MD Alexis Mathian
email: alexis.mathian@aphp.fr

MD, MSc Suzanne Mouries-Martin

PhD Karim Dorgham

Herve Devilliers

PhD Hans Yssel

MSc Laura Garrido Castillo

Fleur Cohen-Aubart

MD, PhD Julien Haroche

MD, MSc Miguel Hie

MD, MSc Marc Pineton De Chambrun

MD Hervé Devilliers

MD, PhD Fleur Cohen- Aubart

MD, PhD Makoto Miyara

MD, MSc Micheline Pha

MD Flore Rozenberg

MD, PhD †3 Guy Gorochov

MD, MSc Zahir Amoura

Ultrasensitive serum interferon-α quantification during SLE remission identifies patients at risk for relapse

Keywords: Systemic lupus erythematosus, interferon-alpha, remission, low disease activity, biomarker, relapse, flare

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

Methods A total of 254 SLE patients in remission, according to the Definition of Remission in SLE (DORIS) classification, were included in the study. Serum IFN-α concentrations were determined at baseline and patients were followed-up for one year. Lupus flares were defined according to the SELENA-SLEDAI Flare Index, whereas the Kaplan-Meier analysis and Cox regression analysis were used to estimate the time to relapse and to identify baseline factors associated with time to relapse, respectively.

Results

Of all patients in remission, 26% displayed abnormally high IFN-α serum levels that were associated with the presence of antibodies specific for RNP, double stranded (ds)DNA and Ro/SSA60, as well as young age. Importantly, elevated baseline IFN-α serum levels and remission duration were associated in an independent fashion, with shorter time to relapse, while low serum levels of C3 and anti-dsDNA Abs were not.

Conclusion

Direct serum IFN-α assessment with highly sensitive digital immunoassay permit clinicians to identify a subgroup of SLE patients clinically in remission, but at higher risk of relapse.

Key messages

-serum IFN-α levels have been poorly studied in SLE patients in remission so far; -the single-molecule array (Simoa) assay is an ultrasensitive assay that quantifies directly IFN-α at attomolar concentrations; -a quarter of SLE patients in remission display elevated serum IFN-α levels; -elevated serum IFN-α levels constitute an independent predictive biomarker of lupus flare; -adding serum IFN-α to the routine laboratory assessments in patient in remission could help clinicians to identify a subgroup of SLE patients at higher risk of relapse.

INTRODUCTION

Systemic lupus erythematosus (SLE) is a chronic autoimmune disease of unknown incompletely known etiology characterized by the presence of anti-nuclear autoantibodies and inflammation in a wide spectrum of organs. [START_REF] Lisnevskaia | Systemic lupus erythematosus[END_REF] Despite the improvement of SLE prognosis in the last decades, SLE patients are still at high risk of disease-related complications and premature death. [START_REF] Bernatsky | Mortality in systemic lupus erythematosus[END_REF][START_REF] Tektonidou | Survival in adults and children with systemic lupus erythematosus: a systematic review and Bayesian meta-analysis of studies from 1950 to 2016[END_REF] Several authors have shown that remission defined as the elimination of disease activity predicted a better disease outcome with a lower burden of damage and a lower risk of relapse. [START_REF] Nossent | Disease activity and damage accrual during the early disease course in a multinational inception cohort of patients with systemic lupus erythematosus[END_REF][START_REF] Zen | Prolonged remission in Caucasian patients with SLE: prevalence and outcomes[END_REF] Thus, remission achievement and its maintenance have become central in the management of SLE patients. [START_REF] Van Vollenhoven | Treat-totarget in systemic lupus erythematosus: recommendations from an international task force[END_REF][START_REF] Van Vollenhoven | A framework for remission in SLE: consensus findings from a large international task force on definitions of remission in SLE (DORIS)[END_REF] Many definitions have been used to better characterize remission states, but a single one has recently made consensus, the DORIS (Definitions Of Remission In SLE). For defining remission, the DORIS uses a clinical index, such as the clinical SLE disease activity index (SLEDAI)=0 with routine laboratory assessments including anti-double stranded DNA (anti-dsDNA) antibodies (Abs) and complement. [START_REF] Van Vollenhoven | A framework for remission in SLE: consensus findings from a large international task force on definitions of remission in SLE (DORIS)[END_REF] Serologically active patients, i.e. patients with an increase in serum anti-dsDNA Abs and/or a complement consumption, are much more likely to experience subsequent flares, as compared to those who are serologically inactive. [START_REF] Van Vollenhoven | A framework for remission in SLE: consensus findings from a large international task force on definitions of remission in SLE (DORIS)[END_REF] However, these two markers fail to reliably predict a lupus flare. [START_REF] Steiman | Prolonged serologically active clinically quiescent systemic lupus erythematosus: frequency and outcome[END_REF][START_REF] Gensous | Predictive biological markers of systemic lupus erythematosus flares: a systematic literature review[END_REF] Consequently, no consensus has yet been reached by the DORIS working group as to a reliable definition that enables the distinction of patients who are serologically active from those who are serologically inactive. [START_REF] Van Vollenhoven | A framework for remission in SLE: consensus findings from a large international task force on definitions of remission in SLE (DORIS)[END_REF] Many authors consider the dysregulation of interferons (IFNs), especially IFN-alpha (IFN-a), to be a central cause of the immunological abnormalities observed in SLE. [START_REF] Theofilopoulos | Type I interferons (alpha/beta) in immunity and autoimmunity[END_REF][START_REF] Obermoser | The interferon-alpha signature of systemic lupus erythematosus[END_REF][START_REF] Ronnblom | Cytokines as therapeutic targets in SLE[END_REF][START_REF] Niewold | Interferon alpha as a primary pathogenic factor in human lupus[END_REF][START_REF] Ronnblom | The type I interferon system in the development of lupus[END_REF][START_REF] Lauwerys | Type I interferon blockade in systemic lupus erythematosus: where do we stand?[END_REF][START_REF] Kirou | Anti-interferon alpha treatment in SLE[END_REF] Transcriptome analysis using microarray technology revealed up-regulation of numerous IFN-stimulated genes (ISGs) in SLE patients' peripheral blood mononuclear cells, constituting an overall "IFN signature". [START_REF] Bennett | Interferon and granulopoiesis signatures in systemic lupus erythematosus blood[END_REF][START_REF] Baechler | Interferoninducible gene expression signature in peripheral blood cells of patients with severe lupus[END_REF] Many reports showed patients' elevated serum-IFN-α levels to be associated with SLE activity and severity, suggesting that monitoring this cytokine might help physicians to better evaluate disease activity, [START_REF] Bennett | Interferon and granulopoiesis signatures in systemic lupus erythematosus blood[END_REF][START_REF] Baechler | Interferoninducible gene expression signature in peripheral blood cells of patients with severe lupus[END_REF][START_REF] Hooks | Immune interferon in the circulation of patients with autoimmune disease[END_REF][START_REF] Preble | Systemic lupus erythematosus: presence in human serum of an unusual acid-labile leukocyte interferon[END_REF][START_REF] Ytterberg | Serum interferon levels in patients with systemic lupus erythematosus[END_REF][START_REF] Friedman | Interferon production in patients with systemic lupus erythematosus[END_REF][START_REF] Shi | Serum interferon in systemic lupus erythematosus[END_REF][START_REF] Kanayama | Possible involvement of interferon alfa in the pathogenesis of fever in systemic lupus erythematosus[END_REF][START_REF] Vallin | Patients with systemic lupus erythematosus (SLE) have a circulating inducer of interferon-alpha (IFN-alpha) production acting on leucocytes resembling immature dendritic cells[END_REF][START_REF] Bengtsson | Activation of type I interferon system in systemic lupus erythematosus correlates with disease activity but not with antiretroviral antibodies[END_REF][START_REF] Dall | Type I interferon correlates with serological and clinical manifestations of SLE[END_REF][START_REF] Kirou | Activation of the interferonalpha pathway identifies a subgroup of systemic lupus erythematosus patients with distinct serologic features and active disease[END_REF][START_REF] Feng | Association of increased interferon-inducible gene expression with disease activity and lupus nephritis in patients with systemic lupus erythematosus[END_REF][START_REF] Petri | Longitudinal expression of type I interferon responsive genes in systemic lupus erythematosus[END_REF][START_REF] Landolt-Marticorena | Lack of association between the interferon-alpha signature and longitudinal changes in disease activity in systemic lupus erythematosus[END_REF][START_REF] Rose | IFNalpha and its response proteins, IP-10 and SIGLEC-1, are biomarkers of disease activity in systemic lupus erythematosus[END_REF][START_REF] Rose | Are interferon-related biomarkers advantageous for monitoring disease activity in systemic lupus erythematosus? A longitudinal benchmark study[END_REF][START_REF] Oke | IFN-lambda1 with Th17 axis cytokines and IFN-alpha define different subsets in systemic lupus erythematosus (SLE)[END_REF][START_REF] Mathian | Monitoring Disease Activity in Systemic Lupus Erythematosus With Single-Molecule Array Digital Enzyme-Linked Immunosorbent Assay Quantification of Serum Interferon-alpha[END_REF] although, unexpectedly, some clinically inactive patients have persistently elevated serum IFN-α levels. [19-23, 25, 35] Since serum concentrations of IFN-a are usually very low and often not detectable by classic immunoassays, monitoring the expression of ISGs is used to evaluate IFN serological activity. The resulting "IFN scores" are calculated based on the expression of several representative ISGs. [START_REF] Feng | Association of increased interferon-inducible gene expression with disease activity and lupus nephritis in patients with systemic lupus erythematosus[END_REF][START_REF] Yao | Development of Potential Pharmacodynamic and Diagnostic Markers for Anti-IFN-alpha Monoclonal Antibody Trials in Systemic Lupus Erythematosus[END_REF][START_REF] Yao | Use of type I interferon-inducible mRNAs as pharmacodynamic markers and potential diagnostic markers in trials with sifalimumab, an anti-IFNalpha antibody, in systemic lupus erythematosus[END_REF] However, the low availability and high complexity of transcriptome-microarray technology implies that IFN scores are not standardized and therefore cannot be easily used in clinical practice. At present, IFN-α overexpression has been poorly studied in patients in remission. The single-molecule array (Simoa) assay, or digital immunoassay, is an ultrasensitive assay based on enumeration of individual enzyme-labeled immunocomplexes of proteins captured on beads in singlemolecule arrays. It enables direct IFN-α quantification at attomolar concentrations, [START_REF] Mathian | Monitoring Disease Activity in Systemic Lupus Erythematosus With Single-Molecule Array Digital Enzyme-Linked Immunosorbent Assay Quantification of Serum Interferon-alpha[END_REF][START_REF] Rissin | Single-molecule enzyme-linked immunosorbent assay detects serum proteins at subfemtomolar concentrations[END_REF][START_REF] Wilson | The simoa HD-1 analyzer: a novel fully automated digital immunoassay analyzer with single-molecule sensitivity and multiplexing[END_REF][START_REF] Rodero | Detection of interferon alpha protein reveals differential levels and cellular sources in disease[END_REF] corresponding to a 5,000-fold-increased sensitivity over classic ELISAs. We and others have shown that at physiological concentrations, the digital immunoassay is as sensitive as ISG expression as a means to quantify IFN-a levels and simpler to perform and standardize. [START_REF] Mathian | Monitoring Disease Activity in Systemic Lupus Erythematosus With Single-Molecule Array Digital Enzyme-Linked Immunosorbent Assay Quantification of Serum Interferon-alpha[END_REF][START_REF] Rodero | Detection of interferon alpha protein reveals differential levels and cellular sources in disease[END_REF] We thus conducted a study to determine the magnitude of serum IFN-α concentrations in SLE patients in remission using the DORIS-validated criteria. [START_REF] Van Vollenhoven | A framework for remission in SLE: consensus findings from a large international task force on definitions of remission in SLE (DORIS)[END_REF] Additionally, in order to improve the definition of remission, we determined the clinical and biological features associated with elevated IFN-α levels in patients experiencing a remission and we investigated whether high serum IFN-α levels at baseline in patients in remission were predictive of a flare in the ensuing year.

PATIENTS, MATERIALS AND METHODS

Study design and patients

We conducted this longitudinal study between September, 2014 and September 2017 at the National Referral Center for SLE, Paris, France. Serum samples were obtained at day 0 (= baseline) from consecutive patients diagnosed with SLE according to the 1997 American College of Rheumatology criteria for SLE classification, regardless of the activity of the disease. [START_REF] Hochberg | Updating the American College of Rheumatology revised criteria for the classification of systemic lupus erythematosus[END_REF] Exclusion criteria were: 1) known or suspected infection or malignancy on the day blood was drawn; 2) increased Hydroxychloroquine (HCQ), prednisone and/or immunosupressant (IS) during the 4 weeks preceding day 0. SLE clinical characteristics (see online supplement), SELENA-SLEDAI, [START_REF] Bombardier | Derivation of the SLEDAI. A disease activity index for lupus patients. The Committee on Prognosis Studies in SLE[END_REF][START_REF] Buyon | The effect of combined estrogen and progesterone hormone replacement therapy on disease activity in systemic lupus erythematosus: a randomized trial[END_REF][START_REF] Petri | Combined oral contraceptives in women with systemic lupus erythematosus[END_REF] SLEDAI-2K, [START_REF] Gladman | Systemic lupus erythematosus disease activity index 2000[END_REF] class of lupus nephritis according to ISN/RPS-2003, [START_REF] Weening | The classification of glomerulonephritis in systemic lupus erythematosus revisited[END_REF] and therapeutic regimen were recorded on day 0. Lupus flares were defined according to the SELENA-SLEDAI Flare Index. [START_REF] Buyon | The effect of combined estrogen and progesterone hormone replacement therapy on disease activity in systemic lupus erythematosus: a randomized trial[END_REF][START_REF] Petri | Combined oral contraceptives in women with systemic lupus erythematosus[END_REF] The term "clinical" SLEDAI (cSLEDAI) refers to symptoms, signs and routine laboratory testing and disregards only the points that can be given for the presence of anti-dsDNA Abs and/or low complement. [START_REF] Van Vollenhoven | A framework for remission in SLE: consensus findings from a large international task force on definitions of remission in SLE (DORIS)[END_REF] Five exclusive disease activity statuses were defined, according to the DORIS [START_REF] Van Vollenhoven | A framework for remission in SLE: consensus findings from a large international task force on definitions of remission in SLE (DORIS)[END_REF] and following Wilhelm et al. [START_REF] Wilhelm | Remission in systemic lupus erythematosus: durable remission is rare[END_REF] and Ugarte-Gil et al. [START_REF] Wojdyla | Remission and Low Disease Activity Status (LDAS) protect lupus patients from damage occurrence: data from a multiethnic, multinational Latin American Lupus Cohort (GLADEL)[END_REF] without physician global assessment (PGA) and serum C4 analysis:

-Complete remission off treatment: cSELENA-SLEDAI=0, no corticosteroids, no immunosuppressant (IS), no anti-dsDNA Abs and no C3 decrease; -Clinical remission off treatment: cSELENA-SLEDAI=0, no corticosteroids, no IS.

Anti-dsDNA Abs and/or C3 decrease present; -Complete remission on treatment: cSELENA-SLEDAI=0, prednisone 1-5mg/day, IS allowed, no anti-dsDNA Abs and no C3 decrease; -Clinical remission on treatment: cSELENA-SLEDAI=0, prednisone 1-5mg/day, IS allowed. Anti-dsDNA Abs and/or C3 decrease present; -Not in remission: cSELENA-SLEDAI>0 and/or prednisone >5mg/day. HCQ was allowed in all groups. Duration of remission was recorded. Over a consecutive 5year period of remission, the patient was considered in "prolonged remission", as proposed by Steiman et al. [START_REF] Steiman | Prolonged clinical remission in patients with systemic lupus erythematosus[END_REF] and treated in the statistical analysis as a 5-year remission. Alternatively, patients not in remission but fulfilling Lupus Low Disease Activity State (LLDAS) [START_REF] Wojdyla | Remission and Low Disease Activity Status (LDAS) protect lupus patients from damage occurrence: data from a multiethnic, multinational Latin American Lupus Cohort (GLADEL)[END_REF][START_REF] Franklyn | Definition and initial validation of a Lupus Low Disease Activity State (LLDAS)[END_REF] were included in the "LLDAS without remission" subgroup (see online supplement). Sera from age-and gender-matched healthy donors (n=68) were collected (Établissement Français du Sang, Île-de-France, Pitié-Salpêtrière Hospital, Paris, France) during the same time period.

The local Ethics Committee of the Pitié-Salpêtrière Hospital approved this study (file N° 30052012) and informed consent was obtained from all participants.

Patient follow-up

Patients in remission at day 0 were followed for one year (see online supplement).

IFN-α digital immunoassay

Serum IFN-α concentrations, expressed in fg/mL, were determined at day 0 with digital immunoassay technology (IFN-α Reagent Kit, Quanterix Simoa TM , Lexington, MA, USA), based on a 3-step protocol (see online supplement) using the HD-1 Analyzer (Quanterix TM ). [START_REF] Rissin | Single-molecule enzyme-linked immunosorbent assay detects serum proteins at subfemtomolar concentrations[END_REF] The IFN-α digital ELISA positivity threshold was 136 fg/mL, which is 3 SDs above the mean serum IFN-α concentration calculated from the sera samples from the 68 healthy blood donors.

Statistical analysis

Statistical analyses were performed using GraphPad Prism, v5.0 software (GraphPad Software, San Diego, CA, USA) and SAS 9.4 software (Cary, NC, USA) (see online supplement).

RESULTS

Patient characteristics and distribution according to disease activity

A total of 407 patients were included in the study, with 254 patients in remission (i.e. cSELENA-SLEDAI=0 and prednisone equal or less than 5 mg/day) and 153 not in remission.

Patients' baseline characteristics are described in Tables 1 and2. From the 254 patients in remission, 86 (33.9%) were in complete remission off treatment, 59 (23.2%) in complete remission on treatment, 47 (18.5%) in clinical remission off treatment and 62 (24.4%) in clinical remission on treatment. Sixty-seven (26.3%) patients were in remission for less than 1 year, 101 (39.8%) for 1 to 5 years, and 86 (33.9%) for more than 5 years. The median (range) of remission duration was 5 years (0-5) for patients in complete remission off treatment, 1.6 years (0-5) for patients in complete remission on treatment, 4.2 years (0.1-5) for clinical remission off treatment and 1.6 years (0-5) for clinical remission on treatment. Among the 153 patients not in remission, 19 (12.4%) fulfilled the LLDAS criteria, defining the "LLDAS without remission" subgroup.

Serum IFN-α in remission and LLDAS

The serum IFN-α levels according to the different states of remission are presented in Table 2. A total of 26.0% of patients in remission had still detectable serum IFN-α levels exceeding the positivity threshold. Patients in "clinical remission" had the highest rate of abnormal serum IFN-α: 41.9% for "clinical remission on treatment" and 38.3% for "clinical remission off treatment" [versus 16.3% for "complete remission off treatment", p = 0.0007 and 0.006, respectively]. Among patients in remission, patients in "clinical remission on treatment" had the highest concentration of IFN-a with a median (quartiles) of 109 fg/mL [versus 11 fg/mL (0-81) in patients in "complete remission off treatment", p=0.0002]. Alternatively, we assessed serum IFN-α in different states of remission according to the definition of Zen et al., a definition of remission in which the role of corticosteroids is highlighted in comparison to immunosuppressive treatment. [START_REF] Zen | Prolonged remission in Caucasian patients with SLE: prevalence and outcomes[END_REF] As shown in supplemental table 2, we found similar results: patients in "clinical remission on or off corticosteroids" had the highest rate of abnormal serum IFN-α levels, as compared to those of patients in "complete remission". Thus, a significant number of patients in remission had increased IFNα levels in their serum. Eight (42.1%) patients of the "LLDAS without remission" subgroup displayed abnormal IFN-α serum concentration (OR 3.7 [95% CI 1.3-11.0] and a mean IFN-α level of 111 fg/mL [0-1,647], p=0.02 and p=0.07, respectively, as compared with patients in "complete remission off treatment").

Parameters SLE characteristics associated with abnormal serum IFN-α levels in remission

Elevated IFN-α serum levels in remission were significantly associated, in multivariable analysis, with the presence of serum Abs specific for RNP, dsDNA and Ro/SSA60, young age and lower granulocyte counts (Table 3). In contrast, disease and remission duration, prednisone intake, immunosuppressant therapy, HCQ, and low C3 serum levels did not show a significant association with IFN-α serum levels.

Elevated IFN-α serum levels in SLE patients in remission predicts a lupus flare

Of the 254 patients in remission at day 0, 250 were followed for one year. Twenty-four (9.6%) patients experienced a flare. The median (range) time of the flare occurrence was 141 (25-349) days. The type and severity of the flares are reported in supplemental table 3. A total of 37.5% of the flares were severe. The most frequent type of relapses was arthritis (n=15) followed by cutaneous flare (n=7) and serositis (n=4). Unadjusted cox regression showed a significantly higher risk of relapse in patients who displayed at baseline elevated IFN-α (HR 5.5 [95% CI 2.4-12.5], p<0.0001) or decreased C3 (HR 3.7 [95% CI 1.6-9.1], p=0.003) serum levels, respectively, but not in patients who had a positive Farr assay (HR 1.5 [95% CI 0.7-3.4], p=0.3) (Figure 1). The highest concentrations of IFN-a at baseline were associated with the greatest frequencies of relapse (supplemental figure 1). Other factors at baseline associated with the risk of relapse were prednisone intake 1-5 mg/day (HR 3.2 [95% CI 1.4- Finally, in multivariable analysis, the factors independently associated with the risk of flare were abnormal serum IFN-α levels at baseline (HR 4.0 [95% CI 1.7-9.6], p=0.002) and remission duration (HR 0.7 [95% CI 0.5-0.9], p=0.02, for each year in remission). Low C3 (HR 2.4 [95% CI 0.9-6.2], p=0.07) and prednisone intake (HR 2.4 [95% CI 0.9-5.9], p=0.06) were also kept in the model as associated with a higher risk of flare but these associations were not statistically significant. We performed a sensitivity analysis using a lower concentration of IFN-α as the threshold of elevated IFN-α levels and found similar results

(data not shown).

Additionally, the risks of relapse according to combined SLE biomarkers (low C3 complement, positive Farr assay and positive IFN-a) were independently analysed with a proportional risk cox model (supplemental table 4). In this model, isolated positive IFN-α was a predictive factor of lupus flare (HR of 5.5 [95% CI 1.7-18.1], p = 0.005). In contrast, isolated positive Farr assay and isolated low C3 were not predictive of lupus flare.

Digital immunoassay, complement C3 and Farr assay performances to predict a flare

The time-dependent ROC area under the curve (AUC) (Figure 2) estimates for the IFN-a digital immunoassay to predict a flare was 0.73, better than that of anti-dsDNA Abs (0.60, p=0.055), and complement C3 serum levels (0.56, p=0.2). The time-dependent ROC AUCs for the three biomarkers were highest around day 90.

DISCUSSION

The significance of monitoring IFN-α in SLE for the assessment of remission and the risk to develop flares has been poorly documented as yet. In the present study, we show that a significant proportion of patients despite being in remission have high serum IFN-α levels that were found to independently predict the risk of subsequent SLE flares, thereby emphasizing the interest of measuring the production of this cytokine to monitor the course of disease.

Earlier publications have reported that between 3 and 32% of SLE patients without active disease present elevated IFN-α serum levels depending on the type of assay used to determine the presence of this cytokine. [19-23, 25, 35] However, because different definitions of disease inactivity were used in these studies, the results cannot directly be compared with our study that takes into account the recently formulated consensual definition of disease remission. [START_REF] Zen | Prolonged remission in Caucasian patients with SLE: prevalence and outcomes[END_REF][START_REF] Van Vollenhoven | A framework for remission in SLE: consensus findings from a large international task force on definitions of remission in SLE (DORIS)[END_REF][START_REF] Wilhelm | Remission in systemic lupus erythematosus: durable remission is rare[END_REF] Contrary to previous report, [START_REF] Steiman | Lack of Interferon and Proinflammatory Cyto/chemokines in Serologically Active Clinically Quiescent Systemic Lupus Erythematosus[END_REF] we noted that serum concentrations of IFN-α above the positive threshold values varied between different remission subgroups. Patients in clinical remission, i.e. with serological activity, presented more frequently elevated serum levels of IFN-α than patients in complete remission. The presence of serum Abs specific for RNP, dsDNA and Ro/SSA60 were found to be independently associated with the magnitude of serum IFN-α levels. These associations have previously been shown in SLE [START_REF] Feng | Association of increased interferon-inducible gene expression with disease activity and lupus nephritis in patients with systemic lupus erythematosus[END_REF][START_REF] Petri | Longitudinal expression of type I interferon responsive genes in systemic lupus erythematosus[END_REF][START_REF] Landolt-Marticorena | Lack of association between the interferon-alpha signature and longitudinal changes in disease activity in systemic lupus erythematosus[END_REF][START_REF] Hua | Functional assay of type I interferon in systemic lupus erythematosus plasma and association with anti-RNA binding protein autoantibodies[END_REF][START_REF] Niewold | High serum IFN-alpha activity is a heritable risk factor for systemic lupus erythematosus[END_REF][START_REF] Niewold | Association of the IRF5 risk haplotype with high serum interferon-alpha activity in systemic lupus erythematosus patients[END_REF][START_REF] Weckerle | Network analysis of associations between serum interferon-alpha activity, autoantibodies, and clinical features in systemic lupus erythematosus[END_REF][START_REF] Ko | Activation of the Interferon Pathway is Dependent Upon Autoantibodies in African-American SLE Patients, but Not in European-American SLE Patients[END_REF][START_REF] Connelly | Association of MIF, but not type I interferon-induced chemokines, with increased disease activity in Asian patients with systemic lupus erythematosus[END_REF] but, to the best of our knowledge, never been reported for patients in remission. These data are in accordance with those from previous studies that showed a key role of DNA/RNAassociated immune complexes through the activation of TLR7 and TLR9 for the induction of type I IFN production. [START_REF] Banchereau | Type I interferon in systemic lupus erythematosus and other autoimmune diseases[END_REF][START_REF] Bengtsson | Role of interferons in SLE[END_REF] The DORIS group has recently agreed that the subsequent occurrence of flares was among the most appropriate outcome variables for defining the prognostic value of remission and furthermore suggested the inclusion of serological criteria for this definition. [START_REF] Van Vollenhoven | A framework for remission in SLE: consensus findings from a large international task force on definitions of remission in SLE (DORIS)[END_REF] Results from previous reports on smaller SLE patient cohorts, based on the analysis of expression of ISGs in peripheral blood cells by microarray, failed to demonstrate an association between IFN scores and the longitudinal risk of relapse. [START_REF] Petri | Longitudinal expression of type I interferon responsive genes in systemic lupus erythematosus[END_REF][START_REF] Landolt-Marticorena | Lack of association between the interferon-alpha signature and longitudinal changes in disease activity in systemic lupus erythematosus[END_REF] It is to be noted that type I and type II IFNs largely overlap in the genes that they control, making it difficult to distinguish the signatures of IFN-gamma (IFN-g) from IFN-a and IFN-beta (IFN-b). Indeed, the results from a modular repertoire analysis have emphasized that IFN signatures in SLE are not restricted to IFN-α, but also involve IFN-β and IFN-γ, thus underscoring the nonspecific nature of IFN scores. [START_REF] Chiche | Modular transcriptional repertoire analyses of adults with systemic lupus erythematosus reveal distinct type I and type II interferon signatures[END_REF] Therefore, in a disease like SLE in which IFN-α appears to be central in the pathogenesis, it is likely that clinical activity better correlates with the values of IFN-α serum levels, directly measured by a highly specific digital ELISA, than with the less specific expression of IGSs. Moreover, the IFN scores are likely to be rather poorly sensitive to changes in IFN-a serum concentrations and therefore of little use in monitoring the risk of relapse of disease. The results of our study suggest that the measurement of additional interferons, including IFN-b, -g and -l with ultrasensitive digital immunoassay, might help to determine whether the expression of other IFN members also correlates with disease activity or specific characteristics of the disease. [START_REF] Oke | IFN-lambda1 with Th17 axis cytokines and IFN-alpha define different subsets in systemic lupus erythematosus (SLE)[END_REF][START_REF] Munroe | Altered type II interferon precedes autoantibody accrual and elevated type I interferon activity prior to systemic lupus erythematosus classification[END_REF][START_REF] Oke | High levels of circulating interferons type I, type II and type III associate with distinct clinical features of active systemic lupus erythematosus[END_REF] Nonetheless, our results corroborate those from an earlier study showing the usefulness of monitoring expression levels of certain IFN-regulated chemokines to predict future flares: serum levels of CXCL10, CCL2 and CCL19 chemokines were found to be linked with SLE activity, and performed better than other laboratory tests to predict a flare over the following year. [START_REF] Bauer | Interferon-regulated chemokines as biomarkers of systemic lupus erythematosus disease activity: a validation study[END_REF] Yet, these chemokines can be induced by other SLE-associated cytokines beyond IFN-α, such as IFN-g and their monitoring remains difficult in routine practice. As reported by others, we did not find an association between the presence of anti-dsDNA Abs and the risk of flare. Not surprisingly, the duration of remission was significantly associated with a poor risk of flare in the following year, thus identifying a subgroup of patients in prolonged remission with less relapsing risk and for whom clinical monitoring can probably be lightened.

The sustained presence of serum IFN-α in serum of SLE patients in remission may have pathological consequences by itself. IFN-α overexpression could be an explanation of chronic fatigue, depression and reduction of sleep secondary to the stimulation of dopamine metabolism by IFN-α in the central neurological system. [START_REF] Raison | Depression during pegylated interferon-alpha plus ribavirin therapy: prevalence and prediction[END_REF][START_REF] Raison | Chronic interferonalpha administration disrupts sleep continuity and depth in patients with hepatitis C: association with fatigue, motor slowing, and increased evening cortisol[END_REF][START_REF] Felger | Tyrosine metabolism during interferon-alpha administration: association with fatigue and CSF dopamine concentrations[END_REF] IFN-α plays also a prominent role in endothelial cell damage and up-regulation of the expression of scavenger receptors in monocyte and macrophages, leading to increased lipid uptake and foam cell formation, a process that may be at the origin of the accelerated atherosclerosis observed in SLE. [START_REF] Kaplan | How does interferon-alpha insult the vasculature? Let me count the ways[END_REF][START_REF] Denny | Interferon-alpha promotes abnormal vasculogenesis in lupus: a potential pathway for premature atherosclerosis[END_REF][START_REF] Li | Interferon-alpha priming promotes lipid uptake and macrophage-derived foam cell formation: a novel link between interferon-alpha and atherosclerosis in lupus[END_REF] These data suggest that for patients in clinical remission, return of IFN-α to normal values could become one of the objectives of the treatment.

Our study has some limitations. It unfortunately lacks data on patients' ethnicity, which is known to bias serum IFN-α levels. [START_REF] Weckerle | Network analysis of associations between serum interferon-alpha activity, autoantibodies, and clinical features in systemic lupus erythematosus[END_REF] We also used a definition of remission and LLDAS in the absence of PGA that has not been assessed in our cohort. However, other teams have already adapted the definition of remission and LLDAS arguing that in the SLE Response Index, the SLEDAI is the variable with the highest impact on the definition of response and that even without PGA, a modified definition of remission or LLDAS is still entirely valid. [START_REF] Wojdyla | Remission and Low Disease Activity Status (LDAS) protect lupus patients from damage occurrence: data from a multiethnic, multinational Latin American Lupus Cohort (GLADEL)[END_REF][START_REF] Navarra | Efficacy and safety of belimumab in patients with active systemic lupus erythematosus: a randomised, placebocontrolled, phase 3 trial[END_REF] Finally, the serum IFN-α concentrations were not assessed during the longitudinal part of the study. Therefore information regarding the intra-individual variability over time of serum IFN-α levels is lacking. These important data will have to be studied in new studies.

In conclusion, our data confirm that a large number of SLE patients in remission display an elevated serum IFN-α concentrations, especially in the presence of anti-dsDNA, anti-ribonucleoprotein Abs (i.e. anti-Ro/SSA 60, anti-RNP), as well as young age. This overexpression is an independent predictive biomarker of lupus flare in the following year.

Adding serum IFN-α measurement to the routine laboratory assessments in patient in remission could help clinicians to identify a subgroup of SLE patients clinically in remission but who still overexpress IFN-a and are at higher risk of relapse. These data suggest that the return of normalcy of serum IFN-α could become one of the objectives of the treatment. Our results must be validated in other independent cohorts. IFN-α = interferon alpha; C3 = complement C3. Serum IFN-α digital immunoassay, anti-dsDNA Abs by Farr assay and complement C3 levels were assessed at baseline (day 0). SLE patients in remission were followed for one year. Lupus flares were defined using the SELENA-SLEDAI Flare Index. Patients who had a flare in any organ system were recorded.

The diagnostic performances of the baseline serum-IFN-α digital immunoassay (red line), Farr assay (blue line) and complement C3 (green line) to predict SLE flare were investigated by computing cumulative time-dependent ROC curves, with lupus flares serving as the gold standard for those analyses. The dashed line represents the upper and the lower 95% confidence interval (CI). The cumulative time-dependent ROC area under the curve (AUC) estimated to predict a flare are given and were compared based on Uno et al.. [START_REF] Uno | On the C-statistics for evaluating overall adequacy of risk prediction procedures with censored survival data[END_REF] Values are expressed as n (%), unless stated otherwise.

* reference group for statistical analysis a bivariable analysis using Mann-Whitney U-test compared to "complete remission off treatment" as the reference.

b bivariable comparison using Fisher's exact test compared with patients in "complete remission off treatment" as the reference.

NS, Non Significant; IFN-a, interferon alpha; fg/mL, femtogram/milliliter; cSLEDAI, clinicalSLEDAI; SD, standard deviation.

29

7. 5 ]

 5 , p=0.007), positive anti-RNP Abs (HR 3.1[1.4-7.0], p=0.006), age <40 years (HR 0.4 [95% CI 0.2-0.9], p=0.02) and disease duration <10 years (HR 0.2 [95% CI 0.1-0.6], p=0.003). The remission duration was a protective factor for the probability of flare (HR 0.6 [95% CI 0.5-0.8] for each consecutive year of remission completed, p=0.0002).

Figures legendsFigure 1 .

 1 Figures legends

Figure 2 .

 2 Figure 2. Cumulative time-dependent receiver operating characteristics (ROC) curves.

Table 1 . Disease parameters characteristics in SLE patients at baseline 1

 1

	Patients (N=407)

Table 2 . Serum IFN-a levels at baseline in SLE patients in remission or not in remission (according to Wilhelm et al. [47] modified).

 2

	Abnormal	Odds Ratio	p value a	Serum IFN-α fg/mL,	p value b
	serum IFN-α level	[95% CI]		median (Q1, Q3)

Table 3 . Parameters Disease characteristics associated with serum IFN-a levels at baseline in SLE patients in remission IFN-α Bivariable p value a Multivariable p value b Adjusted odds ratio b

 3

	[95% CI]

Acknowledgements

We thank the patients, the healthy donors, the nurses and the Department of Internal Medicine 2 staff who participated in this study. We thank Prof. Jean-Christophe Lega for its advices.

Contributors SMM, AM, HD, KD, HY, GG, FR and ZA contributed to the conception and design of the study; SMM, AM, KD, FCA, JH, MH, MM, DS, MP, DBLTH, FR and ZA were involved in the acquisition of data; SMM, AM, HD, KD, HY, MPDC, GG, FR and ZA contributed to the analysis and interpretation of data. All authors contributed to drafting and/or revising the manuscript.

Competing interests none

Patient and Public Involvement none

Positive Farr test 198 [START_REF] Steiman | Prolonged clinical remission in patients with systemic lupus erythematosus[END_REF] Positive anti-RNP Abs 118 [START_REF] Feng | Association of increased interferon-inducible gene expression with disease activity and lupus nephritis in patients with systemic lupus erythematosus[END_REF] Positive anti-Sm Abs 51 [START_REF] Niewold | Interferon alpha as a primary pathogenic factor in human lupus[END_REF] Positive anti-Ro/SSA 52 Abs 97 [START_REF] Kanayama | Possible involvement of interferon alfa in the pathogenesis of fever in systemic lupus erythematosus[END_REF] Positive anti-Ro/SSA 60 Abs 151 [START_REF] Yao | Use of type I interferon-inducible mRNAs as pharmacodynamic markers and potential diagnostic markers in trials with sifalimumab, an anti-IFNalpha antibody, in systemic lupus erythematosus[END_REF] Positive anti-La/SSB Abs 42 [START_REF] Theofilopoulos | Type I interferons (alpha/beta) in immunity and autoimmunity[END_REF] Low C3 98/398 ‡ (25)

Positive IFN-α 163 [START_REF] Rodero | Detection of interferon alpha protein reveals differential levels and cellular sources in disease[END_REF] Values are expressed as n (%), unless stated otherwise.

* Defined using SELENA flare index [START_REF] Buyon | The effect of combined estrogen and progesterone hormone replacement therapy on disease activity in systemic lupus erythematosus: a randomized trial[END_REF][START_REF] Petri | Combined oral contraceptives in women with systemic lupus erythematosus[END_REF]


Vítor Oliveira

Jean Bourgeois

Pedro Ignacio Shmitz

Antoine Zink

C69 -Luminescence Dating Techniques: a User's Perspective Luminescence date and archaeological ages: An epistemology of the luminescence dating

Keywords: datation par luminescence, équation d'âge, incertitude luminescence dating, age equation, uncertainty Θ

A. Introduction

Although the role of the physicist usually stops with the production and the publication of the ages, the ages themselves have a life after. They are an information about artefacts or sites. And then, one expects that they are used as an argument among others in the constitution of the knowledge of the historians (Art historian, historians and archaeologists).

Actually, some times, the age obtained by physical method fully disappears when the site or the object is published by the historians, especially in the communication to the general public, which is very strange when it is obtained after request of the archaeologists and on public funds. In some other cases, it is copied as received without any analysis in review papers, as if they are gospel. A last case, and not the less odd, the historians made a full arbitrary choice between the dates, keeping only the ones in agreement with their own assumptions. In all these cases, the physical age is misused, as it should be used by comparison with other informations to construct the archaeological discourse.

How to present the results (report, papers, list of dates) in view to be useful for the historians?

The problem is how have a rigorous (scientific) discourse with the minimum of technical jargon in a such way that the physical result can be transfer to the historical discourse; keeping the possibilities to other colleagues to control and reproduce our work from the published data.

In the present paper, we are interested by the luminescence dating and the nature of the luminescence age.

Age equation

To well understand the luminescence dating methods, we must remind the physical process involved in luminescence [START_REF] Aitken | Thermoluminescence dating[END_REF]. The luminescence methods are based on the faculty of the minerals to accumulate energy from ambient radioactivity.

Actually, the radioactive energy is transferred to electrons. The electrons are transferred, or ionized, to the conductivity band. From here, they can go freely in all the crystal. Most of them come back to their initial level, emitting some luminescence. It is the fluorescence process. But a minority is trapped by defects in the crystal, the so-called traps. Due to the thermal agitation of the crystal, it has some probability that the trapped electrons are evicted from their traps and come back to their initial level emitting some luminescence. It is the phosphorescence process. The time spent in the trap can be more or less long, from some microseconds to several billion years.

For a trap with large lifetime compare to historical ages, the eviction can be regarded as zero, and the trap accumulates continuously new electrons. It is possible to accelerate the eviction from the traps by giving to the electron some thermal or optical energy. In the first case, we speak about thermoluminescence (TL), and in the second case, about optical stimulated luminescence (OSL).

We must outline that the TL and OSL are irreversible processes: after the heating or the optical bleaching, the traps are empty and the process is stopped. Without a new irradiation, we do not have any new luminescence signal.

Resetting and accumulation are the two characteristics useful to apply the luminescence to dating.

Actually, to be able to date, we need to have a clock; that is a physical process, function of the time with an outstanding instant. In our case, the process is the accumulation of electrons in the traps, or indirectly the absorbed energy, i.e. the dose. It is then a dosimetrical method. The outstanding, or initial, instant is the last empting of the traps. It could be the crystallization of the mineral (stalagmite), the heat at a temperature above 500 °C (ceramic, heated stone), the solar bleaching during a daytime (aeolian or water-laid sediment), or even a shock (seismic fault).

As it is, we can use the luminescence methods to date facts. But, as the most of the clock, it depends of the environment. And they can be used only as a relative method to date objects from the same environment. The dose rate with its uncertainties should reflect our knowledge on the environment (radioelements, wetness...). In this case, the final result is fully correct as a representation of our knowledge on the age.

Uncertainties

Usually, the uncertainties in luminescence dating are based on the works of Aitken and Alldred, summarize in [START_REF] Aitken | Thermoluminescence dating[END_REF].

In this work, the uncertainties are separated in two groups: the uncertainties arising from random B. those which are evaluated by other means.

rather than used the classification of uncertainty components as 'random' and 'systematic'. The nature of the uncertainty as 'systematic' or 'random' is relative depending of the treatment of the measurement.

The table 1 shows an example of uncertainty budget in the case of a Hallstatt site in East of France, with their classification in type A or type B evaluation. As you can see, there is not a simple correspondence between 'systematic'/'random' and 'type A'/'type B' classifications. The wetness is classified by Aitken as an uncertainty arising from a systematic effect, but in the present case is based on several measurements in laboratory, and then a statistical treatment.

Actually, only the uncertainties on luminescence measurements come from random effects. The uncertainties on the dose rate and the wetness, although are evaluated by statistic methods, are related to systematic error. As say before, the dose-rate (including the wetness) are use to correct the error due to the environment, which is a systematic error for all the samples with the same context.

Law of propagation

Actually, the distinction between random and systematic error given by Aitken is best understood as a distinction between type A and type B evaluated uncertainties. But their treatment for several measurements in the same context, their propagation, is best understood with the notion of correlation or uncorrelation between samples as suggested by [START_REF] Aitken | Thermoluminescence dating[END_REF] to identify 'systematic' and 'random' effects.

For the components of the uncertainty uncorrelated between samples, Aitken suggests to use the usual method for combining standard deviations, the "root-sum-of-squares" (square root of the sum-of-the squares). And for the component of the uncertainty correlated between samples, he suggests to take the weighting mean of the individual uncertainties [START_REF] Aitken | Thermoluminescence dating[END_REF].

We can illustrate the difference between correlated and uncorrelated uncertainties between samples in the case of the dating of a stratigraphic unit. A stratigraphic unit is the less archaeological unit which define an age based on chronological links [START_REF] Harris | Principles of Archaeological Stratigraphy[END_REF]. Then it is associated to an unique age (the timespan of the age can be very short or very large). We have measured several samples from the same stratigraphic unit and we want to combine them to obtain the age of the unit.

As suggested by Millard ( 2006), we use a hierarchy between the components of the uncertainty (fig. 1). At a first level, we have the constant parameters and the calibrations of the equipments.

Assuming that only a laboratory produces the date, the uncertainties are fully correlated. At a second level, we have the gamma and cosmic dose-rates. These radiations have large length path and their contribution are generally homogeneous in a single stratigraphic unit. The gamma doserate comes usually from various measurements and then is type A evaluation. We can use an average associated with an uncertainty based on the "root-sum-of-squares" for the stratigraphic unit. For the cosmic dose rate, we take usually reference data (type B evaluation).

We should now consider the alpha and beta dose-rate. They are absorbed quickly in the matter.

And we can not assume the homogeneity of their contribution on the entire unit. They are measured from sub-samples different from the sub-samples used for luminescence measurements, even if they come from a same sample in the stratigraphic unit. Due to their short path range (some micron for the alpha particles), and the a-priori inhomogeneity of the radioelement contents at micro-scale (micro-dosimetry), we can not assume, a-priori, that the alpha and beta dose-rates measured for a sub-sample correspond to the dose-rate for an other sub-sample. Then, as for the gamma dose-rate, but for opposite reasons, we should take the average value of the individual measurements of the alpha and beta dose-rate associated with uncertainties based on the "root-sum-of-squares" for the stratigraphic unit. In this case, we disagree with Millard (2006) who put the alpha and beta dose-rate at lower levels than the stratigraphic unit.

At the level of the sample, we group the parameters calculated by luminescence measurements, and especially the accumulated dose. They arise from the same sub-samples (we neglect the differences between aliquots) and characterise each sub-sample. A priori, it has no reason that the sub-samples are similar. We can say that the age (true value), corrected by the environment (correction factor from a systematic effect) is transform into a particular accumulated dose depending on the nature of the mineral (the nature of the mineral is a-priori independent -uncorrelated-from the other minerals in the vicinity). Then we cannot take the average of this parameters on the stratigraphic unit and it combined "root-sum-of-squares" uncertainty. We must first calculate the age for each sub-samples using the measured value of the accumulated dose and the average for the dose-rates. The uncertainty of the age of the stratigraphic unit is obtain by combining the uncertainties of the average value of the correlated parameters, including the doserate and the "root-sum-of-squares" of the components of the uncertainty due to uncorrelated parameters, including the accumulated dose.

The efficiency alpha is a special case. It is a correction parameter of the alpha dose-rate (systematic effect) measured by luminescence (random effect). We see here the conceptual difficulty of the notion of systematic and random effect. In the present case, we consider that the components of the uncertainty due to the efficiency alpha is an uncorrelated between samples, and is treated as the component of the uncertainty due to the accumulated dose..

Conclusion

The luminescence clock is the accumulated dose by a mineral during some time. [START_REF] Zink | Datation par luminescence du Briquetage de la Seille -Rapport des campagnes de mesures 2004-2005 effectuées à Marsal (Moselle), prospection thématique "Briquetage de la Seille[END_REF]. The subscript associated to the uncertainties refers to the Appendix B from [START_REF] Aitken | Thermoluminescence dating[END_REF], except σ 8 and σ 10 which are adapted to the present case.

Relative uncertainties for a sample (resp. for a stratigraphic unit) source of uncertainties Type A Type B luminescence measurements (s1) 4-5% (1%) dose-rate measurements (s2) 7-9% (3 %) calibrations (sources, alpha counters) (s4) 1% parameters (s5) 3% uranium/thorium ratio (s6) 2% wetness (s7) 5-8 % (3%) calibration (gamma spectrometer) (s8) 5% fading (s10) 2-8 % (1-3%) Combined relative standard uncertainty 13 % (9 %)

  The dating is not limited to the dosimetry of the sample. Actually, to obtain an absolute dating method, we need to calibrate this clock by a term reflecting the environment. It is made by measuring the dose-rate, or annual dose, using analytical or radiometric methods and by dividing the accumulated dose by the dose-rate. Hence, one define the age equation as:

	Equation 1	Age = accumulated dose / annual dose

We must outline that the dimensional analysis associated to this equation: a quantity is divide by its own rate, shows that the result is, physically, a time. It means that we obtain always a calendar age. In comparison, the radiocarbon dating gives a so-called C14-age. To have the corresponding calendar age, we need to use external calibration, generally another dating method as the dendrochronology. The age equation can be split in two terms: the numerator corresponds to the luminescence clock; the denominator plays the role of a correction factor of the error due to the environment. From a physical point of view, it displays what we know about the environment of the sample: the luminescence clock going more or less quickly following the ambient radioactivity. Hence, a granitic soil has a higher radioactivity compared to a loessic environment.

  By dividing the accumulated dose by the annual dose, we convert the luminescence clock in time clock. The annual dose or dose rate is a calibration factor used to reduce the systematic effect due to the environment. Then the result is accurate, i.e. very close to the true age, even though it has a large uncertainty. The luminescence age gives an absolute information to the archaeological age, which is based on temporal relations (e.g. stratigraphical unit). The luminescence dating is a metrology science, giving a measurement in the time dimension. As it is, it has no particular archaeological meaning. It reflects just what the physicist beliefs about the age from his own expertise in luminescence dating. It is only when this measurement is understood as an information for a specific problematic investigated by the archaeologist or the Art historian, that one can speak about a archaeometrical analysis. Table 1 example of uncertainty budget for luminescence dating in the case of the archaeological site of Marsal -Pransieu (Moselle, France) modified from

effects and the uncertainties arising from systematic effects. We prefer here to speak about uncertainty than error, as the term 'error' must be reserved to the difference between the measured value and the true value (VIM). Several sources of uncertainties are identified regrouped into seven components. Two components are related to random effect, they concern the measurement: one for the accumulated dose measurement, and the other for the annual dose measurements. The other components are related to systematic effects and deal with the parameters or the calibration of the equipment. Their mathematical expressions for usual thermoluminescence can be found in Appendix B of [START_REF] Aitken | Thermoluminescence dating[END_REF]. Following the used methods (TL or OSL, fine grains or coarse inclusions, single aliquot or multi-aliquot), they can be adapted. In some cases, other sources of uncertainties can be added (eg. Anomalous fading, external dose rate for museum objects...).

We must keep of mind that in luminescence dating the uncertainty Uc on the age is quoted with a coverage factor of one, or one standard uncertainty. That means that the age A of the sample is believed to lie between a -Uc and a + Uc with a level of confidence of about 2 out to 3 chances (ca. 68 percent), which is commonly written A= a ± Uc. On other terms, if we have measured three ages, for two of them the true age is expected to be inside the confidence interval. But for one of them, it should be outside. The test with samples of known ages gives informations on the evaluation of the uncertainty. In the case where all the true ages are inside of the confidence interval, the uncertainty are overestimate. Opposite, if less than two out of three true ages are inside the confidence interval, the uncertainty is underestimated [START_REF] Zink | Luminescence dating of ceramic works of art: a comparative study. 8Th European Meeting on Ancient Ceramics[END_REF].

Following the recommendation of the International Committee for Weights and Measures CIPM [START_REF] Iso | Guide to the Expression of Uncertainty in Measurement[END_REF][START_REF] Taylor | Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results[END_REF], the scientific community of the metrological science prefers separated the uncertainties in two groups:

A. those which are evaluated by statistical methods,