Dr Florent De Vathaire
email: florent.devathaire@gustaveroussy.fr

Keywords: thyroid cancer genetics, thyroid epidemiology, ionizing radiations, DNA repair, cancer susceptibility

Background: Given the increased use and diversity of diagnostic procedures, it is important to understand genetic susceptibility to radiation-induced thyroid cancer.

Methods: Based on self-declared diagnostic radiology examination records in addition to existing literature, we estimated the radiation dose delivered to the thyroid gland from diagnostic procedures during childhood and adulthood in two case-control studies conducted in France. A total of 1071 differentiated thyroid cancer (DTC) cases and 1188 controls from the combined studies were genotyped using a custom-made Illumina OncoArray DNA chip. We focused our analysis on variants in genes involved in DNA damage response and repair pathways, representing a total of 5817 single-nucleotide polymorphisms in 571 genes. We estimated the odds ratio per milli-Gray (OR/mGy) of the radiation dose delivered to the thyroid gland using conditional logistic regression. We then used an unconditional logistic regression model to assess the association between DNA repair gene variants and DTC risk. We performed a meta-analysis of the two studies. Results: The OR/mGy was 1.02 (95% CI: 1.00, 1.03). We found significant associations between DTC and rs7164173 in CHD2 (p = 5.79 10 -5 ), rs6067822 in NFATc2 (p = 9.26 10 -5 ), rs1059394 and rs699517 both in ENOSF1/THYS, rs12702628 in RPA3, and an interaction between rs7068306 in MGMT and thyroid radiation doses (p= 3.40 10 -4 ). Conclusions: Our results suggest a role for variants in CDH2, NFATc2, ENOSF1/THYS, RPA3 and MGMT in DTC risk.

Impact: CDH2, NFATc2, ENOSF1/THYS and RPA3 have not previously been shown to be associated with DTC risk.

.

Introduction

Differentiated thyroid cancer (DTC) is the most common cancer of the endocrine system (1). The registered incidence of DTC has recently been increasing, especially in developed countries mostly due to increased screening [START_REF] Vanderpump | The epidemiology of thyroid disease[END_REF]. Exposure to thyroid ionizing radiation (IR) during childhood was the first risk factor linked with DTC, an association that has been well characterized over several decades [START_REF] Stepanenko | Estimating individual thyroid doses for a case-control study of childhood thyroid cancer in Bryansk Oblast, Russia[END_REF][START_REF] Modan | Thyroid cancer following scalp irradiation[END_REF][START_REF] Thomas | Integrating Research on Thyroid Cancer after Chernobyl -The Chernobyl Tissue Bank[END_REF][START_REF] Inskip | Radiation-Related New Primary Solid Cancers in the Childhood Cancer Survivor Study: Comparative Radiation Dose Response and Modification of Treatment Effects[END_REF][START_REF] Memon | Dental x-rays and the risk of thyroid cancer: A case-control study[END_REF](8).

In a pooled study performed on doses higher than ≥ 1 Gy (9,10), the excess of DTC relative risk per Gray (ERR/Gy) delivered to the thyroid gland during childhood ranged between 5 and 10. When restricting the pooled analysis to doses lower than 0.2 Gy, however, the ERR/Gy was slightly higher (11). A higher magnitude of excess risk for low dose exposure during childhood was also observed in a cohort study of Japanese atomic bomb survivors [START_REF] Furukawa | Long-term trend of thyroid cancer risk among Japanese atomic-bomb survivors: 60 years after exposure[END_REF]. Nevertheless, some uncertainties remain about how the recent increase in the use of diagnostic procedures involving irradiation, such as CT (computerized tomography), might affect DTC incidence [START_REF] Leung | Low-Dose Childhood Radiation Effects to the Thyroid Follow a Linear Dose-Response Trend and Persist Even 45+ Years After Exposure[END_REF][START_REF] Mazonakis | Thyroid dose from common head and neck CT examinations in children: is there an excess risk for thyroid cancer induction?[END_REF].

Despite being more subject to recall bias than cohort studies, case-control studies may be more helpful for improving understanding of thyroid low-dose radiation risk since casecontrol studies utilize a high number of cases and permit a more detailed investigation of a high number of potential risk cofactors, which are costlier to investigate in cohort studies. Since DTC risk after low radiation dose exposure is also likely modulated by individual susceptibility, investigating the association between DNA variants and DTC risk after low radiation dose could also facilitate an improved understanding of this risk. IR exposure causes DNA damage as well as other physical and chemical biomolecule alterations. DNA double-strand breaks (DSBs) are a characteristic cellular response to IR exposure [START_REF] Mahaney | Repair of ionizing radiation-induced DNA doublestrand breaks by non-homologous end-joining[END_REF]. Exposure to low-dose IR (from levels 50mGy and lower) from X-ray on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited.

Author Manuscript Published OnlineFirst on April 7, 2021; DOI: 10.1158/1055-9965.EPI- examinations has been demonstrated to increase the risk of chromosomal translocation [START_REF] Bhatti | Diagnostic Xray examinations and increased chromosome translocations: evidence from three studies NIH Public Access[END_REF], suggesting the possibility of long-term adverse health effects.

DSBs trigger the DNA repair system, but the effect of these DSBs varies with cumulative exposures and individual susceptibility. To our knowledge, only one published study has investigated an interaction between genetic background and the radiation-related DTC risk after diagnostic radiation exposure [START_REF] Sandler | Germline Variants in DNA Repair Genes, Diagnostic Radiation, and Risk of Thyroid Cancer[END_REF]. This study identified 24 single-nucleotide polymorphisms (SNPs) with a p-value of variant-RI doses interaction was < 0.05 for all types of DTC cases (papillary and follicular). Currently, few genes including FOXE1, ATM, and LIG1 have been associated with DTC risk after IR exposure, but most published studies of these genes were conducted in highly irradiated populations.

Moreover, these identified genes were associated with sporadic DTC [START_REF] Zidane | Genetic susceptibility to radiation-related differentiated thyroid cancers: A systematic review of literature [Internet[END_REF].

Given the increasing use of diagnostic radiology exams and the proliferation of radiology procedure types, it is important to explore the side effects of multiple low-radiation exposures, such as potential effects on DTC development, especially for patients exposed at a young age.

In the current study, we investigated the association between diagnostic low-dose IR exposures and DTC risk. We quantified the doses delivered to the thyroid gland during childhood and adulthood in two French case-control studies. We also investigated the role of genetic variants located in 604 DNA damage signaling and repair genes in modifying the effect of exposure to diagnostic procedure radiation on DTC risk.

Materials and methods

Case-control studies

Our study included cases and controls from two studies conducted in distinct regions from metropolitan France. The CATHY study [START_REF] Cordina-Duverger | Hormonal and reproductive risk factors of papillary thyroid cancer: A population-based case-control study in France[END_REF] Clinical and epidemiological data from both studies were harmonized and aggregated in one database. During this process, 30 subjects were excluded because they were duplicates in the two studies.

Radiologic procedure history

In the questionnaire, participants were asked to report their history of diagnostic radiology examinations by providing the year and the reason for each examination. The exams considered were conventional radiography, CT scans, and nuclear medicine.

Examinations linked to investigating thyroid pathology were excluded and were not considered in the dose estimation or any analysis. Examinations carried out during childhood (before the age of 20 years) and adulthood (over 20 years) were analyzed separately. All procedures reported by participants were classified by period (before 1980, 1980-1989, 1990, and after) to take into account the development of radiologic procedure technology over this time.

Thyroid radiation dose estimates

To estimate the absorbed radiation doses administered to the thyroid gland for different types of diagnostic radiology examinations, we reviewed papers published up to July 2018 that included absorbed dose estimates to the thyroid. From 1970 to 2002, only one study provided estimates of absorbed doses to organs, including the thyroid gland [START_REF] Chang | Thyroid Radiation Dose to Patients from Diagnostic Radiology Procedures over Eight Decades: 1930-2010[END_REF], and was used to calculate dose estimates from conventional radiography.

If sex-specific data were available, a mean dose was used. Since the available data about childhood exams were very limited, specific doses were available only for children under the age of two years old without consideration of the period of exposure. Children older than two years were assumed to receive the same doses as adults. All doses per exam that were equal to or less than 0.01 mGy were considered to be null because of the magnitude of daily natural irradiation in France. Table 1 summarizes the different values used per diagnostic procedure type (conventional radiography, CT scan, nuclear medicine), per period (before 1980, 1980-1989, 1990 and after), and per age at examination (≤ 2 years old, > 2 years).

Genotyping and quality control

DNA was extracted from saliva samples using a semi-automated salt precipitation method. All subjects were genotyped using the Infinium OncoArray-500K BeadChip (Illumina). This array has been previously described in detail [START_REF] Amos | The oncoarray consortium: A network for understanding the genetic architecture of common cancers[END_REF] and contains 499,170 SNPs. We incorporated 13,759 additional custom markers based on prior evidence of association in genes involved in relevant biological pathways, such as thyroid function.

The quality control process was applied to the data of each study separately. A threshold of 5% was applied for a missing call rate per SNP and individual. The Hardy-Weinberg equilibrium (HWE) was also assessed per SNP among controls, using an exact test with a p-value threshold at 10 -5 . Only SNPs with a minor allele frequency (MAF) above 5% were included in the analyses.

The FastPop R package was used to infer intercontinental ancestry with a principal component-derived method [START_REF] Li | FastPop: A rapid principal component derived method to infer intercontinental ancestry using genetic data[END_REF]. Only individuals identified as European were kept in the genetic analyses. A total of 443 cases and 532 controls from CATHY and 629 cases and 656 controls from Young-Thyr were included in the analysis of SNPs.

SNPs of DNA damage signaling and repair genes according to the Gene Ontology database [START_REF] Ashburner | Gene ontology: Tool for the unification of biology[END_REF][START_REF] Carbon | The Gene Ontology Resource: 20 years and still GOing strong[END_REF] were examined. We initially selected exonic and intronic variants in 604 genes. After the quality control steps, a total of 5817 SNPs in 571 genes were retained for the analysis (all genes are listed in the Supplementary Table S1).

Statistical methods

We used a conditional logistic regression model to estimate the odds ratio of DTC per mGy (OR/mGy) of radiation dose received by the thyroid gland. Because in our study, thyroid doses were very low and cell killing not likely to play signification, and because our goal was not to define the best model for thyroid cancer risk after low dose but rather the best model to investigate the interaction between thyroid radiation and genetic factors, we only investigate models with one parameter for the thyroid radiation dose. In this way, we compared a linear model (OR=Cst (1 + α dose) to a "constant" model without a radiation dose (OR= Cst) and other models with one parameter, such as quadratic (OR=1 + α dose2) and exponential (OR=1 + e (α dose)), rather to traditional dose-response models used in radiation epidemiology [START_REF] De Gonzalez | Epidemiological Studies of Low-Dose Ionizing Radiation and Cancer: Rationale and Framework for the Monograph and Overview of Eligible Studies[END_REF]. These comparisons were done using Akaike Information Criterion (AIC) [START_REF] Akaike | Information Theory and an Extension of the Maximum Likelihood Principle BT -Selected Papers of Hirotugu Akaike[END_REF]. Similarly, we investigated the potential role of a dose-response modifier by introducing a term for interaction in the models. The analysis of the radiation dose was performed by using the PECAN module of Epiwin® software. To assess the association between SNPs and DTC risk, odds ratios (ORs) and 95% confidence intervals (95% CIs) were derived from unconditional logistic regression models, assuming a log-additive model since the stratum was not considered in this step. Analyses were first conducted in the Young-Thyr study to filter our SNPs and limit the number of tests to be performed later; only the 100 SNPs with the lowest pvalues from this step were tested in the CATHY study. We also conducted a metaanalysis combining results from both studies; overall z-statistics and p-value for these 100 top SNPs were then calculated from a weighted sum of the individual statistics.

Weights were proportional to the square root of the number of individuals examined in each sample and selected such that the squared weights summed to 1.0, as implemented in the METAL program [START_REF] Willer | METAL: fast and efficient meta-analysis of genomewide association scans[END_REF]. This step aims to improve signal detection in the genetic analysis by avoiding a large number of tests, and to substantiate homologous signals in both studies since our population is relatively limited.

To correct for multiple tests in the main effect analysis, the FDR procedure (29) was calculated for each result of the meta-analysis. We investigated the interaction between SNPs and radiation doses using the likelihood ratio test, comparing models with and without the interaction term following the same steps described above.

All analyses were adjusted for age (five-year period), sex, thyroid cancer family history (yes/no), goiter history (yes/no), radiotherapy history (yes/no), BMI (continuous), height (continuous), educational level (primary school, secondary school, bachelors or higher), smoking status (never/former smoker/smoker), number of pregnancies longer than seven months in women (three classes), and study (CATHY/Young-Thyr) only in the pooled analysis. Analyses of genetic variants were additionally adjusted for the first three principal components to take into account the population stratification. Subgroup analysis was also performed separately for papillary histological type cases and according to tumor size (microcarcinoma and macrocarcinoma).

The log-linear model poses fewer convergence problems than the linear model, for that reason the association and interaction tests between radiation doses and DNA variants were performed using a log-linear model. Since we did not apply any cut-off p-values for SNPs selected to be included in the meta-analysis step, in this study we chose to only show our best five results from each analysis. Association analyses and meta-analyses were performed using R 3.6 and METAL [START_REF] Willer | METAL: fast and efficient meta-analysis of genomewide association scans[END_REF]. SNPs were annotated using the VEP tool [START_REF] Hunt | Ensembl variation resources[END_REF], and gene regions were plotted with LocusZoom software (31).

Results

Demographic characteristics of the pooled study population (Young-Thyr and CATHY) are described in Table 2. More than 75% of our population were women and nonsmokers. Papillary thyroid cancer type was the most frequent type of thyroid cancer observed, with a mean age at diagnosis younger than 40 years old. However, the mean age at diagnosis was lower in the Young-Thyr study than in the CATHY study, as shown in Supplementary Table S2 given after 20 years of age. Among children, the most frequent exam was panoramic dental radiography, which was reported in 971 individuals. Nuclear medicine exams were rarely reported among children; the most frequent exam scan was bone scans reported in 14 children (Table 3). During adulthood, the most frequent conventional radiography exam was chest radiography, which was seen in 30.8% of adults. Skull CT scan was the most common computed tomography exam during adulthood. Nuclear medicine exams were also relatively rarely reported among adults (Table 3). The median thyroid doses delivered during childhood were lower than doses administered during adulthood. The maximum childhood estimated thyroid dose was 194.2 mGy among the whole population, the mean among cases was 2.8 mGy and 2.0 mGy among controls. A total of 1672 subjects reported not having received any thyroid-irradiating diagnostic procedure during childhood. The estimated maximum dose delivered to the thyroid during adulthood in a diagnostic radiology procedure was 260.0 mGy, and the mean dose was 5.6 mGy and 5.5 mGy among cases and controls, respectively (Supplementary Tables S3 andS4). A total of 1466 subjects did not report experiencing any thyroid-irradiating diagnostic procedures during adulthood. Detailed information on diagnostic radiology exams and thyroid doses in cases and controls in each study are shown in Supplementary Tables S2,S3, and S4. Characteristics and thyroid doses among genotyped subgroups from both studies are presented in Table 2. The DTC risk in relation to the radiation doses in this population is detailed in Supplementary Table S5.

Differentiated thyroid cancer risk in relation to thyroid radiation doses

Only estimated radiation dose received by the thyroid gland during childhood was found to be associated with an increased DTC risk, unlike doses received during adulthood. In the linear model, the DTC OR per mGy administered to the thyroid was equal to 1.02 (95% CI: 1.00, 1.03). When restricting the analysis to papillary thyroid carcinoma, the OR per mGy was very similar. The fit of the model was improved by the addition of a quadratic term to take into account a possible higher effect of high doses, although not significant (p = 0.06). No significant difference (p > 0.05) was found between the dose responses for men and for women. No interaction was apparent between the thyroid radiation dose and obese status, age at DTC occurrence, study, number of pregnancies, female sex, smoking status, height, or the personal radiotherapy history. In a log-linear model, the odds ratio for a dose of 1 mGy was 1.01 (95% CI: 1.01, 1.04) (Table 4). Association analysis between DTC risk and the 5817 variants in DNA damage response genes from the Young-Thyr study including all histological types yielded only two SNPs with a p-value lower than 5x10 -4 : rs4962347 (chromosome 10, C10orf90) and rs16983787 (chromosome 10, SMC6). None of the top 100 variants with the lowest pvalues reached the threshold p-value of 5x10 -4 in the CATHY study. In the meta-analysis, results of the association test with DTC risk showed a significantly reduced risk for carriers of the minor allele [T]; both SNPs, rs6067822 in NFATc2 and rs7164173 in CHD2, had a p-value of 5.79x10 -5 and 9.26x10 -5 respectively, under an additive model of inheritance. Associations with both variants were in the same direction in CATHY and Young-Thyr (Table 5A). Other variants in NFATc2 present among the top 100 SNPs associated with DTC in the Young-Thyr study are described in Supplementary Figure 1.

Results from a sub-analysis by tumor size, shown in

Rs7164173 was the only SNP in CHD2 among the top 100 SNPs. Rs105939 and rs699517 in ENOSF1/THYS were in our best results, but statistical significance was not achieved (OR meta-analysis = 1.30, p-value meta-analysis = 7.81x10 -4 ). Only one variant in RPA3 (rs12702628 in 7p21.3) was found to be significantly associated with DTC risk.

When the analysis was restricted to only papillary carcinoma histological types, only rs7164173 was significant (p-value meta-analysis = 9.33x10 -5 ) (Table 5B). In the NFATc2 region, two SNPs, rs77971457 and rs6067822, had respective OR meta-analysis values of 1.45 and 0.77 but did not reach the significance threshold. Rs1290997 and rs1950764 in RAD51B had OR meta-analysis values of 0.74 and 0.60, respectively (Table 5B). The polymorphism rs1950764had a p-value meta-analysis > 5x10 -4 . Detailed results for SNPs in RAD51B are shown in Supplementary Figure 2. Results from the best SNPs in the macrocarcinoma analysis ( (rs72625242, rs16861406) in 2q31.1 in addition to two other SNPs in chromosome 2 (PMSD1and SMC6) and the C10orf90 gene in chromosome 10. In the microcarcinoma analysis, a significant result in 2q31.1 was found (rs75361806, TLK1) (Table 5D). The best results from this later analysis also yielded three SNPs in the MACROD2 gene (20p12.1).

Differentiated thyroid cancer risk related to the interaction between thyroid doses and variants of DNA damage repair and signaling genes

We investigated the interaction between variants in DNA damage response genes and thyroid exposure to radiation in DTC risk. In the meta-analysis, the SNP-radiation interaction term yielded a p-value meta-analysis = 3.4x10 -4 and an OR interaction = 0.65 for rs7068306 in MGMT (Table 6). A second MGMT SNP, rs7087131, was also among the top 100 SNPs identified in the Young-Thyr study. Results on the modifying effect of rs7068306 genotypes on DTC risk according to diagnostic radiation exposure study separately in CATHY and Young-Thyr are presented in Supplementary Table S6.

Discussion

Our main objective was to investigate the potential genetic susceptibility to DTC after exposure to low IR doses from diagnostic procedures performed during childhood. In our study, the estimated OR/mGy for thyroid radiation doses received during childhood (OR/mGy = 1.02 (95% CI: 1.00, 1.03)) was similar to the OR/mGy values of the pooled DTC study by Veiga et al. [START_REF] Veiga | A pooled analysis of thyroid cancer incidence following radiotherapy for childhood cancer[END_REF] when considering analyses restricted to thyroid radiation doses lower than 100 mGy (OR/mGy = 1.010, (95% CI: 1.004 -1.018)) or to thyroid radiation doses lower than 200 mGy (OR/mGy = 1.011, (95% CI: 1.007 -1.02)) (11).

Compared to the latest publication on the US radiologic technologist cohort, including 90,305 radiologic technologists in the U.S. who were followed during 1983-1998, the values of our coefficients for thyroid radiation doses received during childhood are slightly on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from higher than the coefficients estimated in the general analysis and the papillary carcinoma sub-analysis [START_REF] Little | Assessment of thyroid cancer risk associated with radiation dose from personal diagnostic examinations in a cohort study of US radiologic technologists, followed 1983-2014[END_REF]. Our estimates are also slightly higher than estimates in both the most recent analysis among Japanese atomic-bomb survivors [START_REF] Furukawa | Long-term trend of thyroid cancer risk among Japanese atomic-bomb survivors: 60 years after exposure[END_REF] and the IARC study of the highly contaminated area of Belarus following the Chernobyl nuclear accident (8).

The genetic analyses showed an association between DTC risk and SNPs: rs6067822 in intron 1 of NFATc2 (20q11.22), rs7164173 in intron 3 of CHD2 (15q21.3), rs1059394 (3 prime UTR variant), and rs699517 (3 prime UTR variant) both in ENOSF1/THYS (18p11.32), and rs12702628 intron variant in RPA3 (7p21.3). To our knowledge, none of these genes have previously been reported to be associated with DTC risk. The effect direction of these SNPs was similar in the Young-Thyr and CATHY studies and reached the significance threshold for the meta-analysis; furthermore, NFATc2 and CHD2 genes have been implicated in the response to ionizing and ultraviolet radiation in vitro studies [START_REF] Nagarajan | Role of chromodomain helicase DNA-binding protein 2 in DNA damage response signaling and tumorigenesis[END_REF][START_REF] Rajagopalan | Chromodomain helicase DNA-binding protein 2 affects the repair of X-ray and UV-Induced DNA damage[END_REF]. Moreover, cells with mutations in CHD2 were found to be defective in their ability to repair DNA damage, especially after ionizing and ultraviolet radiation exposure [START_REF] Rajagopalan | Chromodomain helicase DNA-binding protein 2 affects the repair of X-ray and UV-Induced DNA damage[END_REF].

Genes of the NFAT family encode for transcription factors, which have a role in cancer progression, and also are important for responding to ionizing and ultraviolet radiation exposure [START_REF] Beals | Nuclear export of NF-ATc enhanced by glycogen synthase kinase-3[END_REF][START_REF] Flockhart | NFAT regulates induction of COX-2 and apoptosis of keratinocytes in response to ultraviolet radiation exposure[END_REF][START_REF] Glover | Low dose ionizing radiation-induced activation of connexin 43 expression[END_REF]; these genes were previously found to be associated with other types of cancer risk, such as melanoma, breast, colorectal and oral cancers [START_REF] Perotti | NFATc2 is an intrinsic regulator of melanoma dedifferentiation[END_REF][START_REF] Kim | Upregulation of Ets1 expression by NFATc2 and NFKB1/RELA promotes breast cancer cell invasiveness[END_REF][START_REF] Shah | Single nucleotide polymorphisms in transcription factor genes associated with susceptibility to oral cancer[END_REF][START_REF] Lang | NFATC2 is a novel therapeutic target for colorectal cancer stem cells[END_REF].

Rs6067822 in NFATc2 and rs7164173 in CHD2 showed a similar stabilizing effect in general and papillary subgroup analyses. Our results from the papillary thyroid carcinoma sub-analysis yielded a significant association of rs1290997 in RAD51B with DTC risk.

Another variant in this gene, rs1950764, was among our top five SNPs but did not reach the significance threshold. These findings suggest a role for RAD51B in the etiology of radiation-related DTC. Interestingly, the RAD51B gene was involved in DNA damage repair after ultraviolet irradiation exposure [START_REF] Havre | The human REC2/RAD51B gene acts as a DNA damage sensor by inducing G1 delay and hypersensitivity to ultraviolet irradiation[END_REF][START_REF] Takata | The Rad51 Paralog Rad51B Promotes Homologous Recombinational Repair[END_REF] and associated with breast cancer risk on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from [START_REF] Lee | Rad51b activity and cell cycle regulation in response to DNA damage in breast cancer cell lines[END_REF][START_REF] Pelttari | RAD51B in Familial Breast Cancer[END_REF]. We report this result with great caution because 525 SNPs in this gene were tested in the first step of the analysis (Supplementary Table S1).

An association was found between two SNPs (rs1059394 and rs699517) falling within the ENOSF1/THYS gene region. These SNPs are non-coding transcript exon variants, and this region is known to be associated with ovarian and endometrial cancers [START_REF] Xu | Association of thymidylate synthase gene with endometrial cancer risk in a chinese population[END_REF][START_REF] Kelemen | rs495139 in the TYMS-ENOSF1 Region and Risk of Ovarian Carcinoma of Mucinous Histology[END_REF].

The polymorphism rs12702628 in replication protein A3 gene (RPA3), which was associated with DTC risk in our study, has previously been found to be involved in tumorigenesis, especially in gastric cancer [START_REF] Dai | Elevated Expression of RPA3 Is Involved in Gastric Cancer Tumorigenesis and Associated with Poor Patient Survival[END_REF].

The macrocarcinoma and microcarcinoma analyses both yielded significant results in 2q31.1. However, since these are subgroups results, they should be taken with caution, especially for the microcarcinoma analysis due to the low number of cases.

The minor allele of MGMT rs7068306 was found to interact with thyroid IR doses during childhood in reducing the risk of DTC after exposure. The first study to report an association between an MGMT variant and radiation-related DTC risk was performed in Belarusian children exposed to radiation [START_REF] Lonjou | Investigation of DNA repair-related SNPs underlying susceptibility to papillary thyroid carcinoma reveals MGMT as a novel candidate gene in Belarusian children exposed to radiation[END_REF]. The polymorphism rs2296675, associated with DTC risk in the Belarusian population, is located 94 kb from rs7068306 in intron 4 of the MGMT region. A correlation coefficient of r 2 = 0.005 was found between rs7068306 and rs2296675. In a study of a Caucasian population, Sandler et al. found an interaction between other MGMT variants: rs1762444, rs4750763, and rs12219606, and exposure to radiation from diagnostic procedures [START_REF] Sandler | Germline Variants in DNA Repair Genes, Diagnostic Radiation, and Risk of Thyroid Cancer[END_REF]. These SNPs are located in intron 2 and are 244kb, 26kb, and 15kb from rs7068306, respectively. The r² values between these three SNPs and rs7068306 are 0.009 and 0.044 (Supplementary Table S7). The r² values between rs7068306 and the SNPs tested in studies by Lonjou and Sandler were estimated in a European reference population of 1000 Genomes project [START_REF] Auton | A global reference for human genetic variation[END_REF] from the present study were obtained after estimation and quantification of thyroid doses, based on a combination of self-reported radiologic procedure history and literature doses separately on childhood and adulthood observations. The Sandler et al. study used a different procedure since no doses were taken into account; only categories of diagnostic procedure exposure based on self-reported history were evaluated. Taken together, results from these different studies highlight the role of MGMT in modulating the effect of IR on cells of the thyroid.

The expression of CLIP2, a gene located on 7q11.22, has been found to be strongly linked with previous radiation exposure in thyroid cancer [START_REF] Heß | Gain of chromosome band 7q11 in papillary thyroid carcinomas of young patients is associated with exposure to low-dose irradiation[END_REF].In our study, only 22 SNPs located on chromosome 7 were tested (Supplementary Table S1), of which, only two were near the CLIP2 gene region. None of these were among the 100 best SNPs in our study, since the low numbers of concerned SNPs prevented us from confirming any results about locus 7q11. [START_REF] Amos | The oncoarray consortium: A network for understanding the genetic architecture of common cancers[END_REF].

Limitations of the study

Investigating the thyroid radiation dose-response from self-reported radiation examinations carried out in case-control studies is sensitive to recall bias. This is particularly true when addressing public health issues highly debated by the public, such as the health effects of irradiation. As Hallquist and Jansson previously showed, in casecontrol studies investigating the impact of self-reported diagnostic radiology procedures on DTC risk, this bias produces under-reporting of examinations by both cases and controls, but significantly more by controls; furthermore, this bias could cause an overestimate of the IR effect [START_REF] Hallquist | Self-reported diagnostic X-ray investigation and data from medical records in case-control studies on thyroid cancer: evidence of recall bias?[END_REF]. We cannot exclude such a bias in our study, which could result in an overestimation of the radiation dose effect. However, in the Young-Thyr study, we previously showed that despite DTC patients being more likely than controls to believe that the consequences of the Chernobyl accident were responsible for DTC occurrences, self-reported vegetable consumption during the two months after the Chernobyl accident, known to be a major source of radioactive contamination, was correlated with the status of participants, cases or controls, but not with their beliefs [START_REF] Xhaard | Are dietary reports in a case-control study on thyroid cancer biased by risk perception of Chernobyl fallout?[END_REF].

Thus, exposure could be over-reported in patients, particularly when they believe that this exposure contributed to their disease. In this type of study, case and control selfdeclarations are often impacted by recall bias, especially in terms of the number of radio diagnostic exams and images in the present study. Despite these caveats, case-control studies could help to improve understanding of the risks associated with low-dose IR radiation by utilizing a large number of cases and permitting more detailed investigations on several potential risk factors, which are costlier to investigate in cohort studies.

For some types of exams, there are no available thyroid dose estimates available in current literature, especially during childhood. This disadvantage could decrease the precision of our estimates; consequently, to harmonize our analyses we considered the same doses for all children older than 2 years. The simplest way to account for age variation of radiation dose exposure (0-2 years compared to older) in our analysis, has probably a limited effect because the reference doses were the same for cases and controls. Thyroid dose estimates were based on self-declarations of diagnostic exam history. In this data, dates for each exam are not precise, causing the impossibility to impose a lagging period and raising the problem of reverse causation. Despite the absence of specific dates for each procedure, we only kept data from radiological procedures that were not carried out for diagnosing thyroid cancer. There is some heterogeneity in demographic and cancer characteristics between our two studies: patients from the Young-Thyr study were younger at cancer diagnosis and inclusion in the study compared to cases from CATHY. Furthermore, diagnostic radiology technologies that were available in childhood differ substantially between the participants of the CATHY and Young-Thyr studies; additionally, the availability and frequency of these examinations differ (Supplementary Tables S2,S3, and S4). To better discern signals from the genetic analysis and to increase the statistical power, we chose to perform a meta-analysis to substantiate homologous signals in both studies by keeping a limited number of SNPs in this step to avoid a high number of tests.

Despite the small size of our study populations, our results suggest a role for NFATc2, CHD2, RPA3, and ENOSF1/THYS that has not previously been associated with DTC risk and confirm the previously demonstrated role of RAD51B and MGMT. However, functional and validation studies are needed to better understand and confirm the biological role of these variants.

Conclusion

We present evidence that DTC risk is significantly increased in higher thyroid radiation doses received during childhood from radio diagnostic examinations. In addition, we demonstrated an interaction between this thyroid radiation dose and the minor allele of rs706830 located in MGMT. Our results also suggest an association between polymorphisms in NFATc2, CHD2, ENOSF1/THYS, RPA3, and RAD51B. Taken together, despite the limited size of both populations studied, these results underline the role of DNA repair pathways in DTC risk. More studies of larger populations are needed to validate and characterize the interaction between DNA repair genes and exposure to low IR doses.

  was a case-control study conducted in Marne, Ardennes, and Calvados, three French administrative areas covered by a cancer registry. Eligible cases were all DTC patients aged 25 years and older that were diagnosed between 2002 and 2007 and resided in these areas. Controls were recruited by selecting and contacting telephone numbers at random, then frequency-matching the individuals to patients by sex and five-year age groups; controls were randomly selected among healthy individuals residing in the same study areas at the time of the matched cases diagnoses. From the 621 cases and 706 controls initially included in the CATHY study, saliva DNA samples (Oragene® DNA testing kit) were available for 583 cases and 643 controls. The Young-Thyr study (20) is a case-control study conducted in eastern regions of France: Alsace, Champagne-Ardennes, Corse, Franche-Comté, Lorraine, Rhône-Alpes, and Provence-Alpes-Côte d'Azur. Eligible cases were all DTC patients diagnosed with DTC between January 1st, 2002, and December 31 st , 2006 that were younger than 35 years of age with their main residence in a region of eastern France. Controls were selected from the general population and individually matched to a single patient of the same sex, year of birth (within one year), and region of residence during the year when the patient was diagnosed with cancer. From the 805 cases and the 876 controls included in the Young-Thyr study, DNA from saliva (Oragene®) was available for 715 cases and 692 controls. Participants from both studies answered similar questionnaires that were collaboratively developed. Information on a personal and familial history of thyroid disease, hormonal and reproductive factors, weight, height, dietary habits, tobacco smoking, and medical history was collected during in-person interviews. Participants from both studies gave their informed written consent before being interviewed by trained interviewers. Both on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on April 7, 2021; DOI: 10.1158/1055-9965.EPI-20-1142 studies were approved by the Ethics Committee and the French National Commission for Data Protection (CNIL).

  (27 years versus 51 years).

3. 1 .

 1 Diagnostic radiation and thyroid cancer risk 3.1.1. Thyroid doses determined by diagnostic radiology examination estimates Estimated IR doses administered to the thyroid during childhood were lower than those

  Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited.Author Manuscript Published OnlineFirst on April 7, 2021; DOI: 10.1158/1055-9965.EPI-

on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from

  Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited.Author Manuscript Published OnlineFirst on April 7, 2021; DOI: 10.1158/1055-9965.EPI-

on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from

  Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited.Author Manuscript Published OnlineFirst on April 7, 2021; DOI: 10.1158/1055-9965.EPI-

on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from

  Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited.Author Manuscript Published OnlineFirst on April 7, 2021; DOI: 10.1158/1055-9965.EPI-

on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from

Table 4 ,

 4 yielded similar DTC risk in relation to thyroid IR doses to these from the whole population analysis. on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from 3.2. Differentiated thyroid cancer risk in relation to DNA damage repair and signaling gene variants

  Table 5C) yielded two SNPs in the MLK7-AS1 gene on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on April 7, 2021; DOI: 10.1158/1055-9965.EPI-20-1142

  . Results on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on April 7, 2021; DOI: 10.1158/1055-9965.EPI-20-1142

  on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on April 7, 2021; DOI: 10.1158/1055-9965.EPI-20-1142

  on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on April 7, 2021; DOI: 10.1158/1055-9965.EPI-20-1142

Table 1

 1 References used for thyroid radiation dose estimates per diagnostic procedure type § : No exposed subject at this age *: No available data for children, adult data used

			Doses in mGy			References
	Exams types	Childhood exposure	Childhood exposure age > 2 years and adulthood exams
		age < 2	Before 1980	1980-1989	1990 and after
	Conventional Radiography
	Skull	- §	3.6	3.6	0.42	Chang et al. 2017
	Dental (panoramic)	- §	0.56	0.07	0.02	Chang et al. 2017
	Paranasal sinuses	- §	0.02	0.04	0.04	Chang et al. 2017
	Intravenous urography	0.38*	0.38	0.21	0.21	Inskip et al. 1995
	Chest	0.13	0.16	0.31	0.19	Almén and Mattsson 1995 / Chang et al. 2017
	Spine	2.8*	2.8	4.5	0.99	Chang et al. 2017
	CT Scan
	Skull	3	0.43	0.49	0.64	Lee et al. 2007 / Chang et al. 2017
	Chest	5.9	15	20.5	22	Mabille et al. 2008 / Chang et al.
	Spine	13.5	17	24	25.5	Mabille et al. 2008 / Chang et al.
	Abdomen	0.17	0.28	0.38	0.41	Mabille et al. 2008 / Chang et al.
	Nuclear medicine
	Bone scan	1.1*	1.1	0.96	1.1	Chang et al. 2017
	Brain scan	- §	1.3	3.6	9	Chang et al. 2017
	Lung scan (perfusion/ventilation)	- §	0.2	0.25	0.25	Chang et al. 2017
	Heart scan	- §	11	17	12	Chang et al. 2017
	Liver scan	- §	0.15	0.15	0.15	Chang et al. 2017
	Renal scan	- §	0.17	0.31	0.17	Chang et al. 2017

Table 2

 2 Clinical and demographic description of the population included in DTC risk in relation to thyroid radiation doses analysis and genetic analysis

		Whole population	The population included in the genetic analysis
		Cases (n = 1393)	Controls (n = 1580)	Cases (n = 1072)	Controls (n = 1188)
	Gender (%)
	Men	300 (21.5)	398 (25.2)	228 (21.3)	302 (25.4)
	Women	1093 (78.5)	1182 (74.8)	844 (78.7)	886 (74.6)
	Age at diagnosis/reference year (years)
	Mean	37.58	37.21	37.4 (15.0)	37.6 (15.2)
	Median [Min, Max]	32.0 [9.00, 83.0]	32.0 [9.00, 83.0]	32.0 [11.0, 83.0]	32.0 [9.00, 80.0]
	Smoking status (%)
	Non-smoker	739 (53.1)	768 (48.6)	232 (52.4)	271 (50.9)
	Former smoker	304 (21.8)	306 (19.4)	140 (31.6)	149 (28.0)
	Smoker	350 (25.1)	506 (32.0)	71 (16.0)	112 (21.1)
	Alcohol consumption (Number of alcohol glasses per week) (%)
	No consumption	778 (55.9)	763 (48.3)	582 (54.3)	559 (47.1)
	Less than 10	504 (36.2)	673 (42.6)	403 (37.6)	521 (43.9)
	More than 10	110 (7.9)	144 (9.1)	87 (8.1)	108 (9.1)
	BMI (Kg/m²)
	Mean (SD)	24.6 (5.21)	24.1 (4.88)	24.7 (5.36)	24.2 (4.89)
	Median [Min, Max]	23.5 [11.0, 51.8]	23.1 [13.4, 49.1]	23.6 [11.0, 51.8]	23.1 [13.4, 48.7]
	Goitre history (%)
	No	899 (64.5)	1468 (92.9)	695 (64.8)	1102 (92.8)
	Yes	494 (35.5)	112 (7.1)	377 (35.2)	86 (7.2)
	Thyroid cancer family history (%)
	No	1542 (97.6)	1322 (94.9)	1023 (95.4)	1158 (97.5)
	Yes	38 (2.4)	71 (5.1)	49 (4.6)	30 (2.5)
	Radiotherapy history (%)
	No	1558 (98.6)	1354 (97.2)	1043 (97.3)	1168 (98.3)
	Yes	29 (2.8)	22 (1.3)	19 (1.7)	20 (1.6)
	Educational level (%)
	Bachelor's degree or higher	765 (54.9)	982 (62.2)	618 (57.6)	743 (62.5)
	Secondary school	418 (30.0)	406 (25.7)	315 (29.4)	311 (26.2)
	Primary school level	210 (15.1)	192 (12.2)	139 (13.0)	134 (11.3)
	Childhood thyroid radiation doses in mGy (%)
	0	1021 (73.3)	1161 (73.5)	777 (72.5)	876 (73.7)
	]0,1]	112 (8.0)	147 (9.3)	89 (8.3)	104 (8.8)
	]1,5]	139 (10.0)	150 (9.5)	116 (10.8)	113 (9.5)
	]5,10]	25 (1.8)	45 (2.8)	18 (1.7)	36 (3.0)
	]10,20]	49 (3.5)	57 (3.6)	35 (3.3)	42 (3.5)
	>20	46 (3.3)	20 (1.3)	37 (3.5)	17 (1.4)
	Mean (sd)	2.79 (10.3)	1.98 (6.18)	2.89 (11.1)	2.11 (6.62)
	Median [Min, Max]	0 [0, 194]	0 [0,80.9]	0 [0, 194]	0 [0, 80.9]

Adulthood thyroid radiation doses in mGy (%)

	0	669 (48.1)	797 (50.4)	523 (48.8)	591 (49.7)
	]0,1]	247 (17.7)	283 (17.9)	187 (17.4)	220 (18.5)
	]1,5]	245 (17.6)	262 (16.6)	182 (17.0)	193 (16.2)
	]5,10]	59 (4.2)	61 (3.9)	46 (4.3)	46 (3.9)
	]10,20]	53 (3.8)	43 (2.7)	44 (4.1)	35 (2.9)
	>20	119 (8.5)	134 (8.5)	90 (8.4)	103 (8.7)
	Mean (sd)	5.63 (17.3)	5.50 (17.9)	5.28 (16.6)	5.54 (17.2)
	Median [Min, Max]	0 [0, 245]	0.02 [0, 262]	0.02 [0, 245]	0.02 [0, 157]
	Number of children (%)
	0 (and men)	666 (47.8)	829 (52.5)	514 (47.9)	622 (52.4)
	1-3	648 (46.6)	529 (43.8)	542 (50.6)	542 (45.6)
	4-6	67 (4.8)	44 (3.4)	10 (0.9)	20 (1.7)
	>6	11 (0.4)	4 (0.3)	6 (0.6)	4 (0.3)
	Study
	Young-Thyr (%)	805 (57.8)	876 (55.4)	629 (58.7)	656 (55.2)
	Cathy (%)	587 (42.2)	704 (44.6)	443 (41.3)	532 (44.8)
	Thyroid cancer histology (%)
	Follicular	140 (10.1)		109 (10.2)
	Papillary	1243 (89.2)		955 (89.1)
	Missing	10 (0.7)		8 (0.7)
	Thyroid cancer size in mm (%)
	< 10	431 (31.0)		341 (31.8)
	> 10	957 (68.8)		729 (68.0)
	Missing	4 (0.28)		2 (0.2)

Table 3

 3 Number of subjects by age and exam typeAuthor manuscripts have been peer reviewed and accepted for publication but have not yet been edited.Author Manuscript Published OnlineFirst on April 7, 2021; DOI: 10.1158/1055-9965.EPI-

		Cases n (%) having at least 1 listed exam	Controls n (%) having at least 1 listed exam
		<20 years	>=20 years	<20 years	>=20 years
	Conventional radiography
	Skull	89 (6.4)	93 (6.7)	94 (5.9)	82 (5.2)
	Sinus	67 (4.8)	124 (8.9)	77 (4.9)	133 (8.4)
	Dental	416 (29.9)	260 (18.7)	555 (35.1)	309 (19.6)
	Spine	180 (12.9)	277 (19.9)	199 (12.6)	296 (18.7)
	Chest	159 (11.4)	451 (32.4)	198 (12.5)	465 (29.4)
	Intravenous urography	27 (1.9)	94 (6.7)	31 (2.0)	74 (4.7)
	CT scan
	Abdomen	7 (0.5)	47 (3.4)	2 (0.1)	33 (2.1)
	Chest	8 (0.6)	46 (3.3)	0 (0)	33 (2.1)
	Skull	53 (3.8)	137 (9.8)	47 (3.0)	117 (7.4)
	Spine	31 (2.22)	122 (8.75)	29 (1.83)	160(10.12)
	Nuclear medicine
	Cerebral	1 (0.1)	3 (0.2)	0 (0)	9 (0.6)
	Heart	1 (0.1)	2 (0.1)	1 (0.1)	7 (0.4)
	Lung	1 (0.1)	3 (0.2)	0 (0)	7 (0.4)
	Bones	8 (0.6)	43 (3.1)	6 (0.4)	52 (3.3)
	Hepatic	0 (0)	2 (0.1)	0 (0)	2 (0.1)
	Renal	4 (0.3)	5 (0.4)	5 (0.3)	13 (0.8)

on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from

Table 5

 5 SNPs with the lowest p-values associated with DTC risk in the meta-analysis among all DTC SNPs with lowest p-values associated with papillary thyroid carcinoma risk in the meta-analysis (563 cases from Young-Thyr and 392 cases from CATHY) SNPs with lowest p-values associated with large thyroid carcinoma (>10mm) risk in the meta-analysis (501 cases from Young-Thyr and 237 cases from CATHY) SNPs with lowest p-values associated with small thyroid carcinoma (<10mm) risk in the meta-analysis (128 cases from Young-Thyr and 206 cases from CATHY) Adjusted on age, sex, childhood IR thyroid doses, thyroid cancer family history, radiotherapy history, goiter history, BMI, height, educational level, smoking status, number of pregnancies, and three first genetic components

		types cases (A), among only papillary DTC cases (B), macrocarcinoma cases (C), and
						microcarcinoma cases (D)
				A/ SNPs with lowest p-values associated with DTC risk in the meta-analysis including all histological types
	SNP	Locus	RA	EA	EAF	Gene	OR a	Young-Thyr P-value	OR a	CATHY	P-value	OR a	Meta-analysis P-value	FDR p-value
	rs12702628	7p21.3	A	G	0.4	RPA3	1.25		1.03 10 -2	1.22		4.37 10 -2	1.24	1.12 10 -03	0.02
	rs7164173	15q26.1	G	T	0.1	CHD2	0.7		1.05 10 -3	0.69		1.06 10 -2	0.68	9.26 10 -05	0.004
	rs1059394	18p11.32	C	T	0.3	ENOSF1/THYS	1.34		2.91 10 -3	1.19		8.97 10 -2	1.3	7.81 10 -04	0.01
	rs699517	18p11.32	C	T	0.3	ENOSF1/THYS	1.34		2.91 10 -3	1.19		8.97 10 -2	1.3	7.81 10 -04	0.01
	rs6067822	20q13.2	G	T	0.3	NFATc2	0.64		1.6 10 -3	0.7		1.13 10 -3	0.64	5.79 10 -05	0.005
	B/ SNP Locus	RA	EA	EAF	Gene	OR a	Young-Thyr P-value	OR a	CATHY	P-value	OR a	Meta-analysis P-value	FDR p-value
	rs1950764	14q24.1	G	A	0.2	RAD51B	0.56		2.87 10 -03	0.66	7.27 10 -02	0.6	6.08 10 -04	0.01
	rs1290997	14q24.1	G	T	0.2	RAD51B	0.77		2.01 10 -03	0.7	7.18 10 -02	0.74	4.36 10 -04	0.01
	rs7164173	15q26.1	G	T	0.3	CHD2	0.69		3.24 10 -03	0.68	1.02 10 -02	0.68	9.33 10 -05	0.009
	rs77971457	20q13.2	G	T	0.1	NFATc2	1.44		1.09 10 -03	1.47	1.76 10 -02	1.45	5.06 10 -04	0.01
	rs6067822	20q13.2	G	T	0.3	NFATc2	0.81		3.47 10 -03	0.72	4.63 10 -02	0.77	5.59 10 -04	0.01
	C/ SNP Locus	RA	EA	EAF	Gene	OR a	Young-Thyr P-value	OR a	CATHY	P-value	OR a	Meta-analysis P-value	FDR p-value
	rs72625242	2q31.1	C	T	0.22	MLK7-AS1	1.927	6.27 10 -4	0.9934	1	1.927	6.25 10 -4	0.004
	rs17619600	2q37.1	T	C	0.15	PMSD1	1.855	1.20 10 -3	1.01	0.9999	1.855	1.20 10 -3	0.004
	rs7578070	2p24.2	A	G	0.41	SMC6	1.538	1.86 10 -3	1.03	0.9998	1.538	1.86 10 -3	0.004
	rs16861406	2q31.1	A	G	0.21	MLK7-AS1	1.912	2.56 10 -3	1.009	1	1.912	2.56 10 -3	0.005
	rs5023821	10q26 ;2	T	C	0.25	C10orf90	0.6249	1.14 10 -3	1.026	0.9998	0.6249	1.14 10 -3	0.004
	D/ SNP Locus	RA	EA	EAF	Gene	OR a	Young-Thyr P-value	OR a	CATHY	P-value	OR a	Meta-analysis P-value	FDR p-value
	rs75361806	2q31.1	A	G	0.05	TLK1	25.55	1.12 10 -2	1.02		1	25.5494	1.12 10 -2	0.03
	rs73234091	20p12.1	T	C	0.05	MACROD2	30.89	6.99 10 -3	1.007		1	30.8891	6.99 10 -3	0.03
	rs17757541	18q21.33	C	G	0.06	BCL2	7.188	1.22 10 -2	1.005		1	7.1877	1.12 10 -2	0.01
	rs116851051	20p12.1	T	C	0.1	MACROD2	28.39	1.12 10 -2	0.9935		1	28.3897	1.12 10 -2	0.035
	rs2327965	20p12.1	A	G	0.05	MACROD2	27.11	1.12 10 -2	1.016		1	27.1096	1.12 10 -2	0.03
	RA=Reference allele
	EA= Effect allele
	EAF= Effect allele frequency

a :

Table 6 Five

 6 SNPs with the lowest p-values in SNPs -diagnostic radiation thyroid doses interaction term from the meta-analysisEAF= Effect allele frequency OR = Odds Ratio for the interaction between Effect Allele and radiation dose, considered as a continuous variable in an exponential dose-response model Adjusted on age, sex, thyroid cancer family history, radiotherapy history, goiter history, BMI, height, educational level, smoking status, number of pregnancies, and three first genetic components

	SNP	Locus	Reference	Effect	EAF	Gene		Young-Thyr		CATHY		Meta-analysis
			allele	allele			OR a	P value	OR a	P value	OR	P value	FDR
													correction
	rs10779613	1q41	T	C	0.4	SMYD2	0.60	1.19 10 -03	0.94	6.08 10 -01	0.80	5.42 10 -03	0.1
	rs17514740	7p11.2	G	C	0.4	EGFR	0.71	9.39 10 -03	1.19	1.84 10 -01	1.30	4.64 10 -03	0.1
	rs7068306	10q26.3	C	G	0.3	MGMT	0.63	1.91 10 -03	0.70	5.85 10 -02	0.65	3.40 10 -04	0.03
	rs10402248	19p13.3	C	T	0.4	MUM1	0.65	4.79 10 -03	0.85	2.54 10 -01	0.75	4.03 10 -03	0.1
	rs6066138	20q13.12	G	A	0.2	EYA2	1.52	9.73 10 -03	1.22	9.01 10 -02	1.32	2.20 10 -03	0.1

a :

on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on April 7, 2021; DOI: 10.1158/1055-9965.EPI-20-1142

a Stratified on age, sex, and study, and adjusted on thyroid cancer family history, radiotherapy history, BMI, height, smoking habits, and number of pregnancies on April 9, 2021. © 2021 American Association for Cancer Research. cebp.aacrjournals.org Downloaded from

Acknowledgement: FDV received the following grants as principal investigator of Young-Thyr study: Fondation de France (Grant number 65391), L'Alliance pour les sciences de la vie et de la santé, « AVIESAN » (Grants number ENV201416 and 2007005070), the Ligue Nationale Contre le Cancer (LNCC) (Grants number EPDAC6036, EPDTP6004, R10127LL). We would like to thank the CEPH-Biobank team, Informatique et Statistique en Anatomie Pathologique en Provence-Alpes-Côte d'Azur (CRISAP PACA) team, as well as Dr C Sattonnet, Dr JL Lassalle, Dr Z Hafdi-Nejjari, Dr P Delafosse, Ms Kami-Marie Moreau, Ms Cyrielle Orenes, Ms Laurianne Sarrazin, Ms Stéphanie Bonnay, Ms Frédérique Chatelain, Ms Maryse Barouh, Ms Evelyne Rapp, Ms Julie Festraëts, Ms Julie Valbousquet, Mr Yusuf Atilgan, Mr Jean Chappellet, Ms Lallia Bedhouche, Mr Florent Dayet and Ms Ziyan Fami for their involvement in Young-Thyr study.

TT received the following grants for CATHY and Young-Thyr studies genotyping Institut National du Cancer (Grant number 9533), the ARC foundation (Grant number PGA120150202302) MZ performed this work during her PhD funded by Ecole des Hautes Etudes en Santé Publique (EHESP) and the ARC Foundation (Grant number ARCDOC42020070002532).

The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.


Yusuf Yigit Pilavci

Pierre-Olivier Amblard

Simon Barthelme

Nicolas Tremblay

Yusuf Yigit Pilavcı

Simon Barthelmé

Variance reduction in stochastic methods for large-scale regularised least-squares problems

Keywords: graph signal processing, smoothing, variance reduction, random spanning forests

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

INTRODUCTION

In linear least-squares problems, given measurements y ∈ R n and predictors A ∈ R n×p , we seek the vector x verifying:

x = argmin x∈R p ||Ax -y|| 2 2 + λx t Px (1)
where λx t Px is a regularization term. x can be computed exactly at cost O(np 2 ), but for very large n or p this is costly, and approximate methods may be used instead. There are dozens of such methods, either deterministic or stochastic in nature. The best known example of the former are the various gradient descent methods [START_REF] Nesterov | Introductory lectures on convex optimization: A basic course[END_REF], while among the latter the most popular is certainly stochastic gradient descent [START_REF] Bottou | Stochastic learning[END_REF]. An attractive alternative to stochastic gradient descent is to use methods based on Determinantal Point Processes, which, roughly, consist in finding a well-chosen, random subset of the rows of A so that solving the least-squares problem for just these rows

This work was partly funded by the French National Research Agency in the framework of the "Investissements d'avenir" program (ANR-15-IDEX-02), the LabEx PERSYVAL (ANR-11-LABX-0025-01), the ANR GraVa (ANR-18-CE40-0005), the ANR GRANOLA (ANR-21-CE48-0009), the MIAI@Grenoble Alpes chairs "LargeDATA at UGA" and "Pollutants" (ANR-19-P3IA-0003).

gives an unbiased estimator for the solution to the full problem [START_REF] Derezinski | Determinantal point processes in randomized numerical linear algebra[END_REF][START_REF] Fanuel | Diversity sampling is an implicit regularization for kernel methods[END_REF]. This contrasts with stochastic gradient descent, where the estimator is generally biased after a finite number of steps.

One drawback of this new class of methods is that sampling a subset of rows with the right properties may be expensive, so that reducing the variance by simply increasing the number of estimates becomes rapidly too costly. We show below that a very simple way to reduce variance is to combine a stochastic estimator with (at least one) step of gradient descent. The result is another unbiased estimator, one that is guaranteed to have lower variance. We apply our technique to Tikhonov regularization on graphs, where DPPbased estimators are particularly well-adapted [START_REF] Yusuf Y Pilavci | Smoothing graph signals via random spanning forests[END_REF][START_REF] Yusuf | Graph tikhonov regularization and interpolation via random spanning forests[END_REF]. As in standard applications of gradient descent, most of the difficulty consists in determining how large the gradient descent step should be. In graphs this problem turns out to be quite tractable, with good heuristics available. Numerical results confirm that the reduction in variance obtained is substantial, at small computational cost.

Main idea

The main idea of the paper is extremely simple. Solving a least-squares problem of the form of Eq.( 1) is equivalent to minimizing a quadratic form

f (x) = 1 2 x t Qx -r t x. (2)
Minimising f by gradient descent consists in taking steps of the form

x t = x t-1 -α∇f (x t-1 ) = x t-1 -α(Qx t-1 -r),
where α is the step size. Since the gradient is zero at the solution, x = argmin f (x) is a fixed point of the iteration. Now suppose that x is an unbiased estimator of x, i.e., a random variable such that E(x) = x. Then, it is easy to check that

E (x -α(Qx -r)) = x,
meaning that x stays unbiased after one step of gradient descent (or indeed several). We show below that setting the step size α correctly guarantees a reduction in variance, and give practical solutions for finding an appropriate step size in a graph signal processing setting.

BACKGROUND

Tikhonov regularization in graphs. The regularised leastsquares estimator we are interested in is graph Tikhonov regularisation (GTR), a method for denoising graph signals. A "graph signal" is a vector of measurements associated with the nodes of a graph, for instance brain activity in n brain regions, where the graph models neural connectivity across regions. GTR also occurs as a subproblem in other methods, like semi-supervised learning [START_REF] Yusuf | Graph tikhonov regularization and interpolation via random spanning forests[END_REF], which is why finding an efficient approximation algorithm is of high interest.

Let us first set notation. We denote a graph by the set G = (V, E, w) with |V| = n vertices and |E| = m edges. w : V × V → R + is called the weight function and is nonzero only for (i, j) ∈ E. In this work, we only consider connected (i.e., there exists a path between any pair of nodes) and undirected graphs (i.e., verifying ∀(i, j) ∈ E, w(i, j) = w(j, i)). In addition, we use certain matrices to depict the algebraic properties of graphs. These are the (weighted) adjacency matrix W = [w(i, j)] i,j ∈ R n×n , the diagonal degree matrix whose diagonal entries are D i,i = n j=1 w(i, j) and the graph Laplacian, L = D -W. It is well-known that L ∈ R n×n is a symmetric positive semi-definite matrix with n eigenvalues λ 1 = 0 < λ 2 ≤ . . . ≤ λ n for any undirected, connected graph [START_REF] Van Mieghem | Graph spectra for complex networks[END_REF].

Given a noisy version y ∈ R n of an underlying graph signal x ∈ R n that one wishes to recover, GTR consists in solving the following minimisation problem to estimate x:

x = argmin z∈R n q||z -y|| 2 2 + z Lz, (3)
where q ∈ R + is a parameter that adjusts the balance between the data fidelity term ||z -y|| 2 2 and the regularization term z Lz, which forces the solution to be smooth over the graph. Note that this is a special case of eq. ( 1) with A = I, P = L and λ = 1/q. The explicit solution to this problem reads:

x = Ky with K = q(qI + L) -1
The direct computation of x requires (a worst-case) O(n 3 ) elementary operations due to the inversion of (qI + L). As n increases, this computation becomes prohibitive. In the next section, we list state-of-the-art methods which avoid this expensive computation.

DPP-based estimators for Graph Tikhonov Regularisation. In the special case of GTR, the most popular methods are deterministic. For large n, state-of-the-art methods can be divided roughly into two groups, namely iterative methods (e.g. conjugate gradient [START_REF] Saad | Iterative methods for sparse linear systems[END_REF]) and polynomial approximations (e.g. Chebyshev polynomials [START_REF] David I Shuman | Chebyshev polynomial approximation for distributed signal processing[END_REF]). Both classes of methods run in linear time with the number of edges, m.

As an alternative stochastic method for GTR, we have proposed in previous works unbiased Monte Carlo estimators for approximating x which also scale linearly with m [START_REF] Yusuf Y Pilavci | Smoothing graph signals via random spanning forests[END_REF][START_REF] Yusuf | Graph tikhonov regularization and interpolation via random spanning forests[END_REF]. Our method can be viewed as a DPP-based subsampling of the rows of a matrix, but the case of GTR is particularly favourable. The appropriate DPP is the random forest process [START_REF] Avena | Two applications of random spanning forests[END_REF], which is easy to sample from, and its analytic properties enable variance reduction via conditional Monte Carlo. The resulting estimator, called x in [START_REF] Yusuf Y Pilavci | Smoothing graph signals via random spanning forests[END_REF][START_REF] Yusuf | Graph tikhonov regularization and interpolation via random spanning forests[END_REF], is unbiased (E(x) = x), can be obtained in O(m) elementary operations, and takes a very simple form: based on the partition formed by a random spanning forest, it averages the signal in each part of the partition. We repeat this process N times and average to get a denoised signal. The details of the estimator can be found in [START_REF] Yusuf | Graph tikhonov regularization and interpolation via random spanning forests[END_REF], but are irrelevant for what we discuss here.

PROPOSED METHOD

In this section, we propose an improved estimator for estimating Ky. As described in the introduction, we combine our unbiased estimator with a gradient descent step to reduce variance. This variance reduction technique can also be viewed as an instance of the control variate method [START_REF] Botev | Variance reduction[END_REF] in the Monte Carlo literature.

The gradient descent update

Note that the solution to (3) also minimizes the cost function:

F (z) = 1 2 z K -1 z -z y.
As stated in the introduction, applying the gradient step to x yields a new estimator:

z := x -α(K -1 x -y). (4)
Proposition 1. z is an unbiased estimator for x. Moreover, assuming1 tr Var(K -1 x) > 0, the MSE of z is a quadratic function of α which is minimized for:

α = tr Cov(K -1 x, x) tr (Var(K -1 x)) . (5)
Proof. Since x is an unbiased estimator, the expectation of

z immediately reads E[z] = E[x]-α(K -1 E[x]-y) = x.
Eq. ( 6) is a quadratic function in α and is minimized at α given in Eq. ( 5):

Connection with control variates. The proposed method is a particular instance of the control variate method. This technique leverages an additional random variable, called control variate, with a known expectation to improve the Monte Carlo performance. In our case, the control variate is K -1 x whose expectation is the input signal y. Implementation. z requires the computation of the control variate per sample in addition to x. The nontrivial part of this computation includes the matrix-vector product Lx. However, we can avoid to repeat this product per sample. Instead, we can calculate the sample mean 1 N N i=1

x(i) , then do the product once to directly compute the sample mean for z.

How to select α?

Unfortunately, calculating the optimal value α requires information that is not readily available. However, as the MSE (Eq. ( 6)) is a quadratic function in α minimized in α , we know that any choice of α ∈ (0, 2α ) will necessarily decrease the variance (see an illustration of this in Fig. 1). We now discuss several options to find such appropriate -yet not optimal-α. Our examination can be separated into two parts, each proposing a choice of α with different motivations. First, we look for a constant for α that is cheap to compute and ensures variance reduction. Second, we consider how to approximate α within the Carlo simulations.

A first option. To ensure variance reduction, z must verify:

E[||z -x|| 2 ] ≤ E[||x -x|| 2 ].
Notice that this inequality is satisfied if the following is true for all x, z ∈ R n :

||z -x|| 2 ≤ ||x -x|| 2 . ( 7
)
We use this inequality to find a safe range for α and propose to choose the largest α within this range. This particular choice costs O(1) to calculate for a given graph.

Proposition 2. Let d max be the maximum degree of the graph. Then, setting α = 2q q+2dmax ensures that:

||z -x|| 2 ≤ ||x -x|| 2 .
Proof. The following must hold to satisfy Eq. ( 7)

||x -x -α(K -1 x -y)|| 2 ≤ ||x -x|| 2 ||(I -αK -1 )(x -x)|| 2 ≤ ||x -x|| 2 . ( 8
)
This inequality holds for all x, x if and only if (I -αK -1 ) is a contraction mapping which means:

|µ i | ≤ 1, ∀i ∈ {1, . . . , n},
where µ i 's are the eigenvalues of the matrix (I -αK -1 ).

Rewriting this constraint in terms of the eigenvalues of the graph Laplacian, we have: ∀i, |1 -α λi q -α| ≤ 1, i.e.: ∀i 0 ≤ α ≤ 2q λi+q . The tightest upper bound is given by λ i = λ n and recalling λ n ≤ 2d max [START_REF] Van Mieghem | Graph spectra for complex networks[END_REF] finishes the proof. A second option. In this section, we approximate α from the samples. Let us define ȳ := K -1 x. Then, Eq. ( 5) may be re-written as α = tr(Cov(x,ȳ)) tr(Var(ȳ)) . Using N samples x(1) , . . . , x(N) and the corresponding ȳ(1) , . . . , ȳ(N) , we can empirically estimate α * with the sample covariance matrices:

α = tr( Cov(x, ȳ))
tr( Var(ȳ))

.

The analysis in [START_REF] Owen | Monte Carlo theory, methods and examples[END_REF]Ch 8.9] shows that along with α, z may yield a biased estimator. However, there are heuristics indicating that the bias diminishes with rate O(N -1 ) which is often negligible for large N w.r.t. the estimation error.

An empirical comparison of these two options for α is given in Fig. 1. In a graph with a regular degree distribution, fixing α to 2q q+2dmax gives a performance close to optimum. However, in the case of a graph with a broad degree distribution, 2q q+2dmax fails to provide a good approximation for α , and one needs to resort to α in order to leverage the full variance reduction potential offered by this gradient descent step.

EXPERIMENTS

We illustrate the improved estimator z over real data sets and compare it with x. Tikhonov denoising. The first data set consists of the trip records of taxis in New York City2 over 260 zones. From their geographical positions, we build a k = 5-nearest neighbour graph. The signal, in our case, is the median of the total amount charged to passengers at 260 drop-off zones. In the experiments, we add artificial Gaussian noise to the signal and reconstruct it via Tikhonov denoising and its estimates x and z. Fig. 2 summarizes the results. In Fig. 2d, we can clearly see the improvement via z w.r.t. x in denoising performance. We observe that z with a constant α slightly outperforms the case with α. This is probably due to the poor estimation of α with N = 2.

Node classification. In the second illustration, we use z for solving the semi-supervised node classification problem. The purpose is to classify each vertex by leveraging the underlying graph while the class information is available over only a few vertices. We define a labeling Y = [y 1 , . . . , y k ] ∈ R n×k for k classes where y l (i) is 1 whenever node i is known to be in class j, otherwise it is 0. Given the set of labeled vertices , typically | | |V|, the goal is to find a classification function F = [f 1 , . . . , f k ] ∈ R n×k . One approach is generalized semi supervised learning framework by Avrachevkov et al. [START_REF] Avrachenkov | Generalized optimization framework for graph-based semi-supervised learning[END_REF] which calculates the following solution: where µ ∈ R + and σ ∈ [0, 1] are the hyperparameters of the algorithm. The cumbersome operation in this solution occurs in the calculations involving K due to the matrix inversion. In [START_REF] Yusuf Y Pilavci | Smoothing graph signals via random spanning forests[END_REF], we have already showed that x can approximate these calculations with a certain setting:

F = D 1-σ KD σ-1 Y with K = (D + 2 µ L) -1 D (10)
z = D 1-σ (x -α(K -1 x -y l ))D σ-1 .
Adapting the calculations in Prop. 2, one obtains the safe option as α = 2µ µ+4 . In the experiments, we examine the classification accuracy of the exact solution and RSF estimates on the benchmark data sets Cora and Citeseer citation network 3 . Fig. 3 presents the classification accuracy given by x, x and ẑ. We observe that z with the constant α performs quite similar to z with α while both outperforming x: for this particular example 2µ µ+4 gives a very good approximation for α .

CONCLUSION

The main idea in this work is that, given an unbiased estimator of the solution to a large-scale least-squares problem (such as in the recent lines of works based on DPPs [START_REF] Derezinski | Determinantal point processes in randomized numerical linear algebra[END_REF][START_REF] Fanuel | Diversity sampling is an implicit regularization for kernel methods[END_REF]), then one (or in fact several) step of classical deterministic gradient descent leaves the estimator unbiased while potentially significantly reducing its variance, for a very small extra cost. We illustrate this idea on graph Tikhonov regularization via random spanning forests, where we show that the variance of the estimator may easily be divided by several factors if one chooses correctly the gradient descent step α. The simplest (and free to compute) choice for α is by far 2q/(q + 2d max ). Even though this choice is shown to necessarily decrease the variance, its performance is hindered when the degree distribution of the graph is broad and d max becomes a crude upper bound of the distribution's mode.

A natural workaround that we will explore in future work is to precondition the gradient step by D -1 yielding (still unbiased) estimators of the form z := x -αD -1 (K -1 xy).

  Now, let us focus on the variance of this new estimator: tr (Var(z)) = tr (Var(x)) + α 2 tr Var(K -1 x) -2α tr Cov(K -1 x, x) .

Fig. 1 :

 1 Fig. 1: Empirical squared error of x (orange horizontal line) and z (blue parabola) w.r.t α on two graphs generated by random models. On the left is a random regular graph with n = 1000 and m = 10000. On the right is a Barabasi-Albert model with parameter k = 10 resulting in n = 1000 and m = 9900. The green (resp. red) vertical dashed line shows α = 2q q+2dmax (resp. the estimated α from the samples). The blue dot represents the best possible variance reduction obtained for α = α . The number of Monte Carlo samples is set to N = 10 and the error results are averaged over 200 realizations. The signal is a random vector generated from N (0, I).

  PSNR vs q, N = 2

Fig. 2 :

 2 Fig. 2: Tikhonov denoising on New York City's taxi network. A k = 5-nn graph with |V| = 260, |E| = 777 is built based on the proximity of the zones. The original signal in (a) is the median of the total amount charged to passengers in drop-off locations. The noisy signal (b) is generated by adding noise drawn from a Gaussian distribution N (x, 25). (c) is the exact solution Ky with q = 0.32. In (d), peak signal to noise ratio is plotted for y, x, z with α = 2q q+2dmax and z with α as in Eq. (9).

Fig. 3 :

 3 Fig. 3: Classification performance on the Cora and Citeseer datasets. m denotes the number of labeled vertices per class. In the experiments, we use µ = 1.0, σ = 0 and α = 2µ µ+4 . The number of Monte Carlo samples is 50 and the experiments are repeated 100 times for each m.

Looking closely at the definition of x in[START_REF] Yusuf | Graph tikhonov regularization and interpolation via random spanning forests[END_REF] as well as its variance property, one can show that tr Var(K -1 x) = 0 only arises when y is a constant vector, in which case x is always equal to y whatever the sampled forest, such that by Eq. (4), z = x and there is no point in using z.

The dataset is available at https://www1.nyc.gov/site/tlc/ about/tlc-trip-record-data.page

These datasets are available at https://linqs.soe.ucsc.edu/data


Fernando Mariño
email: fernando@di.fcen.uba.ar

Claude Descorme

Daniel Duprez

Noble metal catalysts for the preferential oxidation of carbon monoxide in the presence of hydrogen (PROX)

Keywords: Preferential oxidation of CO, PROX, hydrogen purification, Noble metals, Platinum, Iridium, Palladium, Supported catalysts, Acido-basicity, Redox, Oxygen mobility, Fuel cells, WGSR

Oxide-supported noble metal catalysts were tested in the preferential oxidation of carbon monoxide (PROX) reaction in the temperature range between 50 and 300 • C. Both the influence of the noble metal nature (Pt, Ir, Pd), the support physical and chemical properties (redox, acidity, basicity) and the reaction conditions (oxygen stoichiometry) on the catalyst activity and selectivity was evaluated. Platinum and iridium were shown to be the most active and selective catalysts in the whole temperature range compared with palladium. Furthermore, noble metals supported over ceria-based oxides were shown to be active and selective, especially at low temperature. Additionally, it was observed that the higher the molar fraction in ceria in the oxide, the higher the activity and the selectivity in the PROX reaction. Ceria, with the highest oxygen mobility at the oxide surface, was shown to be the best support. Accordingly, on simple oxides (CeO 2 , SiO 2 -Al 2 O 3 ,Al 2 O 3 , SiO 2 ,La 2 O 3 and MgO), the induced mobility of the oxygen atoms at the surface of the support determined elsewhere, well correlated with the basicity of the support, was shown to be one key parameter for the performances of the catalysts in the PROX reaction. Finally, the formation of water (hydrogen oxidation) at high temperature and high oxygen excess was shown to be responsible for the increasing activity of the catalysts in the conversion of CO to CO 2 via the water gas shift reaction (WGSR).

Introduction

Proton exchange membrane fuel cells (PEMFC) have been extensively studied in the past decades. Applications in mobile energy sources have been paid an increasing attention. Pure hydrogen is the ideal fuel for such systems. However, mature technologies for a safe and efficient storage of hydrogen on-board of the vehicle are still not commercially available. As an alternative, hydrogen could likely be generated on-board using a reformer. Natural gas, gasoline or alcohols (methanol, ethanol) are the potential hydrogen sources [1].

In any case, hydrogen is produced together with significant amounts of CO. Because of the high sensitivity of the PEMFC anode catalysts towards even traces of CO, tech-nologies have to be developed to decrease the CO level, at least below 50 ppm for the state of the art Pt-Ru anodes. After the reformer, CO is partially converted to CO 2 via the water gas shift reaction (WGSR). Since the conversion of CO is thermodynamically limited to levels of about 0.5-1%, further purification treatments of the hydrogen stream are required.

To achieve high purification levels, several physical and/or chemical methods have been considered. The preferential oxidation of CO (PROX) appears as the most promising approach and the lowest cost technique. Nevertheless, the oxidation of hydrogen competes with the oxidation of carbon monoxide. Consequently, one critical point is to find a catalyst that is both highly active and highly selective towards the oxidation of carbon monoxide to carbon dioxide. The operating temperature should be somewhere in between the low-temperature WGS unit (250-300 • C) and the temperature of the PEMFC (80-100 • C). Finally, such catalyst should be able to operate under transient conditions, as the power demand will vary considerably.

Noble metals, which ones are highly active for the oxidation of pure carbon monoxide, were some of the first catalysts to be proposed for the preferential oxidation of carbon monoxide (PROX). Oh and Sinkevitch [2] studied the activity and the selectivity of several catalytic systems based on noble metals. The best results were obtained with alumina-supported Pt, Ru and Rh catalysts.

Platinum catalysts are by far the most extensively studied catalysts [3][4][5][6]. Some authors in particular have examined the kinetics and the mechanism of the PROX reaction over Pt/Al 2 O 3 catalysts [7][8][9]. Gold catalysts were also tested for this reaction. In fact, while pure gold is a poor catalyst for most reactions, mainly due to the weak interactions with most adsorbates, several Authors have shown that highly dispersed gold supported on metal oxides was active at low temperatures (even below 0 • C) in the CO oxidation reaction [10][11][12][13][14][15]. Unfortunately, it was observed that supported gold catalysts deactivate much rapidly than the corresponding platinum catalysts [16].

In the present work, oxide-supported platinum, iridium and palladium catalysts were studied. In fact, Pt, Ir and Pd were shown to be highly active in the CO oxidation reaction under oxygen lean conditions, upon three-way catalysis [17][18][19] and we thought that some analogies could be found with the PROX reaction. Ceria and ceria-zirconia supports are traditionally used as supports for three-way catalysts. In fact, such supports were evidenced to behave as oxygen buffers, capable to feed the metal with oxygen under oxygen lean conditions. Ceria-based supports were compared with other metal oxides-based supports. A large variety of supports (CeO 2 ,Ce x Zr (1-x) O 2 , SiO 2 -Al 2 O 3 ,Al 2 O 3 , SiO 2 , La 2 O 3 and MgO), with different redox, acidic and basic properties, were investigated. One of the main purposes of the present study was to understand what could be the role of the different functions on the catalysts, especially the support.

Methods

Catalysts

Noble metal (Pt, Pd, Ir) catalysts supported over ceria or ceria-zirconia were first prepared and characterized before testing in the preferential oxidation of CO. The preparation conditions were adjusted in order to optimize the metal dispersion [17,18].

The first series of catalysts consisted in ceria-zirconiasupported Pt, Pd and Ir catalysts. Rhodia Electronics and Catalysis (La Rochelle, France) provided us with the supports. These supports were pre-calcined at 900 • C for 6 h. For comparison purposes, the metal loading was fixed at about 100 m of metal atoms per gram of catalyst, that is 1 wt.% for Pd and 2 wt.% for Pt and Ir.

Platinum and palladium catalysts were prepared by wet impregnation of the supports with aqueous solutions of Pt(NH 3 ) 4 (OH) 2 and Pd(NO 3 ) 3 , respectively. After impregnation, the samples were dried overnight at 120 • C and finally calcined in flowing dry air (30 mL min -1 )a t5 0 0 • C for 4 h.

In the case of iridium, the catalysts prepared by classical impregnation had shown very poor metal dispersions [20]. For that reason, the iridium catalysts under study were prepared by impregnation in an ultrasonic bath using an acetone solution of Ir[CH(COCH 3 ) 2 ] 3 . The samples were further dried overnight at 120 • C and reduced in flowing hydrogen (30 mL min -1 )a t50 0 • C for 4 h.

The second series of supported catalysts was prepared with a nominal platinum content of about 3 wt.%. Several oxide supports were tested with very different redox, acidic and basic properties (CeO 2 , SiO 2 -Al 2 O 3 ,A l 2 O 3 , SiO 2 ,L a 2 O 3 and MgO).

The samples were prepared by classical wet impregnation of the supports with a Pt(NH 3 ) 4 (OH) 2 solution at pH 11, dried overnight at 120 • C, treated in flowing dry air at 450 • C four 4 h and finally reduced in hydrogen at 500 • C for 8 h.

A summary of the physical and chemical characteristics of the supports and the catalysts we prepared in the present study is given in Table 1.

Characterization

Specific surface areas (S BET expressed in m 2 g -1 ) were measured by N 2 adsorption at -196 • C on a Micromeritics Flowsorb II apparatus. For seek of rapidity, the single point method was selected. Before the measurement, the sample was first outgassed under He/N 2 at 350 • C for 2 h.

Metal dispersions (D M ) were derived from H 2 chemisorption measurements carried out in a homemade apparatus described elsewhere [21]. The samples were first reduced under pure hydrogen (30 mL min -1 )at400 • C for 1 h and further outgassed under argon (30 mL min -1 ) for 3 h at the same temperature. H 2 chemisorption was performed at -85 • C following an optimized procedure earlier described in details [22]. In fact, one critical point was to avoid any hydrogen spillover onto the support, especially in the case of ceria-based supports.

Both the specific surface areas (S BET ) of the supports and the metallic dispersion of the catalysts are reported in Table 1.

Reactor setup and calculations

Catalytic tests were carried out in an atmospheric continuous flow reactor. Tubing and connections were made from stainless steal. The catalyst was introduced in a glass fixed bed reactor placed in an electrical oven. Prior to the reaction, the catalysts were preconditioned in situ in flowing air (100 N ml min -1 )a t3 0 0 • C for 30 min. About 100 mg of catalyst was used for each run. Because of the small size of the catalyst bed (8 mm in diameter and 4 mm in height), it was assumed that there was no significant temperature profile in the bed. Nevertheless, in a few selected experiments the temperatures at the top and bottom of the bed were measured to confirm the absence of temperature profile.

Analytical grade cylinders (Alphagas-1 from Air Liquide) of hydrogen, nitrogen, CO and O 2 were used. The inlet gas flow rates were controlled using BROOKS mass flow controllers previously calibrated for each specific gas. In a typical experiment, the total inlet gas flow rate was fixed at 100 N ml min -1 . The reaction mixture consisted in 70% H 2 , 2% CO (20 000 ppm), 1-4% O 2 and N 2 as a balance. The oxygen excess, λ, could vary from 1 (stoichiometric) to 4.

During the reaction, the reactor temperature was progressively ramped from 50 to 300 • C at a rate of 1 • C min -1 using a temperature controller. A restricted number of steady-state experiments carried out at a few fixed temperatures (100, 150 and 200 • C) could verify that the conversions and the selectivities measured under temperature programmed experiments were the same as the steady-state values. Then, the equilibrium seems to be reached instantaneously.

At the reactor outlet, the product analysis was performed using a combination of two gas chromatographs. One chromatograph was equipped with a CTR column and helium was used as the carrier gas while the other chromatograph was equipped with a 5 Å molecular sieve filled column and nitrogen was used as the carrier gas. The second one was used to determine the H 2 concentration in the outlet gases. In both cases, TCD detectors were used. Finally, for the concentrations in carbon monoxide below 2000 ppm a specific infrared spectrometer could be used. Only CO 2 and H 2 O were detected as the reaction products and CO 2 production is in good agreement with CO consumption. Therefore, we concluded that the conversion of CO and/or CO 2 to CH 4 in the presence of large excess of hydrogen (methanation) do not take place under the selected reaction conditions over the catalysts under study.

The oxygen and the carbon monoxide conversions were classically defined as follows:

x O 2 = F in O 2 -F out O 2 F in O 2 x CO = F in CO -F out CO F in CO
where F in i and F out i are the inlet and outlet molar flows of gas i, respectively.

The selectivity towards CO 2 was calculated as the ratio of the desired reaction (CO oxidation) to the overall O 2 consumption:

S CO 2 = F out CO 2 2(F in O 2 -F out O 2 )
It must be mentioned that the product of the oxygen conversion (x O 2 ) by the selectivity towards CO 2 (S CO 2 ) does not directly result in the CO conversion. In fact, for λ >1 , the oxygen excess (λ = 2F in O 2 /F in CO 2 ) must be taken into account:

x CO = x O 2 S CO 2 λ

Results

Influence of the metal nature

The results we obtained over M/Ce 0.63 Zr 0.37 O 2 catalysts (M = Pt, Ir, Pd) are presented in Fig. 1. Ceria-zirconia-supported platinum and iridium catalysts showed a similar behavior. The same trends were observed for both catalysts and a maximum appeared at about 100 • C in the evolution of the CO conversion as a function of temperature. Complete oxygen conversion was reached at ca. 100 • Ci nt h e case of platinum and ca. 130 • C in the case of iridium. Above these temperatures, the selectivity towards the CO oxidation reaction decreases continuously as the temperature increases. Consequently, the maximum selectivity was observed at the lowest temperature. In fact, ceria-zirconia supports are well-known reducible oxides, highly active for the oxygen storage [22,23]. This specific property of these oxides could explain the high activity and selectivity of these samples, especially at much lower temperatures compared to alumina-supported noble metal catalysts [2,[7][8][9].

At temperatures higher than 175 • C, the CO conversion increases once again due to the incidence of the WGSR. This effect is more noticeable for the iridium catalyst. For the platinum catalysts, this result can be more readily observed at higher λ values (as it will be presented in Fig. 3).

On the contrary, palladium showed a very poor activity in the CO oxidation reaction. However, the oxygen conversion on 1%Pd/Ce 0.63 Zr 0.37 O 2 was even higher at low temperature compared to the corresponding Pt and Ir catalysts. In fact, the hydrogen oxidation appeared to be greatly favored. As a result, the selectivity towards CO 2 formation was very low. For that reason, we did not continue with palladium as the active phase.

Influence of the mixed oxide composition in Ce

x Zr (1-x) O 2 supports
After the selection of the most active noble metals, the influence of the composition of the mixed oxide phase was investigated. The activity and the selectivity of platinum and iridium catalysts supported on Ce x Zr (1-x) O 2 (x = 0.15, 0.5, 1) are presented in Fig. 2. One can observe that both the conversion of CO and the selectivity towards CO 2 formation increase as the atomic fraction in cerium (x) in the mixed oxide increases.

Influence of the oxygen excess (λ)

To go further, the influence of the gas phase composition was checked, especially the oxygen excess (λ). Though all the platinum and iridium catalysts tested present a similar behavior, Fig. 3 shows the results obtained with samples 2%Pt/Ce 0.15 Zr 0.85 O 2 and 2%Ir/Ce 0.15 Zr 0.85 O 2 , for which the trend seems to be more marked.

In the two cases, both the CO and H 2 oxidation increase as λ increase. However, the effect of the oxygen excess is much more pronounced on the hydrogen oxidation. As a result, the selectivity towards CO 2 formation decreases as the oxygen excess increases. This result is in agreement with the results obtained on a Pt/Al 2 O 3 catalyst [24].I n both cases (Pt/Al 2 O 3 and Pt/CeO 2 ), platinum has showed a natural selectivity towards CO oxidation as lower λ values resulted in higher selectivities.

Above 175 • C, the conversion of CO and the selectivity towards the formation of CO 2 increase once again for both platinum and iridium catalysts. The water gas shift reaction (WGSR) was thought to be responsible for this phenomenon. In fact, Barbier et al. [25] studied a series of Pt/Al 2 O 3 catalysts doped with ceria. The authors found that platinum was very active in the conversion of CO to CO 2 at relatively low temperature as they used an O 2 /CO/H 2 O mixture. The authors concluded that the CO oxidation occurs together with the WGSR. The authors also observed that ceria strongly enhances the WGSR activity of the catalyst. Whereas Ir deposited on alumina is not very active in WGSR [26], it seems here much more active when deposited on ceria-zirconia, in accordance with the promoter role of ceria or ceria-zirconia in this reaction.

The WGS reaction is favored by the high λ values. This effect can be simply explained by the fact that the higher the oxygen concentration, the faster the hydrogen oxidation. As a result, more water is formed and the WGSR is strongly favored.

Influence of the acid-base properties of the supports

The role of the support was tentatively confirmed using a larger variety of oxides (CeO 2 , SiO 2 -Al 2 O 3 ,A l 2 O 3 , SiO 2 ,La 2 O 3 and MgO). As one can see, both acidic and basic supports were selected in addition/combination to/with reducible oxides. The effect of the support was examined through the evaluation of a series of 3 wt.% platinum catalysts.

Hydrogen chemisorption measurements carried out at -85 • C showed that platinum is better dispersed on the acidic supports (see Table 1). However, as one can see from Fig. 4, the samples prepared on basic supports were more active for the CO oxidation reaction than the corresponding samples supported on acidic ones. The ability of the catalyst to convert CO appeared to be somehow correlated with the ability of the catalyst to activate the oxygen. In fact, some kind of parallel does exist between the evolution of the CO conversion and the oxygen consumption.

The 3%Pt/CeO 2 catalyst showed in Fig. 4 behaves in a completely different way compared to the other oxides and similarly to 2%Pt/CeO 2 in Fig. 2. Such a specific behavior that could be attributed to the redox properties of ceria is not affected whatever the metal loading or the metal dispersion are.

Discussion

Among the noble metals we studied, both platinum and iridium catalysts were shown to be active in the oxidation of carbon monoxide in the presence of large excess in hydrogen (70% H 2 , 2% CO, 1-4% O 2 and N 2 as a balance). Nevertheless, platinum appeared as the best. High activities were measured even at low temperatures (T < 100 • C).

Unfortunately, noble metals may adsorb all the reactants involved in the CO preferential oxidation (CO, H 2 ,O 2 ). As a result, the undesired hydrogen oxidation reaction also proceeds in competition with the oxidation of CO. In fact, as the reaction temperature increases the hydrogen oxidation becomes faster than the CO oxidation reaction and, at some point, a decrease of the selectivity towards CO 2 formation was systematically observed. Furthermore, since the oxygen activation takes place easily on these metals, the hydrogen oxidation rate is also accelerated when the oxygen concentration in the feed increases. In other words, the selectivity loss is more pronounced at high λ values.

In contrast, some very bad results were obtained with palladium catalysts. The heat of formation of palladium oxide, which is low compared to the rest of the noble metals, could justify this atypical behavior. In fact, above 60 • C, the palladium starts to oxidize to palladium oxide (PdO), which one is practically inactive for the PROX reaction [2]. For that reason, palladium was discarded as we looked forward for the optimum catalytic formulation.

As we have seen, the support has a real impact on the performances of the catalysts in the preferential oxidation of CO. For platinum catalysts, a completely different picture could be drawn depending if we looked at a reducible support, active for oxygen storage such as CeO 2 or at the other "classical" oxides (Fig. 4). Furthermore, as we studied the mixed oxide phase composition, we observed that the less active catalysts were the one supported on oxides with the higher concentration in zirconium (Fig. 2). This could be explained by the fact that zirconium oxide is not an active support for the surface oxygen mobility.

In the case of the catalysts supported on "non-active" supports, such as Al 2 O 3 , the CO preferential oxidation (PROX) was historically described using competitive Langmuir-Hinshelwood kinetics. However, from all what we have seen above, it can be postulated that a different reaction mechanism applies in the case of the catalysts supported on reducible oxides. Other authors [27,28] have shown that surface oxygen atoms from ceria do participate in the oxidation of CO at low temperature. Accordingly, we proposed that the preferential oxidation of CO over ceria-supported catalysts could occur via a non-competitive Langmuir-Hinshelwood mechanism. Such a mechanism should involve the reaction between the CO adsorbed on the noble metal (Pt or Ir) particles and the oxygen atoms previously activated on the support. Such a mechanism was previously reported for Fe-oxide promoted Pt/alumina catalysts [29].

Finally, we observed from Fig. 4 that the oxygen conversion on the different catalysts varies as follows: CeO 2 >A l 2 O 3 > MgO > La 2 O 3 > SiO 2 > SiO 2 -Al 2 O 3 .I fo n e excludes the alumina-supported catalyst, this classification does perfectly match the basicity scale for these oxides [30]. Furthermore, a correlation between the oxygen surface diffusion coefficient and the basicity of these oxides had been already reported [31]. Alumina was again an exception and the oxygen mobility, in comparison, was much higher than it would have been expected from the basicity of this oxide. Consequently, the oxygen mobility on the oxide support appears to have a major impact on the catalyst performances in the PROX reaction.

Conclusions

Ceria-based supported platinum or iridium catalysts were shown to be suitable for the removal of CO in the presence of large quantities of hydrogen via the preferential oxidation of CO. Further work must be performed to evaluate the performance and stability of these samples in the presence of water and/or CO 2 .

The optimum performances were obtained at low temperatures (T < 100 • C). In fact, at higher temperature the hydrogen oxidation also takes place and the selectivity towards the formation of CO 2 markedly decreases.

However, even at low temperature, the CO oxidation activity was still not high enough to achieve the low CO levels acceptable to operate a fuel cell, at least after a single step PROX reactor. The best CO overall removal level was obtained on Pt/Ce 0.15 Zr 0.85 O 2 at 225 • C and λ = 4. Under such reaction conditions, the CO concentration in the outlet feed was reduced down to approximately 700 ppm via the simultaneous PROX and WGS reactions.

Fig. 1 .

 1 Fig. 1. CO preferential oxidation on 2%Ir/Ce 0.63 Zr 0.37 O 2 , 1%Pd/Ce 0.63 Zr 0.37 O 2 , and 2%Pt/Ce 0.63 Zr 0.37 O 2 catalysts. CO conversion, O 2 conversion and CO 2 selectivity as a function of reaction temperature. Mass of catalysts: 100 mg; total flow: 100 N ml min -1 ; and flow composition: 70% H 2 , 27% N 2 , 2% CO, 1% O 2 (λ = 1).

Fig. 2 .

 2 Fig. 2. CO preferential oxidation on 2%M/support catalysts. M: Ir, Pt. Supports: Ce 0.15 Zr 0.85 O 2 (᭡), Ce 0.50 Zr 0.50 O 2 (), CeO 2 (᭺). CO conversion, O 2 conversion and CO 2 selectivity as a function of reaction temperature. Mass of catalysts: 100 mg; total flow: 100 N ml min -1 ; and flow composition: 70% H 2 , 27% N 2 , 2% CO, 1% O 2 (λ = 1).

Fig. 3 .

 3 Fig. 3. CO preferential oxidation on 2%M/Ce 0.15 Zr 0.85 O 2 catalysts. M: Ir, Pt. CO conversion, O 2 conversion and CO 2 selectivity as a function of reaction temperature and oxygen excess (λ). Mass of catalysts: 100 mg; total flow: 100 N ml min -1 ; and flow composition: 70% H 2 , 2% CO, 1-4% O 2 (λ = 1-4), and rest N 2 .

Fig. 4 .

 4 Fig. 4. CO preferential oxidation on 3%Pt/support catalysts. Supports: SiO 2 -Al 2 O 3 (), Al 2 O 3 (᭡), SiO 2 (ᮀ), La 2 O 3 (△), MgO (᭺), CeO 2 (-). CO conversion, O 2 conversion and CO 2 selectivity as a function of reaction temperature. Mass of catalysts: 100 mg; total flow: 100 N ml min -1 ; and flow composition: 70% H 2 , 27% N 2 , 2% CO, 1% O 2 (λ = 1).

Table 1

 1 Characteristics of the supports and catalysts

	Support	S BET (m 2 g -1 )	Catalysts	D M (%)
	Ce 0.15 Zr 0.85 O 2	27	2%Ir/Ce 0.15 Zr 0.85 O 2	-
			2%Pt/Ce 0.15 Zr 0.85 O 2	-
	Ce 0.5 Zr 0.5 O 2	45	2%Ir/Ce 0.5 Zr 0.5 O 2	-
			2%Pt/Ce 0.5 Zr 0.5 O 2	-
	Ce 0.63 Zr 0.37 O 2	43	2%Ir/Ce 0.63 Zr 0.37 O 2 1%Pd/Ce 0.63 Zr 0.37 O 2 2%Pt/Ce 0.63 Zr 0.37 O 2	29 a 61 a 78 a
	CeO 2	25	2%Ir/CeO 2 2%Pt/CeO 2	38 a 79 a
			3%Pt/CeO 2	33
	MgO	66	3%Pt/MgO	13
	La 2 O 3	≈2	3%Pt/ La 2 O 3	8
	SiO 2	175	3%Pt/SiO 2	22
	Al 2 O 3	215	3%Pt/Al 2 O 3	37
	SiO 2 -Al 2 O 3	525	3%Pt/SiO 2 -Al 2 O 3	53

a Results previously obtained by Bedrane et al.

[18]

.

Acknowledgements

The French Ministry of Research and New Technologies is gratefully acknowledged for financially supporting Dr. Fernando Mariño's post-doctoral stay in France.