CPGs for establishing therapeutic recommendations in antibiotherapy can be formalized by a preference model. This model can be learned from the CPGs and a knowledge base describing the domain. In addition, the model allowed the detection of 106 candidate inconsistencies in CPGs, 55 of which were then validated by a medical expert. We also identified several flaws in the knowledge base. To the best of our knowledge, this is the first study that proposes using preference learning on drug properties for detecting inconsistencies within CPGs.

Discussion on the preference model and the learning process

Our preference model is based on a quantitative approach. It uses a simple utility function, which has the interest of producing results easily understandable by medical experts and physicians. In addition, the method we proposed allowed the learning of a single model from several clinical situations, each situation including several cases, and the various features can depend on the antibiotic, the patient profile, the infectious disease and/or the causative bacteria. As a consequence, the feature values can be assigned at various levels in the knowledge base. We used a formal ontology in OWL 2.0 for managing the knowledge base and for obtaining the feature values for each case, using inheritance. Despite the specificity of each infectious disease and patient profile, we successfully built a generic model satisfying all clinical situations described in CPGs, with the exception of 9 cases related to children.

Our utility function does not consider interactions between features, while in antibiotherapy, there might be some interactions. For example, two features a and b might have an impact on the utility, while the impact of a ∪ b is not the sum of the impact of a and b alone. More sophisticated methods, such as Choquet integral [START_REF] Tehrani | Preference learning using the Choquet integral: The case of multipartite ranking[END_REF], can capture the dependencies between features. In the future, we will aim to study this point.

The proposed method is interesting since it allowed learning not only preferences, but also necessary features (i.e. constraints) that are very important in preference reasoning. In the literature, few models exist that permit modeling both constraints and preferences [START_REF] Benferhat | Two alternatives for handling preferences in qualitative choice logic[END_REF]. For example, let us consider an antibiotic For optimizing weights and thresholds, we reused the AFB metaheuristics. We chose metaheuristics in general because they are known to adapt quite well to many kinds of problems, whatever the size of the solution space is. Furthermore, in the literature, metaheuristics have already been used for preference learning [START_REF] Jinyan | A Methaheuristic approach for preference Learning in multi criteria ranking based on reference points[END_REF]. AFB was chosen since it results from our previous works, and because it was found to be especially adaptable, and quite independent from parameter values.

AFB seems efficient for the problem presented here. We compared it with two other metaheuristics, Artificial Bee Colony (ABC) [START_REF] Karaboga | An idea based on honey bee swarm for numerical optimization[END_REF] and Firefly Algorithm (FA) [START_REF] Yang | Firefly algorithms for multimodal optimization[END_REF], for the learning of the M any model with z = 1. We performed 20 runs for each algorithm. For each run, the optimization process was stopped after 15,000 solutions were tested. Table 8 shows the mean results for each algorithm. AFB yielded the best results, and found the lowest value (82.0) in 7 runs. ABC found the lowest value in only 2 runs. On the contrary, FA never found the lowest value. Therefore, AFB seems an interesting algorithm for preference learning.

We used the default parameter values for AFB. We performed parameter optimization a posteriori, and we obtained better results with slightly different values: p 2 = 0.0049, p 3 = 0.78 and p 4 = 0.068. With those values, the mean result was 82.9 (instead of 83.6), and the best result was obtained 11 times out of 20 runs (instead of 7 times). However, the parameter optimization took half a day, thus it may not worth the time to perform it since the gain is low. This confirms previous results suggesting that AFB has a low sensitivity to parameter values.

Medical discussion of results

The learning process allowed the identification of two types of features: necessary vs preference. This confirms the results of previous works based on the manual analysis of CPGs [START_REF] Tsopra | An algorithm using twelve properties of antibiotics to find the recommended antibiotics, as in CPGs[END_REF][START_REF] Tsopra | Towards evidence-based CDSSs implementing the medical reasoning contained in CPGs: application to antibiotic prescription[END_REF]. The distinction between necessary and preference features allows classifying antibiotics in 3 categories, for a given clinical situation:

(1) the inappropriate antibiotics that should never be prescribed because they are not efficient for treating the infectious disease or they cannot be used for a given patient (i.e. antibiotics not having the necessary features), (2) the appropriate antibiotics that could be prescribed, but that are not the ones recommended because better antibiotics exist (i.e. antibiotics having the necessary features, but not preferred), and (3) the recommended antibiotics (i.e. antibiotics having the necessary features, and preferred). This classification into 3 categories could be helpful in clinical practice.

In addition, the learning process identified the weight of antibiotic features. Not surprising, the feature protocol has an important weight. Indeed, in clinical practice, physicians often prefer to prescribe drugs with short treatment duration and/or single daily dose to increase patient observance. The feature not precious has also an important weight for antibiotic recommended in first line (model M 1 ). This feature is specific to antibiotherapy where the objective is to rationalize the use of antibiotics because of bacteria resistance. Thus, some antibiotics are "preserved", and their use is restricted to specific clinical situations. The weight of the feature no side e f may seem lower than what we may expect. However, this can be explained because infectious diseases often require short treatments (one to 7 days), and thus the probability to develop side effects is lower than for longer treatments. Surprisingly, the features spect and low eco risk have a low weight. Since a current French campaign [START_REF] Ansm | Guidelines -Liste des antibiotiques critiques -Rapport[END_REF] encourages the use of antibiotics with narrow spectrum and low ecological risk, we expected higher weights for these features.

The preference learning on the antibiotic knowledge base allowed the detection of 106 errors. The analysis of these errors by a medical expert leads to the identification of 55 inconsistencies in CPGs (defined as contradictions between arguments retrieved in CPGs and the level of recommendation given in CPGs). Therefore, about half of the candidate inconsistencies were manually validated as inconsistencies in the CPGs. These inconsistencies could correspond to two subcategories: (i) either the level of recommendation given in CPGs is correct, but the arguments retrieved in CPGs are in contradiction, or (ii) the arguments retrieved in CPGs are correct, but the level of recommendation given in CPGs is in contradiction. Distinguishing between those two subcategories would require to gather all the experts who wrote the CPGs, which is hardly feasible.

Perspectives

In the future, we will aim at improving our approach in various ways. The missing antibiotic features (e.g. bioavailability) and medical principles identified during the medical analysis could be added to the knowledge base and the preference model, respectively. We would also like to test our approach in other medical domains. However, this would require a preliminary work by medical experts to identify the drug features involved in the recommendations, and the constitution of a knowledge base for representing the domain. The constitution of this knowledge base may be a long process: for antibiotherapy, it took several months and 5 rounds of Delphi Process. The extraction of the content of the knowledge base was not automated in the presented work, although the design of an automatic process is an interesting perspective.

It would be interesting to test a qualitative model, such as conditional preferences [START_REF] Boutilier | Cp-nets: A tool for representing and reasoning with conditional ceteris paribus preference statements[END_REF], in addition to the quantitative preference model proposed in this paper. We would like to check whether it would allow the detection of additional inconsistencies.

Another perspective is the design of a tool based on our preference model and the knowledge base, for supporting experts during the writing of CPGs. The tool could help experts to detect inconsistencies in their recommendations before CPGs publications, but could also suggest a list of recommended antibiotics for each clinical situation. This could speed up the development process of CPGs, which is currently too long [START_REF] Woolf | Developing evidence-based clinical practice guidelines: lessons learned by the US Preventive Services Task Force[END_REF].

Furthermore, these findings might be used for designing a clinical decision-support system for helping physicians to prescribe antibiotics [START_REF] Tsopra | Comparison of two kinds of interface, based on guided navigation or usability principles, for improving the adoption of computerized decision support systems: application to the prescription of antibiotics[END_REF]. Indeed, the preference model could be used for suggesting antibiotics when no recommendation exists in CPGs. Further works are needed to confirm this hypothesis.

Competitive interest statement

None.

Figure 1 :

 1 Figure 1: General model of the knowledge base.

Figure 2 :

 2 Figure 2: The PR curve (in green for model M 1 and in red for model M any ; the dots corresponds to z = 1).

Table 1 :

 1 Comparison between the different ranking problems.

  infections. In step 2, RT populated the knowledge base. Because of the lack Probably active against the causative bacterium [probably active] Whether the frequency of resistance in the causative bacterium is less than Y% (*) for the antibiotic (e.g. Ceftriaxone is probably active against E.coli)

	# Feature [short name]	Antibiotic Patient	Infectious	Causative
	Definition		profile	disease	bacteria
	1 Naturally active against the causative bacterium [naturally active]	X			X
	Whether the causative bacterium is described as sensitive or of intermediate
	sensitivity for the antibiotic (e.g. Amoxicillin is naturally active against
	Group A streptococci)
	2 X		X	X
	3 Clinical efficacy proven in the disease [proved]	X		X
	Whether the antibiotic is described as clinically effective for treating the
	infection OR is (or has been) indicated/recommended for the infection (e.g.
	Penicillin G has proven its clinical efficacy for pharyngitis treatment)
	4 Absence of contraindications for the patient [no contraindication]	X	X
	Whether there is no absolute contraindication of the antibiotic for the
	patient profile (e.g. Pristinamycin is not contraindicated if the child is more
	than 6 years old)
	5 Convenient protocol [protocol]	X		X
	Whether the antibiotic is prescribed for oral administration AND for a
	duration of less than Z (*) days (e.g. Fosfomycin trometamol has a
	convenient protocol in uncomplicated cystitis)

6 Non-precious class [not precious] Whether the antibiotic doesn't belong to a class of drugs that must be preserved for more serious infections (e.g. Amoxicillin is a non-precious class in sinusitis) X X 7 Absence of serious and frequent side effects [no side e f ] Whether there is no serious side effects mentioned AND the frequency of side effects is sufficiently low for antibiotic prescription to be allowed (e.g. Fosfomycin trometamol gives no serious and rare side effects) X 8 High level of efficacy [e f f icacy level] Whether the antibiotic is described as very effective (high clinical cure percentage, e.g. Levofloxacin is very effective in prostatitis) X X 9 Narrow antibacterial spectrum [spect] Whether the antibiotic is described as having a "narrow" antibacterial spectrum (e.g. Nitrofurantoin has a narrow activity spectrum) X 10 Low level of ecological adverse effects [low eco risk] Whether the antibiotic is described as having a low risk of promoting bacterial resistance (e.g. Pivmecillinam has a low level of ecological risk) X 11 Taste [taste]

Table 2 :

 2 The 11 features of antibiotics in the knowledge base. The last four columns indicate on which the feature value depends. (*) Y and Z are values specific to each infectious disease.

Table 3 :

 3 2.0 ontology. It contains 144,038 RDF triples describing 5,696 classes, 19 properties and 34,483 axioms, and belongs to the ALC(D) family 2 of description logics (DL). Simple example showing the structure of the knowledge base.

	Case x a i (antibiotic) x s i (clinical situation) no contraindication no side e f	protocol ∈ Y reco
	x 1	Drug A	Situation X	False	False	False
	x 2	Drug B	Situation X	T rue	False	False
	x 3	Drug C	Situation X	T rue	T rue	False	yes
	x 4	Drug D	Situation X	T rue	False	T rue	yes
	x 5	Drug E	Situation X	Unknown	T rue	T rue
	x 6	Drug A	Situation Y	Unknown	False	False
	x 7	Drug B	Situation Y	T rue	False	False
	x 8	Drug C	Situation Y	T rue	T rue	False
	x 9	Drug D	Situation Y	T rue	False	T rue	yes
	x 10	Drug E	Situation Y	T rue	T rue	T rue	yes

Table 4 :

 4 Results of the learning process on the example of Table3.

		N j	w j Category
	no contraindication	0% -	Necessary
	no side e f protocol	50% 0.2 Preference 25% 0.3
	t ness t pre f	10%	0.5	Threshold

Table 5 :

 5 Example of Table3with the values of the utility function f (x i ) that are computed during preference learning, and indicating which cases belong to S k cand and S k reco .

	Case x a i (antibiotic) x s i (clinical situation) no contraindication no side e f	protocol ∈ Y reco f (x i ) ∈ S k cand ∈ S k reco
	x 1	Drug A	Situation X		False	False	False		-
	x 2	Drug B	Situation X		T rue	False	False		-0.5	yes
	x 3	Drug C	Situation X		T rue	T rue	False	yes	-0.1	yes	yes
	x 4	Drug D	Situation X		T rue	False	T rue	yes	0.1	yes	yes
	x 5	Drug E	Situation X		Unknown	T rue	T rue		-
	x 6	Drug A	Situation Y		Unknown	False	False		-
	x 7	Drug B	Situation Y		T rue	False	False		-0.5	yes
	x 8	Drug C	Situation Y		T rue	T rue	False		-0.1	yes
	x 9	Drug D	Situation Y		T rue	False	T rue	yes	0.1	yes	yes
	x 10	Drug E	Situation Y		T rue	T rue	T rue	yes	0.5	yes	yes
					M 1				M any
	j	Feature		N j	w j	Category	N j	w j		Category
	1	naturally active	3.9%	-		8.2%	-
	2 3	probably active proved	10.8% 1.0%	--	Necessary	15.3% 0.5%	--		Necessary
	4	no contraindication	3.9%	-		3.6%	-
	5	protocol		51.0%	0.26		52.0%	0.97
	6	not precious		41.2%	0.73		55.1%	0.16
	7	no side e f		42.2%	0.47		49.5%	0.25
	8	e f f icacy level	33.3%	0.0	Preference	40.8%	0.026	Preference
	9	spect		84.3%	0.0		89.8%	0.092
	10 low eco risk		81.4%	0.2		86.7%	0.052
	11 taste		100.0%	0.71		100.0%	0.98
				t

ness = 15% t pre f = 0.015 t ness = 20% t pre f = 0.77

Table 6 :

 6 Results of the learning process (N

j , learned weights and thresholds, for z = 1) for the two preference models M 1 and M any .

Table 7 :

 7 Categorization of the candidate inconsistencies obtained from preference learning. (*) The "total" column is not the sum of the two previous columns, because 26 inconsistencies were discovered twice, once with the M 1 model and once with the M any model.

		M 1	M any Total *
	Inconsistencies in CPGs
	Related to probably active	11	29	29
	Related to proved	6	8	11
	Related to no contraindication	5	9	9
	Related to spect	4	0	4
	Related to several features	2	0	2
	Flaws in the knowledge base
	Missing features	0	9	9
	Precision of the coding	5	3	7
	End of drug commercialization	0	1	1
	Flaws in the preference model
	Missing principles	3	7	7
	Genericity of the model	2	9	9
	Not categorized	12	7	18
	Total	50	82	106 *

Table 8 :

 8 Performance comparison between three metaheuristics: Artificial Feeding Bird (AFB), Artificial Bee Colony (ABC) and Firefly Algorithm (FA). # best is the number of times the best known result (82.0) was found, over the 20 runs.having protocol feature True but no contradiction False. If the learned preference model considers only preference features (e.g. no contradiction is preferred to protocol) as in most proposed learning preferences methods, then it is possible to recommend this antibiotic. However, in our proposed model, it cannot be recommended since the model contains also necessary features or constraints (such as no contradiction) which can be viewed as a propositional formula.

Acknowledgements

This work was supported by the French drug agency (ANSM, Agence Nationale de Sécurité du Médicament et des produits de santé) through the RaMiPA project AAP 2016.