Method for Establishing the Joint Uncertainty Distribution of Qualityof-Life Weights for a Set of Health States

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1 RSNA, /radiol Appendix E1 We performed a PubMed database search to determine point estimates and the uncertainty ranges to use in our probabilistic sensitivity analysis for the probability of developing toxicity after SBRT and RFA, and of incomplete ablation after RFA. For the SBRT literature search, we used the keywords SBRT or stereotactic body radiation therapy or stereotactic body radiotherapy in conjunction with the keywords HCC or hepatocellular carcinoma. We included all published series, which comprised mainly retrospective cohort and phase I-II studies. We conducted a similar search for RFA by using the keywords RFA or radiofrequency ablation in conjunction with the keywords HCC or hepatocellular carcinoma and prospective or randomized. Because there were many more RFA series, we included only prospective cohort or randomized controlled trials of percutaneous RFA, in addition to the Wahl et al (9) study. We excluded articles in which toxicity or incomplete ablation outcomes were not reported. We also excluded studies of RFA delivered concurrently with other therapies, such as chemoembolization, ethanol injection, hepatic arterial occlusion, or iodine 125 seed implantation. The last literature research was conducted on December 19, We extracted probabilities of SBRT and RFA toxicity (grade 3 or higher toxicity events that would require hospitalization and/or intervention) and of incomplete ablation after RFA, calculating toxicity probability per patient treated and incomplete ablation probability per lesion treated. Events of SBRT toxicity included mostly gastrointestinal bleeding and ulceration, ascites, and radiation-induced liver disease, and RFA toxicity included mostly gastrointestinal bleeding and perforation, pneumothorax, ascites, sepsis, cardiac arrhythmias, and death. We then calculated pooled estimates of these probabilities by using a random-effects model with the comprehensive meta-analysis software package (Tables E1 and E2). Given the heterogeneity in patient and tumor characteristics among studies, we widened the uncertainty range used in the probabilistic sensitivity analysis (Table 1) by scaling down the and of the fitted distributions by a factor of 0.5. Appendix E2 Method for Establishing the Joint Uncertainty Distribution of Qualityof-Life Weights for a Set of Health States The joint uncertainty distribution for utilities that respected preference order and preserved each utility s marginal distribution (73) was produced for the probabilistic sensitivity analysis. We assumed the preference order of: NED, local progression, treatment toxicity, and extensive disease, implying utility of NED, utility of local progression, utility of treatment toxicity, and utility of extensive disease. We sorted the random samples from the utility s independent marginal distributions by using induced correlation. First, we created three matrices: a preference order matrix (Q) which specifies the preference ordering of our health states, an independent utility matrix (U) which has the random samples from utility value for each state s marginal distribution, and a reference matrix (R) which has the random samples from independent standard normal distributions with a level of multivariate correlation that is optimized to ensure Page 1 of 9

2 that the utility values for each health state respect the preference order. Then we found the correlation matrix (C), which consists of correlation between each pair of health states and allows a threshold level of preference order violation. The correlation matrix C is not guaranteed to be positive and definite, hence, we decomposed C to eigenvectors (V) and eigenvalues (B), of which negative values were converted to a very small positive numbers (C*). We used Cholesky decomposition of C* to MM and resorted the prior reference matrix R on the basis of the correlation we calculated (R* = RM ). Finally, the utility matrix U is sorted in the same order as the resorted reference matrix R*. Because the algorithm only resorts the samples, the marginal distributions are preserved by construction. This analysis was performed with software (R version 3.1.3; R Foundation for Statistical Computing, Vienna, Austria). Appendix E3 Method for Establishing the Joint Uncertainty Distribution of Transition Probabilities To construct the joint uncertainty distribution of the probability of local progression, distant progression, and mortality, we repeated our calibration of the model s outputs to the upper and lower confidence intervals of the study s overall survival, freedom from local progression, and freedom from distant or regional progression Kaplan-Meier curves, which yielded a range of values for each probability. We used these ranges to form the prior marginal distributions of each probability by fitting distributions whose means were the same as the base case and whose 95% confidence intervals were the same as these ranges. We then sampled one million sets of parameters from these marginal distributions. For each sampled set, we used the model to reproduce Kaplan-Meier curves for overall survival, freedom from local progression, and freedom from distant or regional progression by scoring the sampled set according to comparison of the model-simulated curves relative to the study s curves by using a maximum likelihood approach. We retained the 5000 best-fitting parameter sets those with the highest likelihood relative to the data. We used bootstrap analysis of these sets to generate sampled sets used for the probability sensitivity analysis. This analysis was performed by using software (Stata; Stata, College Station, Texas). References 36. Bibault JE, Dewas S, Vautravers-Dewas C, et al. Stereotactic body radiation therapy for hepatocellular carcinoma: prognostic factors of local control, overall survival, and toxicity. PLoS One 2013;8(10):e Cárdenes HR, Price TR, Perkins SM, et al. Phase I feasibility trial of stereotactic body radiation therapy for primary hepatocellular carcinoma. Clin Transl Oncol 2010;12(3): Choi BO, Jang HS, Kang KM, et al. Fractionated stereotactic radiotherapy in patients with primary hepatocellular carcinoma. Jpn J Clin Oncol 2006;36(3): Huang WY, Jen YM, Lee MS, et al. Stereotactic body radiation therapy in recurrent hepatocellular carcinoma. Int J Radiat Oncol Biol Phys 2012;84(2): Page 2 of 9

3 40. Huertas A, Baumann AS, Saunier-Kubs F, et al. Stereotactic body radiation therapy as an ablative treatment for inoperable hepatocellular carcinoma. Radiother Oncol 2015;115(2): Jang WI, Kim MS, Bae SH, et al. High-dose stereotactic body radiotherapy correlates increased local control and overall survival in patients with inoperable hepatocellular carcinoma. Radiat Oncol 2013;8: Janoray G, Chapet S, Ruffier-Loubière A, Bernadou G, Pointreau Y, Calais G. Robotic stereotactic body radiation therapy for tumors of the liver: radiation-induced liver disease, incidence and predictive factors. Cancer Radiother 2014;18(3): Kang JK, Kim MS, Cho CK, et al. Stereotactic body radiation therapy for inoperable hepatocellular carcinoma as a local salvage treatment after incomplete transarterial chemoembolization. Cancer 2012;118(21): Kwon JH, Bae SH, Kim JY, et al. Long-term effect of stereotactic body radiation therapy for primary hepatocellular carcinoma ineligible for local ablation therapy or surgical resection. Stereotactic radiotherapy for liver cancer. BMC Cancer 2010;10: Méndez Romero A, Wunderink W, Hussain SM, et al. Stereotactic body radiation therapy for primary and metastatic liver tumors: A single institution phase i-ii study. Acta Oncol 2006;45(7): Sanuki N, Takeda A, Oku Y, et al. Stereotactic body radiotherapy for small hepatocellular carcinoma: a retrospective outcome analysis in 185 patients. Acta Oncol 2014;53(3): Scorsetti M, Comito T, Cozzi L, et al. The challenge of inoperable hepatocellular carcinoma (HCC): results of a single-institutional experience on stereotactic body radiation therapy (SBRT). J Cancer Res Clin Oncol 2015;141(7): Seo YS, Kim MS, Yoo SY, et al. Preliminary result of stereotactic body radiotherapy as a local salvage treatment for inoperable hepatocellular carcinoma. J Surg Oncol 2010;102(3): Takeda A, Takahashi M, Kunieda E, et al. Hypofractionated stereotactic radiotherapy with and without transarterial chemoembolization for small hepatocellular carcinoma not eligible for other ablation therapies: Preliminary results for efficacy and toxicity. Hepatol Res 2008;38(1): Tse RV, Hawkins M, Lockwood G, et al. Phase I study of individualized stereotactic body radiotherapy for hepatocellular carcinoma and intrahepatic cholangiocarcinoma. J Clin Oncol 2008;26(4): Xi M, Zhang L, Zhao L, et al. Effectiveness of stereotactic body radiotherapy for hepatocellular carcinoma with portal vein and/or inferior vena cava tumor thrombosis. PLoS One 2013;8(5):e Yamashita H, Onishi H, Murakami N, et al. Survival outcomes after stereotactic body radiotherapy for 79 Japanese patients with hepatocellular carcinoma. J Radiat Res (Tokyo) 2015;56(3): Yoon SM, Lim YS, Park MJ, et al. Stereotactic body radiation therapy as an alternative treatment for small hepatocellular carcinoma. PLoS One 2013;8(11):e Page 3 of 9

4 54. Brunello F, Veltri A, Carucci P, et al. Radiofrequency ablation versus ethanol injection for early hepatocellular carcinoma: A randomized controlled trial. Scand J Gastroenterol 2008;43(6): Chen MS, Li JQ, Zheng Y, et al. A prospective randomized trial comparing percutaneous local ablative therapy and partial hepatectomy for small hepatocellular carcinoma. Ann Surg 2006;243(3): Curley SA, Izzo F, Ellis LM, Nicolas Vauthey J, Vallone P. Radiofrequency ablation of hepatocellular cancer in 110 patients with cirrhosis. Ann Surg 2000;232(3): Feng K, Yan J, Li X, et al. A randomized controlled trial of radiofrequency ablation and surgical resection in the treatment of small hepatocellular carcinoma. J Hepatol 2012;57(4): Huang J, Yan L, Cheng Z, et al. A randomized trial comparing radiofrequency ablation and surgical resection for HCC conforming to the Milan criteria. Ann Surg 2010;252(6): Lencioni RA, Allgaier HP, Cioni D, et al. Small hepatocellular carcinoma in cirrhosis: randomized comparison of radio-frequency thermal ablation versus percutaneous ethanol injection. Radiology 2003;228(1): Lin SM, Lin CJ, Lin CC, Hsu CW, Chen YC. Radiofrequency ablation improves prognosis compared with ethanol injection for hepatocellular carcinoma < or =4 cm. Gastroenterology 2004;127(6): Lin SM, Lin CJ, Lin CC, Hsu CW, Chen YC. Randomised controlled trial comparing percutaneous radiofrequency thermal ablation, percutaneous ethanol injection, and percutaneous acetic acid injection to treat hepatocellular carcinoma of 3 cm or less. Gut 2005;54(8): Livraghi T, Goldberg SN, Lazzaroni S, Meloni F, Solbiati L, Gazelle GS. Small hepatocellular carcinoma: treatment with radio-frequency ablation versus ethanol injection. Radiology 1999;210(3): Llovet JM, Vilana R, Brú C, et al. Increased risk of tumor seeding after percutaneous radiofrequency ablation for single hepatocellular carcinoma. Hepatology 2001;33(5): Raut CP, Izzo F, Marra P, et al. Significant long-term survival after radiofrequency ablation of unresectable hepatocellular carcinoma in patients with cirrhosis. Ann Surg Oncol 2005;12(8): Shibata T, Isoda H, Hirokawa Y, Arizono S, Shimada K, Togashi K. Small hepatocellular carcinoma: is radiofrequency ablation combined with transcatheter arterial chemoembolization more effective than radiofrequency ablation alone for treatment? Radiology 2009;252(3): Shibata T, Iimuro Y, Yamamoto Y, et al. Small hepatocellular carcinoma: comparison of radio-frequency ablation and percutaneous microwave coagulation therapy. Radiology 2002;223(2): Shibata T, Shibata T, Maetani Y, Isoda H, Hiraoka M. Radiofrequency ablation for small hepatocellular carcinoma: prospective comparison of internally cooled electrode and expandable electrode. Radiology 2006;238(1): Page 4 of 9

5 68. Shiina S, Teratani T, Obi S, et al. A randomized controlled trial of radiofrequency ablation with ethanol injection for small hepatocellular carcinoma. Gastroenterology 2005;129(1): Wang C, Wang H, Yang W, et al. Multicenter randomized controlled trial of percutaneous cryoablation versus radiofrequency ablation in hepatocellular carcinoma. Hepatology 2015;61(5): Zhang YJ, Liang HH, Chen MS, et al. Hepatocellular carcinoma treated with radiofrequency ablation with or without ethanol injection: a prospective randomized trial. Radiology 2007;244(2): Ray CE Jr, Battaglia C, Libby AM, Prochazka A, Xu S, Funaki B. Interventional radiologic treatment of hepatocellular carcinoma-a cost analysis from the payer perspective. J Vasc Interv Radiol 2012;23(3): Centers for Medicare and Medicaid Services: Anesthesiologists Center. Baltimore, Md: Centers for Medicare and Medicaid Services, Goldhaber-Fiebert JD, Jalal HJ. Some health states are better than others: using health state rank order to improve probabilistic analyses. Med Decis Making 2016;36(8): Page 5 of 9

6 Table E1. Studies Informing Probability of SBRT Toxicity Study No. of Events No. of Patients at Risk Median Age (y) Child-Pugh Classification No. of Patients according to No. of Lesions per Patient A B C NR Other Andolino et al (25) Bibault et al (36) Bujold et al (28) * 7.2 Cardenes et al (37) Choi et al ( Median Tumor Diameter (cm) Huang et al (39) Huertas et al (40) Jang et al (41) Janoray et al (42) Kang et al (43) Kw on et al (44) * 15.4 Mendez Romero et al (45) Sanuki et al (46) , 2.4 Scorsetti et al (47) # Seo et al (48) Takeda et al (49) Tse et al (50) Wahl et al (9) Xi et al (51) # Yamashita et al (52) Yoon et al (53) Note. The point estimate was 7.8 (95% CI: 5.9, 10.3). NR = not reported. * Data are for number of patients with more than one lesion. Number of lesions was not specified. Data are volume in cubic centimeters instead of diameter Data are for the 35 Gy group and the 40 Gy group, respectively. # Data are the mean. Page 6 of 9

7 Table E2. Studies Informing Probability of RFA Toxicity and Retreatment Author Proportion of Events Mean Age (y) Child-Pugh Classification Toxicity Retreatment No. of Patients according to No. of Lesions per Patient A B C Other Brunello et al (54) 10/ * 2.4 Mean Tumor Diameter (cm) Chen et al (55) 0/71 68/ (37), (34) Curley et al (56) 10/76 6/ Feng et al (57) 8/84 8/ (32), 2 4 (53) Huang et al (58) 5/115 17/ (57), > 3 (27) Lencioni et al (59) 0/52 41/ Lin et al (60) 4/52 2/ Lin et al (61) 3/62 3/ Livraghi et al (62) 5/52 8/ Llovet et al (63) 11/ Peng et al (32) 2/95 7/ Raut et al (64) 7/140 4/ Shibata et al (65) 1/43 3/ Shibata et al (66) 1/36 5/ Shibata et al (67) 1/74 5/ Shiina et al (68) 6/118 20/ (44), > 65 (74) (45), > 2.0 (73) Wahl et al (9) 18/161 8/ Wang et al (69) 6/ (42), 2 4 (138) Zhang et al (70) 0/ (29), (25), (12) Note. The point estimate for toxicity was 6.0 (95% CI: 4.0, 9.0) and for retreatment, 9.1 (5.7, 14.1). Cells with more than one set of data indicate that the study included more than one group. * Data are number of patients with more than one lesion. Data are the median. Number of lesions was not specified. Page 7 of 9

8 Table E3. Cost of SBRT and RFA Treatments Treatment and Code* SBRT Description Unit Cost (2015 $) Intensity-modulated radiation therapy device Basic dosimetry calculation Intensity-modulated radiation therapy planning Radiation therapy planning Simulation Radiation treatment aids Design multileaf collimator device for intensity-modulated radiation therapy SBRT management Special radiation treatment Physics consultation SBRT delivery Set radiation field SBRT total cost RFA CT guidance CT abdomen w ith and w ithout contrast material enhancement US abdomen guidance Percutaneous RFA Percutaneous RFA of the liver (ambulatory surgical center) General anesthesia for liver tumor ablation RFA total cost * Codes are from the Current Procedural Terminology and Healthcare Common Procedure Coding System Five fractions of SBRT based on the ongoing RTOG1112 protocol (21). Ambulatory payment classification. Data are expressed in minutes on the basis of general anesthesia time in a prior study (71). Anesthesia is billed by using a base unit and 15 minute incremental time units: anesthesia cost = (base units + time units [72]) conversion factor. The national anesthesia conversion factor in 2015 was (72). Anesthesia drug costs were not considered. Page 8 of 9

9 Table E4. Model Calibration Outcome Clinical Data (9) Model Calibration* 1 year overall survival 70.9 (64.9, 77.3) 71.1 (69.1, 72.7) 2 year overall survival 50.6 (44.2, 58.0) 49.6 (46.7, 55.6) 1 year freedom from distant and regional 58.9 (2.1, 66.7) 57.0 (54.2, 63.6) progression 2 year freedom from distant and regional 42.7 (35.7, 51.1) 40.9 (37.1, 48.2) progression 1 year freedom from local progression 83.6 (79.5, 89.4) 84.4 (81.4, 7.8) 2 year freedom from local progression 80.2 (76.1, 87.2) 80.1 (76.1, 84.0) * Model results of RFA-RFA. FFLP was calibrated only for RFA. FFLP associated with SBRT was derived from applying the hazard ratio reported in Wahl et al (9). Table E5. Point Estimates Used in Sensitivity Analysis Transition Outcome Point Estimates (monthly) Local progression from posttreatment NED for RFA Death from posttreatment NED Death from local progression or post local progression NED Distant or regional progression from posttreatment NED Distant or regional progression from local progression or post local progression NED Death from distant or regional progression Note. Point estimates used in sensitivity analysis were based on calibration, allowing for local progression, to be associated with increased probability of extensive disease and dying. Page 9 of 9