Emmanuelle Véronique Delcroix
email: vdelcroi@uphf.fr

Grislin-Le Strugeon

François Puisieux
email: francois.puisieux@chru-lille.fr

A knowledge based system for the management of a time stamped uncertain observation set with application on preserving mobility

Keywords: information aging, uncertain information, information quality, probabilistic model, knowledge based system, reasoning with uncertainty, health application

The aim of this study is to maintain up-to-date information about the current state of elderly people that are medically followed for risks of fall. Our proposal consists of an individual information database management system that can provide information on-demand on various variables. Such a system has to deal with several sources of uncertainty: lack of information, evolving information and reliability of the information sources. We consider that the features of the person may evolve with time causing uncertainty due to obsolete information.

Our context includes new information received bit by bit, with no possibility to collect all required information at once. This paper establishes a first proposal to manage a set of uncertain observations, in order to reduce erroneous and obsolete information while keeping the benefit of previously collected information.

We propose an architecture of the system based on a probabilistic knowledge model about the characteristics of interest, a set of decay functions that help to evaluate the confidence degree in previous observations, and a reasoning module to manage new observations, maintain the compatibility and the quality of the observation set. We detail the algorithms of the reasoning module, and the algorithm to update the confidence degree of the observations.

Introduction

The temporal dimension is naturally present in medical reasoning, since situations change, events happen and most properties vary with time [START_REF] Combi | Temporal Information Systems in Medicine[END_REF]. For these reasons, the temporal dimension is a source of uncertainty in elderly persons fall prevention. In this domain, recommendations are made by specialists on the basis of information related to the health and environment of the person [START_REF]American Academy of Orthopaedic Surgeons Panel on Falls Prevention, Guideline for the prevention of falls in older persons[END_REF][START_REF] Bourdessol | Prevention of falls in the elderly living at home, Good Practice Guide, collection Référentiels, INPES[END_REF]. The reasoning to identify adequate recommendations is based on a detailed "snap-shot" of the person and her situation, such as loss of muscle mass, bone fragility, sedentary life style, fear of falling, previous falls, living alone, etc. These are high level static variables that summarize useful temporal patterns. However, it is generally not realistic to collect all this information just at the time it is required. The solution is to use information collected in the past.

But this information may have become obsolete, because of aging or changes in the life of the person. We thus have a situation where information aging and incomplete observations generate uncertainty. We also have to deal with uncertainty due to the natural variability of human characteristics, and incomplete information and knowledge. Finally, an additional source of uncertainty comes from the information sources, since a value can be misread, or a dysfunctioning sensor can provide erroneous data.

The problem is thus to maintain an uncertain observation set with an incomplete data collection over time, in order to provide on-demand reliable information regarding the person's state. This requires to evaluate whether the value (or state) of a variable has changed since it was observed. In this problem, time is involved together with uncertainty since only few properties are timeinvariant, and because of incomplete and uncertain observation over time and information aging.

In order to illustrate the problem of dealing with an uncertain observation set, consider the following two pieces of information about a given person: when we know that she lives alone, we set A = a, else A = ā; when we know that she lives in a retirement home, we set B = b, else B = b. Since living in a retirement home implies not to live alone, the configuration (A = a, B = b) is impossible. This is translated in a general probabilistic model by P (A = a, B = b) = 0, also denoted by P (a, b) = 0. Now let's consider two uncertain observations about that person: the first uncertain observation o A is given by the likelihood vector π A = (0.9, 0.1), stating that it is nine times more likely to observe o A when A = a than when A = ā. The second observation o B is given by the likelihood vector π B = (0.2, 0.8). Since these observations are collected separately, they do not provide information of the likelihood of the four possible combinations of A and B. From the observation set {o A , o B }, the combination (a, b) cannot be excluded whereas it is excluded in the general probability distribution P . This example illustrates the question of the compatibility of an uncertain observation set with a general probabilistic model of knowledge. In this article, we propose the notions of total and partial compatibility in order to model different kinds of possible situations regarding this question. The objective is to maintain the compatibility in a knowledge based system for the management of an observation set when integrating new and uncertain observations. This problem lies at the intersection of the domains of uncertain information fusion [START_REF] Dubois | The basic principles of uncertain information fusion. An organised review of merging rules in different representation frameworks[END_REF], dynamic, iterated, belief revision [START_REF] Papini | Knowledge-base revision[END_REF][START_REF] Dubois | Belief change rules in ordinal and numerical uncertainty theories[END_REF] and temporal reasoning [START_REF] Fisher | Handbook of Temporal Reasoning in Artificial Intelligence[END_REF][START_REF] Combi | Temporal Information Systems in Medicine[END_REF].

The problem is to aggregate observations made at different times with static generic knowledge. Three types of belief change are generally distinguished to address the problem of adding new information to a logical theory [START_REF] Revesz | On the semantics of theory change: Arbitration between old and new information[END_REF][START_REF] Dubois | Belief change rules in ordinal and numerical uncertainty theories[END_REF]: revision, update and arbitration. Our problem context relates to these questions, with additional dimensions of uncertainty, needing other approaches than logical theory.

Information aging has recently acquired a specific interest in the domain of web information. In this domain, the way events and information spread in social networks and news pages is particularly studied. For instance, aging theory is used to model the variations in the quantity of publications related to a topic or an event [START_REF] Chen | Life cycle modeling of news events using aging theory[END_REF][START_REF] Paik | Parameterized decay model for information retrieval[END_REF][START_REF] Sendi | Discovery and tracking of temporal topics of interest based on belief-function and aging theories[END_REF]. To address this problem that shows similarities with ours, the temporal decreases are modeled by decay functions. Decay functions are also used in the domain of sensor data to manage the aggregation of data with different ages: the older is the data, the lighter is its weight in the aggregated data summary [START_REF] Cormode | Time-decaying sketches for sensor data aggregation[END_REF].

Temporal reasoning is addressed by several formal theories of time, including temporal logics, temporal constraints and temporal reasoning techniques [START_REF] Fisher | Handbook of Temporal Reasoning in Artificial Intelligence[END_REF].

About temporal reasoning with uncertainty, a well-known model is the qualitative algebra of time, based on intervals, proposed by Allen [START_REF] Allen | Maintaining knowledge about temporal intervals[END_REF][START_REF] Allen | Towards a general theory of action and time[END_REF]. This model allows to represent imprecise temporal events and is suitable when the variables have a specific duration, but it does not allow to express uncertainty in events or their temporal relationships [START_REF] Van Der Heijden | Describing disease processes using a probabilistic logic of qualitative time[END_REF]. In our context, the variables related to the state of a person can keep stable for years and progressively or suddenly change (e.g., leg strength weakness, goes out, drives or alcohol variables) An interesting alternative is proposed by the probabilistic graphical models, which offer diverse solutions to the problem of temporal reasoning with uncertainty. These models have proven their utility and feasibility in the medical domain, see the detailed presentation of temporal extensions of Bayesian networks used in clinical domain in [START_REF] Orphanou | Temporal abstraction and temporal Bayesian networks in clinical domains: A survey[END_REF]. Dynamic Bayesian networks (DBNs) [START_REF] Murphy | Dynamic Bayesian networks: Representation, inference and learning[END_REF] are temporal probabilistic graphical models that model complex multivariate time series or sequences. However, DBNs are not adapted to our problem since the variables that we consider evolve according to different time scales, making hard the choice of a temporal granularity. Using a small discrete time step would lead to a DBNs with a huge number of slices, making the model intractable. In Continuous Time Bayesian Networks (CTBN) [START_REF] Nodelman | Continuous time Bayesian networks[END_REF], the states of variables evolve continuously over time, and the evolution of each variable depends on the state of its parents in the graph. Although possibly well-adapted to our problem, CTBNs construction requires a level of resource that would be too high regarding the size of the targeted model (this is discussed in the last section of the paper). Irregular-Time Bayesian Networks (ITBN) [START_REF] Ramati | Irregular-time Bayesian networks[END_REF] are another extension of Bayesian Networks that includes a representation of time. ITBNs generalize Dynamic BNs to model irregularities in the time intervals between observations. They allow to remove the constraint of a constant time distance between consecutive observations that is required by the Dynamic BNs. Like CTBNs, ITBNs can represent variables with different time slices. Unlike CTBNs, ITBNs are well adapted to model variables having a continuous state space [START_REF] Liu | A comparison between discrete and continuous time Bayesian networks in learning from clinical time series data with irregularity[END_REF]. However, in the current status of our works, we consider only discrete state spaces.

Finally, temporal Bayesian classifiers have been introduced for medical applications [START_REF] Tucker | A spatio-temporal Bayesian network classifier for understanding visual field deterioration[END_REF][START_REF] Tucker | Temporal Bayesian classifiers for modelling muscular dystrophy expression data[END_REF]. They augment the Bayesian network classifiers with a second root node, whose state is associated with discrete time points. Their inabilities to consider time with different granularities make them inappropriate for our problem.

Since none of these models is fully adequate for our problem, we propose the use of additional mechanisms to maintain a time-stamped uncertain observation set based on a static Bayesian network.

The next section describes the real case context and states the problem, followed by the proposal of an architecture and some specific operations to maintain a set of uncertain observations with an illustrative example. We discuss the possibility of using continuous time Bayesian networks in the last section of this paper, together with other perspectives.

The uncertain observation set management problem

In that section we first present the application-related objective and the main research question, then we explain the need to find a compromise between quality and quantity in the observation set. We propose some definitions and the problem statement.

Application-related objective

Preserving the mobility of an elderly person requires to gather specific information about this person in order to provide adequate recommendations. We observed and analyzed the functioning of the service of the hospital center of Lille specialized in fall prevention. Each patient is served during a complete day by a medical team that collects a set of specific individual pieces of information. This information is focused on the evaluation of risk factors for fall that regroup incidence factors, related with fall causes, and severity factors, related with fall gravity. It concerns in particular environmental factors, behavioral factors, precipitating and predisposing factors such as medication, diseases, physical and mental state, and the number of falls during the past six months. On this basis, a group of experts identifies a small number of adequate recommendations to reduce the risk of fall. These recommendations have to be regularly re-evaluated and must evolve together with the person's situation (abilities, environment, context, etc.). However, each person can not frequently benefits of such a complete consultation since it requires plenty of time, the presence of specialists and specific material to achieve examination. The follow-up is generally made by general practitioners, by whom only little information can be collected at each appointment, making impossible to obtain a complete up-to-date set of information. As a consequence, the reasoning has to be conducted on the basis of incomplete information.

The application-related objective is to develop a system able to provide reliable individual information related to the risk of fall, in the aim to assist practitioners or to be linked to other systems like the Assessment of Risk of Adverse Events proposed in [START_REF] Cattelani | A rule-based framework for risk assessment in the health domain[END_REF] for instance.

However, some information may be missing and there is uncertainty about previously collected information.

Main question and general approach

The main question can be formulated as: what information can be provided by the system on a requested variable when there is no available observation on that variable in the observation set, or when the available observation may be out of date, and/or when the observation comes from an unsure source? In order to answer this question, information to consider comes both from specific observations realized on the patient and from generic knowledge to complete as much as possible the information that is provided.

Generic knowledge concerns the dependency relations between the variables, their variability in the considered population, and their evolution over time, partly provided by experts and partly learned from related data. The data file that we used for the construction of the general knowledge model consists of information about 435 variables for 1173 patients who attended the Lille University Hospital Falls Clinic between January 2005 and December 2014. We conducted a study of these data in collaboration with Lille hospital's experts on fall prevention. This study resulted in a taxonomy of the fall risk factors, represented by an ontology [START_REF] Delcroix | Towards a fall prevention system design by using ontology[END_REF], and the selection of 45 relevant variables associated with the characteristics of the person, the main risk factors for fall and possible causes or consequences of them. From this result, we built and evaluated a first model of the generic knowledge, embedded in a Bayesian network [START_REF] Sihag | Prediction of risk factors for fall using bayesian networks with partial health information[END_REF].

Specific observations concern one patient in particular and are made of collected data about this specific person. The observation set includes uncertain information about any subset of variables of the knowledge model. Among the 45 selected variables, some are frequently observed, meaning that corresponding information is frequently present in the observation set, whereas other variables are rarely observed. Furthermore, the proportion of observed variables is very different from one individual to another when considering the whole population of elderly.

In this work, we consider that generic knowledge is well confirmed and we do not call it into question, even when some observations are in contradiction with it. Conversely, specific observations are more or less reliable, and when a set of observations is not compatible with the generic knowledge, some of them are reconsidered. A first step is to maintain the observation set according to criteria of quality and quantity, which is the subject of that paper. A second step, that is beyond the scope of this paper, is to take benefit from the observation set and the generic knowledge model to provide information about a requested variable.

A compromise between quality and quantity

To provide answers, the system must include as much information as possible but also the most reliable information. This concerns the information quantity and quality.

Data quality, or information quality, is a complex concept which is characterized by multiple dimensions such as accuracy, availability, completeness, consistency, reliability, reputation, timeliness, understandability, validity and others [START_REF] Batini | Data and Information Quality -Dimensions, Principles and Techniques, Data-Centric Systems and Applications[END_REF][START_REF] De Tré | Handling veracity in multi-criteria decision-making: A multi-dimensional approach[END_REF][START_REF] Olson | Data Quality: The Accuracy Dimension[END_REF][START_REF] Pipino | Data quality assessment[END_REF][START_REF] Shamala | Integrating information quality dimensions into information security risk management (ISRM)[END_REF][START_REF] Ziad | Data Quality[END_REF]. Since there is no general agreement on data quality dimensions [START_REF] Shamala | Integrating information quality dimensions into information security risk management (ISRM)[END_REF], the aspects to be considered depend on the information consumers requirements [START_REF] Nouvel | The influence of data quality on urban heating demand modeling using 3d city models[END_REF]. Reputation, reliability, accuracy and timeliness are particularly related to the requirements of our applicative context. To represent these aspects, we propose to qualify the information quality according to a confidence degree defined at two levels of granularity: for a piece of information and for an observation set. Data quality assessment is often based on rules [START_REF] Wang | Improving Usability, Safety and Patient Outcomes with Health Information Technology -From Research to Practice, Information Technology and Communications in Health Conference[END_REF][START_REF] Zolnoori | A systematic framework for analyzing observation data in patient-centered registries: Case study for patients with depression[END_REF], which can also handle uncertainty [START_REF] Heinrich | Assessing data quality -a probability-based metric for semantic consistency[END_REF][START_REF] Timmerman | Measuring data quality in information systems research[END_REF]. We propose to represent the knowledge model by a Bayesian network that embeds data quality rules (e.g. about the domain of variables, possible or impossible combinations between subsets of variables and their values). The idea is to maintain the quality of the observation set by continuously (re)evaluating the confidence degree of each piece of information, whether new or not, and maintain the compatibility with the probabilistic generic knowledge model.

Information quantity is another important aspect in our context.

The quantity is related to the number of observations in the set.

Choosing quantity rather than quality would lead to accept any new information, whatever the source, and to keep observation as long as the set of observations remains compatible with the general knowledge model even if this augments the risk of keeping obsolete information in the observation set. At the opposite, choosing quality rather than quantity leads to accept a new observation only when its source is really sure, and to remove previous observations as soon as they may have become obsolete, but this choice would result in a set with very few observations. We thus have to propose a compromise between quality and quantity in the observation set. To that end, the principle is to remove from the set the observations whose quality is no longer sufficient, and the observations that cause a compatibility problem.

Definitions and problem statement

The information to consider comes both from generic knowledge about the dependency relations between the variables and their variability within a population, and from current and past observed states of the specific patient. Both information types can be managed using a Bayesian network approach [START_REF] Pearl | Probabilistic reasoning in intelligent systems: networks of plausible inference[END_REF] provided that some additional mechanisms are added to address the time-related uncertainty.

Before defining Bayesian networks and associated definitions, we give some notations:

• X, X k denote random variables. Capital letters are used to represent random variables.

• Dom(X) denotes the domain of the variable X. When needed, we use the detailed notation Dom(X) = {x 1 , . . . , x m }, but most often, we denote a value of X by x ∈ Dom(X). Lower-case letters represent the values of a variable.

• X = {X 1 , . . . X n } denotes a set of variables. Bold capital letters correspond to sets of variables.

• x = (x 1 , . . . x n ) denotes a possible value (or assignment) of X, with each x i ∈ Dom(X i ), and x ∈ Dom(X) = Dom(X 1 ) × . . . × Dom(X n ). A bold lower-case letter represents the value of a set of variables.

• X K = {X k1 , . . . , X k K } ⊆ X denotes a subset of variables, with K = {k 1 , . . . , k K } ⊆ {1, . . . , n}.

• x K ∈ Dom(X K ) denotes one of the possible values of X K . We refer to x k ∈ Dom(X k ) as an element of the vector x K .

• P (X) is the probability distribution (P (X = x 1 ), . . . , P (X = x m )).

• P (X) = P (X 1 , . . . , X n ) is the joint probability distribution on the set X.

• P (x) denotes P (X = x) and P (x K ) denotes P (X K = x K ).

A Bayesian network B = (G, P ) consists in a set of random variables X = {X 1 , . . . , X n }, a directed acyclic graph G = (X, E), and a set of parameters Θ including the local conditional probability distributions associated with each variable in X. Together, G and Θ define a probability distribution P over X which factorizes as P (X = x) = Xi∈X P (X i = x | pa(X i )), where pa(X i ) ⊂ X is the set of the parents (immediate predecessors) of X i in the graph G.

In our proposal, all the variables of the observation set are in the Bayesian network, but some variables of the Bayesian network may never be observed. We consider the possibility of uncertain observations. For example, an observation about the diagnosis of a disease can be uncertain because the specialist declares that she is not completely sure about it. The uncertain observation is specified by a likelihood vector or potential as proposed by Pearl [START_REF] Pearl | Probabilistic reasoning in intelligent systems: networks of plausible inference[END_REF][START_REF] Ben Mrad | An explication of uncertain evidence in Bayesian networks: likelihood evidence and probabilistic evidence -uncertain evidence in Bayesian networks[END_REF]. The potential of an uncertain evidence e on a variable X represents the relative likelihoods for the possible observation of every state of the variable π

= P (e | X = x i ).
This kind of evidence is easily propagated in a BN by Pearl's method of virtual evidence. A potential on a variable X is a measure π : Dom(X) -→ R + . We assume that, for any potential on a variable X, at least one value of its potential must be non zero: there exists x ∈ Dom(X) such that π(x) > 0. In order to simplify the notation, we also use π to denote the vector (π(x 1 ), . . . , π(x m )).

The most probable values of X in a potential π is defined as follows:

MPV(π) = {x ∈ Dom(X), π(x) = max x∈Dom(X) (π(x))}. The set MPV(π) includes at least one element, and at most |Dom(X)| elements. Let X K = {X k1 , . . . , X k K } ⊆ X a subset of variables and {π k1 , . . . , π k K } a set of associated potentials. The product Π K = π k1 × . . . × π k K is a measure from Dom(X K ) in R + such that Π K (x k1 , . . . , x k K ) = π k1 (x k1 ) • . . . • π k K (x k K ).
As previously, we also use Π K to denote the vector whose components are the images of the elements of Dom(X K ).

Example 1. Potential of a set of observations

Consider two potentials:

π 1 : {x a , x b } → R + defined by the vector (π 1 (x a ), π 1 (x b )) = (1, 0), and π 2 : {y a , y b } → R + defined by the vector (π 2 (y a ), π 2 (y b )) = (0.3, 0.7).
The product of the two potentials Π 1,2 = π 1 × π 2 is defined by the vector

(Π 1,2 (x a , y a ), Π 1,2 (x a , y b ), Π 1,2 (x b , y a ), Π 1,2 (x b , y b )) = (0.3, 0.7, 0, 0).
The observation set regroups the potentials of the observed variables together with the date of the observation and the sources that provided the information. Definition 1. Time stamped uncertain observation A time stamped uncertain observation o on a variable X is a tuple o = (X, π, t, s) where π is a potential on X that represents the uncertain observation on X, t is the time of the observation, and s is the source of the observation.

In this work, we consider the moment when the state (or value) of a variable is observed and we assume that this moment is very close to the moment when we are trying to add the information in the observation set. The observation does not concern the time at which a variable changes in value, but its value at the moment of the observation. In the following, we often simply use the term time stamped observation or just observation to refer to a time stamped uncertain observation.

When there is a past observation on the variable X and no current observation is available on that variable, we do not know whether its current state is still one of those provided by the past observation. Since we consider the possibility of evolving variables, an observation made at time t may no longer be reliable at time t + ∆t: the observation can become obsolete.

Definition 2. Obsolete observation

A time-stamped observation o = (X, π, t, s) is obsolete when the current value of X -even if not observed -is no longer one of the set of the most probable values MPV(π).

An observation o can become obsolete independently of the arrival of a new observation on X, which makes it difficult to detect. More generally, an observation o = (X, π, t, s) is erroneous when the current value of X -even if not observed -is not one of the most probable ones in π. This includes the case where an observation is erroneous from the beginning, for example due to a poor source of information.

We now consider a set of time stamped uncertain observations in order to store available observations. Definition 3. Time stamped observation set on X A time stamped observation set on X is a set O = {(X, π, t, s), X ∈ X} such that for any variable X ∈ X, there is at most one observation on X in O.

We consider both a generic knowledge model which is given by a Bayesian network, and specific knowledge about an one individual which is given by a set of uncertain observations on a subset of variables of the general model.

Each observation has to be compatible with the general knowledge, and in a set of observations, the pieces of information have to be compatible altogether.

Incompatibility may occur when the probability distribution P of the Bayesian network includes some zeros, and more precisely when there is a value for which P is null and the potential of an observation is not null. When that situation is avoided, the potential of the observation is said to be dominated by P .

Below, we recall the definition of that dominance condition and then we propose the notions of partial compatibility and total compatibility between an observation and a general model of knowledge. Definition 4. Dominance of measures A measure ν is dominated by a measure µ, which is denoted by ν µ, if µ(A) = 0 implies ν(A) = 0 for any measurable A.

In the following, we consider the dominance of a probability measure onto a potential. The probability measure P is part of the Bayesian network that constitutes the knowledge model associated with a set of random variables X.

For simplicity, we also denote by P the marginal probability measures associated with a single random variable X ∈ X or with a set of random variables X K ⊂ X.

When considering an observation o = (X, π, t, S) on a single variable X, the potential π of the observation can be dominated or not by P , more precisely by the marginal probability measure of X defined from P .

Definition 5. Totally compatible uncertain observation

An uncertain observation o = (X, π, t, s) on a variable X ∈ X is totally compatible with the probability distribution P if π is dominated by the marginal probability measure P (X), which means that P (X = x) = 0 implies π(x) = 0 for every x ∈ Dom(X).

In others words, when the knowledge model states that a particular value is impossible, an observation stating the contrary is not totally compatible with the model. Such an observation may however be partially compatible with the model of knowledge when at least one value is possible regarding both the observation and the knowledge model.

Definition 6. Partially compatible uncertain observation

An uncertain observation o = (X, π, t, s) on a variable X ∈ X is partially compatible with the probability distribution P if there exists x ∈ Dom(X) such that P (X = x) > 0 and π(x) > 0.

By extension, we say that an observation is partially compatible or totally compatible with a Bayesian network.

Proposition 1. Let o = (X, π, t, s) be an uncertain observation on a variable X ∈ X; if π is totally compatible with a probability distribution P , then π is partially compatible with P .

Proof. By definition, a potential π includes at least one value non zero; let

x ∈ Dom(X) be a value such that π(x) > 0. Since π is totally compatible with P , π is dominated by P , and thus we must have P (X = x) > 0. We thus have a value x for which both P and π are non zero, which means that π is partially compatible with P .

The opposite is not true: an uncertain observation may be partially compatible with P but not totally compatible as in the example below.

Example 2. An observation partially compatible with P but not totally compatible.

Let Dom(X) = {blue, red, green, yellow}, and P (X) = (α, α, α, 0), where α represents a non zero value; this means that yellow is impossible. Let's consider an observation o stating that the color is either red or yellow, but is neither blue not green. The observation o is specified by the potential π = (0, α, 0, α).

The potential π is partially compatible with P since the value red is possible in both measures, but it is not totally compatible with P since the value yellow is impossible according to P but is possible in the observation.

The next two definitions concern the compatibility of a set of observations with a probability measure. When considering a set of observations O K = {o k , k ∈ K} on a set of variables X K , the potential Π K defined as the product of the potentials can be dominated or not by P , more precisely by the marginal probability measure of X K defined from P .

Definition 7. Totally compatible uncertain observation set

A time stamped observation set O K = {(X k , π k , t k , s k ), X k ∈ X K } is totally compatible with the probability distribution P if the product Π K = π k1 ×. . .×π k K
is dominated by the marginal probability measure P (X K ), which means that for

every x K ∈ Dom(X K ), P (X K = x K ) = 0 implies Π K (x K ) = 0. Proposition 2.
O K = O K \ {o k } and X K = X K \ {X k } the corresponding set of variables. Let x K be an assignment of X K such that P (x K ) = 0 and let's see whether Π K (x K ) is null. Since P (x K ) = 0, for any value x k ∈ Dom(X k ), P (x K , x k ) = 0. Since O K is totally compatible with P , this implies that for any value x k ∈ Dom(X k ), Π K (x K , x k ) = 0. By definition, Π K (x K , x k ) = Π K (x K ) • π k (x k )
. We know that any potential has at least a value non zero. Let x k0 be a value such that π k (x k0 ) = 0. Since

Π K (x K ) • π k (x k0 ) = 0, then Π K (x K ) = 0, which confirms that the subset O K = O K \ {o k } is totally compatible with P .
The opposite is not true (see Example 3).

Example 3. An observation set which is not totally compatible with P whereas each of its observation is totally compatible with P .

Let X = {X, Y, Z} and Dom(X) = {x a , x b , x c }, Dom(Y ) = {y a , y b , y c }, Dom(Z) = {z a , z b , z c }.
The joint probability P on X is given in Table 1. This probability measure includes the following zeros: P (x a , y a , z a ) = 0, P (x c , y b , z a ) = 0, P (x c , y c ) = 0.

The observation o 1 states that X = x c ; it is specified by π 1 = (0, 0, 1). The observation o 2 states that Y is either y b or y c , with y c nine times more probable than y b but Y cannot be y a ; it is specified by π 2 = (0, 0.1, 0.9). From Table 1, the marginal probability distributions of X(respectively Y ) has no zero value. As a consequence, the observation o 1 (resp. o 2 ) is totally compatible with P .

We consider the set of observations {o 1 , o 2 }. The marginal probability distribution of (X, Y ) is represented by the vector (α, α, α, α, α, α, α, α, 0) as shown in Table 1. The only zero value corresponds to (x c , y c ). The product of the potentials of the two observations is Π 12 = π 1 × π 2 = (0, 0, 0, 0, 0, 0, 0, 0.1, 0.9).

We thus have P ((X, Y ) = (x c , y c )) = 0 and Π 12 (x c , y c ) > 0, which means that the set of observations {o 1 , o 2 } on {X, Y } is not totally compatible with P .

P (X, Y, Z) x a x b x c y a y b y c y a y b y c y a y b y c z a 0 α α α α α α 0 0 z b α α α α α α α α 0 z c α α α α α α α α 0 P (X, Y ) α α α α α α α α 0
When a set of observations is not totally compatible with a probability distribution, it may however be partially compatible. This new definition is given below.

Definition 8. Partially compatible uncertain observation set

A time stamped observation set O K = {(X k , π k , t k , s k ), X k ∈ X K } is par-
tially compatible with the probability distribution P if there exists at least one

assignment x K ∈ Dom(X K ) such that P (X K = x K ) > 0 and Π K (x K ) > 0,
where Π K is the product of the local potentials π k , for k ∈ K.

K ∈ Dom(X K ) such that (1) P (X K = x K ) > 0 and (2) Π K (x K ) > 0. Consider an observation o k = (X k , π k , t k , S k ) ∈ O K and the subset O K = O K \ {o k }. Let X K = X K \ {X k }
be the associated subset of variables. The assignment x K can be written as

x K = (x K , x k ) with x K ∈ Dom(X K ), and x k ∈ Dom(X k ). Since P (x K , x k ) > 0,
P (X, Y ) x a x b P (Y ) y a α α α y b 0 α α P (X) α α we have P (x K ) > 0. In addition, Π K (x K ) = Π K (x K ) • π k (x k ) > 0, therefore Π K (x K ) > 0. So the subset O K is partially compatible with P .
The opposite is not true (see Example 4). Proof. Let O K be a set of observations totally compatible with P . By definition, each potential has at least one non zero value. Let x 0 K ∈ Dom(X K ) be such a value for the potential Π K . Since O K is totally compatible with P , Π K (x 0 K ) > 0 implies that P (x 0 K ) > 0, which means that O K is partially compatible with P .

The opposite is not true (see the example below).

Example 3 (continued). A set of observations partially compatible with P but not totally compatible. Observations on several variables could also be considered and specified by a potential on the product of their domain but we do not consider this possibility in detail.

The potential of a variable in an observation represents a first type of uncertainty that relates to the relative likelihood of each possible value. Two other types of uncertainty can modify the initial information: the uncertainty due to unsure source of information and the uncertainty due to the age of the information: as time has passed since the observation, the value of the variable which is concerned may have evolved. To represent these last two types of uncertainty, we define a confidence degree for each observation.

Definition 9. Confidence degree

The confidence degree of a time stamped observation o = (X, π, t, s) at the time t = t + ∆t is a real value c(o, t ) in [0, 1] that represents how much the observation is reliable at t . Note that the confidence degree at the time t of the observation may not be 1; indeed, when the information source is known, the confidence at the time the observation is received depends on the trust in this source.

We extend the definition of the confidence degree to a set of observations. This definition is guided by the two types of decisions that must be taken while maintaining an observation set. [START_REF] Combi | Temporal Information Systems in Medicine[END_REF] When a new piece of information is available, we have to decide whether to add it or not to the observation set. This decision is based both on the compatibility of the new observation with the existing set and on the way it affects the confidence degree of the whole set. In particular, we want to prevent the addition of new observations with too low a confidence degree since a single erroneous observation can lead to unreliable result. (2) When there is a conflict between the new observation and the existing set, the removal of different subsets of observations may allow to restore compatibility. In order to decide which subset should be removed, the number of observations of each subset can be considered, together with the impact on the confidence degree of the observation set. It is expected that removing the set with the lowest confidence degree leads to the highest confidence degree for the resulting set. Moreover, there should be no counterbalance between low and high confidence degrees: the assessment of the quality of the complete set must not hide a low confidence degree for an observation because of the presence of more reliable ones. For

a. if c(O , t) < c(O , t) then c(O \ O , t) ≥ c(O \ O , t) (the subset with the lowest confidence degree should be removed), b. if c(O , t) = c(O , t) then c(O \ O , t) = c(O \ O , t).
Note that the mean function would not be suitable to define the confidence degree of an observation set since it does not verify the properties (2), (3) and (4) (see Example 5).

Example 5. The mean function cannot be used for the confidence degree of an observation set. Consider the following three observation sets: When the confidence degree of an observation becomes too low, the observation is likely to have become obsolete. In the same way, when the confidence degree of an observation set becomes too low, it is likely that the set includes an observation that has become obsolete.

O = {o 1 , o 2 , o 3 , o 4 } with c(o 1 , t) = 0.1, c(o 2 , t) = 0.7, c(o 3 , t) = 0.
We can now define more precisely the problem that we tackle. Let B be a Bayesian network, X the corresponding set of discrete random variables, and O a time stamped observation set on X. Over time, the proportion of obsolete information grows when nothing is made to maintain the observation set. When new observations are received, they may contribute to increase the quantity of observations in the set, but also reveal incompatibilities in the observation set relatively to the general knowledge model.

In that context, we propose to periodically update the observation set in order to (1) take into account recently collected observations by making a compromise between the quantity and the quality of the information, (2) decrease the presence of obsolete or erroneous information and (3) maintain compatibility. These operations are presented in the following section, with the functions for the observation set management.

Observation set management system

This section presents the architecture of the system and details the updating operations.

The architecture of the observation set management system

The system combines individual information contained in the observation set and generic knowledge, to provide on demand the belief and confidence about a variable according to the architecture in Figure 2. The system provides two outputs with uncertainty: (a) the belief on a variable depends on stochastic uncertainty and incomplete information about the considered person; (b) the confidence degree depends on uncertainty due to information aging and trust in sources. The intelligent modules of the system are dedicated to manage the observation set and to evaluate beliefs about requested variables. This study focuses on the management operations: management of new observations, periodic removal of unsure observations and evaluation of the confidence degree associated with each observation along with time. The confidence in an observation depends both on the trust we have in the source of information and on the length of time since the information has been received. We propose to model the loss of confidence in the past observations by the use of decay functions. These functions are either constant or decreasing with time, and provide the confidence degree in an observation according to time. However these functions have distinct shapes, depending on the variable. The shape of the decay functions can be defined from expert knowledge or learned from data. Example 6. The observation "Ms A suffers from depression" which was evaluated as highly reliable at the time of the observation, can be less reliable two months later, and even less reliable four months after, etc. Regarding this information, we can assume to represent the loss of confidence by a decreasing linear function, with a slope to be defined. In contrast, "Ms A lives alone" can be as-sumed to remain stable on a long-term perspective, which would be represented by a quasi-constant confidence degree.

Information about the sources of observation is also recorded in order to evaluate the confidence in new observations, at the moment they are received by the system. In order to keep track of the observation sources, learning techniques can be used to adapt the trust level [START_REF] Nunoo-Mensah | The adoption of socio-and bioinspired algorithms for trust models in wireless sensor networks: A survey[END_REF][START_REF] Israelsen | A Definition, Case for, and Survey of Algorithmic Assurances in Human-autonomy trust relationships[END_REF].

Updating operations

The observation set is periodically maintained up-to-date by the two operations described in the maintain algorithm below. At first, the observation set is inspected to be cleaned from observations that are likely to be obsolete.

When the confidence degree in a past observation falls below a given threshold, the risk for the observation to be obsolete is too high, and thus the observation is removed from the observation set (lines 1-3). Secondly, decisions are made when new observations are received in order to maintain the compatibility of the information base (lines 4-end). These operations call two additional algorithms, confidence and integrateNewObs described below. The confidence algorithm provides the degree of confidence in the observation o at a given time t c . When the confidence to compute concerns a current new observation (line 1), the question is: do we already know the observation source? If the response is yes, we can use the trust in the source to provide a confidence degree (lines 2-3). If no, we decide to start with the highest confidence degree (lines 4-5). When the confidence to compute concerns an observation made in the past (lines 6-7), we apply a decay function to compute the current confidence according to the initial confidence degree in the observation and the duration since it was observed, as described in Section 3. The integrateNewObs algorithm decides whether to integrate or not a new observation in the observation set and updates the set accordingly. The decision to integrate a new observation depends on (i) the confidence in the new observation, (ii) the compatibility of the observation set according to a general model of knowledge and (iii) the quality of the observation set, given by the confidence degree of the observation set. This decision relies thus on the confidence degree that results from the confidence algorithm described above and on the compatibility that is checked by the algorithm isCompatible, which is now presented before the detailed description of the integrateNewObs algorithm.

The algorithm isCompatible checks the compatibility of an observation set regarding the general knowledge represented by the BN joint probability distribution. It may refer to either total compatibility or partial compatibility, as previously defined in Section 2.4. The algorithm checks whether an observation set is totally or partially compatible with a probability distribution P , depending on the value of the parameter cT ype ∈ {'total', 'partial'}. When the probability distribution includes no zero (line 1-2), it follows from Definitions 7 and 8 that any observation set is both totally and partially compatible with P . Else, in order to verify the total compatibility of an observation set (lines 5-12), the assignments of the observed variables that are possible in the observation set, i.e. the assignments x K such that Π K (x K ) > 0, are examined until one of them is found with a null probability (line 11), meaning that the observation set is not dominated by the probability P (line 12). When such an assignment is not found, the observation set is totally compatible with P . In order to verify the partial compatibility of an observation set (lines 13-20), the set of the possible assignments of the observed variables is examined until one is found that have a non zero probability. The existence of such an assignment is sufficient to establish the partial compatibility of the set (line 20).

On the base of these operations, we can now described the integrateNewObs algorithm in details. The first step is to check whether the observation set includes a previous observation on the variable concerned by the new observation (lines 1-6). When the previous observation is more reliable than the new one, the new observation is refused (line 6). In the other case, the previous observation is removed from the observation set. When the new observation is compatible with the observation set according to the general knowledge model, it can be integrated (lines 7-8). When it is not compatible (lines 9-26), the subsets of observations responsible for the incompatibility are sought and the most relevant of them is selected to be removed in order to add the new observation. At worst, the complete set of previous observations can be considered. The search for the subset of the observations likely to be obsolete (lines 10-20) begins with the singletons (line 10), and when no singleton allows to restore the compatibility (line 15), larger subsets are checked (line 20). When several subsets of the same size are found, we consider the one with the lowest confidence degree (lines [START_REF] Murphy | Dynamic Bayesian networks: Representation, inference and learning[END_REF][START_REF] Nodelman | Continuous time Bayesian networks[END_REF][START_REF] Ramati | Irregular-time Bayesian networks[END_REF]. Finally, the confidence degree of the set of the observations likely to

Input: OK = {(X k , π k , t k , S k ), X k ∈ XK } an observation set
Input: P a joint probability distribution Input: cT ype ∈ {'total', 'partial'} the type of compatibility Output: isC a boolean, T rue when O K is compatible with P 1 if P includes no zero then

P (x K ) > 0 for any assignment x K ∈ Dom(X K ) 2 isC ← T rue
any observation set is totally and partially compatible with P 3 else P includes at least one zero

4 ΠK ← π k 1 × . . . × π k K 5
if cT ype = 'total' then aims to test the total compatibility of O try to find an assignment x K s.t.

P (X K = x K ) = 0 and Π K (x K ) > 0 6 isC ← T rue
) next Π K (x K ) > 0 n ← n -1 if P (XK = xK ) > 0 then isC ← T rue 21 return isC
be obsolete is compared with the confidence degree of the new observation and the more reliable is kept whereas the other one is rejected (lines 21-25). When the new observation is refused, the previous observation on the same variable is restored, if it existed (lines 24-25).

When there is some incompatibility, the search for the set of the observations likely to be obsolete is guided by two criteria: first remove the smallest number of observations, in order to minimize the loss of information of the observation set, and second, remove the observation(s) with the lowest confidence degree.

The first criterion is known as the principle of minimal change and is frequently used in belief revision [START_REF] Papini | Knowledge-base revision[END_REF][START_REF] Dubois | Belief change rules in ordinal and numerical uncertainty theories[END_REF]. (1) The definition of the confidence degree of an observation set states that the removal of any observations from O can only increase its confidence degree.

Thus the confidence degree of the modified set after the removal of an observation (lines 4, 22) remains greater or equal to β. Regarding the addition of a new

s ← s + 1 a subset O has been found if confidence(O , Now) < confidence(o, Now) then keeps the new obs when it is more reliable than O O ← (O \ O ) ∪ {o} else the observation set is kept unchanged if prevObs = T rue then O ← O ∪ {o } the previous observation is restored return O observation o, either o is less reliable than O, then c(O ∪ {o}, t) = c(o, t) ≥ β; or o is more reliable than O then c(O ∪ {o}, t) = c(O, t) ≥ β.
(2) Let O be totally (resp. partially) compatible with P ; from Proposition 2 (resp. Proposition 3), any subset of O is also totally (resp. partially) compatible with P , thus the removal of some observations have no impact on the compatibility of the resulting set. Concerning the addition of a new observation in the set, this is done only when the resulting set is totally (resp. partially) compatible with P (lines 7 and 15).

The following example illustrates the use of these operations to manage the observation set.

Illustrative example

We illustrate the process with an observation set related with a general model knowledge about fall prevention [START_REF] Bourdessol | Prevention of falls in the elderly living at home, Good Practice Guide, collection Référentiels, INPES[END_REF][START_REF] Delcroix | Towards a fall prevention system design by using ontology[END_REF]. We consider a scenario about Ms. A that continues Example 6. The evolution of the observation set is monitored over one year, showing the arrival of new information, their removal and the evolution of the confidence degree of each observation.

We have selected 12 variables from the real data set provided by the fall prevention service at the hospital of Lille (France) (Table 3). These variables include temporal aspects such as the presence of a specific event in the past or the number of repetitions of an event, about behavior and habits, and the current state of the person.

The variables have different temporal granularity, from some months up to several years. The variables have been regrouped in three subsets corresponding to the shape of their decay function. The variables of the first group rarely change and the associated confidence degree decreases very slowly. The life span of a piece of information is generally more than 3 years, when the initial confidence degree is high. At the opposite, in the third group, the decay functions decreases much faster, and the life span of an information on a variable is generally less than a year. For those variables, changes may occur several times in a year, and an observation is kept only for a few months in the observation set. The variables in the second group fall between these two extremes.

The structure of the Bayesian network using the variables listed in Table 3 710 has been proposed for the purpose of this article without strong validation from the experts (Figure 3). However, the network parameters have been learned from a thousand of real cases from the fall prevention service using the counting learning algorithm used in NETICA [START_REF] Norsys | Netica Application[END_REF].

In this study, the confidence threshold was set to 0.3, so that any informa- and is considered as much less trusty (0.4). An additional source of observations is a rumor; the trust in this source is low (0.1) and the related information is not integrated in the observation set.

The observation set is given in Table 4, with its evolution during four slices of time. New observations are written using bold characters. The confidence degree is re-evaluated at each time step.

At month M1, Ms A has an appointment in a specialized consultation since she has fallen with no apparent reason. The doctor inputs the following observations in the system: Ms A has no dementia (DEM = no); she took no psychotropic drug before that day (PSY = false); Ms A is likely to have an episode of depression, but the doctor is not completely sure of his diagnosis.

According to him, Ms A is four times as likely to be in that state when she has a depression than when she does not. The doctor thus enters an uncertain observation with the likelihood ratio (0.8, 0.2); Ms A goes out as often has she used to before falling (AVGO = no).

At month M3, a member of family, considered as source of information much less trusty (0.4), reports that it seems very likely that Ms A drinks alcohol. The confidence degree of this new uncertain observation, even if low, is however above the confidence threshold, leading to add the observation in the set.

At M5, the treating doctor clearly remarks that Ms A drinks alcohol. The confidence degree of this observation is updated in the observation set. The doctor also inputs several other observations about the variables ALO, PARK, UWA and PSY. A previous and different observation on the variable PSY was in the observation set. It is replaced by the new one which has a higher confidence degree.

After that, there is no new observation during several months, but the confidence degree on previous observations is regularly re-evaluated and the observations that are likely to be obsolete are removed. For example, previous observations on DEP, UWA and AVGO are removed since their confidence degree has become too low.

At M12, new observations coming from the doctor are entered about variables FEAR and UWA. An additional observation coming from a rumor states that Ms A no longer goes out. It is not integrated because of the very low level of trust associated to that source (0.1).

At any time, the observation set management system can provide information about Ms A about any variable of the model. When the question concerns a variable for which an observation is available in the observation set, the system provides the most probable value(s) in the potential of the observation, together with the confidence degree of that information. For example, at M12, the system can states with a high confidence degree that Ms A lives alone, has neither Parkinson disease nor dementia and that she does not use a walking aid and has no fear of falling. Another information is available about her alcohol consumption from a previous observation but the confidence degree is much lower (0.5) (see Table 4). When the question concerns a variable for which no observation is available, the system uses the general probabilistic knowledge embedded in the Bayesian network to update the belief on that variable based on available observations on other variables. It returns the posterior probability distribution on the variable.

In addition, the system can also return the marginal probability distribution of the same variable without any observation to allow the comparison of the specific case with the baseline population. For example, during the whole sce-M0 M1 M3 M5 M12 nario, there has been no observation about the variables GAIT, LS and ADL, and concerning the variables PSY, DEP and AVGO, some observations have been received but they have been removed from the observation set. The comparison of the initial belief (79.6 %) with the current belief (51.9 %) allows to state that Ms A has much less risk to have gait impairment than the baseline population, but that the risk is however present.

This example illustrates the interest of the observation set management system. It allows to provide information about any variable of the model for a specific person, even when no observation has been collected about that variable. It also provides information about the confidence degree related with previous observations collected about that person.

Discussion and related works

In this section, we discuss about different approaches of modeling and reasoning with uncertain, incomplete or inconsistent knowledge.

First we start with the use of Dempter-Shafer theory for uncertainty modeling, then we continue with several works about uncertain information fusion, belief changes and temporal reasoning, and third, we briefly present Continuous Time Bayesian Networks and discuss the interest of using this knowledge model for the management of a time stamped uncertain observation set.

The last part of the section presents the steps toward a practical implementation of a knowledge based system for the management of an observation set with application on preserving mobility.

Representation and reasoning with uncertain knowledge

The question of modeling and reasoning with knowledge and uncertainty can be handled by several theories of uncertainty, among which the Bayesian probability theory and the Dempster-Shafer theory of belief functions [START_REF] Dempster | Upper and lower probabilities induced by a multivalued mapping[END_REF][START_REF] Shafer | A Mathematical Theory of Evidence[END_REF][START_REF] Smets | The transferable belief model[END_REF].

According to Cobb [START_REF] Cobb | A comparison of bayesian and belief function reasoning[END_REF], "both frameworks have roughly the same expressive power (...) and can be utilized to model knowledge and evidence of varying types". However, "computationally, D-S belief networks are more expensive to evaluate than Bayesian". Uncertain evidence can be specified in the theory of belief functions through masses assigned to the subsets of the domain of a variable. In this article, the domain knowledge is modeled using Bayesian network models, and uncertain evidence. In Definition 1, a time stamped uncertain observation is specified in the form of a likelihood vector, as proposed by Pearl [START_REF] Pearl | Probabilistic reasoning in intelligent systems: networks of plausible inference[END_REF].

Beyond the framework used for modeling and reasoning, we present below some works dealing with problems similar to ours.

In belief revision, an agent changes his beliefs about a static world in the light of new information, whereas in our problem, the world represents the state of a person and its context, and it changes over time. In belief update, an agent keeps his beliefs up to date within an evolving world. This is also the case in our problem but the updating is made on the basis of time stamped uncertain observations and the focus is set on how to maintain that uncertain observation set.

Belief merging studies how to aggregate multiple belief bases into a coherent one [START_REF] Ma | A framework for managing uncertain inputs: An axiomization of rewarding[END_REF]. Our problem is related to multi-source information fusion and it raises the question of the compatibility of the observation set with a well-established knowledge base. Several works propose the use of a confidence degree to manage the reliability of different sources [START_REF] Xu | A novel approach to information fusion in multi-source datasets: A granular computing viewpoint[END_REF] or to fuse several distributions of possibility from different sources with some contradictions [START_REF] Delmotte | Modeling of reliability with possibility theory[END_REF]. In our proposal, the confidence degree is attached with a piece of information and evolves with time. Information correction and fusion for belief functions has been studied when the information items may be irrelevant, and sources may lie [START_REF] Pichon | Relevance and truthfulness in information correction and fusion[END_REF]. In order to merge information on a same variable coming from several sources, the authors consider both the notion of truthfulness and the notion of relevance regarding a given question of interest, assuming that uncertain meta-knowledge on the source's relevance and truthfulness is available. The questions of compatibility concern the information brought by sources and assumptions regarding the epistemic state of the agent about the source state. In our work, we also assume that meta knowledge is available about the trust in sources. However, we consider information collected over a long period of time, while taking into account the fact that this information may have become obsolete over time. We evaluate the confidence that can be placed in old information and check the compatibility of specific uncertain information with a general probabilistic knowledge model.

Our system provides two kinds of information about a requested variable depending on whether an observation on the variable is in the observation set or not. The confidence degree relates to the trust we can have in an old observation, whereas the updated belief, thanks to the Bayesian network, is based on general probabilistic knowledge and specific observations. When a trusted observation of the variable is present, this is the information that is provided; when no trusted observation exists, the other observations and the general knowledge are used.

Combining these two pieces of information in a single one is challenging since the semantics are different. It would require to define how to use the confidence degree in the aggregation of the potential of an observation and the posterior probability of the observed variable.

In this paper, we propose to combine decay functions and a BN to re-evaluate the confidence in a piece of information collected in the past. Continuous Time Bayesian Networks (CTBNs) [START_REF] Nodelman | Continuous time Bayesian networks[END_REF][START_REF] Perreault | Compact structures for continuous time bayesian networks[END_REF] seem to constitute an interesting alternative to gather BN and decay functions in a single model. In CTBNs, the states of variables evolve continuously over time, the evolution of each variable depending on the state of its parents in the graph. The key difference between BNs and

CTBNs is that CTBNs model the distribution over the variable's trajectories, considering a distribution over the dynamics of a variable X(t) given the values of the parents of X at time t -the Conditional Intensity Matrices (CIM)-, whereas BNs use parameters which indicates the conditional distributions of a node X given its parents. The elements of the CIM apart from the diagonal denotes the rate departing from a state and arriving in another state in a given period. The time during which a variable stays in a state is usually assumed to be exponentially distributed. Each transition-rate matrix of a CTBN is associated with a time unit that is the reference to define the transition rates. Several algorithms of inference in CTBNs have been proposed [START_REF] Nodelman | Expectation propagation for continuous time Bayesian networks[END_REF][START_REF] Fan | Importance sampling for continuous time Bayesian networks[END_REF][START_REF] Celikkaya | Factored filtering of continuoustime systems[END_REF][START_REF] Rao | Fast MCMC sampling for Markov jump processes and continuous time Bayesian networks[END_REF][START_REF] Cohn | Mean field variational approximation for continuous-time Bayesian networks[END_REF], associated classifiers have been proposed with specific algorithms [START_REF] Stella | Continuous time Bayesian network classifiers[END_REF], and a non parametric approach is proposed in [START_REF] Yang | Learning continuous-time Bayesian networks in relational domains: A non-parametric approach[END_REF] to learn continuous-time Bayesian network in relational domain. A reasoning and learning engine for CTBN is also available2 [START_REF] Shelton | Continuous time Bayesian network reasoning and learning engine[END_REF]. Different applications use CTBN [START_REF] Xu | Intrusion detection using continuous time Bayesian networks[END_REF]. The drawbacks that we see concern the difficulty to define the CTBN since it requires to identify for each variable of interest the variables that influence its evolution, and the initial BN because of the high number of parameters to adjust: a CTBN with n nodes, each of them having p parents and a domain of size m corresponds to a first step before considering the use of CTBNs whose size may quickly cause it to become intractable [START_REF] Perreault | Compact structures for continuous time bayesian networks[END_REF].

Toward practical implementation

The development of the system such as presented in Figure 2 requires several upstream steps, related to the construction of the Bayesian network, the knowledge about the decay functions according to the variables and about the trust in the sources. Most of these steps require the collaboration of domain experts to be achieved. After the definition of an ontology of the risk factors for fall [START_REF] Delcroix | Towards a fall prevention system design by using ontology[END_REF], we selected the variables that constitute the support of the personal information base. These variables have been used to build the Bayesian network [START_REF] Sihag | Prediction of risk factors for fall using bayesian networks with partial health information[END_REF]. The definition of the decay functions is underway: the current step is to assign the variables to different categories regarding the evolution of the variables with time. The implementation of the algorithms proposed in this paper is a short-term perspective for which we have identified a small subset of variables to focus on.

The first intended users of our system are general practitioners since they are key players in the prevention of fall. They will provide new observations about their patients and benefit from the output of the system for unobserved variables and variables for which previous information may have changed. The development of the first prototype will thus be made in conjunction with some general practitioners related with the PREMOB network, whose main objective is the prevention of falls [START_REF] Mirakovska | PREMOB : Réseau d'investigation clinique de l'interrégion nord-ouest sur la thématique : "prévenir la perte de mobilité et les chutes chez les personnes âgées[END_REF].

Conclusion

This study focuses on real-life situations where it is not possible to instantly gather all the up-to-date information needed to make a decision.It considers information collected over time and from a variety of sources, while taking into account the fact that some information may have become obsolete over time.

We address a real world problem in health context which is to get quickly the adequate information about a person, with sufficient quality and quantity to achieve specific purpose such as fall prevention.

Indeed, the application objective is to manage a set of patient specific observations in complement to the generic knowledge embedded in a Bayesian network.

Our contribution includes three main points:

• the proposition of a knowledge based system architecture and algorithms to manage information quality in a time stamped uncertain observation set;

• the definition of the confidence degree of a piece of observation (respectively of an observation set) to reduce the risk of erroneous information in a personnal observation set;

• the definition of the partial / total compatibility of an uncertain observation (respectively an observation set) with a joint probability distribution to maintain the consistency of the observation set regarding a probabilistic model of knowledge.

We present a part of our application context about fall preventing among elderly people, to illustrate how to maintain a set of observations about a subject, with only a few new inputs at each time step. The compromise between quality and quantity allows to benefit from old observations and to remove or reject those in which remains too little confidence.

Our proposal is guided by the criterion of feasibility in order to implement a first prototype as part of a real system dedicated to fall prevention. Some work remains to be done, regarding both theoretical and applicative aspects. Theoretical future work concerns: how the system can learn to adjust its trust in the information sources; the merging of several pieces of uncertain information for the same variable, coming from different sources at different time, is also an interesting perspective, instead of keeping only the information with the highest confidence degree. CTBN is an alternative to be explored provided that the construction of the model is feasible. In addition, uncertain evidence in CTBN [START_REF] Sturlaugson | Uncertain and negative evidence in continuous time Bayesian networks[END_REF] could be interesting to manage the uncertainty coming from the trust in sources, requiring additional hypotheses as explained above.

Applicative future work concerns the knowledge embedded in the system and more specifically decay functions. The implementation of the maintain algorithm may raise computational questions related with the total or partial compatibility. The development and the evaluation of the maintenance system of an observation set for a real application will involve final users.

Example 4 .Proposition 4 .

 44 An observation set which is not partially compatible with P whereas each observation is partially compatible. Let Dom(X) = {x a , x b } and Dom(Y ) = {y a , y b } and the joint probability distribution P is given in Table2. It follows that the marginal probability distributions P (X) and P (Y ) have no null value. For example P (x a ) = P (x a , y a ) + P (x a , y b ) > 0 since P (x a , y a ) > 0. As a consequence, any potential on X (respectively on Y ) is partially compatible with P . Consider the observations: o 1 on X with π 1 = (1, 0), stating that X = x a , and o 2 on Y with π 2 = (0, 1), stating that Y = y b . The product of the two potentials Π 12 = π 1 × π 2 includes a single non zero value which is Π 12 (x a , y b ). Since there is no value of (X, Y ) such that P and Π 12 are both non zero, the observation set {o 1 , o 2 } is not partially compatible with P whereas separately, each observation is partially compatible with P . Let O K be a set of uncertain observations, if O K is totally compatible with a probability distribution P , then it is partially compatible with P .

  We have seen that the set {o 1 , o 2 } on {X, Y } is not totally compatible with P . Note also that the value (x c , y b ) is possible both in P and in Π 12 which means that the set {o 1 , o 2 } is partially compatible with P . Finally, the observations o 1 and o 2 are separately compatible with P , the set {o 1 , o 2 } is partially compatible with P , but not totally compatible with P .

Figure 1 :

 1 Figure 1: Synthetic view of Propositions 1 to 4, where O is an observation set.

Figure 1

 1 Figure 1 summarizes the last four propositions. Note that, in this article, we consider observations sets in which each observation concerns a single variable.

Definition 10 . 2 . 3 . 4 .

 10234 these reasons, we propose the definition below based on the function minimum. Confidence degree of an observation set The confidence degree of a non empty observation set O = {o 1 , . . . , o k } at the time t is a real value in [0, 1] that represents how much the observation set is reliable at t. It is defined by the confidence degree of the less reliable piece of information of the set: c(O, t) = min(c(o 1 , t), . . . , c(o k , t)) . The properties of this function that are interesting for the management of an observation set are given below: whatever the observation o, the observation set O and two subsets O ⊂ O, O ⊂ O, 1. c({o}, t) = c(o, t) Adding an observation can only decrease the confidence degree of a set or let it stable: c(O ∪ {o}, t) ≤ c(O, t). As a consequence, the addition of a new observation to the set should be done with caution. Removing an observation can not decrease the confidence degree of a set c(O \ {o}, t) ≥ c(O, t) If necessary, to decide which subset among O and O should be removed from O depending on the confidence degree comparison:

6

 6 and c(o 4 , t) = 0.8, O = {o 2 } and O = {o 3 , o 4 }. The mean of the confidence degrees in O (resp. O ) equals 0.7. Let's compare the means of O \ O = {o 1 , o 3 , o 4 } and O \ O = {o 1 , o 2 }. The mean of the first set is (0.1 + 0.6 + 0.8)/3 = 0.5 whereas the mean of the second one is (0.1 + 0.7)/2 = 0.4, which contradicts the property (4.a).

Figure 2 :

 2 Figure 2: General architecture of the observation set management system.

Algorithm 1 : 3 O 6 O

 136 maintain(O, Onew, P , cT ype) Input: O an observation set Input: Onew the set of new observations Input: P a probability distribution Input: cT ype ∈ {'total', 'partial'} the type of compatibility Output: O the updated observation set Data: β confidence threshold 1 foreach o ∈ O do 2 if confidence(o, Now) < β then ← O \ {o} clean the set by removing obs. likely to be obsolete 4 foreach new observation o = X, π , t , s ∈ Onew do 5 if confidence(o , Now) ≥ β then the confidence degree in o is sufficient ← integrateNewObs(O, o , P, cType) 7 return O

Algorithm 2 : 3 c 4 else no knowledge about the source s 5 c ← 1 7 c

 234517 confidence(o, tc) Input: o = X, π, t, s observation π on X provided by the source s at t Input: tc time of the confidence degree computing Output: c the confidence degree in o at time tc Data: S known input sources Data: trust() the trust function applied to known input sources Data: decayX() the decay function of the variable X 1 if tc = t then the confidence concerns a new observation 2 if s ∈ S then there is knowledge about the observation source ← trust(s) by default, the source is trusted 6 else the confidence to compute concerns a previous observation ← decayX(confidence(o, t), tc -t) 8 return c

Algorithm 3 :

 3 isCompatible(O, P , cT ype)

7 n

 7 ← |Dom(XK )| 8 while isC = T rue and n > 0 do 9 xK ← next assignment in Dom(XK ) next Π K (x K ) > 0 n ← n -1 if P (XK = xK ) = 0 then isC ← F alse else aims to test the partial compatibility of O isC ← F alse n ← |Dom(XK )| while isC = T rue and n > 0 do xK ← next assignment in Dom(XK

Proposition 5 . 1 . 2 . 3 .

 5123 Let O be the observation set updated after the arrival of a new observation by the algorithm integrateNewObs, with O the previous observation set, o the new observation, P the joint probability distribution, and cT ype the required compatibility ( partial or total ). We have: If confidence(O, t) ≥ β and confidence(o, t) ≥ β then confidence(O , t) ≥ β If the algorithm aims to test the total compatibility (cT ype = 'total') and the set O is totally compatible with P , then O is totally compatible with P . If the algorithm aims to test the partial compatibility (cT ype = 'partial') and the set O is partially compatible with P , then O is partially compatible with P . Proof. Two main updating operations are performed by integrateNewObs: the removal of some observations (line 4 and 22) and the addition of the new observation (line 8 and 22).

Algorithm 4 : 2 prevObs ← T rue 3 if 4 O

 4234 integrateNewObs(O, o, P , cT ype) Input: O an observation set Input: o = X, π, t, s a new observation with a sufficient confidence degree Input: P a joint probability distribution Input: cT ype ∈ {'total', 'partial'} the type of compatibility Output: O the updated observation set 1 if ∃ o = X, π , t , s ∈ O with t < t then there is a previous observation o on X confidence(o , Now) ≤ confidence(o, Now) then confidence in the old observation is lower than in the new one ← (O \ {o }) remove the old information before managing compatibility 5 else 6 return O quit without any change on O 7 if isCompatible(O ∪ {o}, P, cType) then the new observation does not break the compatibility with P 8 return O ∪ {o} 9 else find a subset of observations that restore compatibility with P s ← 1 begins to check singletons f ound ← F alse while f ound = F alse and s ≤ size(O) do browse the subsets of O foreach S ⊂ O of size s do cM in ← 1 maximum degree of confidence keep the subset with the lowest confidence degree among subsets of size s if isCompatible((O \ S) ∪ {o}, P, cType) then 16 f ound ← T rue 17 if confidence(S, Now) < cM in then 18 O ← S 19 cM in ← confidence(S, Now)

Figure 3 :

 3 Figure 3: Graph of the Bayesian network used in the illustrative example.

715

  tion in the observation set has a higher confidence degree. Several sources of information provide observations about the variables. The two main sources are a doctor who specializes in falls prevention and the treating physician; the trust in what they say is very high (0.95). The third source is a member of the family

  This is the posterior probability P (GAIT = yes | ALO = yes, o P ARK , DEM = no, ALC = yes, U W A = no, F EAR = no) where o P ARK is the uncertain observation on the variable PARK specified by the potential π P ARK = (0.9, 0.1, 0).

  If a time stamped observation set O K is totally compatible with a probability distribution P , then any subset O K ⊂ O K is totally compatible with P . As a consequence, every observation o k ∈ O K is totally compatible with P . Proof. Consider an observation o k ∈ O K , and let

Table 1 :

 1 Joint probability distribution on {X, Y, Z}. The symbol α represents a non zero value.

Table 2 :

 2 Joint probability distribution of {X, Y }, and marginal distributions of X and Y in Example 4. The symbol α represents a non zero value.

Table 3 :

 3 Description of the variables used in the example.

	Group	X	Dom(X)	Meaning
		ALO	(yes;no)	lives alone
	1	PARK (no;probable;confirmed) Parkinson disease
		DEM (no;probable;confirmed) dementia
		ALC	(yes;no)	drinks alcohol
	2	GAIT LS	(yes;no) (yes;no)	gait impairment leg strength weakness
		ADL	([0,2];]2,4];]4,6])	autonomy scale
		PSY	(true;false)	takes at least one psychotropic drug
		DEP	(yes;no)	depression
	3	UWA	(yes;no)	uses a walking aid
		FEAR	(yes;no)	fear of falling
		AVGO	(yes;no)	avoids going out for fear of falling

Table 4 :

 4 The observation set with the potentials and the confidence degrees.

	New observations

Table 5 :

 5 Evolution of P (GAIT | Y i = y i ) where Y i = y i represents the observation available at month Mi.

Table 5

 5 displays the posterior probability distribution of the variable GAIT given the observations for Ms A at each time step of the scenario described above. When no observation is available about Ms A (at M0), the initial belief that she has gait impairment is 79.6%. This rate is the marginal probability of gait impairment in the population represented by the Bayesian network model 1 .

At M12, the belief that Ms A has gait impairment has decreased down to 51.9%.

The Bayesian network model has been learned on the basis of a data set of a thousand of patients received in a department specialized in fall prevention. This population has a high rate of gait impairment

http://rlair.cs.ucr.edu/ctbnrle/

n.2 p .m(m -1) transition rates. Finally, Hybrid time BN is another new kind of probabilistic graphical model for dynamic systems [START_REF] Liu | Hybrid time bayesian networks[END_REF]. It aims to reduce the amount of information required to build the model regarding temporal dimension. However, the model construction may become infeasible for large networks such as in CTBN.

These models could however help to decide whether an observation X = x i collected at time t should be kept or not in the information database. Indeed, when the value of the parents of X are known, the transition rate of the variable X from the value x to another value can be obtained from the CIM matrix of X by adding up the values of the row of x except the value on the diagonal.

When the transition rate is below a threshold, we can decide to keep the information X = x i in the database, whereas in the opposite case, the risk for that information to be obsolete is too high and the information should be removed.

The proposal presented in this paper is a first approach guided by the desire to get a solution that can actually be implemented. This proposal can be considered as a particular simple case of a future proposal using CTBNs. Indeed, the Bayesian network model with the variables of the observation set of our actual proposition could be the first component of a CTBN as the initial distribution of the process. The decay functions proposed in the current approach can be seen as conditional intensities matrices (CIM) of a CTBN drastically simplified. Indeed, when the transition rates of a variable X do not depend on its parents' value, nor on the values of X, all CIMs of the variable X are identical, and composed of a single parameter (except on the diagonal). From this parameter, we can derive the probability that the value of X changes over a given amount of time, which is the same information provided by a decay function when it is linear. In the current paper, we propose a simpler approach since its implementation is based on a Bayesian network. However, when trying to respond effectively to the problem of falls prevention, the Bayesian network involves a large number of features and its construction requires important time for knowledge extraction and lots of data to learn the model. A validation of the current proposal with a Bayesian network involving a large number of characteristics is

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:


MD David Beauvais
email: david.beauvais@chru-lille.fr

Oriane Karleskind

Severine Loridant

Remy Nyga

Marie Lamiaux

Anne-Sophie Moreau

Franck Morschhauser

Suman Mitra

Ibrahim Yakoub-Agha

Boualem Sendid

Potential role of tocilizumab in severe gastrointestinal barrier damage after car t-cell therapy

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Adoptive transfer of chimeric antigen receptor T-cells (CAR T-cell) targeting CD19 has emerged as one of the most promising approaches for treating patients with relapsed/refractory diffuse large B-cell lymphoma (DLBCL). [START_REF] Gauthier | Chimeric antigen-receptor T-cell therapy for hematological malignancies and solid tumors: Clinical data to date, current limitations and perspectives[END_REF][START_REF] Ghobadi | Chimeric antigen receptor T cell therapy for non-Hodgkin lymphoma[END_REF] Accordingly, the two approved anti-CD19 CAR T-cell products, tisagenlecleucel (CTL019, Kymriah TM ) and axicabtagene ciloleucel (axi-cel, Yescarta TM ) have demonstrated durable remission in approximately 30-40% of patients with DLBCL. Yet, this approach can be responsible for severe adverse events, including cytokine release syndrome (CRS) and immune effector cellassociated neurotoxicity syndrome (ICANS). [START_REF] Gauthier | Insights into cytokine release syndrome and neurotoxicity after CD19specific CAR-T cell therapy[END_REF] Therefore, close patient monitoring is a critical part of the treatment protocol for the first two weeks after CAR T-cell infusion. High-grade CRS and ICANS are managed with the use of immunosuppressive agents such as tocilizumab (anti-IL6 receptor) and corticosteroids. [START_REF] Yakoub-Agha | Management of adults and children undergoing chimeric antigen receptor T-cell therapy: best practice recommendations of the European Society for Blood and Marrow Transplantation (EBMT) and the Joint Accreditation Committee of ISCT and EBMT (JACIE)[END_REF] In addition, prior therapies and lymphodepleting conditioning coupled with the use of tocilizumab and corticosteroids can increase patient infection risk. [START_REF] Hill | Infectious complications of CD19-targeted chimeric antigen receptor-modified T-cell immunotherapy[END_REF] We report the first case of a heavily pretreated patient developing severe gastrointestinal (GI) damage leading to unexpected septicemia and further disseminated candidiasis following CAR T-cell therapy. The issue of potential role of tocilizumab in the delayed GI wall repair has been addressed.

A 68-year-old female received CAR T-cells (axi-cel) for heavily pretreated (5 prior lines of therapy) DLBCL evolved from follicular lymphoma. After leukapheresis, a bridging therapy consisting of 2 cycles of DHAP (dexamethasone, high dose aracytine, cisplatin) was given allowing disease stability. Lymphodepleting conditioning (cyclophosphamide 500 mg/m²/day and fludarabine 30 mg/m²/day for 3 days) was initiated. However, the axi-cel infusion at (2 × 10 6 CAR T-cells per kilogram) was delayed and ultimately given 5 days after the end of lymphodepletion (41 days after leukapheresis) due to sudden cauda equina syndrome development related to lymphoma progression with epiduritis. Salvage treatment with dexamethasone 40 mg/day for 4 days and radiotherapy for 5 days were therefore required.

Grade 1 CRS occurred on day 1 after infusion of axi-cel, evolving in grade 2 on day 4 with hypoxemia requiring a single dose of tocilizumab. Grade 3 ICANS occurred on day 6 after axi-cel without fever recurrence requiring 10 mg IV dexamethasone four times a day according to European Society for Blood and Marrow Transplantation recommendations. [START_REF] Yakoub-Agha | Management of adults and children undergoing chimeric antigen receptor T-cell therapy: best practice recommendations of the European Society for Blood and Marrow Transplantation (EBMT) and the Joint Accreditation Committee of ISCT and EBMT (JACIE)[END_REF] On day 8, ICANS resolved and the patient started neutrophil recovery. Dexamethasone was progressively tapered and discontinued on day 13. On day 14 after axi-cel, the patient developed sudden abdominal pain and diarrhea associated with hypotension and cardiac arrest without fever. Despite intensive care management, a second cardiac arrest occurred and was resolved with adrenaline. Meropenem-sensitive Escherichia coli was isolated from peripheral blood cultures. A computerized tomography-scan showed, without clear defect, a thickening of the large intestine walls and almost all the small loops. A laparotomy ruled out mesenteric ischemia. Microbiological examination of peritoneal fluid was sterile. High dose noradrenalin remained necessary and inflammation markers persist (CRP 150 mg/L) contrasting with progressive procalcitonin decrease. On day 20 after axi-cel, high serum levels β-(1,3)-Dglucan (1547 pg/ml) and mannan (>2500pg/ml) raised suspicion of invasive Candida infection. Serum galactomannan was positive (index >6) which contrasted with negative DNAemia for A. fumigatus. The patient died on day 21 and autopsy was performed.

Postmortem analysis

Postmortem analysis macroscopic findings showed diffuse petechiae (lungs, pleura, spleen, liver, heart, omentum, colon, kidney) indicating hypoxia. The sectioning of lungs revealed a thick and viscous brown mucoid bronchial secretion. The peritoneal cavity contained 2-liter hemoperitoneum. In the upper GI tract-from lips to the Treitz ligament-a duodenal ulcer without perforation (3.2 x 2 cm) was found (Figure 1A). In the lower GI tract-from the Treitz ligament to anus-there were no signs of ischemia but presence of pseudomembranous plaques on bowel serosa. No suspect lymph nodes were found. In microscopic examination, the duodenal ulcer was confirmed with total loss of mucosae reaching the musculosa. The mucosae were replaced by yeasts, pseudohyphae and hyphae. Moreover, stomach walls, from mucosa to serosa, and the rest of the bowels had also been invaded by fungal cells (Figure 1B). The pseudomembranes contained numerous fungi. Periodic-acid Schiff and Grocott stains confirmed the presence of mycelial agents (Figure 1C). mycotic emboli were also found in the liver and lungs (Figure 1D and1E). All lymph nodes were lymphoma-free.

Microbiological examination of postmortem samples

Direct microscopic examination of the gut epithelium barrier and bronchial mucus revealed numerous yeasts associated with pseudomycelia and Candida albicans grew in culture on Sabouraud agar and chromogenic media. Abdominal effusion fluid examination revealed rare colonies of C. albicans. One colony of Aspergillus fumigatus grew in bronchial mucus and abdominal fluid cultures but not in the gut epithelium barrier. These mycological findings were associated with the presence of oropharyngeal polymicrobial flora in the two gut samples. Mucorales and A. fumigatus q-PCR were negative on all postmortem samples. Galactomannan (index > 6) and mannan (>2500 pg/mL) measurements in the abdominal effusion fluid were also positive.

Discussion

Besides CRS and ICANS, which are early complications in most patients undergoing CAR Tcell therapy, infectious complications in this setting are frequent but often less severe.

Neutropenia following lymphodepleting conditioning is a commonly reported risk factor of early infectious complications, mainly bacterial infections, affecting 23% of patients.

Conversely B-cell aplasia is a risk factor of late infectious disease events, mainly viral infections, affecting 9% of patients. Recently, 32 days after CAR T-cell infusion, a patient receiving tocilizumab and high dose corticosteroids developed fatal mycobacterium abscesses. [START_REF] Kase | Fatal Mycobacterium abscessus in a recipient of axicabtagene ciloleucel CAR-T: beware of T cells[END_REF] The use of tocilizumab and corticosteroids for lower grades of CRS and ICANS could increase the incidence of early infection. Hill et al. reported 3% of invasive fungal infection (IFI) in patients receiving anti-CD19 CAR T-cell therapy; all patients had severe CRS or ICANS requiring tocilizumab and/or corticosteroids. [START_REF] Hill | Infectious complications of CD19-targeted chimeric antigen receptor-modified T-cell immunotherapy[END_REF] While corticosteroids are a risk factor for invasive hyphae infection such as aspergillosis, their role in invasive candidiasis is controversial. [START_REF] Poissy | Risk factors for candidemia: a prospective matched case-control study[END_REF] Invasive fungal infection could have been sped up by septic shock and aminoglycoside use. This hypothesis is supported by the timing of the invasive candidiasis not found by the laparotomy conducted on D+14.

Although rare after CAR T-cell therapy, radiation-and chemotherapy-induced GI mucositis is a frequent complication in patients with hematological malignancies. GI mucosa repair is observed within two weeks after the end of cytotoxic treatment and usually concomitant to neutrophil recovery. In the current case, a loss of the entire GI mucosae was noted in the postmortem analysis. Severe GI barrier damage due to the use of prior therapies including abdominal irradiation and the further administration of tocilizumab could have promoted antibody against human interleukin-6 (IL-6) receptor, may have contributed to delayed GI wall repair and GI mucosae recovery. As apart from its role in inflammatory response, IL-6 is also known to be involved in mucosal wound healing. [START_REF] Kuhn | IL-6 stimulates intestinal epithelial proliferation and repair after injury[END_REF] Furthermore, tocilizumab is known to cause adverse GI events such as ulcers in the small and large intestine and intestinal perforation among rheumatoid arthritis patients who have received tocilizumab therapy in clinical trials. [START_REF] Monemi | Incidence of Gastrointestinal Perforations in Patients with Rheumatoid Arthritis Treated with Tocilizumab from Clinical Trial, Postmarketing, and Real-World Data Sources[END_REF] Tocilizumab could have inhibited intestinal tissue repair and furthered bacteria translocation leading to the invasion of intestinal mucosa by yeasts. Since invasive fungal infections are uncommon in CAR T-cell recipients, there is no evidence suggesting the use of systematic anti-fungal prophylaxis, but it should be considered for patients with prolonged neutropenia who are on corticosteroids. [START_REF] Yakoub-Agha | Management of adults and children undergoing chimeric antigen receptor T-cell therapy: best practice recommendations of the European Society for Blood and Marrow Transplantation (EBMT) and the Joint Accreditation Committee of ISCT and EBMT (JACIE)[END_REF][START_REF] Haidar | Invasive Mold Infections After Chimeric Antigen Receptor-Modified T-cell Therapy: A Case Series, Review of the Literature, and Implications for Prophylaxis[END_REF] In addition, the use of proton pump inhibitor is to be considered in patients undergoing CAR T-cell therapy, especially when corticosteroids and tocilizumab are administered.

To our knowledge, this is the first report of septicemia and disseminated candidiasis due to delayed GI mucosae repair in a patient treated with anti-CD19 CAR T-cell therapy and tocilizumab. Given its potential GI toxicity, close monitoring of GI events in patients receiving tocilizumab following CAR T-cell therapy is recommended. Furthermore, tocilizumab should be used with precaution in patients having recently received abdominal irradiation or who present other conditions that might alter the GI wall.

Figure legend Figure 1 .

 legend1 Figure legend

Grant support

No funding was received for this work.

Competing Interests

The authors have no conflicts of interest to declare.

Authors' contribution

IYA, BS and FM conceived the study; OK, SL, RN and ML acquired data; DB, OK, SM and ASM analyzed data; DB, OK, SL and BS wrote the original draft; all authors revised and approved the final manuscript