An explorative data-analysis to support the choice between hepatic resection and radiofrequency ablation in the treatment of hepatocellular carcinoma

Digestive and Liver Disease 46 (2014) 257–263

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Digestive and Liver Disease journal homepage: www.elsevier.com/locate/dld

Liver, Pancreas and Biliary Tract

An explorative data-analysis to support the choice between hepatic resection and radiofrequency ablation in the treatment of hepatocellular carcinoma Alessandro Cucchetti ∗ , Fabio Piscaglia, Matteo Cescon, Carla Serra, Antonio Colecchia, Lorenzo Maroni, Laura Venerandi, Giorgio Ercolani, Antonio Daniele Pinna Department of Medical and Surgical Sciences, S.Orsola – Malpighi Hospital, Alma Mater Studiorum – University of Bologna, Bologna, Italy

a r t i c l e

i n f o

Article history: Received 28 May 2013 Accepted 27 October 2013 Available online 24 November 2013 Keywords: Hepatocellular carcinoma Liver function Monte Carlo simulation Radiofrequency ablation Survival Surgical therapy

a b s t r a c t Background: Whether to prefer hepatic resection or radiofrequency ablation as first line therapy for hepatocellular carcinoma is a matter of debate. Aims: To compare outcomes of resection and ablation, in the treatment of early hepatocellular carcinoma, through a decision-making analysis. Methods: Data of 388 cirrhotic patients undergoing resection and of 207 undergoing radiofrequency ablation were reviewed. Two distinct regression models were devised and used to perform sensitivity and probabilistic analyses, to overcome biases of covariate distributions. Results: Actuarial survival curves showed no difference between resection and ablation (P = 0.270) despite the fact that ablated patients were older, with worse liver function and smaller, unifocal tumours (P < 0.05), suggesting a complex, non-linear relationship between clinical, tumoral variables and treatments. Sensitivity and probabilistic analyses suggested that the superiority of resection over ablation decreased at higher Model for-End stage Liver Disease scores, and that ablation provided better results for smaller tumours and higher Model for-End stage Liver Disease scores. In patients with 2–3 tumours up to 3 cm, the two treatments produced opposite comparative results in relation to the Model for-End stage Liver Disease score. Conclusions: The superiority, or the equivalence, of resection and ablation depends on the non-linear relationship existing between treatment, tumour number, size and degree of liver dysfunction. © 2013 Editrice Gastroenterologica Italiana S.r.l. Published by Elsevier Ltd. All rights reserved.

1. Introduction Hepatocellular carcinoma (HCC) is the most frequent primary malignancy of the liver and is closely linked to chronic liver disease [1]. Surveillance programmes of subjects at risk have been developed in many areas of the world; consequently, an increased proportion of HCCs could be diagnosed at early stages [2,3]. In these cases, liver transplantation is theoretically the best treatment, but the scarcity of donors limits this treatment. Currently, hepatic resection (HR) and radiofrequency ablation (RFA) are the first line therapies considered potentially curative in the treatment of HCC and are offered in cases in which transplantation is not an option or for candidates on the waiting-list. In the last

∗ Corresponding author at: Policlinico Sant’Orsola-Malpighi, University of Bologna, Via Massarenti 9, 40138 Bologna, Italy. Tel.: +39 051 6363721; fax: +39 051 304902. E-mail address: [email protected] (A. Cucchetti).

decade, a number of retrospective and randomized controlled trials (RCTs) which directly compared these two treatments have been published. Available RCTs have not resolved the doubts regarding the superiority of one treatment over the other, probably due to the inclusion criteria adopted [4–6]. Observational studies have not helped to clarify this topic since they have clearly shown that the patients undergoing HR or RFA were significantly different as regards the clinical and tumoral characteristics capable of affecting prognosis [7–16]; if all these biases are not adequately handled, the results can be confounding. The aim of the present study was to develop a decision-making analytic model, derived from a large series of patients treated in a tertiary referral hospital, which included those clinical and tumoral features which are the main determinants of treatment assignment and prognosis. A stratification of the analysis, for tumour stage and degree of liver dysfunction, was applied in a sensitivity approach and in a probabilistic simulation, aimed at assessing effectiveness uncertainty of these two competing strategies.

1590-8658/$36.00 © 2013 Editrice Gastroenterologica Italiana S.r.l. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.dld.2013.10.015

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2. Methods The study was planned to develop two distinct proportional hazard prognostic models: one for HR patients and one for RFA patients, and to use results obtained to run sensitivity and probabilistic sensitivity analyses using a decision-tree model (TreeAge Software Inc., Williamstown, MA, USA). This approach allows comparing the two treatment populations, even if the baseline clinical and tumoral characteristics are different inasmuch as the comparison is not directly carried out on observed survival, but on expected survival calculated using corresponding beta-coefficients, and baseline hazard functions. Subsequently, a sensitivity analysis was carried out, in which one prognostic variable was kept fixed, and expected survivals for resection and ablation were compared at different variations of the remaining prognostic variables. A probabilistic analysis aimed at assessing the uncertainty of the model was finally carried out. Additional details of the statistical analyses are reported in the specific section. 2.1. Patient population Between January 1997 and November 2011, 388 cirrhotic patients underwent HR for HCC at a tertiary referral Hospital; the policies of our centre regarding indications for hepatic resection have already been published [17,18]. Details regarding study population selection and surgical approach can be found in Appendix A. Between December 2001 and November 2011, 207 cirrhotic patients underwent RFA for HCC at three clinical units of the same tertiary referral hospital. The diagnosis of HCC was histologically confirmed, before RFA, in 28 cases via percutaneous or open biopsy; in the remaining patients, it was based on guidelines for the noninvasive assessment of HCC which had been released during the study inclusion period [19,20]. Details regarding policy of our Institution and ablation technique can be found in Appendix A. Clinical and tumour characteristics of surgical and ablated patients are reported in Table 1. 2.2. Follow-up Following discharge, all patients were observed periodically at follow-up to exclude a possible recurrence of the HCC; biochemical liver function tests, serum alpha-fetoprotein level measurement, and US or CT/MRI were performed 3 and 6 months after discharge and then according to a semi-annual surveillance programme. Recurrent lesions were managed aggressively by a multimodal approach, which included re-resection, TACE, percutaneous RFA and PEI. For selected patients with transplantable recurrences, salvage liver transplantation was also adopted. The treatment was decided by the pattern of recurrence, liver functional reserve, and the general condition of the patient at the time of the recurrence. Since the end of 2008, Sorafenib (Nexavar® ; Bayer, Leverkusen, Germany) therapy has also been adopted, either alone or in combination with percutaneous approaches or TACE for treatment of recurrences [21,22]. Follow-up data were collected until 31st December 2012. Informed consent was obtained from each patient included in the study and the study protocol conforms to the ethical guidelines of the 1975 Declaration of Helsinki. 2.3. Statistical analysis Categorical variables were reported as number of cases and prevalence, and differences between the subgroups were compared using the Fisher exact test. Continuous variables were investigated for their normal distribution (Kolmogorov–Sminov test) and reported as mean and standard deviation or medians and interquartile ranges (25th and 75th percentiles), as appropriate. Differences

between subgroups were investigated using Mann–Whitney test. All analyses were two-tailed. Effect size was also calculated for each covariate comparison [23]. Overall survival was the primary end point of the study and was computed from the day of HCC treatment (surgery or ablation) until the most recent follow-up or until patient death. Recurrence-free survival was computed from the day of surgery until the most recent follow-up visit or until clinical evidence of tumour recurrence. For RFA patients, the presence of residual tumour at 1 month after the first ablation procedure was not considered as recurrence, which was conversely defined, for these patients, as the occurrence of a new lesion distant from the previously treated nodule, regardless of timing, or tumour relapse of the treated nodule, 3 months after completion of treatment session. Ablated patients who did not achieve a complete response after 3 months were considered as having recurrence at the date of the last imaging technique. Transplanted patients were censored the day prior to transplantation. Two distinct proportional hazard models were developed having patient survival as an outcome measure: one for the 388 surgical patients and one for the 207 RFA patients. Tumour size, number (single versus multiple nodules) and Model for End-stage Liver Disease (MELD) score were selected for the multivariate regression analyses [24–26]. These variables were selected because the decision to perform surgery or ablation is mainly a function of tumour burden and the degree of liver dysfunction. Once beta-coefficients and baseline cumulative hazard were obtained for each proportional hazard model, yearly survival estimation was calculated using the following equation: S0(year) ˆ (EXP(PI)), where: S0(year) = −EXP(baseline cumulative hazard for each year) and PI = betaMELD × MELD(unit) + betamultiple × (1 = two or three nodules; 0 = single nodule) + betasize × tumour size(cm). Betacoefficients together with their 95% confidence intervals were entered in the subsequent sensitivity and probabilistic models up to the 14th decimal place. Proportional hazard assumption for each model was assessed by Schonfeld residuals analysis (P > 0.05 in all cases) and non-linearity exclusion verified by Martingale residuals. Yearly survival estimations obtained from Cox regressions were converted into annual mortality using the DEALE method [27]. Mortality excess due to different age and gender proportions in the two groups were taken into account by subtracting the relative mortalities derived from the Italian National Institute of Statistics (ISTAT) [28]. A sensitivity analysis was carried out to obtain information regarding the treatment preferred in relationship to clinical and tumoral characteristics. In particular, in this analysis, the covariates MELD and number of nodules were maintained fixed at determined values (i.e. MELD = 7–8 and single nodules) while tumour diameter was varied between 1 and 5 cm. Both beta-coefficients and baseline cumulative hazard values, for all the three clinical variables, were varied within their 95% confidence intervals, assuming a triangular distribution. Sensitivity analysis included 388 patients for resection arm and 207 for ablation arm. Uncertainty of the model was further explored by running probabilistic analyses. In particular, different clinical scenarios were simulated according to international guidelines recommendations [19,20]. For each clinical subgroup, tumour diameter and MELD score were assumed having a uniform distribution, while beta-coefficients and baseline cumulative hazards were varied within their 95% confidence intervals, assuming a triangular distribution. For each subgroup, 1000 patients for each treatment arm were assumed. Results of probabilistic analyses were measured with both effect-size and number needed to treat (NNT) [29,30]. The NNT can be thought of as the number of patients who need to be treated in order for one to benefit. In theory, the higher the NNT, the less superior is one treatment against the comparative treatment, because more individuals need to receive the specific treatment to see a benefit in one. A significance level of 0.05 was

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Table 1 Baseline clinical and tumoral characteristics of patients with HCC undergoing hepatic resection (HR) or radiofrequency ablation (RFA). Variable

HR (n = 388)

RFA (n = 207)

P

Effect size

Age (years) Male gender HBsAg+ Anti-HCV+ Serum total protein (g/dL) Serum albumin (g/dL) Total bilirubin (mg/dL) PLT count (×103 /mmc) PLT count ≤100 × 103 /mmc INR Child–Pugh class A MELD score Esophageal varices Single tumoura Largest tumour size (cm)a BCLC stage 0 A B Surgical procedure Wedge Segmentectomy Bisegmentectomy Major hepatectomy Patient survival 1-year (%) (95%C.I.) 3-year (%) (95%C.I.) 5-year (%) (95%C.I.) Recurrence-free survival 1-year (%) (95%C.I.) 3-year (%) (95%C.I.) 5-year (%) (95%C.I.)

65 (58–71) 302 (77.8%) 82 (21.1%) 273 (70.4%) 7.6 (7.2–8.0) 3.9 (3.5–4.1) 0.81 (0.62–1.20) 128 (94–175) 117 (30.2%) 1.15 (1.08–1.22) 374 (96.4%) 8 (7–9) 102 (26.3%) 309 (79.6%) 3.5 (2.5–4.7)

68 (60–75) 142 (68.6%) 33 (15.9%) 136 (65.7%) 7.4 (6.9–7.9) 3.8 (3.4–4.1) 1.12 (0.77–1.75) 104 (73–146) 99 (47.8%) 1.21 (1.13–1.33) 163 (78.7%) 9 (8–12) 123 (59.4%) 184 (88.9%) 2.4 (2.0–3.0)

−0.315 0.262 0.191 0.118 0.339 0.194 −0.614 0.367 −0.415 −0.692 1.089 −0.802 −0.779 −0.395 0.783

27 (7.0%) 257 (66.2%) 104 (26.8%)

39 (18.8%) 162 (78.3%) 6 (2.9%)

0.001 0.017 0.156 0.265 0.001 0.051 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.004 0.001 0.001 – – – – – – – – 0.270 – – – 0.001 – – –

213 (54.9%) 104 (26.8%) 45 (11.6%) 26 (6.7%)

– – – –

88.1 (84.3–90.9) 69.1 (63.5–73.9) 57.4 (50.8–63.4)

92.5 (89.3–94.7) 66.2 (57.5–73.6) 43.2 (32.1–53.8)

74.7 (69.8–80.7) 43.8 (37.8–49.6) 31.0 (24.7–37.4)

56.3 (48.8–63.0) 24.7 (17.9–32.0) 15.4 (9.2–22.9)

−0.542 −0.334 1.382 – – – – −0.261 0.073 0.321 0.454 0.479 0.494

Continuous variables are reported as medians and inter-quartile ranges (25–75th percentiles). For continuous variables, the effect size was measured after Log10 transformation: <|0.1| = very small differences; |0.1|–|0.3| = small differences; |0.3|–|0.5| = moderate differences and >|0.5| = considerable differences. Abbreviations: MELD, Model for End-stage Liver Disease; BCLC, Barcelona Clinic Liver Cancer; PLT, platelet; INR, International normalized ratio. a For surgical patients, these features were radiological and not histological characteristics.

used in all analyses. The statistical analysis was carried out using R-project (cox.zph function; R version 2.13.0; Copyright (C) 2011 The R Foundation for Statistical Computing) and SPSS 10.0 software (SPSS, Chicago, IL, USA).

3. Results The baseline characteristics, comparative analysis and outcomes of the surgical and the RFA patients are reported in Table 1. The two groups were representative of the general clinical and tumoral characteristics which regard the use of one treatment versus the other; in particular, RFA patients were significantly older, with more advanced liver dysfunction and with smaller, and more often single, tumours (P < 0.05 in all cases). A higher male prevalence was observed in surgical patients. The 30-day mortality after surgery was 2.3% and that after ablation was 0.5%; the median in-hospital stay after surgery was 8 days (range: 3 days, 5 months) and 2 days after ablation (range: 0 days, 2 months). The median followup for the surgical patients was 29 months (range: 14 days, 12 years) and that of the ablated patients was 24 months (range: 1 month, 10 years). During these time periods, 142 patients out of the 388 undergoing surgery, and 70 patients out of the 207 ablated patients died. Conversely, 16 surgical (4.3%) and 20 ablated (9.7%) patients were transplanted. In particular, 54 surgical patients died without tumour recurrence (13.9%) and 88 died after recurrence (22.7%) whereas 13 ablated patients died without tumour recurrence (6.3%) and 57 died after recurrence (27.5%). Overall survival was similar between the two groups (P = 0.270) but the survival rates reversed themselves over time, suggesting a different impact of clinical and tumour characteristics in determining prognosis;

Table 2 Results from multivariate Cox regression in patients undergoing hepatic resection and in patients undergoing radiofrequency ablation. Variable Hepatic resection MELD score (per unit increase) Two or three nodules vs. a single nodule Size of the largest tumour (per cm increase) Baseline cumulative hazard 1 year 2 year 3 year 4 year 5 year Radiofrequency ablation MELD score (per unit increase) Two or three nodules vs. a single nodule Size of the largest tumour (per cm increase) Baseline cumulative hazard 1 year 2 year 3 year 4 year 5 year

Beta-coefficient (95% C.I.)

P-value

0.132 (0.011–0.252) 0.408 (−0.022 to 0.838)

0.032 0.063

0.162 (0.086–0.238)

0.001

0.015 (0.010–0.021) 0.026 (0.019–0.034) 0.046 (0.035–0.057) 0.059 (0.046–0.074) 0.070 (0.055–0.087)

– – – – –

0.083 (0.001–0.155) 0.604 (−0.045 to 1.254)

0.049 0.068

0.337 (0.074–0.600)

0.012

0.010 (0.005–0.016) 0.035 (0.023–0.048) 0.057 (0.040–0.077) 0.082 (0.059–0.108) 0.118 (0.085–0.160)

– – – – –

Survival estimation for each year is calculated by the following equation S0(year) ˆ (EXP(PI)), where S0(year) = −EXP(baseline cumulative hazard for each year) and PI = betaMELD × MELD (unit) + betamultiple × (1 = two or three nodules; 0 = single nodule) + betasize × tumour size (cm). Baseline cumulative hazard was calculated by the means of Breslow estimator. Beta-coefficients together with their 95% confidence intervals (inclusive of negative confidence limits regarding tumour number) were used in the subsequent deterministic and probabilistic models. Coefficients and baseline hazard function were entered up to the 14th decimal place.

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conversely, surgery led to significantly better recurrence-free survival (P = 0.001).

Table 3 Second order Monte Carlo simulation of HCC patients undergoing hepatic resection (HR) or radiofrequency ablation (RFA) stratified by tumour size, number and MELD score.

3.1. Sensitivity analysis The results from the multivariate Cox model for the three main determinants of treatment allocation, namely, liver function measured by the MELD score, tumour number and tumour diameter are reported in Table 2, together with baseline hazard function at different time points. Tumour size was the strongest predictor of patient survival in both groups (P = 0.001 after resection and 0.012 after ablation) followed by MELD score (P = 0.032 after resection and 0.049 after ablation) and tumour number (P = 0.063 after resection and 0.068 after ablation). Beta coefficients and 95% confidence intervals were entered together with the baseline hazard function into the model. Since comparative analysis of Table 1 showed a male predominance in surgical patients and an older age in ablated patients, the model was adjusted for these two covariates, as described in Section 2. The results of the sensitivity analysis, with varying tumour sizes and MELD scores in single nodules, are reported in Fig. 1. In patients with a MELD of 7 or 8 and a single HCC (Panel A), RFA demonstrated similar, or even slightly better, life expectancy than resection when the tumour size was <1.8 cm; with a higher MELD score (Panels B and C), the benefit obtainable from ablation extends to tumours up to 3 cm. Beyond this tumour size threshold, surgery results in higher life expectancy. The results of the sensitivity analyses, with varying tumour sizes and MELD scores in two or three nodules, are reported in Fig. 2. In patients with a MELD score of 7 or 8 (Panel A), resection provides better life expectancy than ablation, especially with the increased size of the largest tumour; at higher MELD scores (Panels B and C), the benefit obtainable from resection decreases and ablation results in better life expectancy for smaller tumours (panels b and c). 3.2. Probabilistic analysis The results of the Monte Carlo simulation are reported in Table 3. For patients with single tumours <2 cm and a MELD score <10, the two treatments show very similar survival rates (effect size <|0.3|). Even if survival was slightly longer after ablation, the NNT with RFA was very high; 67 patients needed to be ablated before a survival advantage of one ablated patient over resection was achieved. Conversely, when liver function worsens, namely a MELD score ≥10, RFA offers a greater survival advantage over resection (effect size >|0.5|) and an NNT which drops to 12. For single nodules of 2–3 cm, in patients having a MELD score <10, surgery results in a very modest survival benefit over RFA (effect size: |0.3|–|0.5|) and an NNT of 38 patients; when the MELD score is >10, the scenario changes and RFA has a modest survival benefit in comparison to surgery (effect size <|0.3|) and an NNT of 20. Surgery leads to a large survival benefit over RFA for patients with a MELD score <10 and a single nodule between 3.1 and 5 cm (effect size >|0.5|) and an NNT of only 9 patients; this gain decreases when the MELD score is >10 (effect size <|0.3|) and an NNT which goes up to 31. Similarly, for what was observed for single nodules of 2–3 cm, in patients with a MELD score <10 and two or three nodules up to 3 cm, surgery has a modest survival benefit over RFA (effect size: |0.3|–|0.5|) and an NNT of 18 patients; when the MELD score is >10, the scenario changes, and RFA offers a very modest survival benefit in comparison to surgery (effect size <|0.3|) and an NNT as high as 26.

Single nodule <2.0 cm MELD score 6–9 5-year life-expectancy (years) Expected 5-year survival rate Number needed to treat MELD score ≥10 5-year life-expectancy (years) Expected 5-year survival rate Number needed to treat Single nodule 2.0–3.0 cm MELD score 6–9 5-year life-expectancy (years) Expected 5-year survival rate Number needed to treat MELD score ≥10 5-year life-expectancy (years) Expected 5-year survival rate Number needed to treat Single nodule 3.1–5.0 cm MELD score 6–9 5-year life-expectancy (years) Expected 5-year survival rate Number needed to treat MELD score ≥10 5-year life-expectancy (years) Expected 5-year survival rate Number needed to treat Two or three nodules ≤3.0 cm MELD score 6–9 5-year life-expectancy (years) Expected 5-year survival rate Number needed to treat MELD score ≥10 5-year life-expectancy (years) Expected 5-year survival rate Number needed to treat

HR (n = 1000)

RFA (n = 1000)

Effect size

4.41 ± 0.23 81.0% –

4.46 ± 0.16 82.5% 67

−0.252 – –

3.93 ± 0.59 66.3% –

4.22 ± 0.32 74.9% 12

−0.611 – –

4.30 ± 0.27 77.5% 38

4.21 ± 0.28 74.8% –

0.327 – –

3.74 ± 0.70 60.6% –

3.91 ± 0.46 65.6% 20

−0.287 – –

4.10 ± 0.35 71.3% 9

3.72 ± 0.59 60.3% –

0.783 – –

3.49 ± 0.75 53.5% 31

3.37 ± 0.74 50.2% –

0.161 – –

4.06 ± 0.38 70.1% 18

3.87 ± 0.48 64.4% –

0.439 – –

3.35 ± 0.82 49.6% –

3.49 ± 0.69 53.5% 26

−0.185

Effect size <|0.1| = very small differences; |0.1|–|0.3| = small differences; |0.3|–|0.5| = moderate differences and >|0.5| = considerable differences. The number needed to treat (NNT) gives the number of people you would have to treat with one intervention (compared to the control) to prevent one event. The higher the NNT, the less effective the treatment. Continuous variables are reported as means and standard deviations. For tumour size and MELD score, the distribution was assumed to be uniform. For tumours <2 cm, the size ranged between 0.8 and 1.9 cm; for multiple tumours the size ranged 0.8 and 3 cm; for a MELD score ≥10 values ranged between 10 and 14. Patients were stratified according to tumour features and MELD, following accepted clinical thresholds.

4. Discussion The choice for resection or RFA for the treatment of HCC represents a clinical dilemma which often occurs in clinical practice. A clear example comes from the national conference of the Japan Society of Hepatology, held in 2009 when, to the question “Which treatment would you perform for 2-cm sized HCC nodules in patients with Child–Pugh A liver function?”, 80% of surgeons responded “resection”, and 68% of non-surgeons responded “RFA” [31]. Even if greater agreement was observed when asking about the optimal treatment of 3-cm sized nodules, these conclusions point out the uncertainty related to the optimal therapeutic strategy for HCC patients. The present analysis represents an in-depth evaluation of medical circumstances which can guide the therapeutic strategy of HCC, in cirrhotic patients, towards surgery or ablation. In particular, tumoral and liver function thresholds for an optimization of therapeutic choice were proposed, and the uncertainty related to the natural variability of outcome after each treatment was explored to assess the effect size of one treatment over the other.

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Fig. 1. Results from the sensitivity analysis on a single tumour at varying MELD scores and tumour diameters. Expected values represent the life expectancy achievable with resection or ablation over a 5-year period. The covariates number of nodules and MELD score were maintained fixed at determined values (panel A, MELD = 7–8; panel B, MELD 9–10; panel C, MELD 11–12) while tumour diameter was varied between 1 and 5 cm. Beta-coefficients and baseline cumulative hazard values, for all the three clinical variables, were varied within their 95% confidence intervals, assuming a triangular distribution.

Looking at patient characteristics, it is immediately clear that surgical and ablated patients are significantly different regarding tumoral and clinical characteristics. This is not surprising because, in clinical practice, older patients, with smaller tumours and a more advanced degree of liver dysfunction more often undergo ablation rather than surgery. This finding is very frequently found in the medical literature which compares resection to ablation [4–16]. Of note, in the RCT of Chen, the proportion of patients randomized to ablation who refused treatment was quite high (21%) raising the question as to whether an RCT can really be conducted in a real-life scenario [4,32]. When it is difficult to carry out prospective trials due to different overwhelming practical and ethical problems, as in the instance of HCC, modelling studies can help clarify specific issues. In the present analysis, a different methodological approach was applied. The development of two distinct prognostic models, based on the same clinical and tumoral variables and adequately adjusted for age and sex, allowed a comparison of predicted outcomes of surgery and ablation through sensitivity and probabilistic analyses. In particular, the Monte Carlo simulation gave us the possibility of testing the uncertainty that could be expected from the comparison of the two therapies. The sensitivity analysis pointed out that the benefit of resection over ablation increased with increasing tumour size, which reflected the fact that the larger the tumour, the lower the complete response rate achievable with ablation, and, consequently, the lower the expected survival. At the same time, with an increasing degree of liver dysfunction the benefit of resection decreased more rapidly than that of RFA, allowing ablation to achieve better

survivals for larger tumour diameters. This is because ablation had a lesser detrimental effect on liver functional reserve than resection or, from the opposite point of view, the benefit obtainable from resection in terms of oncological radicality was lost because of the postoperative deterioration of liver function. These results pointed out how the outcomes of surgery and ablation were not linearly related to tumour size or liver function but reversed themselves as these characteristics varied. Such a non-linear relationship can well explain the disagreement observed in the literature and confirm recent expert opinions regarding the impossibility of conducting a reliable RCT [4–16,32]. Prognosis after each therapy is obviously accompanied by the reliability of the estimate consequent to the uncertainty related to the procedure itself. In other words, similar patients could experience different outcomes although undergoing the same procedure. This aspect is pointed out, in the present study, by the probabilistic analysis. In presence of a MELD score <10, RFA and surgery obtained very similar results in treating single nodules <2 cm as seen by an effect size <|0.3| and an NNT of 67. This latter indicator meant that 67 patients were needed to be treated with RFA before an advantage over resection for one single patient was achieved. Obviously, this relatively high number of patients confirmed that the observed difference had no clinical significance and that the two procedures can bring similar outcomes. Nevertheless, the NNT dropped to 12 for the same tumour size but with higher MELD score; in this scenario, RFA could provide a reasonable benefit over resection, as confirmed by an effect size >|0.5|. For tumours between 3.1 and 5 cm, resection can provide better results than RFA, with a

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Fig. 2. Results from the sensitivity analysis on two or three tumours at varying MELD scores (panel A, MELD = 7–8; panel B, MELD 9–10; panel C, MELD 11–12) and tumour diameters. Expected values represent the life-expectancy achievable with resection or ablation over a 5-year period. Confidence intervals were calculated at different tumour diameters, and varying beta-coefficients and baseline cumulative hazard values within their respective ranges.

reasonable NNT of 9 when the MELD score was <10; this benefit was, however, reduced for higher MELD score (NNT: 31). Finally, probabilistic analysis showed that single tumours of 2–3 cm in diameter, and two or three tumours <3 cm represented a grey zone, in which the two procedures could be alternatively suggested depending on the degree of liver dysfunction. The present study has some limitations which deserve specific discussion. First, the ability of the model to achieve a prognosis after treatment is influenced by the characteristics of the population on the basis of which it is constructed. However, surgical and ablated patients, of the present series, were representative of the typical patients who undergo one or the other treatment, thus, limiting the possible bias which could derive from the superselection of individuals needed to find comparable patient groups. Another limitation is represented by the sample size of the two populations. It is logical to expect that larger sample size will produce less uncertainty. This is the reason why we added NNT to the analysis since a statistically significant difference did not necessarily imply a significant clinical difference. It must be also highlighted that, on opposite, the absence of statistical difference did not imply the equivalence of the two treatments. The present modelling study was not aimed at replacing RCTs which remain the best clinical evidence available. However, until RCTs specifically designed to address the outcomes of the two treatments in different settings, related to tumour size and liver function, are carried out, the present analysis can provide useful informations to plan further prospective studies for cases in which both treatments can be chosen. In particular, the possibility to conduct an equivalence trial seems quite unrealistic, and the present analysis can suggests clinical scenarios in which such condition will be encountered. There are some additional aspects that need specific discussion. The study

was conducted on the basis of tumour size, number and MELD to reduce at minimum the complexity of the model. There are, however, some other clinical features that can drive the choice towards one treatment or the other. The degree of portal hypertension, the presence of comorbidities, which can represent contraindications to surgery, and the location of the tumour were not included in the model. While the presence of comorbidities is likely captured from the present age-adjustment, the remaining features probably need to be further investigated. In particular, portal hypertension as a contraindication for surgery is still a matter of debate [33,34] and dedicated comparative studies of the two treatments focused in patients with this feature should better clarify the role of each therapy. Location of the tumour represents another potential confounding variable that was not included in the present model. Even if in the present study an accurate assessment of the tumour deep was not performed, this feature is probably already reflected by the treatment choice, making present results consistent for patients in whom both treatments could be adopted [35]; however, this is probably another aspect that needs dedicated studies. In conclusion, we observed that the superiority, or a possible equivalence, of resection and/or ablation in the treatment of HCC is modified by the relationship existing between tumour number, size, and the degree of liver dysfunction. For patients with a single tumour <2 cm and very well-preserved liver function, the two procedures seem to provide similar results whereas, for tumours of 3–5 cm, resection can be a preferable option. The benefit obtainable from surgery in comparison to ablation is reduced for more advanced degrees of liver dysfunction. For single tumours of 2–3 cm and for multiple tumours, the two therapies provide opposite results in relation to the degree of liver dysfunction. The present results suggest that further studies should be focused on specific

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