M.D Atsushi Tanaka
email: a-tanaka@med.teikyo-u.ac.jp

M.D Junko Hirohara

M.D Toshiaki Nakano

M.D Kosuke Matsumoto

M.D Olivier Chazouillères

M.D Hajime Takikawa

Ph.D Bettina E Hansen

M.D Fabrice Carrat

M.D Christophe Corpechot
email: christophe.corpechot@aphp.fr

Antoine Hospital

Association of Bezafibrate with Transplant-Free Survival in Patients with Primary Biliary Cholangitis

Keywords: PBC, UDCA, Fibrate, Cohort, Transplantation

Background & Aims: Beneficial effect of bezafibrate (BZF) on symptoms and biochemical features of primary biliary cholangitis (PBC) with incomplete response to ursodeoxycholic acid (UDCA) has been reported but long-term efficacy on survival remains unknown. In Japan, BZF has been used as a de facto second-line therapy for PBC since 2000. Herein, we compared the survival rates between patients treated with and those without BZF in a large nationwide Japanese PBC cohort.

Methods: All consecutively-registered patients of this cohort who started UDCA therapy from 2000 onwards and had a follow-up ≥ 1 year were included. Association between BZF exposure and mortality or need for liver transplantation (LT) was assessed using time-dependent, multivariableand propensity score-adjusted Cox proportional hazards models. Clinical benefit was quantified using the number needed to treat (NNT).

Results: Of 3908 eligible patients, 3162 (81%) received UDCA only and 746 (19%) UDCA and BZF over 17360 and 3932 patient-years, respectively. During follow-up, 183 deaths (89 liver-related) and 21 LT were registered. Exposure to combination therapy was associated with a significant decrease in all-cause and liver-related mortality or need for LT (adjusted hazard ratios: 0.3253, 95% CI 0.1936 -0.5466 and 0.2748, 95% CI 0.1336 -0.5655, respectively; p<0.001 for both). This association was consistent across various risk groups at baseline. The NNTs with combination therapy to prevent one additional death or LT in 5, 10, and 15 years were 29 (95% CI 22 -46), 14 (10 -22), and 8 (6 -15), respectively.

Conclusions:

In a large retrospective cohort study of treatment effects in patients with PBC, the addition of BZF to UDCA was associated with improved prognosis.

Abbreviations

Lay summary

The long-term efficacy of bezafibrate (BZF) on liver transplantation (LT) -free survival of patients with PBC with an incomplete response to ursodeoxycholic acid (UDCA) remains to be determined.

In this Japanese nationwide retrospective cohort study, the use of UDCA-BZF combination therapy, compared to UDCA alone, was associated with lower risk in all-cause and liver-related mortality or need for LT. These results indicate that BZF is so far the only drug in PBC to have demonstrated efficacy in improving symptoms, biochemical markers, and long-term outcomes.

INTRODUCTION

Primary biliary cholangitis (PBC) is a chronic cholestatic liver disease, potentially progressing to cirrhosis and liver failure without appropriate treatment. [START_REF] Lleo | Primary biliary cholangitis[END_REF] The burden of PBC is growing worldwide and an increasing trend of the prevalence is universally observed. [START_REF] Tanaka | Increase trend in the prevalence and male-to-female ratio of primary biliary cholangitis, autoimmune hepatitis, and primary sclerosing cholangitis in Japan[END_REF][START_REF] Marzioni | Epidemiology of primary biliary cholangitis in Italy: Evidence from a real-world database. Digestive and liver disease : official journal of the Italian Society of Gastroenterology and the Italian Association for the Study of the[END_REF] PBC is considered a model autoimmune disease because of disease-specific autoantibodies, i.e. anti-mitochondrial autoantibodies (AMA), marked infiltration of mononuclear cells in the vicinity of intrahepatic smallsized bile ducts, and a high prevalence of autoimmune diseases as comorbidities. Nevertheless, immunosuppressing agents such as corticosteroids have no or little effect for altering the natural course, and clinical trials of biologics targeting cytokines or chemokines playing a crucial role in pathogenesis have failed to meet endpoints to date. [START_REF] Hirschfield | Ustekinumab for patients with primary biliary cholangitis who have an inadequate response to ursodeoxycholic acid: A proof-ofconcept study[END_REF][START_REF] De Graaf | NI-0801, an antichemokine (C-X-C motif) ligand 10 antibody, in patients with primary biliary cholangitis and an incomplete response to ursodeoxycholic acid[END_REF][START_REF] Bowlus | Therapeutic trials of biologics in primary biliary cholangitis: An open label study of abatacept and review of the literature[END_REF] This is probably because autoimmune attack against biliary epithelial cells initiating the disease course of PBC may not be a dominant factor contributing to disease progression in clinical settings, and rather chronic cholestasis following bile duct injury should be targeted. [START_REF] Dyson | Novel therapeutic targets in primary biliary cirrhosis[END_REF][START_REF] Tanaka | Emerging novel treatments for autoimmune liver diseases[END_REF] Indeed, a globally-approved first-line treatment for PBC is ursodeoxycholic acid (UDCA), a hydrophilic, tertiary bile acid with choleretic and anticholestatic properties. UDCA was demonstrated to be effective both in decreasing liver biochemical abnormalities 9, 10 and improving the liver transplantation (LT)-free survival of patients with PBC. [START_REF] Poupon | Combined analysis of randomized controlled trials of ursodeoxycholic acid in primary biliary cirrhosis[END_REF][START_REF] Shi | Long-term effects of mid-dose ursodeoxycholic acid in primary biliary cirrhosis: a meta-analysis of randomized controlled trials[END_REF][START_REF] Harms | Ursodeoxycholic acid therapy and liver transplant-free survival in patients with primary biliary cholangitis[END_REF] On the other hand, based on historical criteria, 30-40% of UDCA-treated patients exhibit an incomplete biochemical response resulting in a significantly worse outcome, while treatment failure defined by non-normalization of liver tests is much higher. [START_REF] Pares | Excellent long-term survival in patients with primary biliary cirrhosis and biochemical response to ursodeoxycholic Acid[END_REF][START_REF] Corpechot | Biochemical response to ursodeoxycholic acid and long-term prognosis in primary biliary cirrhosis[END_REF][START_REF] Kuiper | Improved prognosis of patients with primary biliary cirrhosis that have a biochemical response to ursodeoxycholic acid[END_REF][START_REF] Kumagi | Baseline Ductopenia and Treatment Response Predict Long-Term Histological Progression in Primary Biliary Cirrhosis[END_REF][START_REF] Lammers | Development and Validation of a Scoring System to Predict Outcomes of Patients With Primary Biliary Cirrhosis Receiving Ursodeoxycholic Acid Therapy[END_REF][START_REF] Perez | Goals of treatment for improved survival in primary biliary cholangitis: treatment target should be bilirubin within the normal range and normalization of alkaline phosphatase[END_REF] To improve the long-term outcome of these patients, a number of drugs and compounds have been tested. [START_REF] Tanaka | Emerging novel treatments for autoimmune liver diseases[END_REF][START_REF] Corpechot | New treatments/targets for primary biliary cholangitis[END_REF] Currently, the only drug approved for this population is obeticholic acid (OCA), a steroidal farnesoid X receptor agonist. [START_REF] Nevens | A Placebo-Controlled Trial of Obeticholic Acid in Primary Biliary Cholangitis[END_REF] However, OCA is still unsatisfactory for several reasons, including frequent development of pruritus as an adverse effect, uncertainty in terms of improvement of long-term outcome, and potential liver toxicity in patients with advanced disease. [START_REF] Tanaka | Finding the cure for primary biliary cholangitis -Still waiting[END_REF][START_REF] Eaton | Liver Injury in Patients With Cholestatic Liver Disease Treated With Obeticholic Acid[END_REF] Another promising candidate as a second-line treatment for patients with incomplete response to UDCA is bezafibrate (BZF). BZF is a dual pan-peroxisome proliferator-activated receptors (PPARs) / pregnane X receptor (PXR) agonist with efficacy against cholestasis, and officially labeled for hyperlipidemia. [START_REF] Honda | Anticholestatic effects of bezafibrate in patients with primary biliary cirrhosis treated with ursodeoxycholic acid[END_REF] The beneficial effects of BZF in pre-cirrhotic PBC patients was first reported in 1999. [START_REF] Iwasaki | Bezafibrate may have a beneficial effect in pre-cirrhotic primary biliary cirrhosis[END_REF] Thereafter, several pilot studies and prospective, randomized controlled studies in Japan showed the biochemical efficacy of short-term combination therapy with BZF and UDCA, [START_REF] Nakai | Combination therapy of bezafibrate and ursodeoxycholic acid in primary biliary cirrhosis: a preliminary study[END_REF][START_REF] Itakura | Prospective randomized crossover trial of combination therapy with bezafibrate and UDCA for primary biliary cirrhosis[END_REF][START_REF] Iwasaki | The efficacy of ursodeoxycholic acid and bezafibrate combination therapy for primary biliary cirrhosis: A prospective, multicenter study[END_REF] and BZF has been used in this country as a de facto second-line treatment for PBC patients with incomplete response to UDCA. [START_REF]Working Subgroup for Clinical Practice Guidelines for Primary Biliary C. Guidelines for the management of primary biliary cirrhosis: The Intractable Hepatobiliary Disease Study Group supported by the Ministry of Health, Labour and Welfare of Japan[END_REF] Besides, a double-blinded, randomized, placebo-controlled study in France (BEZURSO trial) demonstrated that a 2-year combination treatment with UDCA and BZF resulted in a significantly higher rate of complete biochemical response (defined by normal levels ALP, total bilirubin, and aminotransferases) and improvement of non-invasive measures of liver fibrosis compared to placebo. [START_REF] Corpechot | A Placebo-Controlled Trial of Bezafibrate in Primary Biliary Cholangitis[END_REF] Indeed, ALP normalization in this trial occurred in two thirds of patients in the BZF group compared to only 2% in the control group. Nevertheless, even if reduction in mortality or need for LT has been predicted by prognostic models, [START_REF] Corpechot | Letter: reduction in projected mortality or need for liver transplantation associated with bezafibrate add-on in primary biliary cholangitis with incomplete UDCA response[END_REF][START_REF] Honda | Bezafibrate Improves GLOBE and UK-PBC Scores and Long-Term Outcomes in Patients With Primary Biliary Cholangitis[END_REF] it remains uncertain whether BZF combination therapy truly improves survival of PBC patients, and it is unlikely that large, adequately-powered trials will address this issue because PBC is a slowly progressive disease.

In Japan, nationwide surveys for PBC have been conducted almost every 3 years since 1980, and nearly 10,000 patients with PBC have been registered to date. Clinical information at diagnosis including age, gender, liver biochemistries, histologic stage, and treatment as well as outcome were recorded. In the present study, we took advantage of this large-scale nationwide cohort to determine whether BZF in combination with UDCA may improve transplant-free survival of patients with PBC.

METHODS

Study population

The nationwide surveys in Japan are a cohort study of patients with PBC that was initiated in 1980 and has been conducted almost every 3 years by the Intractable Hepato-Biliary Diseases Study Group for Research on Measures for Intractable Disease, which is supported by Health Labor Science Research Grants in Japan. The survey protocol was previously described by Nakano and colleagues. [START_REF] Nakano | Long-term prognosis of primary biliary cirrhosis (PBC) in Japan and analysis of the factors of stage progression in asymptomatic PBC (a-PBC)[END_REF] It was approved by the Ethics Committee at Teikyo University (approval no. 14-200), as well as the local institutional review board at each participating institution. In the most recent survey (the 16 th in 2017), questionnaires were sent to 556 institutions (including 229 tertiary referral centers and 327 primary/secondary care centers) throughout Japan that were affiliated with active members of the Japan Society of Hepatology and the Japanese Society of Gastroenterology. All patients with PBC, both newly diagnosed and those already followed-up in their institutions, were registered.

To date, 9,919 patients with PBC have been included in the cohort. The diagnosis of PBC was made according to the criteria established by the Intractable Hepato-Biliary Diseases Study Group of Japan. [START_REF]Working Subgroup for Clinical Practice Guidelines for Primary Biliary C. Guidelines for the management of primary biliary cirrhosis: The Intractable Hepatobiliary Disease Study Group supported by the Ministry of Health, Labour and Welfare of Japan[END_REF] Patients who met at least two of the following criteria were diagnosed as having PBC: biochemical evidence of chronic cholestasis; positive AMA in sera; histologic features compatible with PBC. In this registry, center type, date of birth and gender, date of diagnosis, presence of pruritus and biochemical test findings (ALP, total bilirubin, and albumin) at the time of diagnosis, histologic stage (Scheuer's classification), treatment protocol (UDCA and/or BZF), and the final follow-up date and outcomes at that time (LT, liver-related and all-cause death) were recorded.

Longitudinal data, including biochemical liver tests, response to treatment, and histologic stage, were not available.

The patient selection criteria for the primary analysis of the study were as follows: 1) complete data set available in terms of date of birth, gender, diagnosis date, treatment protocol, final followup date and outcome; 2) UDCA therapy initiated in 2000 or after; and 3) follow-up ≥ 1 year. All the patients who met the criteria 1) and 3) were included in a sensitivity analysis covering the whole cohort. In addition to the patients selected for primary analysis, the whole cohort included patients who started UDCA therapy before 2000, and those who received no treatment during their followup.

Data analysis

Total bilirubin and albumin values were categorized into normal and abnormal values, ALP level into low (≤1.67xULN) and high (>1.67xULN) levels, and histologic stage into early (1-2) and late (3-4) stages. Missing values were imputed using a predictive mean matching method. Starting and discontinuation dates for UDCA and BZF were collected for each patient. Inconsistent starting dates, as those prior to diagnosis or those subsequent to the final follow-up date, were considered as missing. Over 2000-2017, UDCA starting dates were missing in 1573 (40%) out of 3908 UDCA-treated patients. They were imputed according to the following rules: when diagnosis was prior to June 1 st , 1987 and the final follow-up was after this date, UDCA was assumed to have been started on June 1 st , 1987, i.e. the year when the efficacy of UDCA was first reported both in English 9 and Japanese literature [START_REF] Wada | The efficacy of ursodeoxycholic acid for primary biliary cirrhosis[END_REF] ; when diagnosis was after June 1 st , 1987, the UDCA starting date was imputed at the date of diagnosis. The median difference between imputed and original dates was 0.01 year (interquartile range -0.03 -0.07). Starting dates for BZF were missing in 108 (14%) out of 746 BZF-treated patients. They were imputed according to a predictive mean matching method based on the covariates at baseline (center type, date of diagnosis, age, gender, total bilirubin, albumin, ALP, pruritus, and histologic stage), assuming that the probability of response to UDCA depends on pretreatment disease features, as recently shown in several large Western and Asian PBC cohorts. [START_REF] Carbone | Pretreatment prediction of response to ursodeoxycholic acid in primary biliary cholangitis: development and validation of the UDCA Response Score[END_REF][START_REF] Yagi | A validation study of the Ursodeoxycholic Acid Response Score in Japanese patients with primary biliary cholangitis[END_REF] When UDCA or BZF treatment was notified as discontinued but with no stopping date available, which occurred in 3% of patients for UDCA and 0.4% for BZF, stopping dates were imputed at the mid-period of time between starting date and last follow-up.

Exposures to UDCA and BZF were handled as time-varying covariates. Two main outcomes were defined: survival without LT, and survival without liver-related death or LT. These outcomes considered the primary model and models 4 and 5 were used as sensitivity analyses. All analyses have been done with 50 imputation datasets combined following the Rubin's rules. Unadjusted and adjusted survival curves were generated based on models' predictions. The absolute efficacy of BZF was assessed using the number needed to treat (NNT) to prevent one death or LT, or one liverrelated death or LT. It was computed as the reciprocal of the difference of predicted event rates between treatment groups at various time points using the primary model estimates. [START_REF] Altman | Calculating the number needed to treat for trials where the outcome is time to an event[END_REF]

RESULTS

A total of 3908 (39%) out of 9,919 patients was eligible for primary analysis (Figure 1). The characteristics of these patients at diagnosis are shown in Table 1. As compared to patients exposed to UDCA only (UDCA-only group, n=3162), patients who were additionally exposed to BZF at any time of the study (UDCA-BZF group, n=746) were more frequently followed-up in tertiary centers, were younger, had higher ALP and albumin levels, and more advanced histologic stage at diagnosis. These 2 groups did not differ according to gender, pruritus frequency, and total bilirubin level.

Treatment exposures

Over 2000-2017, the study included 17360 patient-years of exposure to UDCA in 3908 patients and 3932 patient-years of exposure to BZF in 746 patients. The mean (SD) time of exposure to UDCA was 5.0 (3.5) years in the UDCA-only group and 6.9 (4.0) years in the UDCA-BZF group. In the UDCA-BZF group, BZF was started an average of 1.4 (2.6) years after UDCA began, and the mean time of exposure to BZF was 5.3 (3.8) years. The permanent treatment discontinuation rate was 0.7% (28 out of 3908 patients) for UDCA and 5.9% (44 out of 746) for BZF.

Main outcomes

The overall average (SD) follow-up from UDCA initiation was 5.5 (3.8) years, ranging from 1.0 to 15.9 years. It was 5.2 (3.6) years for the UDCA-only group and 7.3 (4.1) years for the UDCA-BZF group. All-cause death, liver-related death, and LT occurred in 161, 76, and 20 patients, respectively in the UDCA-only group and 22, 13, and 1 patients, respectively in the UDCA-BZF group. The crude incidence rates of these events according to groups are shown in Appendix (Table S1). In all survival models studied, including the imputation-free model, exposure to BZF was associated with a significant decrease in all-cause and liver-related mortality or need for LT as compared to UDCA alone (Table 2). Detailed results are shown in Appendix (Tables S2 -S7). According to the primary model, addition of BZF to UDCA was associated with a 67% decrease in all-cause mortality or need for LT as compared to UDCA alone: adjusted hazard ratio (aHR) 0.3253 (95% CI: 0.1936 -0.5466; p<0.0001). The corresponding aHR for liver-related mortality or LT was 0.2748 (95% CI: 0.1336 -0.5655; p<0.0001). Both unadjusted and multivariable-adjusted survival curves are shown in Figure 2. The survival curves derived from actual data are shown in Appendix (Figure S1). A significant association between exposure to BZF and decreased mortality or need for LT was observed in almost all risk groups at baseline except male gender (Figure 3).

Absolute clinical benefit and sample size calculation

The absolute clinical benefit of UDCA-BZF therapy as compared to UDCA alone was assessed using the NNT to prevent one additional death or LT (Table 3). On average, 29 (95% CI: 22 -46), 14 (10 -22), and 8 (6 -15) patients with UDCA would have to be added on BZF to prevent one death or LT in 5, 10, and 15 years, respectively. The estimated number of subjects that would need to be enrolled in a 5-year clinical trial with a 2-year recruitment period in order to have 80% power at a 5% significance level to detect a treatment effect on LT-free survival is 1000 individuals equally distributed between groups (500 in the control group and 500 in the treatment group).

Complementary analysis

A sensitivity analysis was conducted on all patients with available data registered between 1980 and 2017 (n=8180), consisting of 7030 (86%) patients with UDCA, of whom 6087 (74%) with UDCA monotherapy and 943 (12%) with BZF-UDCA therapy, and 1133 (14%) patients with no treatment. In this full population, aHR of UDCA-BZF therapy vs UDCA alone for all-cause mortality or LT was 0.2305 (95%CI: 0.1498 -0.3546; p<0.0001) while aHR of UDCA alone vs no treatment was 0.5278 (95%CI: 0.4495 -0.6198; p<0.0001). Detailed results and corresponding survival curves are shown in Appendix (Tables S8 -S9, Figure S2).

DISCUSSION

In this nationwide retrospective cohort study of patients with PBC in Japan, combination of UDCA with BZF, as compared to UDCA alone, was significantly associated with a lower risk in allcause and liver-related mortality or need for LT. These findings were consistent in almost all patient subgroups at baseline, including those with abnormal bilirubin or albumin levels, or advanced histologic stage. Since the main indication for BZF adjunctive therapy was biochemical resistance to UDCA, these results support the clinical efficacy of UDCA-BZF combination in patients with PBC and incomplete response to UDCA.

A 2-year placebo-controlled trial of BZF in PBC has recently shown biochemical efficacy in patients with an incomplete response to UDCA. [START_REF] Corpechot | A Placebo-Controlled Trial of Bezafibrate in Primary Biliary Cholangitis[END_REF] Improvement of pruritus reported in this trial has further been confirmed in a short-term, randomized study. [START_REF] De Vries | Fibrates for Itch (FITCH) in Fibrosing Cholangiopathies: A Double-Blind, Randomized, Placebo-Controlled Trial[END_REF] However, it has yet to be proven that these beneficial effects on biochemical features and symptoms of the disease can translate into lower mortality or need for LT. In this regard, it can be estimated from the present data that 1,000 patients equally recruited in the first 2 years of a 5-year placebo-controlled trial would be required to observe a difference in survival. It seems unlikely that such a large trial in PBC can be designed in the future.

Large-scale observational studies seem to be the only way to provide evidence for BZF clinical efficacy in PBC. The present cohort, where BZF was used as a de facto second-line therapy, [START_REF]Working Subgroup for Clinical Practice Guidelines for Primary Biliary C. Guidelines for the management of primary biliary cirrhosis: The Intractable Hepatobiliary Disease Study Group supported by the Ministry of Health, Labour and Welfare of Japan[END_REF] provided us with a unique opportunity to address this issue. While UDCA therapy, compared to no treatment, was confirmed to reduce mortality or need for LT by nearly 50%, in line with a recent report from the Global PBC Study Group, [START_REF] Harms | Ursodeoxycholic acid therapy and liver transplant-free survival in patients with primary biliary cholangitis[END_REF] BZF therapy was associated with a further 70% decrease in risk when added to UDCA. These findings, based on a large-scale retrospective data analysis, are the best currently available evidence of BZF efficacy in UDCA-resistant PBC. Whether BZF and UDCA combination therapy could benefit to all PBC patients, however, remains an outstanding question. [START_REF] Corpechot | Clinical Trials in PBC Going Forward[END_REF] Previous studies of BZF (or fenofibrate) long-term use in PBC have been reported. [START_REF] Honda | Bezafibrate Improves GLOBE and UK-PBC Scores and Long-Term Outcomes in Patients With Primary Biliary Cholangitis[END_REF][START_REF] Hosonuma | A prospective randomized controlled study of long-term combination therapy using ursodeoxycholic acid and bezafibrate in patients with primary biliary cirrhosis and dyslipidemia[END_REF][START_REF] Cheung | Combined ursodeoxycholic acid (UDCA) and fenofibrate in primary biliary cholangitis patients with incomplete UDCA response may improve outcomes[END_REF][START_REF] Chung | Additional fibrate treatment in UDCArefractory PBC patients[END_REF] They were all limited to small or medium-sized PBC cohorts, including no more than 118 patients with fibrates combination therapy as compared with 943 in the present study. All but one has provided findings in line with our data. The only long-term prospective study available, an unblinded randomized trial of UDCA-BZF combination therapy, did not find an improvement in survival despite a significant reduction in the Mayo risk score. [START_REF] Hosonuma | A prospective randomized controlled study of long-term combination therapy using ursodeoxycholic acid and bezafibrate in patients with primary biliary cirrhosis and dyslipidemia[END_REF] However, this study, that included only 27 patients followed-up for 8 years, was not powered enough to assess hard endpoints such as death or LT.

Although BZF has an excellent safety profile during long-term use, a progressive increase in serum creatinine level has been reported as a potential concern. In the BEZURSO trial, creatinine levels in the BZF group increased 5% within the first 3 months and remained stable afterwards until 24 months. [START_REF] Corpechot | A Placebo-Controlled Trial of Bezafibrate in Primary Biliary Cholangitis[END_REF] Dose reduction or discontinuation of BZF could occur because of increased creatinine level. [START_REF] Corpechot | A Placebo-Controlled Trial of Bezafibrate in Primary Biliary Cholangitis[END_REF][START_REF] Hosonuma | A prospective randomized controlled study of long-term combination therapy using ursodeoxycholic acid and bezafibrate in patients with primary biliary cirrhosis and dyslipidemia[END_REF] In the present cohort, data on renal function was lacking. Over 2000-2017, the estimated rate of permanent discontinuation of BZF was approximately 6%. Unfortunately, we were unable to determine whether drug cessation was related to creatinine elevation or other adverse effects like myalgias.

Our study has some limitations mainly related to its retrospective nature and inherent biases.

In addition, many starting dates for UDCA or BZF, as well data on biochemical response to treatment were missing. If imputation of missing starting dates for UDCA was quite easy to assume, considering that treatment was likely initiated at diagnosis in all patients diagnosed after 1987, 9 34 imputing missing starting dates for BZF based on disease characteristics at diagnosis might appear questionable. However, this approach made sense since pre-treatment features have been shown to predict biochemical response to UDCA. [START_REF] Carbone | Pretreatment prediction of response to ursodeoxycholic acid in primary biliary cholangitis: development and validation of the UDCA Response Score[END_REF][START_REF] Yagi | A validation study of the Ursodeoxycholic Acid Response Score in Japanese patients with primary biliary cholangitis[END_REF] In addition, the median time between original and imputed dates was marginal and we took care to valid our findings based on actual data. Nevertheless, whether non-captured, time-dependent confounders may have had an influence on results cannot be completely excluded.

In conclusion, in a large retrospective study of treatment effects in patients with PBC, the addition of BZF to UDCA was associated with improved prognosis. At this time, BZF is the only PBC drug to have shown efficacy evidence on the symptoms, biochemical markers, and prognosis of the disease.

  ratio IPTW, inverse probability of treatment weighting LR, liver-related LT, liver transplantation NNT, number needed to treat OCA, obeticholic acid PBC, primary biliary cholangitis PPAR, peroxisome proliferator-activated receptor PXR, pregnane X receptor UDCA, ursodeoxycholic acid ULN, upper limit of normal range

  were assessed using 5 different survival models: Model 1, time-dependent Cox model unadjusted for baseline covariates; Model 2, time-dependent Cox model adjusted for baseline covariates (center type, age, gender, year of diagnosis, pruritus, total bilirubin, ALP, albumin, and histologic stage); Model 3, inverse probability of treatment weighted (IPTW) Cox model unadjusted for baseline covariates; Model 4, IPTW Cox model adjusted for baseline covariates; and Model 5, imputation-free, time-dependent Cox model adjusted for baseline covariates. Model 2 was

Fig. 1 .

 1 Fig. 1. Flow chart of the study.

Fig. 2 .

 2 Fig. 2. Survival without liver transplantation and survival free of liver-related death or liver

Fig. 3 .

 3 Fig. 3. Adjusted hazard ratio of combination therapy versus UDCA only for all-cause death or liver

Fig. S1 .

 S1 Fig. S1. Multivariable-adjusted survival curves after exclusion of missing BZF starting dates and baseline missing data (p-values for BZF time-dependent, multivariableadjusted Cox model)

Table 1 . Characteristics of patients at diagnosis

 1

	Characteristic	Patients exposed to	Patients exposed to	p-value
		UDCA-only (n=3162)	UDCA-BZF (n=746)
	Age (year)	60.0 ± 11.7	55.7 ± 10.8	<0.0001
	Missing data	0 (0%)	0 (0%)
	Gender
	Female	2679 (85%)	627 (84%)	0.4789
	Male	483 (15%)	119 (16%)
	Missing data	0 (0%)	0 (0%)
	Pruritus
	Absent	2365 (75%)	542 (73%)	0.4796
	Present	788 (25%)	202 (27%)
	Missing data	9 (0%)	2 (0%)
	Total bilirubin (mg/dL)	0.92 ± 1.22	0.99 ± 1.11	0.1277
	Missing data	0 (0%)	0 (0%)
	ALP (xULN)	1.77 ± 1.36	2.31 ± 1.90	<0.0001
	Missing data	0 (0%)	0 (0%)
	Albumin (g/L)	40.1 ± 5.0	40.8 ± 4.6	0.0012
	Missing data	0 (0%)	0 (0%)
	Histologic stage
	Early stage (I-II)	1732 (55%)	453 (61%)	<0.0001
	Late stage (III-IV)	264 (8%)	92 (12%)	(*)
	Missing data	1166 (37%)	201 (27%)
	Center
	Tertiary	2690 (85%)	711 (95%)	<0.0001
	Primary/secondary	472 (15%)	35 (5%)
	Missing data	0 (0%)	0 (0%)
	UDCA start period †
	2000 -2004	853 (27%)	169 (23%)	0.0296
	2005 -2009	1056 (33%)	275 (37%)
	2010 -2015	1253 (40%)	302 (40%)
	Data are expressed as mean ± standard deviation for continuous variables and number (%) for
	categorical variables. UDCA, ursodeoxycholic acid. BZF, bezafibrate. ALP, alkaline phosphatase.
	ULN, upper limit of normal range. P-values are those for the Student's t-test or the Fisher's exact
	test. (*) p=0.0288 when missing data are not considered.

†

The date of diagnosis was used when UDCA starting date was missing.

Table 2 . Hazard ratio for death or liver transplantation in patients exposed to combination therapy versus UDCA only

 2

	Cox model	All-cause mortality or LT	Liver-related mortality or LT
		HR (95% CI)	p-value	HR (95% CI)	p-value
	Model 1	0.3196 (0.1927 -0.5299)	<0.0001	0.3372 (0.1715 -0.6631)	0.0016
	Model 2 †	0.3253 (0.1936 -0.5466)	<0.0001	0.2748 (0.1336 -0.5655)	0.0005
	Model 3	0.2571 (0.1502 -0.4401)	<0.0001	0.2513 (0.1221 -0.5171)	0.0002
	Model 4	0.2832 (0.1643 -0.4880)	<0.0001	0.2649 (0.1252 -0.5607)	0.0005
	Model 5	0.2547 (0.1337 -0.4850)	<0.0001	0.1882 (0.0745 -0.4754)	0.0004

UDCA, ursodeoxycholic acid. LT, liver transplantation. HR, hazard ratio. Model 1: time-dependent Cox regression model unadjusted for baseline covariates; Model 2: time-dependent Cox regression model adjusted for baseline covariates; Model 3: inverse probability of BZF treatment weighted Cox regression model unadjusted for baseline covariates; Model 4: inverse probability of BZF treatment weighted Cox regression model adjusted for baseline covariates; Model 5: time-dependent Cox regression model adjusted for baseline covariates without imputation of missing covariates at baseline and BZF starting dates. † Primary model.

Table 3 . Number needed to treat with combination therapy to prevent one additional death or liver transplantation compared to UDCA only

 3

	Treatment duration	All-cause mortality or LT	Liver-related mortality or LT
		NNT	95% CI	NNT	95% CI
	5 years	29	22 -46	48	34 -81
	10 years	14	10 -22	22	15 -39
	15 years	8	6 -15	13	9 -30
	UDCA, ursodeoxycholic acid. LT, liver transplantation. NNT, number needed to treat. CI,
	confidence interval.

Table S1 .

 S1 Crude incidence rates (95% confidence interval) per 1000 person-years of the main clinical outcomes by treatment group

	Outcomes	UDCA-only	UDCA-BZF	P-value
	All-cause death	9.62 (8.24 -11.16)	4.32 (2.60 -6.78)	0.0005
	Non-liver-related death	5.01 (4.04 -6.15)	1.78 (0.78 -3.52)	0.0029
	Liver-related death	4.55 (3.63 -5.64)	2.54 (1.29 -4.53)	0.0697
	Liver transplantation	1.15 (0.70 -1.78)	0.25 (0.00 -1.42)	0.0928
	P-values are the mid-p values for the Fisher's exact test.

Table S2 .

 S2 Parameters of Model 2 (BZF time-dependent, multivariable-adjusted, 100-dataset imputation of missing BZF starting dates and baseline data): all-cause mortality or liver transplantation

	Parameter	Estimate	SD 95%CI LL 95%CI UL	t-test	P-value
	UDCA-BZF (vs UDCA-
	only)	-1.1231	0.2648	-1.6422	-0.6040	-4.24	<0.0001
	Gender (male)	0.5724	0.1801	0.2195	0.9254	3.18	0.0015
	Age (per decade)	0.3906	0.0756	0.2424	0.5389	5.16	<0.0001
	Pruritus (yes)	0.7999	0.1659	0.4747	1.1251	4.82	<0.0001
	ALP (> 1.67 xULN)	0.4822	0.1518	0.1846	0.7797	3.18	0.0015
	T. bilirubin (> 1.5 mg/dL)	0.9958	0.1962	0.6113	1.3804	5.08	<0.0001
	Albumin (< 35 g/L)	0.9763	0.1948	0.5944	1.3583	5.01	<0.0001
	Histological stage (III-IV)	0.7542	0.1980	0.3653	1.1431	3.81	0.0002
	Diagnosis era (per decade)	-0.1039	0.1704	-0.4379	0.2300	-0.61	0.5419
	Tertiary referral center (no)	-0.1493	0.2533	-0.6457	0.3471	-0.59	0.5556
	SD, standard error. LL, lower limit. UL, upper limit.

Table S3 .

 S3 Parameters of Model 2 (BZF time-dependent, multivariable-adjusted, 100-dataset imputation of missing BZF starting dates and baseline data): liver-related mortality or liver transplantation

	Parameter	Estimate	SD 95%CI LL 95%CI UL	t-test	P-value
	UDCA-BZF (vs UDCA-
	only)	-1.2917	0.3682	-2.0133	-0.5701	-3.51	0.0005
	Gender (male)	0.2403	0.2831	-0.3145	0.7950	0.85	0.396
	Age (per decade)	0.1369	0.0905	-0.0405	0.3142	1.51	0.1304
	Pruritus (yes)	1.4309	0.2504	0.9402	1.9217	5.71	<0.0001
	ALP (> 1.67 xULN)	0.7191	0.2217	0.2846	1.1536	3.24	0.0012
	T. bilirubin (> 1.5 mg/dL)	0.9368	0.2470	0.4526	1.4210	3.79	0.0002
	Albumin (< 35 g/L)	1.1003	0.2560	0.5984	1.6023	4.30	<0.0001
	Histological stage (III-IV)	0.9290	0.2689	0.4009	1.4572	3.46	0.0006
	Diagnosis era (per decade)	-0.2879	0.2479	-0.7738	0.1980	-1.16	0.2455
	Tertiary referral center (no)	-0.4728	0.4057	-1.2679	0.3223	-1.17	0.2438
	SD, standard error. LL, lower limit. UL, upper limit.

Table S4 .

 S4 Parameters of Model 4 (BZF IPTW, BZF time-dependent, multivariable-adjusted, 100-dataset imputation of missing BZF starting dates and baseline data): all-cause mortality or liver transplantation

	Parameter	Estimate	SD 95%CI LL 95%CI UL	t-test	P-value
	UDCA-BZF (vs UDCA-
	only)	-1.2617	0.2777	-1.8059	-0.7175	-4.54	<0.0001
	Gender (male)	0.4932	0.1859	0.1289	0.8576	2.65	0.0080
	Age (per decade)	0.3403	0.0772	0.1890	0.4916	4.41	<0.0001
	Pruritus (yes)	0.8446	0.1688	0.5137	1.1755	5.00	<0.0001
	ALP (> 1.67 xULN)	0.5190	0.1532	0.2186	0.8193	3.39	0.0007
	T. bilirubin (> 1.5 mg/dL)	1.0101	0.2002	0.6176	1.4025	5.04	<0.0001
	Albumin (< 35 g/L)	0.9219	0.2004	0.5290	1.3149	4.60	<0.0001
	Histological stage (III-IV)	0.8141	0.1948	0.4318	1.1963	4.18	<0.0001
	Diagnosis era (per decade)	-0.0922	0.1688	-0.4230	0.2386	-0.55	0.5850
	Tertiary referral center (no)	-0.1847	0.2530	-0.6806	0.3112	-0.73	0.4654
	SD, standard error. LL, lower limit. UL, upper limit.

Table S5 .

 S5 Parameters of Model 4 (BZF IPTW, BZF time-dependent, multivariable-adjusted, 100-dataset imputation of missing BZF starting dates and baseline data): liver-related mortality or liver transplantation

	Parameter	Estimate	SD 95%CI LL 95%CI UL	t-test	P-value
	UDCA-BZF (vs UDCA-
	only)	-1.3282	0.3825	-2.0779	-0.5785	-3.47	0.0005
	Gender (male)	0.1703	0.2915	-0.4011	0.7417	0.58	0.5591
	Age (per decade)	0.0954	0.0923	-0.0855	0.2762	1.03	0.3014
	Pruritus (yes)	1.4337	0.2559	0.9321	1.9353	5.60	<0.0001
	ALP (> 1.67 xULN)	0.7442	0.2214	0.3101	1.1782	3.36	0.0008
	T. bilirubin (> 1.5 mg/dL)	0.9960	0.2580	0.4902	1.5018	3.86	0.0001
	Albumin (< 35 g/L)	1.0241	0.2617	0.5111	1.5372	3.91	<0.0001
	Histological stage (III-IV)	0.9894	0.2644	0.4704	1.5084	3.74	0.0002
	Diagnosis era (per decade)	-0.2593	0.2414	-0.7325	0.2138	-1.07	0.2827
	Tertiary referral center (no)	-0.4912	0.4046	-1.2842	0.3018	-1.21	0.2248
	SD, standard error. LL, lower limit. UL, upper limit.

Table S6 .

 S6 Parameters of Model 5 (BZF time-dependent, multivariable-adjusted, exclusion of missing BZF starting dates and baseline data): all-cause mortality or liver transplantation

	Parameter	Estimate	SD 95%CI LL 95%CI UL	t-test	P-value
	UDCA-BZF (vs UDCA-
	only)	-1.3678	0.3287	-2.0121	-0.7236	-4.16	<0.0001
	Gender (male)	0.5359	0.1840	0.1753	0.8965	2.91	0.0036
	Age (per decade)	0.4019	0.0773	0.2505	0.5533	5.20	<0.0001
	Pruritus (yes)	0.8624	0.1685	0.5321	1.1927	5.12	<0.0001
	ALP (> 1.67 xULN)	0.5146	0.1526	0.2155	0.8136	3.37	0.0007
	T. bilirubin (> 1.5 mg/dL)	0.9076	0.1968	0.5219	1.2934	4.61	<0.0001
	Albumin (< 35 g/L)	0.9653	0.1975	0.5781	1.3524	4.89	<0.0001
	Histological stage (III-IV)	0.7285	0.2066	0.3225	1.1345	3.53	0.0005
	Diagnosis era (per decade)	-0.1290	0.1751	-0.4722	0.2141	-0.74	0.4612
	Tertiary referral center (no)	-0.1531	0.2545	-0.6519	0.3457	-0.60	0.5475
	SD, standard error. LL, 95%CI lower limit. UL, 95%CI upper limit.

Table S7 .

 S7 Parameters of Model 5 (BZF time-dependent, multivariable-adjusted, exclusion of missing BZF starting dates and baseline data): liver-related mortality or liver transplantation

	Parameter	Estimate	SD 95%CI LL 95%CI UL	t-test	P-value
	UDCA-BZF (vs UDCA-
	only)	-1.6703	0.4728	-2.5969	-0.7437	-3.53	0.0004
	Gender (male)	0.2315	0.2901	-0.3372	0.8002	0.80	0.4249
	Age (per decade)	0.1524	0.0937	-0.0312	0.3360	1.63	0.1037
	Pruritus (yes)	1.5648	0.2611	1.0531	2.0766	5.99	<0.0001
	ALP (> 1.67 xULN)	0.7815	0.2224	0.3455	1.2175	3.51	0.0004
	T. bilirubin (> 1.5 mg/dL)	0.8410	0.2448	0.3611	1.3209	3.44	0.0006
	Albumin (< 35 g/L)	1.0641	0.2602	0.5539	1.5742	4.09	<0.0001
	Histological stage (III-IV)	0.9195	0.2813	0.3665	1.4725	3.27	0.0012
	Diagnosis era (per decade)	-0.2979	0.2605	-0.8085	0.2127	-1.14	0.2529
	Tertiary referral center
	(yes)	-0.4672	0.4082	-1.2673	0.3330	-1.14	0.2525

SD, standard error. LL, lower limit. UL, upper limit.

Table S9 .

 S9 Parameters of model 2 (BZF time-dependent, multivariable adjusted, 10-dataset imputation of missing BZF starting dates and baseline data) after inclusion of all analyzable patients since 1980: liver-related mortality or liver transplantation

	Parameter	Estimate	SD 95%CI LL 95%CI UL	t-test	P
	UDCA-BZF (vs UDCA-
		-1.604819 0.286463	-2.16629	-1.04335
	only)					-5.60	<0.0001
	UDCA-only (vs Never-
		-0.686600 0.100929	-0.48864	-0.88456
	treated)					-6.80	<0.0001
	Gender (male)	0.331910 0.117433	0.10171	0.56211	2.83	0.0047
	Age (per decade)	0.014742 0.037957	-0.05969	0.08918	0.39	0.6978
	Pruritus (yes)	1.241546 0.088035	1.06854	1.41455	14.10	<0.0001
	ALP (> 1.67 xULN)	0.321271 0.105823	0.10795	0.53459	3.04	0.0040
	T. bilirubin (> 1.5 mg/dL)	1.231081 0.089981	1.05455	1.40761	13.68	<0.0001
	Albumin (< 35 g/L)	0.727706 0.113454	0.50280	0.95261	6.41	<0.0001
	Histological stage (III-IV)	0.603724 0.096301	0.41305	0.79439	6.27	<0.0001
	Diagnosis era (per decade) -0.231400 0.053992	-0.33727	-0.12553	-4.29	<0.0001
	Tertiary referral center (no) -0.471934 0.111893	-0.69145	-0.25242	-4.22	<0.0001
	SD, standard error. LL, 95%CI lower limit. UL, 95%CI upper limit.

Intercept, Cymabay, Calliditas, Albireo, Mirum, and consultant fees from ChemoMab and Genfi; Dr. O. Chazouillères, receiving grant support from Aptalis, fees for teaching from Mayoly Spindler, consulting fees from Genfit, and fees for teaching and consulting fees from Intercept; Dr. C. Corpechot receiving grants from Arrow and Intercept France, consulting fees from Intercept France, Inventiva Pharma and Genkyotex, and fees for teaching from Intercept France and GlaxoSmithKline France; No other potential conflict of interest relevant to this article was reported. Financial support: This work was supported by a Health and Labor Sciences Research Grant (research on intractable hepatobiliary disease) issued by the Ministry of Health, Labor, and Welfare of Japan. The sponsor had no role in the study. -designer, coordinating investigator, data acquisition,

Data availability statement:

The dataset generated during this study is available from the corresponding author upon reasonable request.

Association of bezafibrate with transplant-free survival in patients with primary biliary cholangitis

Atsushi Tanaka, Junko Hirohara, Toshiaki Nakano, Kosuke Matsumoto, Olivier Chazouillères, Hajime Takikawa, Bettina E. Hansen, Fabrice Carrat, Christophe

Corpechot

Table of contents


Etienne Lehembre

Jean-Luc Lamotte

Abdelkader Ouali

Christophe Couronne

Bruno Crémilleux

Alban Lepailleur

Jean-Luc Manguin

Ronan Bureau

Albrecht Zimmermann

Bertrand Cuissart

Towards lattice-based interactive pharmacophore exploration

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

TOWARDS LATTICE-BASED INTERACTIVE PHARMACOPHORE EXPLORATION

Etienne Lehembre a , Jean-Luc Lamotte b , Abdelkader Ouali a , Christophe Couronne a , Bruno Crémilleux a , Alban Lepailleur b , Jean-Luc Manguin a , Ronan Bureau b , Albrecht Zimmermann a , Bertrand Cuissart a a : GREYC, CNRS UMR 6 , UNICAEN, Normandy Univ. Caen, France Computing key structural configurations from ligands is a major challenges in drug design. In the InvolvD project , we designed a pharmacophore mining method to discover structural layouts potentially linked to a biological activity.

. Method overview

) Defining pharmacophoric features.

) Representing molecular data-set as pharmacophore graphs.

) Extracting pharmacophores by mining the pharmacophore graphs [ ] via Norns a .

) Structuring pharmacophore set into a concept lattice [ ].

) Computing quality of each pharmacophore by applying the Pharmacophore Activity Delta (PAD) measure, the latter being based on the Growth Rate. ) Object / Attributes : pharmacophores / molecules.

Then, the lattice is condensed by building equivalence classes which group pharmacophores occurring in the same set of molecules as soon as they constitute a connected part.

F

: Pharmacophore lattice (left) and its corresponding condensed lattice (right)

Orange nodes from left figure have been separated because :

) They are not connected by a common direct ancestor nor a common direct descendant.

) One is not the ancestor nor the descendant of the other.

. PAD : a new quality measure F : Pharmacophore Activity Delta By using the condensed lattice and the Growth Rates of the pharmacophores, one computes the Pharmacophore Activity Delta :

) Select a node in the lattice (red node).

) Identify the ancestors (red arrows).

) Identify the siblings (green nodes).

) Compute the family standard deviation.

) Compute node delta from its quality and the standard deviation.

PAD has been inspired by the notion of an Activity Cliff [ ]

. Results

Data-set : , 8 ligands from CHEMBL-ABL. Lattice-set :

, 6 pharmacophores extracted from the data-set. Pharmacophores have been extracted with the following parameters :

) Minimal frequency : . ) Size : to features.

PAD have been computed on the condensed lattice with a minimum selecting threshold of times the family standard deviation.

F.

  a. https ://forge.greyc.fr/projects/norns From a pharmacophore lattice to a condensed lattice In order to structure the pharmacophores of interest composing our molecules, we use a lattice structure ) Order relation : sub-graph inclusions.


Guillaume Fontes
email: guillaume.fontes@powerdesign.tech

François Boige

Alvaro Morentin

Guillaume Delamare

Thierry Meynard

Nicolas Videau

Semiconductor loss estimation in an innovative global power converter designer

This paper proposes an approach to quickly evaluate semiconductor losses. This approach combines a fast solver with ideal switch models and detailed loss data stored in multidimensional lookup-tables. This alternative offers a good compromise between accuracy and speed. It is implemented in PowerForge®, an innovative software to benchmark different power semiconductor devices or topologies. Results comparing PLECS, PSIM and PowerForge to evaluate the accuracy is proposed.

Introduction

Designing power converter is mostly a trade-off between efficiency and power density. While power density is mainly driven by the passive elements and heatsink volume, the efficiency is mainly impacted by the semiconductor losses (conduction and switching). Estimating accurately the losses of these devices is crucial for the converter efficiency as well as for the volume of the heatsinks. Usually, this loss estimation is performed with simple equations or with detailed simulations. This paper describes an approach that combines ideal switch models with detailed loss data to provide an efficient and accurate alternative to detailed device simulations at a minimum cost. This approach is used in PowerForge® [START_REF] Powerforge | Power Design Technologies SA[END_REF], which is an innovative software to benchmark different topologies (including multilevel topologies such as NPC, T-type, flying capacitor) and different power semiconductor devices. This paper purpose is to detail how the losses are estimated and how accurate they are compared to time-based circuit simulation tools. In a first section, the general principle of the approach is described which relies on several distinct mechanisms: a frequency domain solver to compute waveforms, a storage in lookup tables of the loss data for a given component and an iterative loop to compute the junction temperature and exact losses. In a second section, the generation of the loss data are detailed. In a third section, the results are compared to time-based circuit simulation tools PLECS® [START_REF] Plecs | The Simulation Platform for Power Electronic Systems[END_REF] and PSIM® [START_REF]Powersim: PSIM Electronic Simulation Software[END_REF].

General principle

The approach to compute semiconductor losses is based on two key steps to provide a fast evaluation of these losses as shown in Fig. 1: Fig. 1: General principle • Steady-state waveforms of the whole circuit are directly determined thanks to a frequency domain solver adapted to the switching cell. From these waveforms are extracted the switched currents and voltages for each switch event.

• The values of current and voltage are used to read the resulting dissipated energy and power losses from multidimensional lookup tables for both conduction loss and switching loss. The junction temperature considered is an average temperature over the modulation period. The losses and the junction temperature are determined with an iterative computation as the losses depend on the temperature and the temperature depends on the losses. This iterative loop ends when the difference of the junction temperature between two steps is below 0.5°C.

Steady-state Waveform Determination with a Frequency Solver

This method has been presented in [START_REF] Fontes | Fast Solver to Get Steady-State Waveforms for Power Converter Design[END_REF]. The solver is adapted to commutation cells and based on the modified nodal analysis (MNA) [START_REF] Ho | The modified nodal approach to network analysis[END_REF]. It provides a very fast generic method to get steady-state waveforms of the power converters based on commutation cells with hard switching. The commutation cell is modelled by a current source 𝐼 𝐻𝑉 at high voltage side and a voltage source 𝑉 𝐿𝑉 at low voltage side as shown in Fig. 2 with the model of a simple dc-dc chopper.

Where 𝐷(𝑡) is the duty cycle of the commutation cell.

The solving process can be summarized with the three steps shown in Fig. 3:

• The frequency spectrums of current 𝐼 𝐻𝑉 and voltage 𝑉 𝐿𝑉 are first obtained with the Fast Fourier Transform (FFT) algorithm.

• The MNA resolution is applied on all frequencies of the spectrum and the different voltages or currents of the circuits (𝐼 𝐿𝑉 , 𝑉 𝐻𝑉 , 𝑉 𝑐ℎ , 𝐼 𝑏𝑢𝑠 … ) are determined. • The Inverse Fast Fourier Transform (IFFT) algorithm is used to reconstruct the timedomain quantities at both sides of the commutation cell.

Loss Data Storage with Multidimensional Lookup Tables

Switching energy and voltage drop data are stored as multidimensional lookup tables for each power semiconductor device, as following:

𝐸 𝑜𝑛|𝑜𝑓𝑓|𝑟𝑟 = 𝑓(𝑉 𝐻𝑉 , 𝐼, 𝑇 𝑗 ) (2)
𝑉 𝑜𝑛 = 𝑓(𝐼, 𝑇 𝑗 ) (3) A linear interpolation can be performed between the points stored in the lookup tables, resulting in a continuous surface presented in Fig. 5 for Eq° [START_REF] Plecs | The Simulation Platform for Power Electronic Systems[END_REF] and in continuous curves presented in Fig. 6 for Eq° [START_REF]Powersim: PSIM Electronic Simulation Software[END_REF]. The lookup tables consider the dependence on the temperature, which is computed as an average temperature over a modulation period with the interaction of the cooling device. Loss data stored in these lookup tables are extracted from manufacturer datasheets or estimated with a SPICE model as presented in the following section.

Switching Loss Data Generation for Si-MOSFETS

In this case, the switching energies are obtained by a double-pulse measurement SPICE simulation. The classical double pulse simulation schematic is presented in Fig. 7. The turn-on and turn-off voltages are the nominal ones from the manufacturer datasheet. The pulse times are swept in order to obtain the switching energies for a large panel of drain currents as well as gate

V on (V) I on (A) T j 25 C 66.7 C 108.3 C 150 C V HV R Gon, R Goff V Goff DUT L test V Goff V Gon G D S C DG C GS C DS L D L S I ch Body Diode R Gint v L k.v L R L L Perfect Diode K A
resistors and bus voltages (VHV). The model of the device under test (DUT), including the body diode, is based on [START_REF] Courtay | MAST power diode and thyristor models including automatic parameter extraction[END_REF]. The schematic of the MOSFET and the body diode are presented in Fig. 8 and Fig. 9.

The MOSFET drain current is described with the following equations:

𝐼 𝑐ℎ = 𝑠𝑖𝑔𝑛(𝑉 𝐷𝑆 ) • min (𝐼 𝑝𝑜𝑡 , | 𝑉 𝐷𝑆 𝑅 𝐷𝑆𝑜𝑛 |) (4)
With: 𝑖𝑓 (𝑉 𝐺𝑆 -𝑉 𝑡ℎ ) > 0, 𝐼 𝑝𝑜𝑡 = 𝐾 𝑝 • (𝑉 𝐺𝑆 -𝑉 𝑡ℎ ) 2 𝑒𝑙𝑠𝑒 𝐼 𝑝𝑜𝑡 = 0 [START_REF] Ho | The modified nodal approach to network analysis[END_REF] and 𝐾 𝑝 the transconductance parameter, 𝑅 𝐷𝑆𝑜𝑛 the channel resistance, 𝑉 𝑡ℎ the threshold voltage.

All the parameters are extracted from the manufacturer datasheet in particular CDG(VDS) and CDS(VDS).

The body diode recovery current is modeled by identifying three parameter values L, RL and k based on the MOSFET electrical characteristics (IRRM,QR) as described in [START_REF] Courtay | MAST power diode and thyristor models including automatic parameter extraction[END_REF].

The temperature dependence is possible if the parameters are given for different temperatures.

Conduction Loss Data

Voltage drops, introduced in Eq° (3), for computing conduction loss are obtained by digitalizing the manufacturer datasheets, typically 𝑅 𝐷𝑆(𝑜𝑛) = 𝑓(𝑇 𝑗 ) curves for MOSFET and 𝐼(𝑉) curves at different 𝑇 𝑗 for IGBT and diodes. These curves are always taken at nominal gate drive voltage.

Reverse conduction of MOSFETS with or without external diode

When conducting reverse current, synchronous rectification is used if the transistor's technology makes it possible (e.g. MOSFET). The transistor gate is assumed to be driven high, so that the channel can contribute to reverse current conduction. In this case, the reverse current may be split between controlled and spontaneous reverse conduction mechanisms (e.g. diode and channel) in a ratio that depends on total reverse current and on each junction temperature as illustrated in Fig. 10. The proposed approach handles this and pre-computes the conduction ratio between the two conduction mechanisms as shown in Fig. 11. Fig. 12 shows the different device contributions in reverse conduction and the resulting voltage drop depending on the total current. This result shows the benefit of the diode conduction at high current level for Si-MOSFET.

Results and Comparison

The proposed approach is implemented in a computer-aided engineering platform dedicated to benchmark different power semiconductor devices or topologies for power converter design: Powerforge® [START_REF] Powerforge | Power Design Technologies SA[END_REF].

𝑅 𝑡ℎ 𝑅 𝑡ℎ 𝐼 𝑜 𝐼 𝑜𝑠𝑓 𝑡 𝐼 𝑠 𝑡𝑐ℎ 𝑇 ℎ 𝑡𝑠 𝑛
The losses are compared between PowerForge, PLECS [START_REF] Plecs | The Simulation Platform for Power Electronic Systems[END_REF] and PSIM [START_REF]Powersim: PSIM Electronic Simulation Software[END_REF] software for three cases:

• a DC-DC conversion stage composed of two 3level flying capacitor switching cells in parallel (ncell(FC)=2 and ncell(par)=2) , • a 2-level 3-phase inverter, • a motor drive application where two topologies are compared: a 3-level T-type and a 3-level flying capacitor.

The comparison of the results shows the sum of the losses in the diode and the transistor for switching and conduction losses, junction temperatures of each device and the relative errors. The semiconductors losses curves have been extracted from the manufacturers datasheet for different temperatures as explained above.

Case 1: DC-DC conversion stage

This conversion stage is composed of two flying capacitor cells connected in parallel and interleaved as shown in Erreur ! Source du renvoi introuvable.. The characteristics of this conversion stage are presented in Table 1. A first comparison of the iterative thermal computation has been performed using waveforms generated by PLECS and have been re-injected in PowerForge to compute the losses and the junction temperatures. This comparison showed a relative error below 10 -5 , due to the convergence of the thermal computation in PowerForge. Indeed, this thermal computation includes an iterative loop (Fig. 1) which ends with a small tolerance on the junction temperature between two computation steps.

A full comparison has then been performed between PowerForge, PLECS and PSIM and results are shown in Table 2. Most of difference are below 1% except for the switching losses computed with PSIM. These small differences can be explained with the differences between the currents and voltages switched values which are computed with different solvers.

Case 2: 2-level 3-phase inverter

The second comparison is based on a 2 level 3-Phase inverter as shown in Fig. 13. The characteristics of this second comparison case are shown in Table 1. The comparison results of the second case are shown in Table 4. Switching and conduction losses are the sum of transistor and conduction losses.

In this case of a 3-phase inverter, where the HF current ripple is only 20% peak-to-peak, the influence of the solver on the waveforms and on the values of the switched currents is less important. Thus, PSIM simulation shows closer results than in previous case. Moreover, PSIM performs an averaged thermal computation on the modulation period in the same way as PowerForge and shows closer results than PLECS, which dynamically computes the junction temperatures with the instantaneous loss computation.

Case 3: Motor drive application

At last, the losses of a T-type inverter, shown in Fig. 14, for a motor drive application are compared:

• Power: 200 kW,

• Phase-to-phase voltage: 690 V AC.

The characteristics of the T-type inverter are shown in Table 5. In this case, again, PLECS simulation shows différence that are a little bit higher than PSIM simulation, which is due to the different process of the thermal computation. This approach is based on the frequential solver previously described that is much faster than time solvers. Losses evaluation is, therefore, quicker for a huge number of different power converter solutions. This technological advance is paving the way for power converter design automation.

Fig. 2 :

 2 Fig. 2: Commutation cell model of a simple dc-dc chopper The values of current source 𝐼 𝐻𝑉 and voltage source 𝑉 𝐿𝑉 are analytically computed from: 𝑉 𝐿𝑉 (𝑡) = 𝐷(𝑡) • 𝑉 𝐻𝑉 (𝑡) 𝐼 𝐻𝑉 (𝑡) = 𝐷(𝑡) • 𝐼 𝐿𝑉 (𝑡)

Fig. 3 :

 3 Fig. 3: Frequency resolution adapted to the commutation cell From these waveforms are extracted the switched values of current and voltage as shown in Fig. 4.

Fig. 4 :

 4 Fig. 4: Switched power and current

Fig. 5 :Fig. 6 :

 56 Fig. 5: Switching energies for different currents, voltages and temperatures

Fig. 7 :

 7 Fig. 7: Double pulse schematic

Fig. 10 :

 10 Fig. 10: Thermal model and current sharing between the couple MOSFET and diode

Fig. 13

 13 Fig. 13 Circuit of a 2-Level 3-phase inverter

Fig. 14

 14 Fig. 14 Circuit of a T-Type 3-phase inverter

  interpolated or extrapolated especially for 𝑉 𝐻𝑉 . If the manufacturers do not provide loss measurement results (i.e. low voltage Si-MOSFET), the authors developed a doublepulse SPICE simulation to estimate 𝐸 𝑜𝑛|𝑜𝑓𝑓|𝑟𝑟 = 𝑓( 𝐼, 𝑇 𝐽 , 𝑉 𝐷𝑆 ). This last process will be detailed in next section.

3.1 Switching Loss Data

Switching energies, introduced in Eq° (2), are obtained by digitalizing the manufacturer datasheets, 𝐸 𝑜𝑛|𝑜𝑓𝑓|𝑟𝑟 = 𝑓( 𝐼) curves at different 𝑇 𝑗 are stored in the lookup tables. The switching energy is linearly

Table 1 :

 1 Parameters of the DC-DC conversion stage

	Switch reference	IKB20N60H3
	Rth(c-s) per switch	1.14 K / W
	Rth(s-a)	0.2 K / W
	Tambient	25 °C
	VHV	450 V
	VLV	300 V
	iLV	40 A
	ncell(FC)	2
	ncell(par)	2
	fsw	10 kHz
	Cfly	297 µF
	LLV	100 µH
	Rwinding L	1 m
	CLV	1 mF

Table 2 :

 2 Comparison results for the DC-DC conversion stage between PowerForge, PLECS and PSIM

		PF	PLECS	PSIM
		Value	Value	Δ(%) Value	Δ(%)
	Psw(High) [W]	4.62	4.6	0.4	4.36	5.6
	Pcond(High) [W]	31.30	31.2	0.3	31.25 0.2
	Pcond(Low) [W]	15.10	15.10	0	15.10 0
	Psw(Low) [W]	0	0	0	0	0
	Tj(T-High) [°C]	138.4	138.9	0.4	137.6 0.6
	Tj(D-High) [°C]	106.9	107.4	0.5	106.3 0.3
	Tj(T-Low) [°C]	83.1	83.6	0.6	82.8	0.5
	Tj(D-Low) [°C]	111.7	112.3	0.5	111.4 0.6

Table 3 :

 3 Parameters of the 2-level 3-phase inverter

	Switch reference	FGH12040WD
	Rth(c-s) per switch	1.14 K / W
	Rth(s-a)	0.2 K / W
	Tambient	25 °C
	UDC	750 V
	UAC RMS	400 V
	PAC	20 kW
	f0	50 Hz
	fsw	10 kHz
	LAC	1.27 mH
	Rwinding L	0.24 
	CAC	14.9 mF

Table 4 :

 4 Comparison results for the 2-Level 3-phase inverter between PowerForge, PLECS and PSIM

		PF	PLECS	PSIM
		Value Value	Δ(%)	Value Δ(%)
	Psw [W]	25.81 25.76	0.2	25.83 0.07
	Pcond [W]	29.60 29.59	0.04	29.62 0.06
	Tj(T) [°C]	150.1 149.8	0.2	150.2 0.06
	Tj(D) [°C]	139.2 138.8	0.3	139.2 0

Table 5 :

 5 Parameters of the 3-level T-type inverter

	Module reference	SEMiX305TMLI17E4C
	Rth(c-s) per switch	0.018 K / W
	Rth(s-a)	0.072 K / W
	Tambient	25 °C
	UDC	1070 V
	UAC RMS	690 V
	PAC	200 kW
	f0	50 Hz
	fsw	2.5 kHz
	LAC	211e-6 µH
	Rwinding L	0.07 
	CAC	26.9 mF

Table 6

 6 • from the different solvers which are used (between PLECS, PSIM and PowerForge) which can give different values of the switched current and voltages, • from the different processes of the thermal computation. On one side, PSIM and PowerForge perform a thermal computation of averaged junction temperature over a modulation period. On the other side, PLECS

	: semiconductor losses for two topologies
		estimated with three software
		PF	PLEC		PSIM
		Value	Value	Δ(%)	Value Δ(%)
	Psw(inner) [W]	10.1	9.4	7	10.2	1
	Psw(outer) [W]	55.1	55.1	0	55.4	0.5
	Pcond(inner)	36.1	36.1	0	36.1	0
	[W]
	Pcond(outer)	129.5	129.7	0.2	129.3 0.2
	[W]
	Tj(T inner)	129.8	128.4	1	129.9 0.08
	Tj(T outer)	149.9	148.5	1	150.0 0.07
	Tj(D inner)	133.7	132.2	1	133.9 0.1
	Tj(D outer)	135.2	133.8	1	135.3 0.07
	5 Conclusion
	This paper presents a fast and accurate method to
	estimate semiconductor losses in various power
	converter topologies. The fast frequential solver is
	used to determine waveforms, i.e. the switched
	voltages and currents and the currents through the
	devices. Therefore, these quantities are used to
	read lookup tables to evaluate switching and
	conduction losses and each chip temperature. The
	lookup table data are extracted from the
	manufacturer datasheets or estimated with a
	double-pulse measurement of a SPICE simulation
	(typically for low-voltage Si-MOSFETS). Finally,
	the described approach is compared with two well-
	known simulation tools, PSIM® and PLECS®
	showing a good accuracy with a maximum
	difference -for the considered examples -below
	1% for PSIM and maximum 7% for PLECS. The
	differences can be explained: