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Original Article

Beta-Adrenergic–Antagonist Drugs in the Prevention of Gastrointestinal Bleeding in Patients with Cirrhosis and Esophageal Varices — An Analysis of Data and Prognostic Factors in 589 Patients from Four Randomized Clinical Trials

Thierry Poynard, M.D., Ph.D., Paul Calès, M.D., Linda Pasta, M.D., Gaetano Ideo, M.D., Jean-Pierre Pascal, M.D., Luigi Pagliaro, M.D., Didier Lebrec, M.D., and the Franco—Italian Multicenter Study Group*

N Engl J Med 1991; 324:1532-1538May 30, 1991

Abstract
Abstract

Background.

The value of beta-adrenergic—antagonist drug therapy for the prevention of initial episodes of gastrointestinal bleeding in patients with cirrhosis and esophageal varices is uncertain, both positive and negative study results having been reported.

Methods.

In this study, we analyzed data on individual patients from four randomized, controlled trials to assess the efficacy of this treatment. Of the 589 patients studied, 286 received a beta-adrenergic—antagonist drug (propranolol in 203 and nadolol in 83) and 303 received placebo.

Results.

After two years, the mean (±SE) percentage of patients who had had no upper gastrointestinal bleeding was 78±3 percent in the beta-adrenergic—antagonist treatment group and 65±3 percent in the control group (P = 0.002). The percentage of patients without fatal bleeding was 90±2 percent in the treatment group and 82±3 percent in the control group (P = 0.01). The percentage of patients surviving after two years was 71 ±3 percent in the treatment group and 68±3 percent in the control group (P = 0.34). After age and severity of cirrhosis were taken into account, the survival rate was better in the treatment group (P = 0.09). The percentage of surviving patients who had had no bleeding after two years was 62±3 percent in the treatment group and 53±3 percent in the control group (P = 0.04). Both propranolol and nadolol prevented a first episode of bleeding. Severe cirrhosis and especially the presence of ascites were associated with bleeding (P<0.001) and death (P<0.001) in both groups. The efficacy of beta-adrenergic—antagonist therapy in the prevention of bleeding (P<0.001) and of fatal bleeding (P = 0.004) and in the prevention of bleeding or death (P = 0.005) was the same after adjustment for cause and severity of cirrhosis, ascites, and size of varices.

Conclusions.

Propranolol and nadolol are effective in preventing first bleeding and reducing the mortality rate associated with gastrointestinal bleeding in patients with cirrhosis, regardless of severity. (N Engl J Med 1991; 321:1532–8.)

Media in This Article

Figure 1Mean (±SE) Percentage of Patients with Cirrhosis Who Had No Upper Gastrointestinal Bleeding during the Two-Year Treatment Period.
Figure 2Mean (±SE) Percentage of Patients with Cirrhosis Who Did Not Die of Bleeding during the Two-Year Treatment Period.
Article

THE continuous administration of beta-adrenergic—antagonist drugs induces a sustained decrease in portal pressure in patients with cirrhosis.1 2 3 4 As a result, these drugs have been used to prevent gastrointestinal bleeding, a leading cause of death in patients with portal hypertension. There are published reports of four randomized clinical trials of beta-adrenergic—antagonist drug treatment — two using propranolol5 , 6 and two using nadolol7 , 8 — to prevent a first episode of gastrointestinal bleeding due to portal hypertension in patients with cirrhosis.

The percentages of patients who had no bleeding and the survival rates were dissimilar in these four trials. In two studies, the treatment was more effective than placebo in the prevention of a first episode of bleeding,5 , 7 but in the other two studies the treatment was effective only in certain subgroups of patients —namely, those who complied with the regimen9 and those with no ascites.6 In one trial the survival rate was significantly higher in the patients who received active therapy.5

In an attempt to clarify the discrepant findings, we combined the data, including prognostic factors, on all the patients studied in the four trials, to determine the effect of beta-adrenergic—antagonist drug therapy on the risk of bleeding and the survival rate and to identify the variables associated with the efficacy of the drugs.

Methods

Patients

The criteria for the inclusion and exclusion of patients in the four studies and the study protocols have been described in detail elsewhere.5 6 7 8 The base-line characteristics of the patients are shown in Table 1.Table 1Characteristics of the Patients at the Time of Entry into Each Trial of Beta-Adrenergic-Antagonist Drug Treatment for the Prevention of First Bleeding in Patients with Cirrhosis.* All the patients in the four trials had cirrhosis and esophageal varices identified by endoscopy, but no history of variceal bleeding. The patients were treated with either propranolol or nadolol in doses that reduced the heart rate by approximately 25 percent. Although the patients did not know whether they were receiving active treatment, the attending physicians did. In one study,7 the patients in the control group received ranitidine instead of placebo, and in another study6 the control group received vitamin K. The size of the varices and the severity of cirrhosis varied among the trials. In two trials, patients with moderate-sized varices were included: the varices ranged in size from 4 to 6 mm in one trial8 and were of Grade II in the other.5 In the remaining two trials, only patients with large varices that filled more than one third of the esophageal lumen were included. Patients with severe liver disease manifested by intractable ascites, hepatic encephalopathy, a serum bilirubin level above 100 μmol per liter, or any combination of these were excluded from one trial,8 and patients with tense ascites resistant to diuretic treatment, chronic or recurrent hepatic encephalopathy (more than three episodes per year), or a serum bilirubin concentration above 513 μmol per liter were excluded from another.6 Pascal et al. excluded patients with severe cirrhosis, as defined by a Child—Pugh score over 13,5 and Ideo et al. excluded patients with intractable ascites.7 The follow-up period was designed to last one year in two studies5 , 8 and two years in the other two studies.6 , 7 One of the two studies with a one-year follow-up8 was continued in 40 patients; the results after two years are included in this analysis. The characteristics of the patients during follow-up are shown in Table 2Table 2Characteristics of the Patients in Each Trial, According to the Events Occurring during Two Years of Follow-up.*, including the occurrence of hepatocellular carcinoma, noncompliance with the study protocol, lack of abstinence from alcohol, and absence of permanent reduction of the heart rate by 25 percent. Noncompliance was defined as the failure to take the active drug or placebo for at least two consecutive days, as reported by the patient or the patient's family. Abstinence from alcohol was defined as the total cessation of consumption of alcohol, as reported by both the patient and the patient's family.

Statistical Analysis

The results were collected from the responses of the patients' physicians, who all received an identical questionnaire requesting information on the following 12 characteristics of the patients at the time of inclusion in the study: study center, sex, age, cause of cirrhosis, presence of ascites, presence of hepatic encephalopathy, serum bilirubin level, prothrombin time, serum albumin level, size of the largest varix, presence of red signs on the mucosa overlying the varices, and type of treatment. Four items related to the risk of bleeding were recorded during follow-up: occurrence of hepatocellular carcinoma, noncompliance with the study protocol, lack of abstinence from alcohol, and absence of reduction of the heart rate by 25 percent. The other items were used to estimate the end points: first episode of bleeding during the two-year period (with time and cause), death in two years (with time and cause), and duration of follow-up for patients lost to follow-up. Since the size of the varices was assessed differently in the four trials, we defined large varices as those classified as F3 by Ideo et al.7 and the Italian Multicenter Project,6 those classified as Grade III by Pascal et al.,5 and those more than 6 mm in diameter as measured by Lebrec et al.8 Varices classified as Grade II by Pascal et al.5 and measuring between 4 and 6 mm in diameter were defined as being of moderate size.

We chose four end points for comparison after two years of follow-up: the percentage of patients who had had no bleeding, the percentage who had not had fatal bleeding, the percentage who survived, and the percentage who survived without any bleeding. An episode of bleeding was defined as one in which there was hematemesis, melena, or blood in a gastric aspirate. Fatal bleeding was defined as occurring when a patient died within six weeks of a bleeding episode. These definitions were agreed on at a consensusdevelopment workshop, "Definitions, Methodology, and Therapeutic Strategies in Portal Hypertension," held in Baveno, Italy, on April 5 and 6, 1990. The percentages were calculated according to the Kaplan–Meier method, expressed as means ±SE, and compared at the end of two years with the log-rank test. The percentages of patients with and without ascites who had no bleeding and of those with a Child—Pugh score ≥8 or <8 were compared by the adjusted log-rank test.

The results of a meta-analysis using the data on the individual patients were compared with the results of a meta-analysis using the published data from each center. For the meta-analysis of the data on individual patients, the proportional-hazards model was used, stratified according to center or not stratified, or the log-rank test was used, adjusted according to center. The meta-analysis of the published data was done with the MantelHaenszel test.

All P values were two-tailed. Quantitative variables were expressed as means ±SD. The chi-square test or Fisher's exact test was used to compare qualitative variables, and either Student's t-test or the Mann—Whitney nonparametric test was used to compare quantitative variables. Proportional-hazards models were used to identify the factors independently associated with each end point, including the treatment assignment. To ensure proportionality, we checked that there was a constant vertical difference, independent of time, between the plots of estimates of log minus log survival function. The significance of each factor was expressed by the regression coefficient and tested by the likelihood-ratio test. For each factor tested, the regression coefficients were calculated separately for the treatment and the control groups. When the coefficients were not similar, they were given separately, and when they were similar, a common coefficient was given.

The absence of a permanent reduction of the heart rate by 25 percent was recorded only in the patients who received beta-adrenergic—antagonist treatment, and therefore its independent prognostic value was tested only in those patients. Since three factors —red signs on varices, the occurrence of hepatocellular carcinoma, and noncompliance — were not recorded by Pascal et al.,5 the proportional-hazards model for these factors was estimated only for the patients in the other three trials. Since the severity of cirrhosis can be estimated either by the Child—Pugh score, which combines values for ascites, hepatic encephalopathy, serum bilirubin level, scrum albumin level, and prothrombin time, or by any of these five variables separately, the prognostic value of the severity of cirrhosis was evaluated on the basis of two proportional-hazards models —one using the Child—Pugh score and another using the five variables individually.

All the end points were assessed with the intention-to-treat method. That is, the patient was included in the randomized group even if the treatment was stopped. Only end points that occurred during the first two years were considered. New data were available from Lebrec et al. after two years of follow-up; the original report from that study analyzed the data collected after one year.8 For the study by Pascal et al.,5 certain end points that occurred after two years were reported in the original publication, which accounts for the appearance of different figures here.

Results

Bleeding

Altogether, there were 286 patients receiving beta-adrenergic—antagonist drugs and 383 receiving placebo. Forty-nine patients in the beta-adrenergic—antagonist group and 82 patients in the control group had upper gastrointestinal bleeding during the study period. The mean (±SE) percentage of patients who had no bleeding during the two-year period was 78±3 percent in the treatment group and 65±3 percent in the control group (log rank = 9.2, P = 0.002) (Fig. 1Figure 1Mean (±SE) Percentage of Patients with Cirrhosis Who Had No Upper Gastrointestinal Bleeding during the Two-Year Treatment Period.). The presence of ascites, a low serum albumin level, a high Child—Pugh score, and treatment with a beta-adrenergic—antagonist drug were the only independent variables that influenced the incidence of bleeding (Table 3Table 3Prognostic Analysis of the Risk of Reaching the Four Study End Points, According to Proportional-Hazards Analysis.*). The presence of red signs on the varix and noncompliance were associated with bleeding in the treatment group but not the control group.

Among the 131 patients with bleeding, 85 had bleeding from esophageal varices (35 in the treatment group and 50 in the control group), 24 from portal hypertensive gastropathy (6 in the treatment group and 18 in the control group), and 22 from unknown sources (8 in the treatment group and 14 in the control group). After two years, the percentage of patients who had had no bleeding from varices was 83 ±3 percent in the treatment group and 77±3 percent in the control group. The percentage of patients who had had no bleeding from portal hypertensive gastropathy was 97±1 percent in the treatment group and 90±2 percent in the control group. The percentage of patients who had had no bleeding from an unknown source was 97 ±1 percent in the treatment group and 94±2 percent in the control group. The significant effects of beta-adrenergic—antagonist drug therapy persisted after adjustment for the source of bleeding.

Table 4Table 4Percentage of Patients Free of Bleeding after Two Years, According to the Presence or Absence of Ascites and the Severity of Cirrhosis. shows the percentage of patients who had had no bleeding after two years, according to the presence or absence of ascites and the severity of cirrhosis. The difference between the beta-adrenergic—antagonist and placebo groups was greater in those with poor liver function or ascites than in those with relatively good liver function or no ascites.

Fatal Bleeding

Twenty-one patients in the treatment group and 43 patients in the control group had fatal bleeding. The percentage of patients who did not have fatal bleeding was 90±2 percent in the treatment group and 82±3 percent in the control group (log rank = 6.4, P = 0.01) (Fig. 2Figure 2Mean (±SE) Percentage of Patients with Cirrhosis Who Did Not Die of Bleeding during the Two-Year Treatment Period.). The presence of ascites, a high Child—Pugh score, the presence of red signs, and beta-adrenergic—antagonist drug treatment were the only independent variables to influence the incidence of fatal bleeding (Table 3).

Death

Seventy patients in the treatment group and 86 patients in the control group died. The percentage of patients surviving after two years was 71 ±3 percent in the treatment group and 68±3 percent in the control group (log rank = 0.89, P = 0.34) (Fig. 3Figure 3Percentage of Patients with Cirrhosis Who Survived the Two-Year Treatment Period.). Age, red signs, ascites, low serum albumin level, high serum bilirubin level, high Child—Pugh score, occurrence of hepatocellular carcinoma, and beta-adrenergic—antagonist drug treatment (P<0.09) were the only variables that influenced survival (Table 3).

Death or Bleeding

Eighty-nine patients in the treatment group and 121 patients in the control group had bleeding, died, or both. The percentage of patients surviving with no bleeding was 62 ±3 percent in the treatment group and 53±3 percent in the control group (log rank = 4.7, P = 0.04). The presence of ascites, low serum albumin level, high serum bilirubin level, high Child—Pugh score, occurrence of hepatocellular carcinoma, and beta-adrenergic—antagonist drug treatment were the only independent variables to influence the incidence of bleeding or death (Table 3).

Comparison between Patients with and without Alcoholic Cirrhosis

Among the 383 patients with alcoholic cirrhosis, the percentage of patients who had no bleeding during the two-year study period was 80±4 percent in the treatment group and 65±5 percent in the control group. Among the 206 patients with nonalcoholic cirrhosis, these percentages were 76±5 percent in the treatment group and 66±5 percent in the control group. After we adjusted for the cause of cirrhosis, the efficacy of beta-adrenergic—antagonist drug treatment was statistically significant for the time of first bleeding (P = 0.003), for fatal bleeding (P = 0.01), and for the prevention of bleeding or death (P = 0.03).

Efficacy of Propranolol and Nadolol

For the patients taking propranolol or nadolol, the percentages who reached the four study end points are shown in Table 5.Table 5Efficacy of Nadolol and Propranolol for Preventing Patients from Reaching a Study End Point.* There was no statistically significant difference in efficacy between the two drugs.

Comparison of Meta-analyses Using Data on Individual Patients or Published Data

The results of four different meta-analyses are shown in Table 6.Table 6Efficacy of Beta-Adrenergic—Antagonist Agents as Assessed by Four Different Meta-analyses.

Discussion

This analysis was not a classic overview (meta-analysis) of the published results of four randomized clinical trials, but instead an analysis of the data on individual patients, including prognostic factors. This method allowed us to demonstrate the efficacy of beta-adrenergic—antagonist drugs in preventing the first episode of bleeding and reducing the mortality associated with bleeding. It also allowed us to identify the independent prognostic factors for bleeding and death in a population of patients with cirrhosis who had varices. Finally, it demonstrated the advantages of an analysis that combines individual data as compared with one using only published results.

The results demonstrate the efficacy of propranolol and nadoloi in preventing a first episode of upper gastrointestinal bleeding in patients with cirrhosis who have esophageal varices. This efficacy was greatest in patients with good compliance who did not have ascites and in patients in good condition. The two drugs were also effective, however, in patients with ascites or severe cirrhosis, as demonstrated by the multidimensional and adjusted analyses. For example, patients with ascites who received active treatment had a greater probability of having no bleeding during the two-year study period than patients with no ascites who received placebo (Table 4). The efficacy of treatment for the prevention of first bleeding has already been reported by Pascal et al.5 and Ideo et al.7 In the trial conducted by Lebrec et al.,8 efficacy was shown only in patients in whom compliance was good. In the trial of the Italian Multicenter Project,6 active treatment with propranolol prevented bleeding only in patients who did not have much ascites.

Among the 589 patients included in this overview, the effect of beta-adrenergic—antagonist drug treatment on survival was small. As assessed by the proportional-hazards model, survival was predictable mainly on the basis of the Child—Pugh score, age, and the occurrence of hepatocellular carcinoma. When these three factors were taken into consideration, treatment had a small favorable effect. The small effect of treatment on survival after two years may be due to the small number of deaths related to bleeding. In the control group, half the deaths (43) were related to bleeding, as compared with 30 percent (21) in the treatment group. Forty-four deaths in the control group and 49 in the treatment group were unrelated to bleeding. These results also suggest that in the event of hemorrhage, propranolol and nadoloi have no deleterious effects. After two years of treatment with these drugs, the occurrence of fatal bleeding was reduced from 18 percent to 10 percent, a savings of 8 lives among 100 patients during the period.

We also found that treatment increased the percentage of patients who survived with no bleeding. This end point is reached frequently when the risk of bleeding or death is approximately 50 percent in the control group.

Propranolol and nadoloi had similar efficacy in the prevention of bleeding or fatal bleeding, but the two drugs were not compared directly. Their direct comparison in a randomized trial would be difficult because of the large sample needed. However, indirect comparison using the proportional-hazards model showed no difference after adjustment for prognostic factors. This is another advantage of using data on individual patients and prognostic factors in an analysis.

In our overview, we identified several independent factors associated with bleeding and death. Ascites and severe cirrhosis were strongly associated with bleeding, fatal bleeding, and death in both the control and the treatment groups. The negative effect of ascites was similar in both groups. Ascites was a risk factor for bleeding independently of other known prognostic criteria, such as high serum bilirubin level, low serum albumin level, prolonged prothrombin time, and hepatic encephalopathy.

Noncompliance was independently associated with lower efficacy of beta-adrenergic—antagonist drug treatment for the prevention of bleeding. This effect of decreased compliance was noted previously in studies of the prevention of recurrent gastrointestinal bleeding with propranolol.9 The presence of red signs on varices was also an independent risk factor for bleeding in the patients in the treatment group. Age, sex, and cause of cirrhosis were not independently associated with the risk of bleeding.

Burroughs et al. have published recommendations for trials to prevent a first episode of bleeding,10 and our overview took most of these recommendations into consideration. We used three of their four characteristics of patients, two of the four criteria for follow-up, and two of the four statistical considerations. There are two main weaknesses in the four trials we evaluated. First, the protocols were not double-blind, although it is difficult to organize such trials for this type of drug. Second, there was no standardization of the emergency treatment of patients with bleeding, a possible source of differences in mortality rates. Although we do not have data on each patient, the investigators all stated that every patient with bleeding was treated similarly within each center.

An analysis such as ours is time-consuming, but it has several advantages over a meta-analysis that combines only published data. First, prognostic factors and censored data can all be taken into account. Second, data obtained after the same period of follow-up can be combined. Also, by combining data on individual patients, one can compare the proportional-hazards models and adjusted log-rank tests. Finally, and most important, the definition of data requested on the questionnaire used in the analysis can be standardized. With classic meta-analysis it is impossible to identify the risk factors for bleeding or to assess the effect of treatment on fatal bleeding. Unlike our analysis, the two recent classic meta-analyses of beta-adrenergic—antagonist drug treatment11 , 12 did not take into account prognostic variables, censored data, or combined end points for different periods of follow-up (range, 12 to 34 months). Nor did they demonstrate the efficacy of treatment in patients with ascites, severe cirrhosis, or large or moderate-sized varices, and they did not compare propranolol and nadolol.

Since this analysis has demonstrated the efficacy of beta-adrenergic—antagonist drug treatment for preventing both bleeding and fatal bleeding, we conclude that patients with cirrhosis and large or moderatesized varices should be treated with one of these drugs. Because there is a treatment that reduces the risk of fatal bleeding, it now seems justified to screen patients with cirrhosis for large or moderate-sized varices. Furthermore, cooperation between investigators working in the same area can make overviews unnecessary and help reduce the need for expensive new randomized clinical trials.

Address reprint requests to Dr. Poynard at the Hôpital Antoine Beclère, F-92141 Clamart, France.

*The following persons participated in the Franco—Italian Multicenter Study Group: for the Nadolol French Multicenter Study Group — Didier Lebrec, M.D., Bernard Rueff, M.D., and Jean-Pierre Benhamou. M.D. (Clichy); Thierry Poynard, M.D., Ph.D., Dominique Roulot, M.D., Jean-Claude Chaput, M.D., and Said Aitoussy, M.D. (Clamart); Jean-Pierre Capron. M.D. (Amiens); Patrick Hillon, M.D. (Dijon); and Patrick Geoffroy, M.D. (Reims); for the Propranolol French Multicenter Study Group — Jean-Pierre Pascal, M.D., Paul Calès, M.D., André Rivet. M.D., and Philippe Cabarrot, M.D. (Toulouse); André Quinton, M.D., and Hervé Lamouliatte, M.D. (Bordeaux); Jean Paccalin, M.D., and Henry Dabadie, M.D. (Bordeaux 2); Gilles Bommelear, M.D., Michel Dapoigny, M.D., and Jean-Michel Scotto, M.D. (Clermont-Ferrand); Michel Rachail, M.D,, and Jean-Paul Zarski, M.D. (Grenoble); Jean-Claude Paris, M.D., Jean Mudry, M.D., and Christian Lemba, M.D. (Lille); Bernard Pillegand, M.D.. and Denis Sautereau, M.D. (Limoges); Louis Descos, M.D., and JeanPierre Marin-Lafleche, M.D. (Lyon); André Gauthier, M.D., and Danielle Botta, M.D. (Marseille); Henri Michel, M.D., Paul Bauret, M.D., and Jean-Paul Aubin, M.D. (Montpellier 1); Franççois Blanc, M.D., and Eric Monin, M.D. (Montpellier 2); Pierre Gaucher, M.D., and Bruno Champigneulle, M.D. (Nancy); Louis Le Bodic, M.D., and Philippe Jutel, M.D. (Nantes); Jean Delmont, M.d., and Gérard Fratini, M.D. (Nice); Henri Parlier, M.D., and Philippe Le Bourgeois, M.D. (Boulogne); Brigitte Patouillard, M.D., and Gérard Patouillard, M.D. (Saint-Etienne); Raymond Colin, M.D., and Jean-Luc Trouvez, M.D. (Rouen); Jean-Pierre Vinel, M.D. (Toulouse 2); Etienne-Henry Metman, M.D., Pierre Le Marchand, M.D., and Alain Margulies, M.D.(Tours); René Bockel, M.D., and Michel Doffoel, M.D. (Strasbourg 1); and Jean-Pierre Weill, M.D., and Bernard Duclos, M.D. (Strasbourg 2); for the Italian Multicenter Project for Propranolol in Bleeding — Luigi Pagliaro, M.D., Gennaro D'Amico, M.D., Linda Pasta. M.D., M. Gabriella Filippazzo, M.D., and Salvatore Le Moli, M.D. (Palermo); Alberto Ferrari, M.D. (Modena); Giovanni De Pratis, M.D., and Federico Oberhollenzer, M.D. (Bolzano); Giorgio Marenco, M.D. (Pietra Ligure); Mariano Amuso, M.D.. Sonia Di Piazza. M.D., Giovanna Gatto, M.D., Gandolfo Giannuoli, M.D., Alberto Maringhini, M.D., Ugo Palazzo, M.D., Giovambattista Pinzello, M.D., R. Giovanna Simonetti, M.D., Maria Caltagirone, M.D., Silvio Magrin, M.D., M. Pia Marceno, M.D., Mario Traina, M.D., Miriam Turri, M.D., Maria Vinci, M.D., Roberto Virdone, M.D., Giovanni Vizzini, M.D., Mario Cottone, M.D., Elio Sciarrino, M.D., and Fabio Tine, M.D. (Palermo); Giampiero Rigo, M.D., and Alberto Merighi, M.D. (Modena); Maurizio Valentini, M.D., Harald Steiner, M.D., and Lucia Piazzi, M.D. (Bolzano); Antonio Giudici Cipriani, M.D., Gialuigi Dante, M.D., and Giorgio Menardo, M.D. (Pietra Ligure); Alberto Morabito, M.D. (Milano); for the Italian Nadolol Study Group — Gaetano Ideo, M.D., Giorgio Bellati, M.D., Edoardo Fesce, M.D., and Daniela Grimoldi, M.D. (Como).

We are indebted to Dr. M.D. Rosset (Squibb France) and Dr. Zourabichvili (Quanta Medical, France) for their help, and to B. Hautecoeur and C. Fritsch for assistance in the preparation of the manuscript.

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