Drs Frangakis, Georgiades, and Geschwind respond

Letters to the Editor Re: Prognostic Accuracy of 12 Liver Staging Systems in Patients with Unresectable Hepatocellular Carcinoma Treated with Transarterial Chemoembolization From: Yun Ku Cho, MD Department of Radiology Seoul Veterans Hospital 6-2 Dunchon-dong, Gangdong-gu Seoul 134-060, Korea Editor: In the October 2006 issue of JVIR, Georgiades et al (1) reported the comparative analysis of 12 liver staging systems. The authors evaluated 12 different staging systems based on the error reduction rate in predicting survival. I agree that error reduction rate can be a good measure of the discrimination ability of the systems. I would, however, like to comment about some points made in the article. First, the monotonicity of the gradients for each staging system should have been also discussed (2). The mean survival time for a group classified as favorable with any system should be longer than the survival times noted in less favorable groups (2). Second, the 5th edition of the American Joint Committee on Cancer TNM staging manual, not the 6th edition (3), was used in the study. The 6th edition is the most recent TNM staging system and was reported to be more effective than that in the 5th edition (4). Third, in the statistical analysis, I think that there is some fault in the following equation for the estimated error reduction with various staging systems: Ês ⫽ (1 ⁄ n) 兺兺 i (tⱖ0) ⱍt ⫺ Ĝ(X )ⱍ␦Ŝ(tⱍX s,i s,i ) I think that the above-mentioned n should denote the number of stratification levels instead of the total number of patients, as was mentioned in the text. When the number of the stratification level becomes 1, the above-mentioned equation should become identical to the following equation for the estimated error reduction without the staging system, as it is: Êns ⫽ 兺 (tⱖ0) ⱍt ⫺ Ĝⱍ␦Ŝ(t) This means that the n should denote the number of stratification levels. References 1. Georgiades CS, Liapi E, Frangakis C, et al. Prognostic accuracy of 12 liver staging systems in patients with unresectable hepatocellular carcinoma treated with transarterial chemoembolization. J Vasc Interv Radiol 2006; 17:1619 –1624. 2. Ueno S, Tanabe G, Sako K, et al. Discrimination value of the new western prognostic system (CLIP score) for hepatocellular carcinoma in 662 Japanese patients. Hepatology 2001; 34:529 – 534. 3. Vauthey J, Lauwers GY, Esnaola NF, et al. Simplified staging for hepatocellular carcinoma. J Clin Oncol 2002; 20:1527–1536. DOI: 10.1016/j.jvir.2007.01.009 4. Varotti G, Ramacciato G, Ercolani G, et al. Comparison between the fifth and sixth editions of the AJCC/UICC TNM staging systems for hepatocellular carcinoma: multicentric study on 393 cirrhotic resected patients. Eur J Surg Oncol 2005; 31:760 –767. Drs Frangakis, Georgiades, and Geschwind respond: We agree that monotonicity is another valid way to rank the staging systems. We have briefly looked into it, and our statistician’s preliminary comment is as follows: “With only a few exceptions, for most staging systems and for most levels of each system, the median survival decreases monotonically with increasing levels of the system.” This further supports our conclusions. Indeed there is a 6th edition, “newer” TNM classification system. This, however, is used only for patients with resectable hepatocellular carcinoma (HCC). In addition, the article cited by the authors (1) failed to conclude that the 6th edition (or the 5th for that matter) was an important prognostic factor. On the contrary, it concluded that even for patients with resectable HCC the Child-Pugh remains the most important prognostic factor, which supports our conclusions. To quote the article referenced by the author: “Univariate and multivariate analysis of this study showed that the number of nodules (single vs multiple) and the child classification (A vs B–C) were the two most important prognostic factors affecting both overall and disease-free survival rates, confirming that the prognosis of patients suffering from HCC or cirrhosis is strongly influenced either by the tumour characteristics or by the status of the underlying hepatic disease.” What does the “n” in statistical formulas represent? As designated in our article, n is the number of patients, not the number of stratification levels as suggested above. For a detailed explanation, please read our statistician’s comments: There is one issue of definition and two issues of results that are relevant to the reader’s comment, and it is useful to address each of them in order. First, if, for a cohort of patients {i}, Ti is the survival of patient i, and G(Xs,i) a function of that patient’s staging level Xs,i based on system s, then it is a definition that “the average error of predicting Ti based on G(Xs,i),” ⱍ ⱍ Es ⫽ Average Ti ⫺ G(Xs,i) , is the average over patients i of the errors |Ti ⫺ G(Xs,i)|. Therefore, with data from a total of n patients, this average is estimated as the average over patientsover patientsover patientsover patients i as Ês ⫽ (1 ⁄ n) 兺 i⫽1 1, . . . , n 兺 (tⱖ0) ⱍt ⫺ Ĝ(X )ⱍ s,i ⫻ ␦Ŝ(tⱍXs,i), (1) as we stated in the article. Second, if Xs,i has only one value (ie, if there is only one DOI: 10.1016/j.jvir.2006.12.738 455 456 • March 2007 Letters to the Editor stratum), which is the setting that the reader also mentioned, then all Xs,i are the same across i; Ĝ(Xs,i) reduces by definition to Ĝ, the median over all patients; ␦Ŝ(t|Xs,i) reduces by definition to ␦Ŝ(t), the decrements of the Kaplan-Meier curve over all patients and, hence, the outer summation over patients i in Equation (1) sums the same quantity, ⌺(t ⱖ 0)|t ⫺ Ĝ|␦Ŝ(t), n times, giving (1 ⁄ n) * n * 兺 (tⱖ0) ⱍt ⫺ Ĝⱍ␦Ŝ(t) ⫽ 兺 ⱍt ⫺ Ĝⱍ␦Ŝ(t), (tⱖ0) (2) which is the formula that we gave in the article for using no strata information. Thus, there is no contradiction with the special case. Third, suppose now we want to correctly re-express Equation (1) with a summation over strata, say k ⫽ 1, . . . , K. Specifically, if the stratum k has nk patients, then Xs,i is the same for those patients; thus, Equation (1) reduces to Ês ⫽ (1 ⁄ n) ⫽ 兺 兺 k⫽1. . .K 兵*n * 兺 ⱍt ⫺ Ĝ(X )ⱍ␦Ŝ(tⱍX )其 兵(n ⁄ n) * 兺 ⱍt ⫺ Ĝ(X )ⱍ␦Ŝ(tⱍX )其 , (3) k⫽1. . .K k k s,k (tⱖ0) (tⱖ0) s,k s,k s,k where Ĝ(Xs,k) now denotes the median of survival in stratum k and ␦Ŝ(t|Xs,k) the decrements of the Kaplan-Meier is stratum k. From this, we see that the correct re-expression of the average error as a summation over strata, which is Equation (3), cannot generally be obtained by using the reader’s suggestion—to simply change the summation in Equation (2) to be over strata as opposed to over patients. This is because the correct expression (Eq [3]) weighs the strata by (nk/n). When these weights are not the same (ie, when the strata do not all have the same number of patients), then omitting the weights does not give the correct result (Eq [3]). Constantine Frangakis, PhD Christos S. Georgiades, MD, PhD Jean-Francois Geschwind, MD Division of Vascular and Interventional Radiology Johns Hopkins University 600 N Wolfe St Blalock 545 Baltimore, MD 21287 Re: Prognostic Accuracy of 12 Liver Staging Systems in Patients with Unresectable Hepatocellular Carcinoma Treated with Transarterial Chemoembolization JVIR chemoembolization (TACE) of hepatocellular carcinoma (HCC). In the authors’ cohort of 172 consecutive patients, the use of the Child-Pugh nominal scoring system was associated with a smaller deviation from predicted survival than the Model for End-Stage Liver Disease (MELD), among other systems, leading the authors to conclude that the Child-Pugh nominal staging system should be “adopted as the standard for HCC staging in [patients undergoing TACE].” As the authors point out, there is inherent difficulty in current scoring systems that use only biochemical variables because other disease states unrelated to the liver disease may produce elevation of the variables used in the score. What the authors may have overlooked is that their assessment of Child-Pugh scores in individual patients may be highly reproducible at their institution but that does not mean the Child-Pugh scoring system is highly reproducible in the general medical community. The Child-Pugh system is flawed in that two of its five variables—the presence and severity of ascites and encephalopathy—are subjective assessments. Moreover, the level of albumin can be iatrogenically modified with the infusion of albumin. It was these limitations that produced great difficulty in triaging livers for transplantation because the potential recipient’s ChildPugh score might differ as much as four points, depending on the physician performing the scoring. For this reason, the United Network for Organ Sharing abandoned their use of the Child-Pugh system in February 2002 in favor of MELD. Because it is calculated with only biochemical parameters, MELD is reproducible between examiners (2). It is also less susceptible to the “ceiling effect” that occurs with the Child-Pugh system. Although MELD is far from ideal, advocating the use of the Child-Pugh nominal system over MELD for predicting survival after TACE would seem to be a step in the wrong direction. The authors may want to consider taking advantage of their large-volume TACE practice to develop an objective scoring system that can help predict survival outcomes better than MELD. References 1. Georgiades CS, Liapi E, Frangakis C, et al. Prognostic accuracy of 12 liver staging systems in patients with unresectable hepatocellular carcinoma treated with transarterial chemoembolization. J Vasc Interv Radiol 2006; 17:1619 –1624. 2. Wiesner R, Edwards E, Freeman R, et al. Model for end-stage liver disease (MELD) and allocation of donor livers. Gastroenterology 2003; 124:91–96. Editor: We read with interest the article by Georgiades et al (1) concerning the use of various scoring systems of hepatic disease to predict the survival of patients after transarterial Drs Georgiades and Geschwind respond: One of the reasons we embarked on the time- and effortconsuming task of ranking 12 liver staging systems is the fact that the literature is replete with scientifically unsubstantiated statements regarding the accuracy of one or the other system. The claim that “The Child-Pugh system is flawed in that two of its variables—the presence and severity of ascites and encephalopathy—are subjective assessments” is yet one more of these statements. On the contrary, performance status, encephalopathy, and ascites (despite being subjective in their grading) are very strong predictors DOI: 10.1016/j.jvir.2007.01.009 DOI: 10.1016/j.jvir.2006.12.737 From: Timothy W. I. Clark, MD New York University School of Medicine 530 First Avenue New York, NY 10016