Audrey Muratet
email: muratet@mnhn.fr

; Porcher

; Poncet

; Moret

A Robert

Biodiversity studies

Keywords: data quality, floristic diversity, monitoring, sampling effort, species richness Biodiversity studies

Large monitoring programs exist in many countries and are necessary to assess present and past biodiversity status and to evaluate the consequences of habitat degradation or destruction. Using such an extensive data set of the floristic richness in the Paris Ile-de-France region (France), we compared different sampling efforts and protocols in different habitat units to highlight the best methods for assessing the actual plant biodiversity.

Our results indicate that existing data can be used for a general understanding of site differences, but analysts should be aware of the limitations of the data due to nonrandom selection of sites, inconsistent observer knowledge, and inconsistent sampling period. The average species diversity recorded in a specific habitat does not necessarily reflect its actual diversity, unless the monitoring effort was very strong.

Overall, increasing the sampling effort in a given region allows improvement of the (i) number of habitats visited, (ii) the total sampled area for a given habitat type, (iii) the number of seasons investigated. Our results indicate that the sampling effort should be planned with respect to these functional, spatial and temporal heterogeneities, and to the question examined. While the effort should be applied to as many habitats as possible for the purpose of capturing a large proportion of regional diversity, or comparing different regions, inventories should be conducted in different seasons for the purpose of comparing species richness in different habitats.

Introduction

It is now widely recognized that the current extinction rates of plant and animal species are between a hundred and a thousand times higher than the background rates throughout life's history on Earth [START_REF] May | The future of biological diversity in a crowded world[END_REF]. However, documenting species extinction only, i.e. the most obvious manifestation of biodiversity loss, is not sufficient to develop effective conservation policies, partly because extinction rates carry no information regarding changes in community composition, which may have dramatic consequences for ecosystem stability [START_REF] Worm | Biodiversity, productivity and stability in real food webs[END_REF]. There is an urgent need to quantify the spatiotemporal changes in biodiversity by considering community composition and trends in species abundances (Convention on Biological Diversity in Rio, 1992). Such information is necessary to identify the mechanisms (e.g. environmental variables, human-induced disturbances, etc.) controlling the variation in species richness through space and time, as well as to identify sites of conservation concern and appropriate policies to improve the current biodiversity.

Ideally, this quantification would require large scale, long-term surveys based on standardized methodologies to allow comparisons in space and time. Such protocols already exist in a limited number of cases or are just starting to be implemented. The British Countryside Survey (CS) [START_REF] Firbank | Assessing stock and change in land cover and biodiversity in GB: an introduction to Countryside Survey 2000[END_REF][START_REF] Haines-Young | Changing landscapes, habitats and vegetation diversity across Great Britain[END_REF], for example, was established in 1978 in the United Kingdom and focuses on several taxonomic groups, including plants. The Biodiversity Monitoring Program (BDM) in Switzerland [START_REF] Weber | Scale and trends in species richness: considerations for monitoring biological diversity for political purposes[END_REF][START_REF] Plattner | Data quality in monitoring plant species richness in Switzerland[END_REF] was launched in 1995 and focuses on local plant diversity. Other protocols have been implemented to survey the diversity of particular taxonomic groups, as exemplified by breeding bird surveys in different countries (since 1966 in North America, [START_REF] Sauer | The North American Breeding Bird Survey Results and Analysis[END_REF]since 1994 [START_REF] Julliard | Common birds facing global changes: what makes a species at risk? Glob[END_REF]. Such surveys are based on formatted sampling protocols generally occurring twice a year within different discrete classes of habitat at the national scale. In these examples, the inventory protocol is generally standard and well defined, which allows the sampling effort to be homogeneous among observers, constant in time, or clearly quantified, so that any statistical inference can be made independently of the monitoring effort. Moreover, inventory protocols are designed to ensure that sampling is proportional to the area occupied by each habitat / settlement type in the region of interest.

Although such large scale monitoring schemes are crucial to document future changes in biodiversity, they will unfortunately not suffice to quantify the present changes in biodiversity, and specifically to evaluate the 2010 biodiversity target. A complementary approach to quantify changes in biodiversity could be to use the large amounts of existing inventory data collected by various biodiversity stakeholders (some of which are compiled in the Global Biodiversity Information Facility, GBIF 2008).

However, because such data come from a very large number of observers and geographic locations, they were generally collected using very different methodologies and are highly heterogeneous in nature. The question that immediately arises is whether such heterogeneous data can be exploited to document reliably the trends in biodiversity.

Here we address this issue using plant inventory data from Paris Basin (France).

We analyzed data from thousands of inventories carried out between 2001 and 2005 by botanists who were involve in the same Botanical Conservatory but who were not instructed to follow a given standardized protocol. Focusing on the proportion of total Biodiversity studies 6/27 vascular plant species detected as a function of (1) annual number of visits per habitat type and (2) season of data collection, we investigated different options for data analysis and survey protocol, to optimize the use of existing data and improve future monitoring.

We specifically addressed the following questions: 1) Are one time surveys of floristic diversity indicative of the total diversity of a region, and do species richness estimated from one time surveys vary across habitats, seasons and years? 2) What is the benefit of increasing survey effort, by increasing either the number of survey habitats or the time span of surveys? Biodiversity studies 7/27

Material and methods

Study area

The Ile-de-France region, including the city of Paris (48°68' N; 0°17' E) and the surrounding area, covers 12,072 km² (Fig. 1). The climate is oceanic with continental trends (mean annual temperature 12 °C, with a minimum in January and a maximum in July; average monthly rainfall 57 mm) and the relief is relatively flat (elevation between 11 and 217 m a.s.l.). The population density is 952 inhabitants/km² (INSEE 2006), which makes Ile-de-France the most densely populated administrative region of France.

A total of 1225 plant species were encountered in the study area between 2001 and 2005, as calculated from records of the FLORA database (National Botanical Conservatory of the Paris Basin, CBNBP 2008 and see below for a description of the database). Of these species, 11% were naturalized species, i.e. non-indigenous species that reproduce and sustain populations without direct intervention by humans [START_REF] Richardson | Naturalization and invasion of alien plants: concepts and definitions[END_REF].

Inventory protocol

The data used in this study were collected between 2001 and 2005 by botanists from the National Botanical Conservatory of the Paris Basin (hereafter CBNBP), a

French public organization aiming to study and protect the flora of the Paris basin. One central objective of CBNBP is to describe the geographical distribution of all species growing in the area, which dictates the methodology used to collect data. Every year, a total of 149 botanists (both professionals and competent amateurs) visited the 'communes' (French administrative municipalities) of the region between March and October and recorded as many plant species as they could observe within a Biodiversity studies 8/27 municipality, as well as the spatial locations of each species. There was no standardized protocol: the duration of data collection, sampling locations and total area sampled were left to the appreciation of the observers and varied greatly among individuals. For example, sampling locations within a municipality were not randomly distributed, but were instead usually chosen to maximize the total number of species observed.

Database contents and study data

Inventory data were pooled in FLORA, a database built by CBNBP. The database includes information on species (scientific and common names), observer, date of observation, location (municipality) and habitat type according to CORINE land cover nomenclature [START_REF] Bissardon | Biological Diversity in Rio[END_REF], and contains more than one million observations (i.e. one species recorded at a given time and in a given site) for the Ile-de-France region (CBNBP 2008).

We chose to work with data collected between 2001 and 2005, because the quality and quantity of data are much lower before this period. For statistical reasons, we also discarded all observations from rarely sampled habitats, i.e. habitats that were visited less than once a month between 2001 and 2005, so that data from eight habitat types only were retained (see Table 1). For this study, this yielded a total of 237,884 observations corresponding to 7,358 different sites (i.e. the total area covered by a given habitat type in a given place) within the Ile-de-France region.

Data analysis

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Because the database contains very little information on species abundance or frequency, and does not allow estimating species detection probabilities, plant communities were characterized by the observed species richness only.

Species richness at the site level

We first analyzed the variation in species richness at the site level by fitting an analysis of variance model using the R software (Core Team 2007), where site richness was a function of (1) habitat type (2) inventory month, (3) inventory year, and (4) all pairwise interactions.

As this analysis showed statistical differences among years on the richness recorded, all years were considered separately in subsequent analysis.

Assessment of optimal monitoring effort

To optimize monitoring programs, monitoring effort should be minimum, but large enough to provide accurate estimates of species richness (and, ideally, other parameters of community composition). To evaluate this, we performed random resampling in the database to simulate various monitoring efforts, by varying the number of sites, habitats, or months sampled.

a) Increasing effort within a given habitat

To estimate the species accumulation curve within each habitat type, we plotted the ratio of observed vs. total species richness as a function of the number of inventories, x, as follows. Within a given year, x inventories (= x sites) were sampled at random, each in a different month, and the overall species richness (excluding redundancies) of this sample was computed. This species richness was then divided by the total number of species observed in this habitat type. For each x and each habitat Biodiversity studies 10/27 type, the procedure was repeated 50,000 times and the average ratio of observed vs. total species richness was plotted.

b) Correlation between sampled and total species richness

To test whether the number of species recorded in x inventories was representative of the "true" floristic richness of the different habitats, we compared the number of species recorded in x inventories within a year in each habitat to the overall number of species in each habitat, using a Spearman rank correlation across habitats.

This procedure was performed 50,000 times for each habitat, and the average correlation coefficient, rs, as well as the proportion of significant correlations at the 5% level were plotted as a function of the number of inventories per habitat, x.

c) Optimization of the number of habitats or months sampled

We compared the benefit of increasing the number of months or the number of habitats sample, given a constant effort. To this end, we plotted the observed species richness as a function of number of habitats (respectively months) visited, with a constant number of inventories. Keeping the number of inventories (8) constant allowed us to test for a habitat or month effect without confounding area effects. Within a given year, eight sites were chosen at random among x habitat types (respectively months) and the overall species richness in these eight inventories (i.e., excluding redundancies) was computed. The procedure was repeated 50,000 times and the average species richness in x habitats (respectively months) was plotted against the number of habitats (months).

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Results

Variation in average observed species diversity

Site species richness varied significantly across years, months (maximum species richness in June (36.5), minimum in August ( 28)), and habitat types (maximum number of species in cities and industrial sites (41), minimum in stagnant freshwater (18), Table 2). In addition, all interactions were also significant, so that the difference in species richness among habitats were highly variable within and across years (Table 2).

Species accumulation curves within habitats

The shape of the species accumulation curves varied greatly across habitats (Fig. 2). The proportion of total species recorded appeared to reach a plateau at five inventories per habitat in mesophile meadows, cultures, cities and industrial sites or wastelands. Note however that the fraction of total species observed remained low (between 15 and 25%). In contrast, the species accumulation curves did not appear to saturate in stagnant fresh water, circle of water edges, deciduous forest or urban parks and gardens.

Correlation between observed and total species richness across habitats

As expected, the correlation between observed and total species richness across habitats was close to zero and non-significant when the number of inventories per habitat was small (x < 6, Fig 3). However, seven or eight inventories per habitat provided a better picture of the total species richness (Spearman correlation coefficient significantly different from 0, Fig. 3a). Note however that mean correlation coefficients remained relatively low (fig 3a), suggesting that yearly monitoring protocols with few Biodiversity studies 12/27 inventories in each habitat do not allow to compare species richness in the different habitats.

Optimization of monitoring effort by increasing the number of habitats or months

As expected, observed species richness increased (+ 12%) when the number of habitats increased for a constant monitoring effort. Similarly, there was a lower but non negligible benefit (+7%) of increasing the number of inventory months.

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Discussion Biodiversity inventories are costly in time and money, and maximizing the number of species observed during a given monitoring effort is therefore an important task. Our study focuses on the use of existing, non standardized inventory data to address the optimization of monitoring effort.

Non-standardized data and minimal monitoring effort

Our results reflect the well-known heterogeneity of plant communities in time (year) and among habitat types: the observed species richness depends on the habitat, season, year and their interactions. When dealing with non-standardized data, this raises the issue of how to disentangle actual ecological sources of heterogeneity (e.g. true differences among habitat, seasons, years…) from sampling or methodological sources of variation. In particular, owing to the lack of randomization and to observer variability, among-inventory differences in species richness were not only due to differences in the period of sampling (month and year), but also to differences in sites themselves (inventories performed in different months were not necessarily conducted on the same sites). This for example implies that classical methods to estimate species richness (e.g. those derived from the CAPTURE program, [START_REF] Rexstad | User's guide for interactive program CAPTURE[END_REF] cannot be used with such non-standardized inventory data. Hence, total species richness in a given habitat was estimated as the total number of species observed over a large number of inventories. Although this probably results in an underestimation of species richness, we nonetheless believe that it provided a reasonably good picture of community composition.

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General guidelines about minimal monitoring efforts can be inferred from the results above. We showed that one to five yearly inventories per habitat do not provide an accurate picture of habitat richness (Fig. 4), at least in the semi-natural habitats commonly encountered in Île-de-France. Sampling effort is clearly an important issue regardless of the survey method used [START_REF] Metcalfe-Smith | Effect of sampling effort on the efficiency of the timed search method for sampling freshwater mussel communities[END_REF][START_REF] Walther | Species richness estimation of bird communities: how to control for sampling effort[END_REF], and other studies have reached similar conclusions regarding minimal sampling efforts. For example, De [START_REF] Solla | Effect of sampling effort and species detectability on volunteer based anuran monitoring programs[END_REF] showed that, in anuran monitoring programs, the average observed species richness was only 25.1% of the total richness with a single sampling night, but reached an average of 80% of the total species richness with 12 sampling nights. [START_REF] Archaux | Effects of sampling time, species richness and observer on the exhaustiveness of plant censuses[END_REF] showed that on 400 m² forest quadrats, the level of exhaustiveness of plant censuses increased in a semi-logarithmic way with sampling time. The study of [START_REF] Estevez | Analysis of the movement and use of space of animals in confinement: The effect of sampling effort[END_REF] Although the information collected in the aforementioned monitoring programs is useful to document long-term trends, or to compare trends among habitat types (especially for the most frequent species, and when directional variations in species Biodiversity studies 15/27 abundances are high), our results suggest that it will not be sufficient to compare the absolute species numbers present in the different habitat types. In the present data set, the variability across observers and sites tended to overwhelm the differences among habitat types when there were fewer than six inventories per year (Fig. 4), which represents a large monitoring effort in comparison with most survey programs.

Optimization of sampling effort

The outcome of a given protocol depends, among others, on the area sampled as well as on seasonal and habitat effects, so that the sampling effort should be judiciously planned and implemented to optimize the number of species recorded. In general, the financial and time costs of a field inventory do not vary across seasons or habitat types and protocols can be optimized via a selection of seasons and habitats visited. For example, with a constant effort, the observed species richness was increased by 6.5% if inventories were conducted in two different seasons vs. a single season, and by 11 % if they were conducted in two vs. one habitats. This is consistent with the generally accepted idea that plant functional beta diversity is larger than seasonal beta diversity.

However, the choice of maximizing either the number of seasons or habitats sampled should depend on the question investigated.

If a monitoring program aims to maximize recorded species richness in the study region (e.g. for the purpose of comparing biodiversity across regions or examining annual trends), maximizing habitat types would be the most efficient strategy. In fact, our results indicate that (i) increasing the number of habitats is always more efficient than increasing the number of months; (ii) beyond three months, any further increase in the number of months sampled has no notable effect on the observed species richness Biodiversity studies 16/27 for a constant number of sites visited (Fig. 4). In contrast, to compare species richness across habitats, inventories should be conducted throughout as many sites as possible to ensure that actual differences among habitats can be detected. Assuming that the total species richness was a proxy for true total species richness, we showed that the average species richness observed during a single inventory per habitat was not representative of total richness. First, the average species richness observed in a single inventory was only 4.24 ± 2.84 % of total richness on average. Second, (b) observed richness is not representative of the total richness of the habitat unless the sampling effort is extremely strong (> 5 inventories a year, figure 3). It follows that for a constant sampling effort, among habitat comparisons require to use few habitats with many inventories per habitat.

Conclusion

There is general agreement that biodiversity conservation should be guided by biodiversity assessment. As an important part of this assessment, inventory protocols should be designed with care, to identify the specific conservation target that a project ultimately would like to influence [START_REF] Salafsky | Improving the Practice of Conservation: a Conceptual Framework and Research Agenda for Conservation Science[END_REF]. Ideally inventories should include (1) sites randomly sampled according to a standard protocol (for example, using a sampling effort stratified by habitat types), (2) observers with a knowledge level as uniform as possible (3) identical observation periods. As we promote these goals we will promote high quality data for monitoring and other purposes. Existing large data sets collected by various biodiversity stakeholders do not generally meet these criteria, and they should be used with caution to infer biodiversity trends, e.g. in combination Biodiversity studies 17/27 with resampling methods to correct for their heterogeneity. The large number of existing inventory data can however be exploited to address other conservation issues, e.g. to quantify floristic index over a homogeneous region [START_REF] Muratet | Evaluation of floristic diversity in urban areas as a basis for habitat management[END_REF]

  on the movement of animals in confinement clearly indicated that sampling effort had a tremendous impact on the study outcome. Nonetheless, several European countries have started to implement floristic monitoring programs, generally based on one or two inventories per year. For instance, in the United Kingdom, the British Countryside survey (Haines-Young et al. 2000) is based on annual inventories of several hundred of randomly sampled fix plots classified into 32 land use classes. In Switzerland, The Biodiversity Monitoring Program (Hintermann et al. 2002) consists in a grid-sampling program based on five settlement types within which plots are randomly drawn. The local plant diversity is inventoried in these plots every five years.

FiguresFig. 1 Fig. 2

 12 Figures

Fig. 3 Fig. 4

 34 Fig. 3 Correlation between overall and recorded species richness in the different

  in UK,Newson et

	Biodiversity studies
	al. 2005; since 1989 in France,
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Table 1

 1 . Description of habitats types. The distribution of the number of inventories across habitat types between 2001 and 2005 and the spatial distribution of habitats

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Table 2

 2 Result of the analysis of variance, where site richness was a function of (1) habitat type (2) inventory month, (3) inventory year, and (4) all pairwise interactions.

	405

Acknowledgments

We thank Gérard Arnal and Sébastien Filoche of the CBNBP, coordinators of the floristic inventories in the Paris Ile-de-France region. Emmanuelle Porcher was partly funded by Agence Nationale de la Recherche (ANR Grant #2006-JCJC-0032).

Biodiversity studies 19/27


Johanne Bakalara

Temporal models of care sequences for the exploration of medico-administrative data

Keywords: Temporal logics, Ontologies, pharmacoepidemiology

Pharmacoepidemiology with medico-administrative databases enables to study health products impact in real-life settings. However, querying this data in a medical perspective is still a challenge because of the complexity of temporal constraints for medical patterns. This PhD thesis aims at proposing a formal framework for the analysis of temporal medical patterns that would support a well-founded tool for querying care trajectories. This paper presents our problematic and introduce a use-case which illustrates the comparison of several querying formalisms.

Introduction

Pharmacoepidemiology studies the benefits and risks of drugs usage on population in real life settings. As such, pharmacoepidemiology deals with positive impact as well as safety concerns. Patients with health events are identified according to their individual characteristics, their treatments and their concomitant treatments. Collecting information to answer one specific epidemiological question requires a lot of time and is very expensive. Using medico-administrative databases is an attractive potential alternative because of their large population coverage and their availability. For instance, the SNDS 3 database contains individual information of French patients: age, sex, location; and health reimbursement information: drug deliveries, medical acts or medical visits and hospitalisations (date of arrival, leaving date, diagnosis code) but it does not contain medical reports. The interest of using this medico-administrative database has been demonstrated by the suspension of benfluorex [START_REF] Weill | Benfluorex and valvular heart disease: a cohort study of a million people with diabetes mellitus[END_REF].

Epidemiologists use the SNDS database to find patients that experienced some medical events of interest. All the medical events that are stored in the database compose the care trajectory of a patient. For epidemiologists, the challenge is to define selection criteria that would reconcile those actual patient information with the medical semantic. The definition of these criteria composes a health pattern called care pathway. For example, the care trajectory of a patient "delivery at date t of anticoagulant with ATC code B01AF01 " would match the care pathway "patients exposed to anticoagulant for 3 to 6 months under the assumption of a monthly delivery".

The problem that we address is to enable epidemiologists to query the database of care trajectories with care pathways. The complexity is twofold:

use of ontological concepts ("Doppler imagery act"/"anticoagulant"/"vascular specialist"): the code of the medical act performed on a patient is given, but is more precise than the criterion "anticoagulant drug" and symbolic domain knowledge is required to reconcile both. Here ,"Anticoagulant" refers to a class of drugs that is described in the ATC taxonomy. 4 use of temporal constraints ("in the week after"/"within 4 months"): the temporal order of cares, numerical duration/delays specifies the temporal organisation of the events.

Problem statement

The objective of this work is to propose a formal framework that would support a well-founded and efficient tool for querying care trajectories in the context of pharmacoepidemiology.

Generally speaking, let T = (T i ) i∈[n] be a set of n care trajectories and ϕ a care pathway abstract description. ϕ holds in a care trajectory T ∈ T , denoted T |= ϕ, iff the care trajectory verifies the care pathway. The formalisation problem is threefold, we define:

a formalism to model care trajectories, T , which represent the SDNS data a formalism to model care pathways, ϕ, which specifies an abstract care pathway a computational model that can evaluate whether T entails ϕ: T |= ϕ.

As we noticed in the introduction, specifying care pathways requires to manipulate: temporal concepts (time constraints and time window), medical concepts and knowledge (ontologies). The ideal formal framework should capture these dimensions, enable intuitive queries to be expressed for a wide range of pharmacoepidemiological studies and be computationally efficient.

It is of paramount importance to base choices on solid theoretical foundations. Expressiveness and efficiency are known to be antagonist objectives [START_REF] Levesque | Knowledge representation and reasoning[END_REF]. A wellfounded approach would be the basis for proposing long-term solutions, make possible future improvements and facilitate its application to a broad range of contexts (i.e., various databases, queries).

Related works

This section presents four families of formalisms related to the problem: model checking; Complex Event Processing (CEP); temporal databases; and Knowledge Representation and Reasoning (KR). The formalism should represent data (care trajectories), query (care pathway) and compute the answers of the queries on data. The last two families have been further explored in medical context [START_REF] Combi | Temporal information systems in medicine[END_REF] than the two others.

Model checking [START_REF] Clarke | Model checking[END_REF] verifies if a model satisfies a property or a formula. This research line is interested in representing dynamic systems with formal temporal formalisms (discrete event models, M, describing how the system evolves) to prove some properties specified by formula ϕ. A formula ϕ is true iff ϕ is true for any trace that can be generated from model M. The most common formalisms for timed formula in Model Checking are LTL, CTL or MTL (temporal LTL).

To apply such methods in our context, the events of care trajectory are represented by one finite trace of the system (and there is no system model in our case) and the care pathway is represented by a timed logic formula. The care trajectory is selected iff the trace satisfies the formula. These methods are interesting because they provide formal results (expressiveness, completeness, equivalences) on the representation of timed systems, but they neither manage reasoning nor ontological representation. In the medical domain, model checking has been used to study the compliance of care pathways [START_REF] Bottrighi | Adopting model checking techniques for clinical guidelines verification[END_REF].

Complex Event Processing (CEP) [START_REF] Giatrakos | Complex event recognition in the big data era[END_REF] is a research line that aims at processing log-streams with patterns. Log-streams are streams or sequences of timed events. The CEP processes these logs to detect or to locate complex events (or patterns) defined by the user. This domain defines formalisms that aim at being very efficient to process streams and expressive to specify patterns. Temporal constraint networks [START_REF] Cabalar | Temporal constraint networks in action[END_REF] or Chronicles [START_REF] Dousson | Chronicle recognition improvement using temporal focusing and hierarchization[END_REF] are simple temporal models that are interesting for their graphical representation, but are limited to simple events. Some more complex formalisms, e.g. ETALIS [START_REF] Anicic | ETALIS: Rule-based reasoning in event processing[END_REF] or logic-based event recognition [START_REF] Giatrakos | Complex event recognition in the big data era[END_REF] propose very expressive representations of complex events, including reasoning techniques (encompassing ontologies) which enrich the CEP capabilities.

In our context, care trajectories are logs, and care pathways are the complex events. We are not interested in the stream dimension, but their formalisms to represent complex events can be adapted in the context of static logs.

Temporal databases [START_REF] Snodgrass | Temporal databases[END_REF] extend the notion of database to timestamped data. Databases cover data representation problems but also specific querying language problems. This family encompasses the temporal extension of relational databases (e.g. TSQL) but also Semantic Web approaches which combine query languages (e.g. SPARQL) and expressive description languages. Care trajectories are facts in the temporal database and the querying of care pathways becomes a problem of specifying care pathways in the query language. [START_REF] Rivault | queryMed: Semantic Web functions for linking pharmacological and medical knowledge to data[END_REF] shown that the Semantic Web is a relevant approach for our problem, but does not explicitly address the problem of timed queries.

Finally, Knowledge Representation and Reasoning (KR) [START_REF] Levesque | Knowledge representation and reasoning[END_REF] is "the study of how what we know can at the same time be represented as comprehensibly as possible and reasoned with as effectively as possibly". In this research domain, temporal KR is focused on representing and reasoning about time. It gives rise to several logics [START_REF] Long | A review of temporal logics[END_REF], for instance: Allen's logic, McDermott's logic, Event Calculus or Halpern & Shoham's logic. KR is a general framework to study how to represent care trajectories and how to model reasoning-based queries on care pathways. Approaches from the other families may be represented with appropriate logics. Studying KR formalisms seems of paramount importance as it provides common foundations to compare various approaches. Description Logic (DL) [START_REF] Baader | The description logic handbook: Theory, implementation and applications[END_REF] is a KR formalism allowing ontology-mediated query answering (OMQA) [START_REF] Bienvenu | Ontology-mediated query answering: harnessing knowledge to get more from data[END_REF]. Artale et al. [START_REF] Artale | Ontology-mediated query answering over temporal data: A survey[END_REF] present a temporal extension of DL that may be suitable for our problem. For instance, [START_REF] O'connor | Knowledge-data integration for temporal reasoning in a clinical trial system[END_REF] developed a tool based on OWL for research data management with a temporal reasoning in a clinical trial system. [START_REF] Bienvenu | Ontology-mediated query answering: harnessing knowledge to get more from data[END_REF] Comparison of approach on a use case

Rational

This section introduces a real use case. In this example, pharmacoepidemiologists want to select patients with Venous Thromboembolism (VTE) from the data contained in the SNDS. Venous thromboembolism, i.e. deep vein thrombosis (DVT) or pulmonary embolism (PE), is a frequent and potentially fatal disease [START_REF] Delluc | Real-world incidence of cancer following a first unprovoked venous thrombosis: Results from the EPIGETBO study[END_REF][START_REF] Oger | EPI-GETBO: Incidence of venous thromboembolism: a community-based study in western france[END_REF]. The motivation is to survey how many people are concerned, if the number of patients increased and if a specific drug has an impact. The difficulty for epidemiologists lies in the description of the care pathways that will accurately identify VTE from the SNDS data. The description below describes two care pathways that physicians proposed to identify VTE.

In clinical practice facing a clinical suspicion of VTE, physicians first prescribe anticoagulant and then confirm or not the diagnosis through specific medical acts: for instance Doppler ultrasonography or CT scan. Patients with suspected PE are often hospitalized whereas patients with suspected DVT are managed on a ambulatory basis. If the suspicion is confirmed, anticoagulant deliveries continues for 3 to 12 months or sometimes longer duration. Hence, diagnosis (through medical act) is preceded or followed by anticoagulant initiation within a time window of at most 1 to 2 days, keeping in mind that PE suspicion leads to hospitalisation during which medical act to confirm the diagnosis are performed and then anticoagulant is observed only after the patient comes back home.

Through these observations, pharmacoepidemiologists identified the following two care pathways to detect patients with VTE from SNDS data:

1. A diagnosis (DVT or PE) or a medical act (Doppler or CT scan) during or prior to anticoagulant (AC) deliveries for 1 to 2 days and delivery lasts a minimum of 3 months and a maximum of 12 months (sometimes longer). Each delivery is separated by 0 to 2 months. 2. A diagnosis PE during an hospitalisation followed by AC delivery. These care pathways are ordered and also contain time constraints between events (for instance number of days) or duration of events (time window). Searching for such patterns requires high expressiveness that make databases query B01(Pierre, n1) B01(Pierre, n2) P E(Pierre, n3) B01AF 01(Paul, n1) B01AF 01(Paul, n3) EDQM 001(Paul, n4) n1 < n2 < n3 < n4 languages (SQL, TSQL) practically difficult to use. The next section illustrates formalisms that will allow the generalization of the representation of care pathways and care trajectories. Note that this use case illustrates the problem of formalizing care pathways of patients suffering from VTE. But, for sake of generality, our formalism has to specify the care pathway patterns of a broad range of care studies.

Fig. 1. ABox B01AF 01 B01AF B01AF B01 B01 B Fig. 2. TBox D D [0,60] D [0,60] VTE [-92,1] (♦D ∧ (♦D) ∧ (♦D)) ∧ (♦(DV T ∨ P E)) ♦(DV T ∨ P E) ⇒ ((♦ [0 24] D) ∧ (♦ [0 60] D) ∧ (♦ [0 60] D) ∧ (♦ ≥365 ( (¬D)))

Comparison of different models

This section illustrates several formalisms: Description Logic (DL) to represent care trajectories and Chronicles, LTL and MTL to express queries. These queries represent care pathways. We discuss their expressivity in our use case.

DL is used to describe and to reason about concepts on data. The first one consists in defining the data and the data form (called ABox ) which contains knowledge at the instance level: a set of assertion defining concepts, roles and a countably infinite set of individuals names. Concepts with individuals names and roles with individuals names are forming atoms.

The second step is to define a base of knowledge (TBox ) which is a set of concepts inclusions. For instance, the concept B01AF 01 (Rivaroxaban) representing anticoagulant drugs is the leaf concept in the hierarchy of concept modeling the ATC classification: B01AF (Direct Xa inhibitor), B01 (Antithrombotic agents) and B (Blood and blood forming organs).

Considering the CCAM (medical acts) code for the Doppler: EDQM 001 (iliac and lower limb arteries), we could construct the ABox of Fig. 4.2, where Pierre and Paul are patients and n i are dates of medical events. TBox of Fig. 4.2 is issued from the previous ATC classification.

The third step is to define a query to extract information from knowledge contained in ABox and TBox. Usually, queries are expressed with a first order logic. [START_REF] Artale | Ontology-mediated query answering over temporal data: A survey[END_REF] designed a temporal DL: TQL that extends the standard ontology language: OWL 2QL. However, to express queries with temporal delays, several formalisms seem to be adapted. For example, the chronicle formalism represents a care pathway as a temporal constraint graph. Chronicles allow the expression of sequential order of events with temporal constraints such as interval of time. Furthermore, negative time in the interval expresses that an event may occur before or after another one. Fig. 3 specifies patients having at least three AC deliveries separated by 0 to 60 days, and a diagnosis DVT before, after or during deliveries. DVT occurs 92 days earlier or one day after the third delivery. However, we can not explicitly restrict the number of deliveries to 12 months as defined in the use case. We also can not use the notion of no event (event does not occur).

Model checking offer the possibility to express no event. Such as an example we propose the LTL formula Fig. 3 as an example applied to our case of study:

The LTL formula represents a care pathway with at least three deliveries and a diagnosis DVT or PE. We literally read it: in the future (♦), there is the delivery of B01 and (∧) it is followed ( ), in the future, by the delivery of B01 and it is followed, in the future, by a delivery of B01 and, in the future, there is a DVT (or ∨) PE) diagnosis. LTL only contains ordered events and does not contain time constraints. The expressivity of such formula is too limited for our problemThe MTL formula adds the capability to express quantitative temporal constraints. Fig. 3 is a MTL formula which represents a care pathway with a DVT or PE followed by three AC deliveries separated between 0 to 60 days, and no deliveries occur after 365 days. MTL can explicitly restrict the number of deliveries and temporal constraints but the notion of sequences is manually found by the multiple use of ♦.

From a computational aspect, chronicle recognition is a space/time-efficient task. Simple LTL formula would also be space/time-efficient to check but it is expressively poor. In contrast, MTL is more expressive but it is known to be undecidable. This is a theoretical limitation but not necessarily a practical constraint [START_REF] Ouaknine | On the decidability of metric temporal logic[END_REF].

Conclusion

Current researches are based on comparing temporal models and on studying their suitability for pharmacoepidemiology studies. Participating to this doctoral consortium would be an opportunity to discuss existing temporal model in medical applications and to identify other similar use cases that will highlight other needs. Expectation from the doctoral consortium is to guide me for the future evolution of my thesis.

Fig. 3 .

 3 Fig. 3. Example of care pathway representation of the case study in three formalisms. Top left: Chronicles, top right: LTL formula and bottom: MTL formula (D denotes an anticoagulant delivery event).

SNDS: French National System for Health Data (previously SNIIRAM).

Acknowledgments This multidisciplinary PhD thesis began six months ago. It is supervised by the pharmacoepidemiologist E. Oger in the REPERES team and by computer scientists, T. Guyet and O. Dameron in the IRISA laboratory, and A. Happe in the REPERES team.