Norbert A ' Campo

Bernard Teissier

On the paper Un résultat sur la monodromie

Présentation

The local study of complex hypersurfaces in C n+1 , n = 0, 1, • • • has a long history.

First let us study the case n = 0. Let U ⊂ C be an open connected neighborhood of 0 and let f : U → C be a non constant holomorphic function that vanishes at 0. Then after shrinking U , there exists on U a complex coordinate function z, that vanishes at 0, such that f equals z m , m = 1, 2, • • • . So the complex hypersurface

H f = {p ∈ U | f (p) = 0} is the singleton H f = {0}. The complex hypersurface H f -t = {p ∈ U | f (p) =
t} consists for |t| small enough of m points provided t = 0. If t = t(τ ) = r(cos(τ ) + i sin(τ )), τ ∈ [0, 2π] the set H f -t moves in such a way that the graph τ ∈ [0, 2π] → H f -t(τ ) is a braid in [0, 2π] × U (Fig. 1). The monodromy of this braid is a cyclic permutation of the set H f -t .

The cases n ≥ 1 are more complicated. As before, 0 ∈ U ⊂ C n+1 , and let f : U → C be a non-constant holomorphic function that vanishes at 0. Two assumptions will simplify the study : the differential df does not vanish on U \ {0} and, instead of the open U , one considers a euclidean closed ball B = B(0, R) of small radius R. A seminal Theorem of F. Bruhat and H. Cartan, see [B-C], [W-B], valid for real analytic, semianalytic or subanalytic sets, is essential. The Theorem goes today under its name given by Milnor : Curve Selection Lemma. Using this Lemma, a transversality result of Milnor follows : the radius R can be chosen such that for all 0 < r ≤ R the intersections of the spheres ∂B(0, r) and the complex hypersurface H f are transverse. It follows that the space H f ∩ B(0, R) is contractible and that 0 is the only critical value of the restriction of f to the interior of B. Moreover, there exist ρ > 0 such that for all

t ∈ C, 0 < |t| ≤ ρ, the intersection X f,t = B∩H f -t is a manifold with boundary. Putting t(τ ) = ρ(τ ) = ρ(cos(τ ) + i sin(τ )), the graph of τ ∈ [0, 2π] → X t(τ ) sweeps out a cobordism W f,ρ from X f,ρ = X f,t(0) back to X f,ρ . A trivialisation of W f,ρ induces a diffeomorphism T : X f,ρ → X f,ρ .
The isotopy class of T is called the local monodromy at 0 of the complex hypersurface H f . The induced map by T on the homology is commonly called the monodromy.

Only few monodromies were known at the time of the work of Sebastiani and Thom. The local monodromy of the quadratic function

f = z 2 0 + z 2 1 + • • • + z 2 n :
1 C n+1 → C by Picard and Lefschetz and the cohomological monodromy for functions

f = z a0 0 + z a1 1 + • • • + z an n : C n+1 → C, a 0 , a 1 , • • • a n ≥ 2
, by Pham. These polynomials f do not seem very complicated, and the discoveries of Brieskorn and Hirzebruch showing that many exotic spheres previously discovered by Milnor appear as boundaries ∂X f,0 came as a surprise. Milnor gave a course on this topic at Princeton ; see the well known book [M].

The work of Sebastiani and Thom is an extension of the work of Pham. First let us explain very briefly the work of Pham. For

f = z a0 0 + z a1 1 + • • • + z an n : C n+1 → C, a 0 , a 1 , • • • , a n ≥ 2, Pham constructs inside X f,t = B(0, R) ∩ H f -t , 0 < |t| << R, a simplicial complex Φ f,t on which X f,t retracts by de- formation. The complex is a union of n-simplices ∆ µ (t) ⊂ X f,t that are para- metrized by the standard n-simplex ∆ n = {s 0 , s 1 , • • • , s n | s i ≥ 0, n i=0 s i = 1} as follows : φ µ(t) : (s 0 , s 1 , • • • , s n ) ∈ ∆ n → (s 1 a 0 0 µ 0 (t), s 1 a 1 1 µ 1 (t), • • • , s 1 an n µ n (t)) ∈ X f,t where µ(t) = (µ 0 (t), µ 1 (t), • • • , µ n (t)) and µ i (t) is a chosen a i -th root of t.
The number of possible choices, i.e., the number of n-simplices in Φ f,t , is the product a 0 a 1 . • • • .a n of the exponents. Moreover, the realization Z f,t of Φ f,t is homeomorphic to the join U a0 * U a1 * • • • * U an where U ai ⊂ C is the set of a i -roots of unity. The dimension of Z f,t is half the real dimension of X f,t . The simplicial map induced by the primitive cyclic permutations of U ai is a homotopic model for the local monodromy of f .

The ramification of the integrals

t → ∆µ(t) z b dz 0 ∧ dz 1 ∧ • • • ∧ dz n /df for monomials z b = z b0 0 • • • z bn n with 0 ≤ b i < a i
is studied by Pham and he computes the monodromy action on the De Rham cohomology of X f,t .

The work of Sebastiani and Thom concerns hypersurfaces defined by po-

lynomials f = f 0 + f 1 + • • • + f k : C N +1 → C, k ≥ 2 where N + 1 = (n 0 + 1) + (n 1 + 1) + • • • + (n k + 1
). The term f 0 depends only on the first (n 0 + 1) variables, f 1 depends only on the next (n 1 + 1) variables, ... . Again assume f i (0) = 0, i = 1, 2, • • • , k, and that df has an isolated zero at 0 ∈ C N +1 . Clearly, df i has an isolated zero at 0 ∈ C ni+1 . Let T i : X fi,t → X fi,t be a monodromy diffeomorphism for the hypersurface {f i = 0} ⊂ C ni+1 , well defined up to isotopy. Here X fi,t is constructed as above for 0 < |t| << R i .

A concrete example with k = 2, n 0 = 1, n 1 = 0 would be f = ((z 3 0 + z 2 1 ) 2 + z 5 0 z 1 ) + z 3 2 . In this language, and with above notations, Sebastiani-Thom's Theorem reads as follows :

Theorem 1.1 (Sebastiani & Thom). Let f be as above. Choose R, R i for f, f i with R i << R. Choose 0 < |t| << Min{R i } for f . Choose monodromy diffeo- morphisms T i : X fi,t → X fi,t . For s ∈ ∆ k define Y f,t,s = X f0,s0t × X f1,s1t × • • • × X f k ,s k t ⊂ X f,t ⊂ C (n0+1)+(n1+1)+•••+(n k +1) Define Y f,t = ∪ s∈∆ k Y f,t,s . Then Y f,t ⊂ X f,t is a deformation retract of X f,t . Moreover, the space Y f,t is homotopic to the join Z f,t = X f0,t * X f1,t * • • • * X f k ,t and the join map T 0 * T 1 * • • • * T k : Z f,t → Z f,t is a homotopic model for the local monodromy of f at 0 ∈ C N .
Remark. If k = n + 1, i.e. for polynomials studied by Pham, the spaces Y f,t and Z f,t coincide and are a polyhedron of real dimension n inside the fiber X f,t of real dimension 2n. If 2 ≤ k < n + 1, i.e. for polynomials studied by Sebastiani and Thom, the space Y f,t is a closed semi-algebraic subset of real dimension 2N -k + 1 in X f,t . The homotopy equivalence with the join Z f,t is due to the homotopy equivalences Y fi,0 ∼ { * }.

In case of sums

f = f 0 + f 1 + • • • + f k of
functions in disjoint sets of variables having at 0 non-isolated singularities, the Curve Selection Lemma still applies and extends Milnor's transversality result in stratified sense. As a consequence, the homotopy equivalences Y fi,0 ∼ { * } and, without any change of words, that the above Theorem of Sebastiani and Thom remains valid in case of summands with non-isolated singularities.

Commentaires

The addition defined by Sebastiani-Thom has turned out to have many more applications than the construction of many explicit examples of monodromies and boundaries of isolated singularities, such as exotic spheres. First of all, the proof constructs not only the monodromy of the sum, but also its Seifert form and hence the intersection form of vanishing cycles.

Assuming isolated singularities, keep notations, and introduce the notation of X f,t for the Milnor fiber obtained by pushing the tube fiber X f,t radially, by constant argument of t, into the sphere of ambiant space. This is possible as done by Milnor, again using the Curve Selection Lemma. The spaces X f,t , X f,t , X f,t + are canonically homotopic. Here t + denotes a complex number e 2πδ t for small positive δ. The subspaces X f,t , X f,t + in the local sphere are disjoint, and X f,t + is a homotopy retract of X f,t , so by the Alexander linking one obtains a nondegenerate pairing

A f : HN (X f,t , Z) × HN (X f,t + , Z) → Z
of reduced homology groups, which together with above homotopy equivalence yields the Seifert form

S f : HN (X f,t , Z) → ( HN (X f,t , Z)) *
Remember the join formula S N = S n0 * S n1 * • • • * S n k for the local ambient spheres. Also remember that the reduced homology of a join product is canonically isomorphic to the graded-shifted tensor product of the reduced homologies of the factors. The shift is by k -1. Now it is straightforward that

S f = ±S f0 ⊗ S f1 ⊗ • • • ⊗ S f k
holds for the Seifert form. The Seifert S form determines the intersection I form on the reduced homology and also the homological monodromy T by I = S ± S t and T = ±S • (S t ) -1 .

As one sees by considering Sebastiani-Thom sums such as U (z 0 , . . . , z n )f (z 0 , . . . , z n ) + g(w 0 , . . . , w m ),

where U is a unit, the analytic isomorphism type of the sum is not in general well defined by the analytic type of the summands. However, its equisingularity class for any reasonable definition of equisingularity is well defined and this may partly explain its usefulness in the study of geometric invariants. Here are some examples :

-The study of special case of the Thom-Sebastiani operation where one adds a function of a single variable, f (z 0 , . . . , z n ) + w k = 0 is already quite rewarding. From a differential topology viewpoint the intersection of this hypersurface with a small 2n + 3-sphere centered at the origin in C n+2 is a k-fold cyclic covering of the sphere S 2n+1 ramified along its intersection with f (z 0 , . . . , z n ) = 0. -Thom had asked whether any hypersurface with isolated singularity is a generic hyperplane section of a hypersurface with isolated singularity, that is, a section by a hyperplane which is not a limit of tangent hyperplanes at non singular points. In [Te] it is shown that when the integer k is larger than the largest polar invariant (see the commentary to the manuscript "Un résultat sur la monodromie" at the end of this volume) η(f ) ∈ Q >0 of the hypersurface with isolated singularity f (z 0 , . . . , z n ) = 0, then the hyperplane w = 0 is a generic hyperplane section of the hypersurface with isolated singularity f (z 0 , . . . , z n ) + w k = 0. The same type of argument, based on the study of the polar invariants of a Sebastiani-Thom sum, is used there to show that [η(f )] + 1 is the degree of topological sufficiency of the map germ f : (C n+1 , 0) → (C, 0). -Integral dependence criteria for equisingularity imply that if F (t, z 0 , . . . , z n ) = 0 and G(t, w 0 , . . . , w m ) = 0 determine two germs of families of isolated singularities of hypersurfaces which are both equisingular in the sense that the t-axis is the singular locus and a Whitney stratum, then the Sebastiani-Thom sum F (t, z 0 , . . . , z n )+G(t, w 0 , . . . , w m ) = 0 is also equisingular. In [Te], applying this with G = F is the key to a proof of the constancy, in an equisingular family of hypersurfaces with isolated singularities, of the Jacobian Newton polygon, and in particular of the polar invariants. -There have recently appeared many generalizations of the Thom-Sebastiani addition ; we can mention :

-Goulwen Fichou and Yimu Yin have in [F-Y] proved a Sebastiani-Thom formula for the non-archimedean Milnor fiber introduced by Hrushovski-Loeser which, in their words, is "a richer embodiment of the philosophy of the Milnor fiber".


Valérie Rochaix Vieillesse

come     Vieillesse, old-age and lǎonián Analysis of a discursive construction of care in the context of Alzheimer disease

Faculty of Foreign Languages, Sun-Yat-Sen University, Guangzhou, China 16/11/2023

Vieillesse, old-age and lǎonián Analysis of a discursive construction of care in the context of Alzheimer disease

Valérie Rochaix, University of Tours, Laboratoire Ligérien de Linguistique (UMR 7270), membre associé au Prefics (UR 4246)

Alzheimer's disease is not a direct consequence of ageing, but it mainly concerns older people. In France, it affects one in 5 people over the age of 80. The carers of people diagnosed with Alzheimer's therefore have to deal with people who are gradually losing their abilities as a result of both old age and disease. We invite here to look at the lexical representation of old age, in particular, in French, English and Chinese Mandarin, on the basis of their respective definitions in language dictionaries, in order to understand how the different languages take account of this period of life through this denomination and how these representations rooted in a languageculture can say/act on the ability of family carers to look after their relative. We then illustrate the discursive (de-)construction of this representation in French, as carried out in the Accmadial corpus (Accompagnants des Malades diagnostiqués Alzheimer) AAP 'handicap et autonomie, IRESP 2020-2022, CPER DI2L2S MSH 2018) consisting of semi-directive interviews conducted with spouses/partners, children and grandchildren of people affected by this neurodegenerative disease in Western France. This is be done from two perspectives : a linguistic one, in order to illustrate the semanticopragmatic and semantico-discursive mechanisms of meaning construction; and an intercultural one, in order to explore, on the basis of linguistic clues, representations of the world perceived and modalised across three language-cultures. Drawing on the distinction set forth by the philosopher of language John Searle (1990[START_REF] Searle | The Construction of Social Reality[END_REF] between brute facts, such as illness and death, which require no human institution, and institutional facts, which result from a collective intention, such as the way in which they are accompanied, and its associated definitions of regulatory and constitutive rules, we start by identifying what, in old age and its consequences, are natural facts or social constructions, over which institutions, in the broadest sense, have leeway. Secondly, we describe the words "vieillesse", in French, "old-age", in English and "老年" (lǎonián), in Chinese Mandarin on the basis of the definitions, collocations and associated examples by, in French, the Grand Robert de la langue française ( 2009), the Grand dictionnaire des Lettres Larousse (1989), the Petit Larousse (2023), the dictionnaire érudit de la langue française Lexis (2014), the Quillet dictionary (1990) and the TLF-i [on-line], as far as concerns English, the Oxford English Dictionary [online], the Cambridge English Dictionary [online] and The Collins English Dictionary [online] and for the Chinese part, the Xiàndài hànyǔ cídiǎn, electronic version and 7th paper edition, as well as the Hànyǔ dà cídiǎn. To do so, we rely on the theoretical framework of the Semantics of Argumentative Possibilities [START_REF] Galatanu | La sémantique argumentative intégrée et ses enjeux pour l'analyse linguistique du discours[END_REF](Galatanu, , 2007(Galatanu, , 2009(Galatanu, , 2013[START_REF] Galatanu | La sémantique des possibles argumentatifs. Génération et (re)construction discursive du sens linguistique[END_REF], whose strata-based modelling (core, stereotypes, argumentative possibilities and argumentative deployments) allow, among other things, to isolate what constitutes the essential properties of the word from its less stable properties, "argumentative associations of the essential properties with other semantic representations, more kinetic because rooted in cultural kinetics" [START_REF] Galatanu | Construction discursive des valeurs sociales complexes et sémantisme des valeurs modales épaisses. Retour à une vie normale[END_REF]. This step provides clues about the recurring properties in the language dictionaries, as well as it does about the differences that the latter reflect between the semantic representation of the word in the 3 languages and the anchoring of the notion of old age in its natural and/or social dimensions.

Finally, we look at the discourse mechanisms used in France, particularly by carers of Alzheimer's patients, as evidenced by the Accmadial corpus (184 texts; here, 102 texts, 1,026,781 occurrences, 18,421 forms and 7,577 hapaxes). Based on a textometric analysis, using the Iramuteq software developed by P. Ratinaud and P. Marchand, and a contextual analysis of occurrences of "vieillesse" (old-age)", "maladie" (illness), we identify how they put the experience of help into words, and how they describe care in relation to old age, illness and dependency. More specifically, we focus on two observations : (i) the overall weakening of physiological functions and mental faculties and the difficulties in carrying out the tasks relating to these functions and faculties are, in this corpus and on the basis of this approach, minimized by their relationship not to an exceptional situation but to the normal development of the relative over which the carers have no control ; (ii) in comparison, the carer who becomes aware of the gradual dependence of his or her relative suffering from Alzheimer's disease says this care mainly in relation to the disease. "If old age, an ontological fact, is said to carry very negative values, which subjectivize its expression, it is also used to attenuate the seriousness of the symptoms of the disease, to minimize the "abnormal" behaviour of the patient due to illness. The description of the semantic representation of the denomination of a raw, ontological fact leads us to distinguish what, in the analysis of discourse, can provide elements of an answer to the relationship between the argumentative links constructed by speakers and their capacities for adherence" (Rochaix, à paraitre).


Gildas Carlin

Ian Manifacier

Jean-Louis Milan

Stochastic model of cell migration over curved substrate

Trajectories of T-cells on sinusoidal substrate

Scale bar : 50µm

The greater the curvature, the greater cell migration is contained in the valleys of the substrate [START_REF] Song | Sinusoidal wavy surfaces for curvature-guided migration of T lymphocytes[END_REF]. The cell is triggered by cell-scale curvature, this phenomenum named "curvotaxis" leads cells toward concave areas [START_REF] Pieuchot | Curvotaxis directs cell migration through cell-scale curvature landscapes[END_REF].

  model on flat substrate : Mean Square Displacement (MSD) and Velocity Autocorrelation Function (VACF) are calculated (red curves) and compared with experimental data (blue curves) [3] --> the model behaves like cells It gives parameters independant with curvature What is the strategy of the cell to measure curvature ? Stochastic model of cell migration over curved substrate Gildas Carlin(1,2), Ian Manifacier(1,2), Jean-Louis Milan(1,2) 1.Aix Marseille University, CNRS, ISM, Marseille, France 2.APHM, Institute for Locomotion, Department of Orthopaedics and Traumatology, St Marguerite Hospital, Marseille, France


Jeremy Charriot
email: j-charriot@chu.montpellier

Vincent Descamps

Roger Jankowski

Milka Maravic

Arnaud Bourdin

Keywords: severe asthma, atopic dermatitis, nasal polyposis, urticaria, T2 diseases, biologics --

Background:

Several biologics (Bx) and targeted synthetic drugs (TSD) exist to treat T2 diseases, including chronic spontaneous urticaria (CSU), severe asthma (SA), chronic rhinosinusitis with nasal polyposis (CRSwNP) or atopic dermatitis (AD).

Objective:

To identify patients treated with Bx/TSD from a dynamic dispensing database using an algorithm-based methodology.

Methods:

We used the LRx database (Lifelink Treatment dynamics, IQVIA) which covers nearly 45% of the French retail pharmacies. Patients who had at least one Bx/TSD dispensing from April 2021 to March 2022 were included. An algorithm was designed to determine the indication of the Bx/TSD prescription analyzing all previous drug dispensation since March 2012 following a 3-steps procedure.

Results:

A total of 21,677 patients received at least one Bx/TSD between March 2021 and April 2022. The algorithm identified 91.7% (n = 19,884) patients with a T2 disease (AD = 18.4%, CRSwNP = 1.5%, SA = 59.5%, and CSU = 12.4%), the rest having either an association of diseases (1%) or an undetermined one (7.3%). SA was the main reason for Bx/TSD initiation (52%), followed by AD (29%), CSU (14%) and CRSwNP (5%). For SA patients already under biologic at entry, omalizumab was the most frequently prescribed (48%) followed by benralizumab, mepolizumab (22% each) and dupilumab (8%). Dupilumab was mostly prescribed for AD patients (89% for patient-initiated vs 96% for patient-renewed) followed by baricitinib.

Conclusion:

The algorithm was able to identify patients with T2 diseases under Bx/TSD treatments. This tool may help to follow the evolution of prescription patterns in the future.

Plain Language Summary:

Nowadays, physicians have a choice of multiple biologics. Although some prospective cohorts of patients receiving those therapeutics exist, there are very few large up-to-date databases. Our algorithm based on a nationwide dynamic dispensing database was able to identify the T2 diseases of patients under biologics or targeted synthetic drugs and to characterize this population. This is a step toward a better understanding and monitoring of prescription patterns in a nationwide setting.

Multiple Biologics for Multiple T2 Diseases: A Pharmacoepidemiological Algorithm for Sorting Out

Patients by Indication

Introduction

Chronic inflammatory diseases have seen their therapeutic sphere turned upside down by the revolution provided by the rise of monoclonal antibodies and other "small molecule" agents.

Especially, new biologics targeting diseases gathered under the type 2 (for type 2 inflammation) umbrella such as severe asthma (SA), atopic dermatitis (AD), chronic spontaneous urticaria (CSU) and chronic rhinosinusitis with nasal polyps (CRSwNP)1 have transformed their burden: omalizumab (Anti-IgE), mepolizumab (Anti-IL5), reslizumab, benralizumab (Anti-IL5Rc) and dupilumab (Anti-IL4/13Rc). The multiple actions of these molecules stem from the pathophysiology of type 2 inflammation which is a fine balance between tolerance and intolerance to the external environment through the airways, the skin or the digestive tract. Indeed, it is driven by both the innate immune system triggered by pollutants, viral or fungal infections involving type 2 innate lymphoid cells (ILC2) and the adaptive immune system, triggered by contact with an allergen involving type 2 T-helper (Th2) cells. Both ILC2 and Th2 cells produce the type-2 cytokines (interleukin (IL)-4, IL-5 and IL-13), each with several roles in the inflammation cascade.2

One of the first monoclonals, omalizumab, was first approved for SA and then for CSU. More recently, it has been approved for CRSwNP. Then mepolizumab, reslizumab, benralizumab and finally dupilumab have proved efficacy in severe eosinophilic asthma in reducing exacerbations, oral steroids use and in improving symptoms.3 They have also shown great results in CRSwNP in improving nasal and endoscopic scores,4-7 though only dupilumab, mepolizumab and omalizumab are approved in this indication in France. Reslizumab was not approved in France because of the intravenous route. Among those drugs, dupilumab is the only one to be approved for atopic dermatitis thanks to a drastic mitigation of disease activity in Phase III studies.8 Baricitinib, initially approved for rheumatoid arthritis (RA)9 and further for moderate-to-severe AD,10 has a special place because it is not a biological treatment as such, rather a selective immunosuppressant which inhibits the enzymatic activity of Janus Kinases 1 and 2.

CSU, AD, SA and CRSwNP share some pathophysiological mechanisms gathered under the T2 acronym, and as a consequence Bx/TSD has progressively acquired overlapping indications. Moreover, initially restricted to tertiary care center specialists, their prescriptions are now authorized in secondary care centers. This situation likely modified the profile of patients initiated with these molecules, making the collection of real-life data paramount.

Long-term data from open-label extension studies11 or from early access programs12 and "real-world data" are now available. [START_REF] Pilette | REALITI-A Study: real-world oral corticosteroid-sparing effect of mepolizumab in severe asthma[END_REF][START_REF] Dupin | Effectiveness and safety of dupilumab for the treatment of severe asthma in a real-life French multi-centre adult cohort[END_REF][START_REF] Humbert | Real-life omalizumab exposure and discontinuation in a large nationwide population-based study of paediatric and adult asthma patients[END_REF] The latest mostly derived from national healthcare databases, which implies a significant delay between the last available data and present time, imposing very frequent updates.16 Accordingly, a real-time updating tool describing Bx/TSD prescription pattern is needed, as no large cohort of patients exists in France (the prospective French cohort RAMSES (recherche sur les asthmes sévères, AP-HP, NCT04077528) involves currently less than two thousand patients).

Lifelink Treatment dynamics (LRx) is a dynamic dispensing database regrouping 45% of the French retail pharmacies (see Materials and Methods). Using that database, we aimed to develop an algorithm able to describe and sort the population treated or initiated by Bx/TSD drugs (disease identification, demographic data, co-treatments) at a large scale, starting from the dispensation of these drugs over a given period of time.

Materials and Methods

Design

We designed a retrospective observational study using non-medical sources. A longitudinal assessment of patients' dispensations since March 2012 is possible due to its unique identifier regardless of the pharmacy where the dispense occurred. Data do not include treatments delivered during hospitalizations.

Drugs of Interest

The algorithm focused on the Bx/TSD prescribed in the management of AD, CRSwNP, SA, and CSU delivered in outpatient care setting by a private or hospital-based practice physician. Patients identified with rheumatoid arthritis (RA) were excluded (as RA is not considered as a T2 disease and is targeted only by Baricitinib in our study). The Bx/TSD of interest was benralizumab, dupilumab, mepolizumab, and omalizumab for Bx, and baricitinib for TSD.

The first indication and the date of following indication were based on the date of their approval in France (ie, date of the transparency committee).

Sorting Rules Using TD

In order to discriminate the different diseases, the tracking drugs (TD) usually prescribed for each were assessed and set up to feed the algorithm described below. For AD, the TD included those delivered before Bx/TSD initiation (alitretinoin, fusidic acid for topical use, clobetasone), and those co-prescribed with Bx/TSD (ciclosporin or methotrexate in association with emollient or topical tacrolimus or topical corticosteroids and topical tacrolimus). For SA, dispense of inhaled corticosteroids (ICS) and long-acting beta-2 agonist (LABA) combination was recorded. More specifically, at least 1 delivery of ICS/LABA (irrespective of the dosing) co-prescribed with a Bx/TSD during the study period, and/or at least ≥2 deliveries of an (high/medium dose) ICS/LABA combination in a historical period of CRSwNP and CSU (Figure 1). We also focused on prescribed drug(s) to evaluate either the burden of each disease or the adequacy with the guidelines (Table S1). For each drug, at least one prescription during the study period was considered.

3-Step Algorithm for Diagnosis Identification

Patients from the LRx database who had at least one Bx/TSD dispensing from April 2021 to March 2022 were included in the present study. Then, an algorithm was designed to determine the indication (ie, which disease of interest) for which a patient received a Bx/TSD. This algorithm analyzed all previous drug dispensing since March 2012 for each patient following a 3-steps procedure if needed (Figure 1):

Step1: Firstly, the indication for which each Bx/TSD dispense during a 10-year historical period was analyzed. At this stage, a patient could be sorted as having one disease in case of mono-indication of the Bx/TSD dispenses or common indication shared by at least two Bx/TSD dispensed for the same patient.

Step2: If a patient was not classified in the first step (multiple indications for the prescribed biologic), after assigning a score of 5 for each indication in competition, the algorithm proceeded to the next step. In this step, only the specialty prescribing the Bx/TSD having an ability to differentiate the disease (dermatology, ENT, and pulmonology) were analyzed. A score of 3 was added to each indication related to the prescriber's specialty. If multiple physicians from different specialties were associated to one patient's prescriptions over the study period, this score was attributed to each indication related to different specialties, regardless of the number of prescriptions. For CRSwNP, only a biologic initiated and prescribed by an ENT allowed to classify the patient.

Step3: If the biologic prescribed for one patient had more than one indication (disease not identified in step 1) AND if the prescriber specialty was not able to differentiate the disease (disease not identified in step 2), the third step considered the previous dispensations, focusing on several TD (described above) dispensed before Bx/TSD initiation and/or ±30 days around the Bx/TSD dispensation. A score of 2 was attributed to these TD, regardless of the number of dispensations throughout the follow-up.

If a patient was not classified at the first step, a global score for each indication was computed from the subscores obtained at each step, and the patient was then classified as having the disease with the highest score. In case of equal scores for two indications, the patient was considered as having both diseases. If the algorithm could not determine the indication accurately, the patient was classified as having an "undetermined disease" (ie, ≥3 indication, if at least one Bx/ TSD dispense with multiple indication without information regarding prescriber's specialty and no TD, with Bx/TSD indication in one disease and another with other indication not shared with the previous Bx/TSD dispense) (Figure 1).

Statistical Analysis

The total raw number of patients receiving Bx/TSD from April 2021 to March 2022 was described from the LRx database. The following characteristics of patients classified as having a specific disease were described: demographic characteristics (age category, gender), Bx/TSD (initiated or not during the study period) and co-treatments dispensed at least once during the study period. An initiation was defined as no Bx/TSD delivered 12 months before the first Bx/TSD recorded during the study period from April 2021 to March 2022. Only descriptive statistics were performed. Quantitative data were expressed by mean and standard deviation, and qualitative data as percentages.

Ethics

Access to and processing of data were done in compliance with applicable laws and regulations including GDPR.

Results

Identification of Diseases by the Algorithm and Demographic Characteristics

In the LRx database, 21,677 patients received at least one Bx/TSD from March 2021 to April 2022. The algorithm identified 91.7% (n = 19,884) patients as having a unique disease. Among them, a majority had SA (59.5%), then AD (18.4%), CSU (12.4%) and CRSwNP (1.5%). One percent were sorted as suffering from an association of diseases, whereas the indication remained undetermined for 7.3% (Table 1).

Patients with AD were on average younger (mean age = 43.3 years; SD = 20) versus other conditions: 56.5 (SD = 18.5) for SA, 55 (SD = 14.1) for CRSwNP and 49.6 (SD = 18.3) for CSU. Men were mostly represented in CRSwNP (66.1%) and women in CSU (66.1%) (Table 1 and Figure 2).

Repartition of Bx/TSD Prescriptions

Among the 19,884 patients classified in one specific disease, 34.5% (n = 6.925) were initiated with a Bx/TSD mainly for SA (52%) followed by AD (29%), CSU (14%), and CRSwNP (5%). In SA, omalizumab was the first biologic initiated (32%) followed by equivalent respective parts of prescription for the anti-IL5/IL5Rc and IL4/13 monoclonal antibodies (mepolizumab, benralizumab, dupilumab), respectively, 23%, 22% and 22%. Dupilumab and omalizumab represented the only initiated or renewed biologic for CRSwNP and CSU, respectively. Dupilumab was mostly prescribed for AD patients (89% for patient-initiated vs 96% for patient-renewed) followed by baricitinib. For SA patients already under biologic before the study period, omalizumab was the most frequent biologic (48%) followed by benralizumab and mepolizumab (22% for each) and dupilumab (8%) (Table 2).

Co-Treatments of Interest

Figure 3 described the frequency of oral corticosteroid (OCS) dispenses among patients under Bx/TSD during the study period: SA and CRSwNP represented the main diseases for which patients had at least 2 OCS delivery during the study period (41.5% and 40.5% respectively). Hypnotics and sedatives are frequently co-prescribed in T2 diseases and AD, with the highest proportion for CSU (28.5%). Antibiotics and especially penicillin were mostly co-prescribed in CRSwNP (34.8%) and SA (35.6%). Influenza vaccine prescriptions were detected in almost half of patients identified with SA (47.8%) (Table 3).

Discussion

Our 3-step algorithm identified almost 20,000 patients under Bx/TSD for a T2 disease, in a real-life setting, and provided interesting data about their demographic characteristics and their co-treatments. The accuracy of the data we obtained becomes more meaningful when compared to "real-life" studies. Indeed, in accordance with the results of the CHRONICLE cohort which concerns 2793 patients in the United States, we here found approximately the same proportion of biologic prescriptions for severe asthma: 48% for omalizumab, an equal proportion for mepolizumab and benralizumab and the rest for dupilumab. The age-class distribution was similar,20 as was the proportion of adult women within the SA group. [START_REF] Chowdhury | Sex and gender in asthma[END_REF] The well-known burden of oral corticosteroids (OCS) in SA or CRSwNP was also highlighted in our research, with a similar number of OCS bursts over a one-year period,22,23 The psychological comorbidities and the prescriptions related to them were also in line with published data; indeed, we found a high prescription of anxiolytics or hypnotics among patients with SA or severe CRSwNP.24,25 Based on the classification of patients we obtained, we were then able to depict accurately the repartition of the prescription of each Bx/TSD according to the identified underlying diseases, and their trends in terms of prescription shares over the study period; indeed, in addition to the Bx/TSD dispenses observed at the beginning of the period of interest (renewed), we were able to capture all new drug dispensing from March 2021 to April 2022 (initiated). Thus, we observed a decreasing number of prescription of omalizumab, as opposed to the increased prescription of dupilumab, in SA, that fits with the reality of the successive marketing-authorizations in this indication.

We were also able to detect the co-treatments: this way, we and highlighted the burden of such severe diseases from an iatrogenic perspective with a significant proportion of antibiotics or oral corticosteroid bursts, which are far from being harmless.26,27

The reliability of our algorithm comes from the fact that it has also proved efficient in previous studies in different settings. For instance, it was able to identify patients with type 1 and type 2 diabetes, which could be helpful to monitor changes in strategies to control blood glucose.17 In a completely different field, that of epidemiological monitoring of acute gastroenteritis, the data obtained with our algorithm had a strong agreement with validated primary care French surveillance network data collected during winter months in the overall population.19

One strength of our study is that it relies on a large dispensing database which represent 45% of the French retail pharmacies. As a consequence, we obtained a representative sample of the French population. Another strength of our study is that the LRx database may be queried anytime starting from past month, allowing real-time updates and evolving Bx/TSD prescription patterns. This might be particularly relevant to monitor adherence to guidelines according to the evolution of marketing-authorizations of each molecule. Although this kind of pharmacoepidemiological tool appears obviously useful for companies, many interests can be identified also for clinicians, regulators, payers and policy makers, varying with the level of granularity (level of zoom) chosen: trends in incidence, regional specificities and heterogeneities, impact of new safety warnings when applicable, trends in costs, trends in OCS sparing, adherence to comedications, and needs for targeted continuous medical education. In addition, the 3rd step of our algorithm, based on Tracking Drugs to classify patients not previously categorized, is particularly original as it provides insights into the "polymedication" burden of patients with T2 diseases. These data plaid for a therapeutic de-escalation that Bx/TSD might bring some day: after oral corticosteroids, this could concern inhaled treatment tapering or discontinuation in patients with severe asthma controlled with Bx.

Besides, our study has limitations. First, as for any algorithm, some patients could not be classified in one disease. However, this represents a minor fraction of the general population of the study (7.3%). Secondly, the fact that no relevant Tracking Drugs were identified as relevant for CSU and AD could be perceived as a pitfall, despite the test of multiple combinations. For instance, high-dose anti-histaminics were tested for AD but did not change the performance of our algorithm in terms of disease classification. Moreover, during our period of interest, dupilumab was the only marketed monoclonal available for CSU and AD; as a consequence, the step 2 (based on the prescriber specialty) was reliable enough to classify the patients. At last, one limitation is the absence of a validation cohort with clinically established firmed diagnosis. Thus, we are not able to fairly extrapolate our results to the national population, though our database represents 45% of the retail pharmacies.

Conclusion

The algorithm was able to identify and describe the current landscape of T2 diseases treated by Bx/TSD. This tool could be helpful to monitor the general adherence to guidelines and the temporal evolution of the dispensed drugs according to their market authorizations in a reallife setting.

  LRx database was authorized by the French Data Protection Authority (CNIL) on the 21st of October 2011 [reference: DE-2011-097] and updated on July 2018 for compliance with the GDPR (Délibération 2018-289 du 12 septembre 2018 -Légifrance (legifrance.gouv.fr)).

Acknowledgments

The authors would like to thank the IQVIA Team and particularly Deborah Desprez, Eric Martinho and Daniel Poitevin.

Abbreviations

AD, atopic dermatitis; CRSwNP, chronic rhinosinusitis with nasal polyps; CSU, chronic spontaneous urticaria; OCS, oral corticosteroids; LRx, Lifelink Treatment dynamics; RA, rheumatoid arthritis; SA, severe asthma.

Disclosure

A.B. received payment or honoraria for lectures, presentations, speakers, bureaus, manuscript writing or educational events from AstraZeneca, GSK, Sanofi, Chiesi, Regeneron, ABScience, Novartis, and was principal investigator in clinical trials for AstraZenaca, GSK and Boehringer Ingelheim. J.C. received payment or honoraria for lectures, presentations, speakers, bureaus, manuscript writing or educational events from AstraZeneca, GSK, Sanofi, Chiesi. V. D. received payment or honoraria for lectures, presentations, speakers, bureaus, manuscript writing or educational events from ABBVIE, Janssen, Lilly, Novartis and Sanofi. R.J. reports personal fees from IQVIA, during the conduct of the study; personal fees from Sanofi, outside the submitted work. M.M is affiliated with IQVIA. The authors report no other conflicts of interest in this work.