Is Serum Bilirubin Concentration the Only Valid Prognostic Marker in Primary Biliary Cirrhosis?

Transcription

1 Is Serum Bilirubin Concentration the Only Valid Prognostic Marker in Primary Biliary Cirrhosis? PIOTR KRZESKI, 1 WLODZIMIERZ ZYCH, 1 EWA KRASZEWSKA, 2 BOHDAN MILEWSKI, 3 EUGENIUSZ BUTRUK, 1 AND ANDRZEJ HABIOR 1 From the many prognostic models for primary biliary cirrhosis (PBC) patients based on Cox s regression analysis, the Mayo model has gained the most popularity and was successfully validated in some centers. The aim of our study was to validate the Mayo survival model for Polish PBC patients and, in case of its inapplicability, to select prognostic variables and to create time-fixed and time-dependent survival models for the patients. We used database information on patients from 6 medical centers in Poland, fulfilling clinical, serological, and/or pathological criteria of PBC. The Mayo model was validated using data from 116 PBC patients. The time-fixed and time-dependent models were created using data on clinical and biochemical variables used in the Mayo model from 162 and 208 patients, respectively. The Mayo model validation was performed graphically and by one-sample log-rank tests after dividing the study sample into 3 groups of high, medium, and low risk. The survival analysis was performed using Cox s proportional hazards regression method on clinical and biochemical variables used in the Mayo model. Treatment with ursodeoxycholic acid (UDCA) was included in the time-dependent analysis. Validation showed that the Mayo model overestimated death risk in Polish PBC patients. Of the variables used in the Mayo model, serum bilirubin concentration appeared to be the only variable of prognostic importance. The analysis shows that serum bilirubin concentration holds most of the prognostic information for our PBC patients irrespective of prior treatment with UDCA. (HEPATOLOGY 1999;30: ) Primary biliary cirrhosis (PBC) is a rare, chronic disorder involving intrahepatic bile ducts. Its cause remains unknown Abbreviations: PBC, primary biliary cirrhosis; OLT, orthotopic liver transplantation; UDCA, ursodeoxycholic acid. From the 1 Department of Gastroenterology, Medical Center for Postgraduate Education, Oncology Center, Warsaw, Poland; 2 Department of Biostatistics, Oncology Center, Warsaw, Poland; and 3 Department of Gastroenterology, National Food and Nutrition Institute, Warsaw, Poland. Received February 16, 1999; accepted July 20, Supported by grants KBN 4PO 5C from the Polish State Committee for Scientific Research and CMKP /97 from the Medical Center for Postgraduate Education. Parts of this article were adapted from Krzeski P, Habior A, Zych W, Kraszewska E, Milewski B. Survival model for Polish population with primary biliary cirrhosis (in Polish). Gastroenterol Pol 1998;5: with permission from the Publisher and the authors. Address reprint requests to: Piotr Krzeski, M.D., Department of Gastroenterology, Medical Center for Postgraduate Education, Oncology Center, Roentgena 5, Warsaw, Poland. AHAB@coi.waw.pl; fax: (48) Copyright 1999 by the American Association for the Study of Liver Diseases /99/ $3.00/0 865 and the only effective treatment in its advanced stage is orthotopic liver transplantation (OLT). Years of relatively symptom-free survival may be expected between the time of diagnosis and the time that occurrence of complications leading to liver transplantation supervene. Precise timing of liver transplantation is therefore crucial to fulfill the National Institutes of Health criteria of no opportunity for spontaneous stabilization and a fair chance of the procedure success. 1 Prognostic models based on Cox s regression give an estimation of survival probability and have served in PBC to help in OLT timing. 2-5 So far, the survival model for PBC patients developed in the Mayo Clinic has gained the greatest popularity. It was developed on relatively numerous groups of PBC patients, and it comprised easily obtainable variables of age, serum bilirubin and albumin concentration, prothrombin time, and presence of edema at the moment of disease diagnosis. 6 The Mayo model was cross-validated on several independent groups of patients in different American and European centers The time-dependent extension of the original Mayo model can be used to predict survival at any moment of follow-up for limited time periods. 11 According to preliminary reports, the estimated prevalence of PBC in Poland is probably one of the lowest in the world. 12 However, PBC constitutes one of the major indications for OLT in the recently established national liver transplantation program. The aim of our study was to establish a tool for helping the clinician decide the moment for OLT in Polish PBC patients. Because our preliminary analysis showed that the Mayo model could inadequately estimate their survival, 13 initially we validated the Mayo model on a representative group of Polish PBC patients. Our next step was to find important prognostic variables for the patients at the time of disease diagnosis and incorporate them into our own survival model. Finally, we developed a time-dependent extension of the model in which the prognostic variables are allowed to vary over time. It is therefore more precise and can be formally used for making survival estimation based on follow-up data as opposed to the time-fixed model. PATIENTS AND METHODS Our database contains 232 patients (215 women and 17 men) who fulfill clinical, laboratory, pathological, and serological criteria of PBC, diagnosed from 1972 through Of the 232 patients, 153 were from our Warsaw centers. The rest of the patients originated from 4 other tertiary referral centers in Poland. The mean follow-up period was 3.8 years, ranging from 0 to 22 years from the moment of PBC diagnosis to death or censoring. At the time of analysis 85 patients died (death of any cause was considered failure for the survival analysis purposes), 103 were alive, and 24 were lost to follow-up. Nineteen patients were only seen once at the time of

2 866 KRZESKI ET AL. HEPATOLOGY October 1999 diagnosis (follow-up time 0 years). These patients were not included in the analysis. OLT was performed in 1 patient and was treated as failure in survival analysis. Cross-validation of the Mayo Model. Data from 116 patients with available values of the Mayo model variables at the time of PBC diagnosis were used for cross-validation. Their detailed characteristics are shown in Table 1. There were missing values because of the retrospective nature of data collection. At the moment of PBC diagnosis, there was no information regarding the value of bilirubin concentration in 20 cases, albumin concentration in 36, and prothrombin time in 97. The missing values were independent of the end-point, i.e., patient s death. Cross-validation of the Mayo model was performed using a one-sample log-rank test. 14 Patients eligible for cross-validation were divided according to Mayo model prognostic index R into 3 groups with an equal number of deaths in each group. The model prognostic index R is the weighted sum of the prognostic variables, selected in Cox s regression analysis, weights being the regression coefficients. Group I of low risk included patients whose R value was less than Group II of medium risk included patients whose R value was between 6.33 and Group III of high risk included patients whose R value was higher than The one-sample log-rank test was used to compare the observed number of deaths in each group with the number of deaths predicted by the Mayo model. The predicted survival curve for each group, i.e., the average of the predicted survival functions for each patient in that group, was graphically compared with the observed survival in each group, i.e., Kaplan-Meier survival curves. 15 Time-Fixed Model. Our own survival model was created based on data obtained at the moment of diagnosis from 162 PBC patients. We decided to limit variables selection to those used in the Mayo model with the exception of prothrombin time in seconds which was substituted for the prothrombin index, which is more generally used in Poland. Follow-up time was restricted to 7 years. Patients were randomly divided into 2 equal groups of 81 patients (split-sample technique). There were 26 deaths during the 7 years of follow-up in each group. Characteristics of the groups are shown in Table 2. The survival model was created using data from the first group of 81 patients. We used the Cox proportional hazards regression method for creation of our own prognostic model. 16 The estimation procedure maximized the log-likelihood of the regression model via Newton-Raphson iterations. Using backward selection, we chose significant variables at levels of 0.05 (Wald test 17 ). The proportional hazards assumption was checked using significance testing of interaction: variable multiplied by the time function. 18 We also performed graphical testing of the proportional hazards assumption. Testing goodness of fit of our model was performed graphically using Schoenfeld residuals against follow-up time and martingale residuals against selected independent variables and linear index: variable multiplied by its regression coefficient. 19,20 We used standard transformations of the selected variables (square root, second power, natural logarithm) for fitting purposes. The model was validated on the independent, second group of 81 patients, who were divided according to our model prognostic index R value into 3 groups with equal numbers of deaths in each group. Group I of low risk included patients whose R value was less than Group II of medium risk included patients with R value between 1.65 and Group III of high risk included patients whose R value was higher TABLE 1. Characteristics of 116 Patients Included in the Cross-validation of the Mayo Model Variable Median (mean) Age (years) 53.8 (50) Serum bilirubin concentration (mg/dl) 2.3 (4.22) Serum albumin concentration (g/dl) 3.74 (3.68) Prothrombin time (s) 15.5 (16.44) Presence of edema (percent of patients) 18 Mean value of prognostic index R (Mayo model) 6.09 TABLE 2. Characteristics of Two Groups of Patients Used for Creation of Our Model and Its Validation Variable Model Creation Group (n 81) Median (Mean) Model Validation Group (n 81) Median (Mean) Age (years) 49.6 (50.75) 53.8 (53.0) Serum bilirubin concentration (mg/dl) 1.7 (3.8) 3.0 (5.0) Serum albumin concentration (g/dl) 3.78 (3.74) 3.7 (3.63) Prothrombin index (%) 98 (96.4) 100 (95.7) Presence of edema (percent of patients) than The one-sample log-rank test was used to compare the observed number of deaths in each group with the number of deaths predicted by our model. Predicted survival was graphically compared with the observed survival in each group using Kaplan-Meier survival curves. The test and the validation groups were then combined to obtain the final, more accurate prognostic model. The 95% confidence intervals for survival curves predicted by our model were obtained according to the method described by Lin et al. 21 for 3 values of our prognostic index (R 0.322; 1.608; 2.798) that corresponded to mean values of 3 risk groups of all 162 patients included in the analysis. Time-Dependent Model. Data from 208 patients were used for the creation of our time-dependent model. The data consisted of the variables selected in the time-fixed analysis. In the time-dependent analysis, we also decided to include variables related to treatment with ursodeoxycholic acid (UDCA), which was repeatedly reported to influence survival and serum bilirubin concentration. 22,23 The variables related to UDCA treatment included categorical variables: UDCA treatment during at least 6 months preceding data collection, serum bilirubin concentration high or low (using median for cut-off), and multiplicative interaction of the two. The data were collected during whole follow-up period from the moment of diagnosis in yearly intervals ( 3 months) up to the patient s death or censoring. Because of the small number of patients followed and missing values of variables under consideration, all observations were censored after 6 years of follow-up. The patients were randomly divided into 2 groups with equal number of deaths in each group. The test group, which served for the model creation included 103 patients with 43 deaths, 32 of which took place during the first 6 years of follow-up. The validation group included 105 patients with 43 deaths, 28 of which took place during the first 6 years of follow-up. A total of 48 patients in each group received UDCA treatment for a median of 2.3 and 1.9 years in the test and validation group, respectively. The patients who were treated with UDCA were followed-up for a median of 3 and 2.45 years in the test and validation group, respectively. The patients who were not treated with UDCA were followed-up for a median of 3.15 and 4 years in the test and validation group, respectively. A total of 12 of 32 and 10 of 28 deaths in test and validation group, respectively, were not included in the analysis because of missing data on variable values less than 1 year before the event. We used Cox s regression model for time-dependent variables. 24,25 The values of selected variables were updated every year. We assumed that the values did not change during the period between the observations, i.e., during 1 year. Testing goodness of fit of the time-dependent model was performed graphically drawing martingale residuals against ordered failure times and predicted and observed 1-year survival probability against prognostic index R values (all observations were divided into 10 groups of increasing R value; average 1-year observed survival was compared with the predicted by the model probability of surviving the next 1 year at the beginning of the interval). We compared the number of deaths observed and predicted by the model during 6 years of

3 HEPATOLOGY Vol. 30, No. 4, 1999 KRZESKI ET AL. 867 follow-up in 3 groups of patients divided according to serum bilirubin value using one-sample log-rank test. The time-dependent model was validated using the second independent group of patients. Similarly as in testing goodness of fit of the model, we compared graphically predicted and observed 1-year survival probability against the prognostic index R value. We compared the number of deaths observed and predicted by the model during 6 years of follow-up in 3 groups of patients divided according to serum bilirubin values using one-sample log-rank test. For this purpose we used arbitrarily the 60th (3 mg/dl) and the 90th (14.4 mg/dl) quartile of serum bilirubin concentration, although another quintile selection could also be used without affecting the results of the analysis. Analysis was performed using STATA (Computing Resource Center, Santa Monica, CA) and StatSoft Statistica (Statsoft, Tulsa, OK) software. RESULTS Cross-validation of the Mayo Model. Of the 116 patients included in the analysis, 42 died over the 7 years of follow-up. The number of deaths predicted by the Mayo model and observed in the 3 groups of patients were and 14 (P.026) for the low risk group, and 14 (P.001) for the medium risk group, and and 14 (P.001) for the high risk group, respectively (Fig. 1). Results indicate that the Mayo model does not fit the Polish population of PBC patients. Time-Fixed Model. Our own model was created on data from the test group of 81 patients. Proportional hazard assumptions were fulfilled for all 5 variables that were the subject of analysis, i.e., serum bilirubin and albumin concentration, prothrombin index, age, and presence of edema at the time of diagnosis. Using backward selection procedure and standard transformations of the variables, we found that serum bilirubin concentration was the only prognostic marker statistically significant at the assumed level. A survival model based on the natural logarithm of serum bilirubin concentration provided the best fit to our test group. The new model was cross-validated on the second, independent group of 81 patients. The number of deaths predicted by the model and observed in the 3 groups of patients were and 9 (P.13) for the low risk group, and 9 (P.32) for the medium risk group, and and 8 (P FIG. 2. Comparison of observed survival curves (Kaplan-Meier) and predicted survival by our model in 3 groups of patients of high (R 2.87), medium (2.87 R 1.65), and low risk (R 1.65). Reprinted with permission ) for the high risk group, respectively (Fig. 2). Because of the good fit to the independent group, both groups were combined to increase the accuracy of the model. The final model formula obtained on 162 patients is exp1.11[ln(bilirubin in mg/dl)] S(t, X) S 0 (t) where S(t,X) stands for survival probability at time t of a patient with values of prognostic variables X (i.e., serum bilirubin concentration in our model) and S 0 (t) is the baseline survival function that is estimated for each moment up to 7 years from the time of diagnosis (Fig. 3). Time-Dependent Model. Analysis revealed the best fit of the model based on serum bilirubin concentration ( 1.348, SE 0.225, P.001). The addition of variables related to UDCA treatment did not improve fit of the model significantly. The cumulative baseline hazard for the timedependent model over 6 years of observation changed approximately linearly following the formula: H 0 (t) t(years) Cross-validation of the time-dependent model on the independent data set showed its generalizability (Fig. 4). The model well predicted survival during 6 years of follow-up in patients FIG. 1. Comparison of observed survival curves (Kaplan-Meier) and predicted survival by the Mayo model in 3 groups of patients of high (R 7.59), medium (7.59 R 6.33), and low risk (R 6.33). Reprinted with permission. 30 FIG. 3. Baseline survival function S 0 (t) for our prognostic model.

4 868 KRZESKI ET AL. HEPATOLOGY October 1999 FIG. 4. Cross-validation of the time-dependent model on the independent data set (average 1-year observed survival and predicted by the model probability of surviving next year related to the prognostic index R value at the beginning of the interval). of low, medium, and high risks (divided according to serum bilirubin concentration): observed and predicted deaths were respectively 0 and 1.64 (P.2069), 6 and 8.31 (P.4263), and 12 and (P.767). Our time-dependent model has the following formula: exp51.348[ln(bilirubin in mg/dl) 0.157]6 S(t, X) S 0 (t) where S 0 (t) stands for baseline survival and has the value of for 6 months and for 1 year. DISCUSSION In several previous analyses the Mayo model established its generalizability to independent PBC populations. However, to our knowledge, it was never applied to patients from Central or Eastern Europe. Cross-validation results of the Mayo model for Polish PBC patients clearly show that the observed survival is significantly higher than the predicted values. Although the Mayo model seems to well stratify the patients according to risk of death, it cannot be used for survival estimation and selection of timing for liver transplantation in these patients. The characteristics of Polish PBC patients and the Mayo Clinic patients whose data served for the model creation suggest that the diagnosis of PBC in Poland is made in a more advanced disease stage than in the United States. However, the Mayo model overestimated the risk of death in our patients. A possible explanation is that PBC in Poland is diagnosed during a symptomatic exacerbation of the disease. It is implied by the low prevalence of symptom-free patients with the PBC diagnosis in Poland. 12 Another reason for the differences between Polish and Mayo Clinic PBC patients may be the fact that the patient data were taken at different time points. In the Mayo model it was the moment for randomization to a clinical trial and in Poland it was the time of the disease diagnosis. One of the predictive variables in the Mayo Clinic model is prothrombin time in seconds. The results of this test depend on the type of thromboplastin used and laboratory reference range. 26 To check the hypothesis that a survival model with the same variables as those used in the Mayo Clinic model could work for the Polish patients, we performed an analysis using the Mayo model variables except that prothrombin time was substituted for prothrombin index (unpublished data). The substitution would help to eliminate the abovementioned differences between centers. We presumed that all variables of the Mayo model (serum and albumin concentration, edema, age, and prothrombin index instead of prothrombin time) enter the model irrespectively of their formal statistical significance. The analysis led to a paradox of negative (although statistically insignificant) regression coefficients for the edema variable. Although overall fit of the model was good, this meant that a patient with edema had a better survival probability than a patient without it. In consequence we rejected the model and created a new survival model fulfilling formal and logical assumptions of the analysis. We think that it is necessary to perform a similar analysis of any survival model that was based on different patient populations before implementing it in clinical practice. Incorporation of UDCA-related variables into the timedependent analysis did not influence the predicted 1-year survival. As recently shown by Bonnand et al., 27 UDCA treatment effect on survival may be explained by serum bilirubin concentration and, therefore, it is insignificant by itself. Our analysis based on regression survival models also shows that serum bilirubin concentration holds most prognostic information irrespective of prior treatment with UDCA. Another possible interpretation is that longer UDCA treatment is necessary for the drug to take effect. Our model is simple and easy to use in everyday clinical practice. It is noteworthy that in 1979, before the publications of any survival models for PBC patients based on Cox s regression, Shapiro et al. 28 on the basis of clinical observations concluded that serum bilirubin was the most important predictive variable. Our analysis confirms his findings for time-dependent as well as for time-fixed data sets. Serum bilirubin concentration seems to be so strongly associated with survival of PBC patients that it overshadows the influence of other variables. Its importance is confirmed by the fact that it is repeatedly included in all prognostic models. Although such a historical step back may appear an oversimplification, our analysis based on a sufficient group of patients and correct statistical tools does allow this conclusion. It is supported by Christensen 29 who postulated simplification and uniformity of existing models to make them more thoroughly applicable in practice. Acknowledgment: The authors thank Prof. Jan Dzieniszewski from the Food and Nutrition Institute in Warsaw, Prof. Zbigniew Gonciarz from Silesian Medical School in Sosnowiec, Prof. Jozef Bogdal from Jagiellonian University in Cracow, Prof. Krzysztof Marlicz from Pomeranian Medical School in Szczecin, Dr. Jan Lypik from Zeromski Hospital in Cracow, and Dr. Hanna Wasyluk from the Medical Center for Postgraduate Education in Warsaw for providing data on their PBC patients. REFERENCES 1. Benhamou J-P. Indication for liver transplantation in primary biliary cirrhosis. HEPATOLOGY 1994;20(Suppl):11S-13S. 2. Roll J, Boyer JL, Barry D, Klatskin G. The prognostic importance of clinical and histologic features in asymptomatic and symptomatic primary biliary cirrhosis. N Engl J Med 1983;308: Christensen E, Neuberger J, Crowe J, Altman DG, Popper H, Portmann B, Doniach D, et al. Beneficial effects of azathioprine and prediction of prognosis in primary biliary cirrhosis. Gastroenterology 1985;89:

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