From Higgs to the Hospital: Normal Tissue Complication Probability Modeling in Radiation Therapy

1. From Higgs to the Hospital: Normal Tissue Complication Probability Modeling in Radiation Therapy Eric Williams Memorial Sloan-Kettering Cancer Center New York, NY January 17, 2014

2. Overview • Introduction What does the Higgs have to do with it? • The α, β, γ’s of Radiation in Medicine Discovery and modern use • Normal Tissue Complication Probability Modeling NTCP → DVH → NTD: A short history of acronyms • Radiation induced Chest-Wall Pain A retrospective analysis • Radiation Therapy & Global Health A digression • Conclusions Seriously though, whats the deal with the Higgs? E. Williams (MSKCC) Higgs → Hospital January 17, 2014 1 / 29

10. Introduction From Higgs: ↓ ↓ To Health: E. Williams (MSKCC) Higgs → Hospital January 17, 2014 2 / 29

12. Radiation in Medicine – Discovery • Radiation (x-rays) discovered by Wilhelm Roentgen (1895) while Henri Becquerel concurrently discovered radioactivity (uranium) • Following, Marie Curie pioneered research in radioactivity with radium and polonium • Potential to medicine quickly realized (Figure 1) • Within a month, radiographs were under production • Within 6 months, they were used in battle to locate bullets in soldiers • Dangers of radiation also quick to surface: Figure 1: The ﬁrst x-ray of Bertha Roentgen’s hand. “If one leaves a small glass ampulla with several centigrams of radium salt in ones pocket for a few hours, one will feel absolutely nothing. But in 15 days afterwards redness will appear on the epidermis, and then a sore, which will be very diﬃcult to heal. A more prolonged action could lead to paralysis and death.” – Pierre Curie, Nobel lecture 1903 E. Williams (MSKCC) Higgs → Hospital January 17, 2014 3 / 29

15. Radiation in Medicine – Modern Use • Diagnostic tools: • X-ray images → computed tomography (CT ) • Positron Emission Tomography (PET ) • Magnetic Resonance Imaging (MRI ) • Therapeutic tools: Eleckta Linear Accelerator • Brachytherapy : radioactive sources place near disease • Nuclear medicine: Radioactive material injected or injested by patient • External beam radiotherapy: intense radiation from external source is focused on the cancerous tissue → Nearly 2/3 of all cancer patients will receive radiation therapy ← during the course of their treatment.1 E. Williams (MSKCC) Higgs → Hospital January 17, 2014 4 / 29

19. NTCP Modeling: Purpose A key challenge in radiotherapy is maximizing radiation doses to cancer cells while minimizing damage to surrounding healthy (normal) tissue Successful tumor control depends principally on the total dose delivered, but tolerances of surrounding normal tissues limit this dose.3 Goal: To model Normal Tissue Complication Probability (NTCP), based on clinical and dosimetric predictors, to reduce future toxicities and allow higher doses to the target for greater tumor control. E. Williams (MSKCC) Higgs → Hospital January 17, 2014 5 / 29

20. NTCP Modeling: Dose-Volume Histograms To obtain useful predictors, need to simplify complicated 3D dosimetric and anatomic information from treatment plans: Dose-Volume Histogram Lung Treatment Plan → E. Williams (MSKCC) Higgs → Hospital January 17, 2014 6 / 29

21. NTCP Modeling: Dose-Volume Histograms Dose-volume histograms (DVH) • DVHs summarize dose-volume information for a particular structure (e.g. tumor, or organ) • A point on the DVH represents: The volume (V) of the given structure that received at least dose (D) VD : Vol. (V ) receiving ≥ dose (D) V20Gy = 40% V50Gy = 15% E. Williams (MSKCC) Higgs → Hospital January 17, 2014 7 / 29

24. NTCP Modeling: Model Building • NTCP models use these DVH reduction values (e.g. VD ) as predictive parameters to produce a single measure: probability of complication → ??? → ??? Common NTCP independent variables • • • • Common NTCP complication probability models Dose/Volume parameters: e.g. VD or DV Min/Max/Mean dose to organ Generalized Equivalent Uniform Dose Clinical inputs (e.g. age, KPS, smoke) E. Williams (MSKCC) Higgs → Hospital • • • • Logistic Regression ROC Analysis Cox Proportional Hazards Logrank + Kaplan-Meier January 17, 2014 8 / 29

25. NTCP Modeling: Model Building • NTCP models use these DVH reduction values (e.g. VD ) as predictive parameters to produce a single measure: probability of complication → VD,i → VD Common NTCP complication probability models Common NTCP independent variables • • • • Dose/Volume parameters: e.g. VD or DV Min/Max/Mean dose to organ Generalized Equivalent Uniform Dose Clinical inputs (e.g. age, KPS, smoke) E. Williams (MSKCC) Higgs → Hospital • • • • Logistic Regression ROC Analysis Cox Proportional Hazards Logrank + Kaplan-Meier January 17, 2014 8 / 29

26. NTCP Modeling: Model Building • NTCP models use these DVH reduction values (e.g. VD ) as predictive parameters to produce a single measure: probability of complication Mean → Dosei → Dmean Common NTCP complication probability models Common NTCP independent variables • • • • Dose/Volume parameters: e.g. VD or DV Min/Max/Mean dose to organ Generalized Equivalent Uniform Dose Clinical inputs (e.g. age, KPS, smoke) E. Williams (MSKCC) Higgs → Hospital • • • • Logistic Regression ROC Analysis Cox Proportional Hazards Logrank + Kaplan-Meier January 17, 2014 8 / 29

27. NTCP Modeling: Model Building • NTCP models use these DVH reduction values (e.g. VD ) as predictive parameters to produce a single measure: probability of complication → F(Di , Vi , ...)→ F(D, V, ...) Common NTCP complication probability models Common NTCP independent variables • • • • Dose/Volume parameters: e.g. VD or DV Min/Max/Mean dose to organ Generalized Equivalent Uniform Dose Clinical inputs (e.g. age, KPS, smoke) E. Williams (MSKCC) Higgs → Hospital • • • • Logistic Regression ROC Analysis Cox Proportional Hazards Logrank + Kaplan-Meier January 17, 2014 8 / 29

28. NTCP Modeling: Model Building • NTCP models use these DVH reduction values (e.g. VD ) as predictive parameters to produce a single measure: probability of complication → ??? → ??? Common NTCP independent variables • • • • Common NTCP complication probability models Dose/Volume parameters: e.g. VD or DV Min/Max/Mean dose to organ Generalized Equivalent Uniform Dose Clinical inputs (e.g. age, KPS, smoke) E. Williams (MSKCC) Higgs → Hospital • • • • Logistic Regression ROC Analysis Cox Proportional Hazards Logrank + Kaplan-Meier January 17, 2014 8 / 29

29. NTCP Modeling: Model Building • NTCP models use these DVH reduction values (e.g. VD ) as predictive parameters to produce a single measure: probability of complication 0.5 log10(a) = 0.6 0.45 p−val: 1.33e−04 → ??? → Complication probability 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 10 20 30 40 50 60 gEUD [Gy] Common NTCP independent variables • • • • Common NTCP complication probability models Dose/Volume parameters: e.g. VD or DV Min/Max/Mean dose to organ Generalized Equivalent Uniform Dose Clinical inputs (e.g. age, KPS, smoke) E. Williams (MSKCC) Higgs → Hospital • • • • Logistic Regression ROC Analysis Cox Proportional Hazards Logrank + Kaplan-Meier January 17, 2014 8 / 29

30. NTCP Modeling: Model Building • NTCP models use these DVH reduction values (e.g. VD ) as predictive parameters to produce a single measure: probability of complication → ??? Common NTCP independent variables • • • • Common NTCP complication probability models Dose/Volume parameters: e.g. VD or DV Min/Max/Mean dose to organ Generalized Equivalent Uniform Dose Clinical inputs (e.g. age, KPS, smoke) E. Williams (MSKCC) → Higgs → Hospital • • • • Logistic Regression ROC Analysis Cox Proportional Hazards Logrank + Kaplan-Meier January 17, 2014 8 / 29

31. NTCP Modeling: Model Building • NTCP models use these DVH reduction values (e.g. VD ) as predictive parameters to produce a single measure: probability of complication → ??? Common NTCP independent variables • • • • Common NTCP complication probability models Dose/Volume parameters: e.g. VD or DV Min/Max/Mean dose to organ Generalized Equivalent Uniform Dose Clinical inputs (e.g. age, KPS, smoke) E. Williams (MSKCC) → Higgs → Hospital • • • • Logistic Regression ROC Analysis Cox Proportional Hazards Logrank + Kaplan-Meier January 17, 2014 8 / 29

32. NTCP Modeling: Model Building • NTCP models use these DVH reduction values (e.g. VD ) as predictive parameters to produce a single measure: probability of complication → ??? Common NTCP complication probability models Common NTCP independent variables • • • • Dose/Volume parameters: e.g. VD or DV Min/Max/Mean dose to organ Generalized Equivalent Uniform Dose Clinical inputs (e.g. age, KPS, smoke) E. Williams (MSKCC) → Higgs → Hospital • • • • Logistic Regression ROC Analysis Cox Proportional Hazards Logrank + Kaplan-Meier January 17, 2014 8 / 29

34. SBRT Induced Chest-Wall Pain: Purpose Chest-wall pain (CWP) is among the most common adverse eﬀects of stereotactic body radiation therapy (SBRT) for thoracic tumors. The purpose of this (and similar) normal tissue toxicity study is both: Predictive→ Build predictive models of the incidence of CWP using dose/volume and clinical parameters. Prescriptive→ Derive clinically implementable dose/volume guidelines (thresholds) to be imposed in future treatments. E. Williams (MSKCC) Higgs → Hospital January 17, 2014 9 / 29

37. SBRT Induced Chest-Wall Pain: Patient Cohort Patient and Tumor Characteristics • 316 lung tumors in 295 patients treated between 2006-2012 were retrospectively analyzed N Median age Median KPS Tumor Primary NSCLC Oligometastatic Recurrent Doses x Num Fx. 18 − 20 Gy × 3 12 Gy × 4 9 − 10 Gy × 5 Other Percent (%) 77 (49 − 95)y 70 (50 − 100) E. Williams (MSKCC) 285 13 18 90.2 4.1 5.7 113 114 62 27 35.8 36.1 19.6 8.5 Higgs → Hospital January 17, 2014 10 / 29

38. SBRT Induced Chest-Wall Pain: Chest-wall deﬁnition Deﬁnition of chest wall (CW) Chest wall contoured for each patient: 2cm expansion of the lung in rind around ipsilateral lung • 4 CT slices (0.8 cm) above and below the tumor • E. Williams (MSKCC) Higgs → Hospital January 17, 2014 11 / 29

39. SBRT Induced Chest-Wall Pain: Outcome Definition Definition of Chest-Wall Piain (CWP) CWP Grade Description Grade 1 Grade 2 Mild pain, not interfering with function Moderate pain interfering with function but not ADLs, requiring NSAIDs/Tylenol Severe pain interfering with ADLs, requiring narcotics, or needing intervention Grade 3 CTCAE v4.0 with specifications E. Williams (MSKCC) Higgs → Hospital January 17, 2014 12 / 29

40. SBRT Induced Chest-Wall Pain: Outcome Definition Definition of Chest-Wall Piain (CWP) CWP Grade Description Grade 1 Grade 2 Mild pain, not interfering with function Moderate pain interfering with function but not ADLs, requiring NSAIDs/Tylenol Severe pain interfering with ADLs, requiring narcotics, or needing intervention Grade 3 CTCAE v4.0 with specifications CWP outcome studied ≥ 2 Grade. E. Williams (MSKCC) Higgs → Hospital January 17, 2014 12 / 29

41. SBRT Induced Chest-Wall Pain: Modeling Inicidence of grade >= 2 Chestwall Pain Actuarial analysis necessary due to inherent latency of chest-wall pain 0.35 0.3 0.25 0.2 0.15 Median onset time: 0.61 yr 0.1 0.05 0 0 1 2 3 4 5 6 Years Univariate and multivariate Cox Proportional Hazards (CPH) model used to identify predictive factors of CWP • Regression analysis for survival data • ROC analysis and Logrank test with Kaplan-Meier method used to assess correlation of risk factors to CWP • E. Williams (MSKCC) Higgs → Hospital January 17, 2014 13 / 29

42. SBRT Induced Chest-Wall Pain: Univariate Results Variable V39Gy V30Gy Presc. Dose (Tx) Dose/Fx Num. of Fx Dist. GTV to CW BMI Coef. Std. Err ln L CPH p-value 0.0207 0.0129 0.0008 0.001 −0.47 −0.52 0.04 0.0032 0.0022 0.0002 0.0003 0.18 0.18 0.02 −320.30 −322.65 −329.76 −331.90 −333.85 −330.17 −335.32 1.1 × 10−10 7.8 × 10−10 6.8 × 10−5 7.5 × 10−4 7.5 × 10−3 1.4 × 10−3 0.031 Predictors not signiﬁcant in univariate CPH: KPS, Sex, Age Variable beta se ln L KPS Sex Age -0.02 -0.18 -0.01 0.01 0.26 0.01 -337.06 -337.45 -337.68 E. Williams (MSKCC) Higgs → Hospital p-value 0.25 0.48 0.83 January 17, 2014 14 / 29

43. SBRT Induced Chest-Wall Pain: Univariate Results Variable → → • V39Gy V30Gy Presc. Dose (Tx) Dose/Fx Num. of Fx Dist. GTV to CW BMI Coef. Std. Err ln L CPH p-value 0.0207 0.0129 0.0008 0.001 −0.47 −0.52 0.04 0.0032 0.0022 0.0002 0.0003 0.18 0.18 0.02 −320.30 −322.65 −329.76 −331.90 −333.85 −330.17 −335.32 1.1 × 10−10 7.8 × 10−10 6.8 × 10−5 7.5 × 10−4 7.5 × 10−3 1.4 × 10−3 0.031 VD is a common dose-volume metric utilized by planners in the clinic, from literature,5 to limit: • Radiation pneumonitis in NSCLC treatments, V20Gy < 30% • Late rectal toxicity in prostate cancer treatments, V50Gy < 50% • Acute esophagitis in thoracic treatments, V35Gy < 40% Note: V30Gy < 70cc already implemented as CW constraint E. Williams (MSKCC) Higgs → Hospital January 17, 2014 14 / 29

44. SBRT Induced Chest-Wall Pain: Univariate Results Variable → → Coef. V39Gy V30Gy Presc. Dose (Tx) Dose/Fx Num. of Fx Dist. GTV to CW BMI Std. Err ln L CPH p-value 0.0207 0.0129 0.0008 0.001 −0.47 −0.52 0.04 0.0032 0.0022 0.0002 0.0003 0.18 0.18 0.02 −320.30 −322.65 −329.76 −331.90 −333.85 −330.17 −335.32 1.1 × 10−10 7.8 × 10−10 6.8 × 10−5 7.5 × 10−4 7.5 × 10−3 1.4 × 10−3 0.031 • Since goal of study is produce clinically implementable prescriptive models, we must take many practicalities into consideration, e.g. • • • • Complexity added to treatment planning systems Ease of implementation (many constraints already in place) Oncologists understanding/comfort Study ﬁndings in relation to current constraints → For these reasons V30 E. Williams (MSKCC) Gy is chosen as variable of interest over V39 Higgs → Hospital January 17, 2014 Gy 14 / 29

45. SBRT Induced Chest-Wall Pain: Univariate Results Variable → Coef. ln L CPH p-value 0.0207 0.0129 0.0008 0.001 −0.47 −0.52 0.04 V39Gy V30Gy Presc. Dose (Tx) Dose/Fx Num. of Fx Dist. GTV to CW BMI Std. Err 0.0032 0.0022 0.0002 0.0003 0.18 0.18 0.02 −320.30 −322.65 −329.76 −331.90 −333.85 −330.17 −335.32 1.1 × 10−10 7.8 × 10−10 6.8 × 10−5 7.5 × 10−4 7.5 × 10−3 1.4 × 10−3 0.031 0 10 −2 10 −325 CPH p−value CPH log−likelihood −320 −330 −335 −340 0 Low 68% CI Low 95% CI Max LogL = −320.3 at D39 Gy −4 10 Min p−val = 1.1e−10 at V39 Gy −6 10 −8 10 −10 10 20 30 40 50 60 10 0 (VD) Dose [Gy] E. Williams (MSKCC) 10 20 30 40 50 60 (VD) Dose [Gy] Higgs → Hospital January 17, 2014 14 / 29

46. SBRT Induced Chest-Wall Pain: Univariate Results Variable → V39Gy V30Gy Presc. Dose (Tx) Dose/Fx Num. of Fx Dist. GTV to CW BMI Coef. Std. Err ln L CPH p-value 0.0207 0.0129 0.0008 0.001 −0.47 −0.52 0.04 0.0032 0.0022 0.0002 0.0003 0.18 0.18 0.02 −320.30 −322.65 −329.76 −331.90 −333.85 −330.17 −335.32 1.1 × 10−10 7.8 × 10−10 6.8 × 10−5 7.5 × 10−4 7.5 × 10−3 1.4 × 10−3 0.031 V30 threshold Sensitivity Speciﬁcity TP T P +F N TN T N +F P 30cc 50cc 70cc 0.891 0.828 0.656 0.294 0.524 0.0726 AU C = 0.73 [0.66 − 0.81 (95%CI)] E. Williams (MSKCC) Higgs → Hospital January 17, 2014 14 / 29

47. SBRT Induced Chest-Wall Pain: Univariate Results Variable → V39Gy V30Gy Presc. Dose (Tx) Dose/Fx Num. of Fx Dist. GTV to CW BMI Coef. Std. Err ln L CPH p-value 0.0207 0.0129 0.0008 0.001 −0.47 −0.52 0.04 0.0032 0.0022 0.0002 0.0003 0.18 0.18 0.02 −320.30 −322.65 −329.76 −331.90 −333.85 −330.17 −335.32 1.1 × 10−10 7.8 × 10−10 6.8 × 10−5 7.5 × 10−4 7.5 × 10−3 1.4 × 10−3 0.031 V30Gy splits at 30cc, 50cc, 70cc all signiﬁcant • Recommend: V30Gy ≤ 50cc • Greater protection than 70cc • More achievable than 30cc • E. Williams (MSKCC) Higgs → Hospital January 17, 2014 14 / 29

48. SBRT Induced Chest-Wall Pain: Univariate Results Variable → V39Gy V30Gy Presc. Dose (Tx) Dose/Fx Num. of Fx Dist. GTV to CW BMI Coef. Std. Err ln L CPH p-value 0.0207 0.0129 0.0008 0.001 −0.47 −0.52 0.04 0.0032 0.0022 0.0002 0.0003 0.18 0.18 0.02 −320.30 −322.65 −329.76 −331.90 −333.85 −330.17 −335.32 1.1 × 10−10 7.8 × 10−10 6.8 × 10−5 7.5 × 10−4 7.5 × 10−3 1.4 × 10−3 0.031 V30Gy splits at 30cc, 50cc, 70cc all signiﬁcant • Recommend: V30Gy ≤ 50cc • Greater protection than 70cc • More achievable than 30cc • E. Williams (MSKCC) Higgs → Hospital January 17, 2014 14 / 29

49. SBRT Induced Chest-Wall Pain: Univariate Results Variable → → → Coef. V39Gy V30Gy Presc. Dose (Tx) Dose/Fx Num. of Fx Dist. GTV to CW BMI Std. Err ln L CPH p-value 0.0207 0.0129 0.0008 0.001 −0.47 −0.52 0.04 0.0032 0.0022 0.0002 0.0003 0.18 0.18 0.02 −320.30 −322.65 −329.76 −331.90 −333.85 −330.17 −335.32 1.1 × 10−10 7.8 × 10−10 6.8 × 10−5 7.5 × 10−4 7.5 × 10−3 1.4 × 10−3 0.031 But we’ve forgotten something! Number of Fractions Dose per Fraction (Gy) Prescription Dose (Gy) 3 4 5 18 − 20 12 9 − 10 54 − 60 60 45 − 50 What is a ‘fraction’ and how does it eﬀect treatment? E. Williams (MSKCC) Higgs → Hospital January 17, 2014 14 / 29

50. SBRT Induced Chest-Wall Pain: Fractionation Eﬀects Radiation therapy is a (3 + 1) − D problem! ‘Fractionation’ refers to how the radiation is delivered over TIME (one fraction = one serving of radiation) E. Williams (MSKCC) Higgs → Hospital January 17, 2014 15 / 29

51. SBRT Induced Chest-Wall Pain: Fractionation Eﬀects Radiation therapy is a (3 + 1) − D problem! ‘Fractionation’ refers to how the radiation is delivered over TIME (one fraction = one serving of radiation) Conventional fractionation (old school): 2 − 3 Gy/fraction → overall treatment times of months! SBRT /Hypo-fractionation (new school): 8 − 20 Gy/fraction (!)→ overall treatment times of week(s) High risk of severe toxicities without sophisticated beam delivery E. Williams (MSKCC) Higgs → Hospital January 17, 2014 15 / 29

52. SBRT Induced Chest-Wall Pain: Fractionation Eﬀects Radiation therapy is a (3 + 1) − D problem! ‘Fractionation’ refers to how the radiation is delivered over TIME (one fraction = one serving of radiation) Conventional fractionation (old school): 2 − 3 Gy/fraction → overall treatment times of months! SBRT /Hypo-fractionation (new school): 8 − 20 Gy/fraction (!)→ overall treatment times of week(s) High risk of severe toxicities without sophisticated beam delivery Why does this matter?? → The biological response of tissues (normal and tumor) depends on the fractionation regime (how much dose per fraction)! E. Williams (MSKCC) Higgs → Hospital January 17, 2014 15 / 29

53. SBRT Induced Chest-Wall Pain: Fractionation Eﬀects How does this eﬀect this study? E. Williams (MSKCC) Higgs → Hospital January 17, 2014 16 / 29

54. SBRT Induced Chest-Wall Pain: Fractionation Effects How does this effect this study? Number of Fractions Cohort has various SBRT fractionation schemes! → Dose per Fraction (Gy) Prescription Dose (Gy) 3 4 5 18 − 20 12 9 − 10 54 − 60 60 45 − 50 Problem: If tissues respond differently to different fractionation schemes (see above), how can we infer dose-responses relationship in a mixed cohort? Solution: Linear-Quadratic Model!2 Proposed as solution to this problem for conventional radiotherapy in the 80s E. Williams (MSKCC) Higgs → Hospital January 17, 2014 16 / 29

55. SBRT Induced Chest-Wall Pain: Fractionation Effects How does this effect this study? Number of Fractions Cohort has various SBRT fractionation schemes! → Dose per Fraction (Gy) Prescription Dose (Gy) 3 4 5 18 − 20 12 9 − 10 54 − 60 60 45 − 50 Problem: If tissues respond differently to different fractionation schemes (see above), how can we infer dose-responses relationship in a mixed cohort? Solution: Linear-Quadratic Model!2 Proposed as solution to this problem for conventional radiotherapy in the 80s E. Williams (MSKCC) Higgs → Hospital January 17, 2014 16 / 29

56. SBRT Induced Chest-Wall Pain: Fractionation Effects How does this effect this study? Number of Fractions Cohort has various SBRT fractionation schemes! → Dose per Fraction (Gy) Prescription Dose (Gy) 3 4 5 18 − 20 12 9 − 10 54 − 60 60 45 − 50 Problem: If tissues respond differently to different fractionation schemes (see above), how can we infer dose-responses relationship in a mixed cohort? Solution: Linear-Quadratic Model!2 Proposed as solution to this problem for conventional radiotherapy in the 80s Currently unclear whether LQ model extends to SBRT → a goal of this study! E. Williams (MSKCC) Higgs → Hospital January 17, 2014 16 / 29

57. SBRT Induced Chest-Wall Pain: LQ Model The LQ Model accounts for the eﬀect of fractionation on cell-killing through a single, tissue dependent, parameter α/β (for more detailed explanation see [Hall 2012]) → Normalized Total Dose (NTD), replaces ‘physical’ dose, and allows for comparison between diﬀerent fractionation schemes: N T Dα/β = (nd)× α β α β +d +2 n − number of fractions d − dose per fraction Using NTD results in models that are easily implementable in the clinic (important). Therefore it would be of much interest if LQ formalism can be applied to predictive models in SBRT cohorts... E. Williams (MSKCC) Higgs → Hospital January 17, 2014 17 / 29

58. SBRT Induced Chest Wall Pain: LQ Model Question: Does using LQ model N T D instead of ‘physical’ dose improve our NTCP models? Method: Compare VD CPH models (previous results) to models using VN T Dα/β for a range of α/β E. Williams (MSKCC) Higgs → Hospital January 17, 2014 18 / 29

59. SBRT Induced Chest Wall Pain: LQ Model Question: Does using LQ model N T D instead of ‘physical’ dose improve our NTCP models? Method: Compare VD CPH models (previous results) to models using VN T Dα/β for a range of α/β −319 Log−likelihood, Cox model −320 Log−likelihood for best VNTD Cox Model −318 Max ln(L) at V39 −322 −324 −326 −328 −330 −332 −334 0 50 100 VD [Gy] 150 200 Physical Dose Best fit ln(L) = −320.3 −319.5 −320 −320.5 −321 −321.5 0 2 4 6 8 10 12 14 16 18 20 22 24 α/β [Gy] Answer: E. Williams (MSKCC) Higgs → Hospital January 17, 2014 18 / 29

60. SBRT Induced Chest Wall Pain: LQ Model Question: Does using LQ model N T D instead of ‘physical’ dose improve our NTCP models? Method: Compare VD CPH models (previous results) to models using VN T Dα/β for a range of α/β −317.8 −318 CPHM NTD −324 Log−likelihood for best V Log−likelihood, Cox model −322 −326 −328 −330 −332 −334 0 NTD Dose Best fit ln(L) = −317.87 at α/β = 2.1 −317.9 −320 −318 −318.1 −318.2 Low 68% CI −318.3 −318.4 Physical Dose Best fit ln(L) = −320.3 −318.5 −318.6 −318.7 50 100 VD [Gy] 150 200 −318.8 0 2 4 6 8 10 12 14 16 18 20 22 24 α/β [Gy] Answer: E. Williams (MSKCC) Higgs → Hospital January 17, 2014 18 / 29

61. SBRT Induced Chest Wall Pain: LQ Model Question: Does using LQ model N T D instead of ‘physical’ dose improve our NTCP models? Method: Compare VD CPH models (previous results) to models using VN T Dα/β for a range of α/β −317.8 −318 CPHM NTD −324 Log−likelihood for best V Log−likelihood, Cox model −322 −326 −328 −330 −332 −334 0 NTD Dose Best fit ln(L) = −317.87 at α/β = 2.1 −317.9 −320 −318 −318.1 −318.2 Low 68% CI −318.3 −318.4 Physical Dose Best fit ln(L) = −320.3 −318.5 −318.6 −318.7 50 100 VD [Gy] 150 200 −318.8 0 2 4 6 8 10 12 14 16 18 20 22 24 α/β [Gy] Answer: Yes, using NTD with any α/β value < 17.7 Gy results in a better SBRT CWP VN T D model than physical dose! E. Williams (MSKCC) Higgs → Hospital January 17, 2014 18 / 29

62. SBRT Induced Chest Wall Pain: LQ Model Question: Does using LQ model N T D instead of ‘physical’ dose improve our NTCP models? Method: Compare VD CPH models (previous results) to models using VN T Dα/β for a range of α/β −317.8 −318 CPHM NTD −324 Log−likelihood for best V Log−likelihood, Cox model −322 −326 −328 −330 −332 −334 0 NTD Dose Best fit ln(L) = −317.87 at α/β = 2.1 −317.9 −320 −318 −318.1 −318.2 Low 68% CI −318.3 −318.4 Physical Dose Best fit ln(L) = −320.3 −318.5 −318.6 −318.7 50 100 VD [Gy] 150 200 −318.8 0 2 4 6 8 10 12 14 16 18 20 22 24 α/β [Gy] Answer: Yes, using NTD with any α/β value < 17.7 Gy results in a better SBRT CWP VN T D model than physical dose! Best ﬁt VN T D model at α/β = 2.1 Gy → V99Gy2.1 (Gyα/β normalized dose units) E. Williams (MSKCC) Higgs → Hospital January 17, 2014 18 / 29

63. SBRT Induced Chest-Wall Pain: CPH Model Results Variable → Coef. Std. Err ln L CPH p-value V99Gy2.1 V30Gyphys Presc. Dose (Tx) Dist. GTV to CW BMI 0.0175 0.0129 0.0008 −0.52 0.04 0.0035 0.0022 0.0002 0.18 0.02 −317.87 −322.65 −329.76 −330.17 −335.32 4.3 × 10−12 7.8 × 10−10 6.8 × 10−5 1.4 × 10−3 0.031 E. Williams (MSKCC) Higgs → Hospital January 17, 2014 19 / 29

64. SBRT Induced Chest-Wall Pain: CPH Model Results Variable → → Coef. Std. Err ln L CPH p-value V99Gy2.1 V30Gyphys Presc. Dose (Tx) Dist. GTV to CW BMI 0.0175 0.0129 0.0008 −0.52 0.04 0.0035 0.0022 0.0002 0.18 0.02 −317.87 −322.65 −329.76 −330.17 −335.32 4.3 × 10−12 7.8 × 10−10 6.8 × 10−5 1.4 × 10−3 0.031 Model: V99Gy2.1 + T x CPH p-value V99Gy2.1 Tx ln L AIC 1.1 × 10−7 0.58 -317.7 639.4 No surprise: LQ-model NTD accounts for diﬀerent fractionations, prescription dose is correlated with # of fractions, should drop out E. Williams (MSKCC) Higgs → Hospital January 17, 2014 19 / 29

65. SBRT Induced Chest-Wall Pain: CPH Model Results Variable → → Coef. Std. Err ln L CPH p-value V99Gy2.1 V30Gyphys Presc. Dose (Tx) Dist. GTV to CW BMI 0.0175 0.0129 0.0008 −0.52 0.04 0.0035 0.0022 0.0002 0.18 0.02 −317.87 −322.65 −329.76 −330.17 −335.32 4.3 × 10−12 7.8 × 10−10 6.8 × 10−5 1.4 × 10−3 0.031 Model: V99Gy2.1 + cm2cw CPH p-value V99Gy2.1 cm2cw E. Williams (MSKCC) ln L AIC 4.3 × 10−7 0.33 -317.4 638.8 Higgs → Hospital January 17, 2014 19 / 29

66. SBRT Induced Chest-Wall Pain: CPH Model Results Variable → → Coef. Std. Err ln L CPH p-value V99Gy2.1 V30Gyphys Presc. Dose (Tx) Dist. GTV to CW BMI 0.0175 0.0129 0.0008 −0.52 0.04 0.0035 0.0022 0.0002 0.18 0.02 −317.87 −322.65 −329.76 −330.17 −335.32 4.3 × 10−12 7.8 × 10−10 6.8 × 10−5 1.4 × 10−3 0.031 Model: V99Gy2.1 +BMI CPH p-value V99Gy2.1 BMI ln L AIC 3.6 × 10−10 0.035 -315.7 635.3 Valid bi-variate CPH model! E. Williams (MSKCC) Higgs → Hospital January 17, 2014 19 / 29

67. SBRT Induced Chest-Wall Pain: CPH Model Results Variable → → Coef. Std. Err ln L CPH p-value V99Gy2.1 V30Gyphys Presc. Dose (Tx) Dist. GTV to CW BMI 0.0175 0.0129 0.0008 −0.52 0.04 0.0035 0.0022 0.0002 0.18 0.02 −317.87 −322.65 −329.76 −330.17 −335.32 4.3 × 10−12 7.8 × 10−10 6.8 × 10−5 1.4 × 10−3 0.031 Two signiﬁcant CPH NTCP models: V99Gy2.1 V99Gy2.1 +BMI CPH p-value V99Gy2.1 ln L AIC 4.3 × 10−12 −317.87 637.7 E. Williams (MSKCC) CPH p-value V99Gy2.1 BMI Higgs → Hospital ln L AIC 3.6 × 10−10 0.035 −315.7 635.3 January 17, 2014 19 / 29

68. SBRT Induced Chest-Wall Pain: CPH Model Results Variable → → Coef. Std. Err ln L CPH p-value V99Gy2.1 V30Gyphys Presc. Dose (Tx) Dist. GTV to CW BMI 0.0175 0.0129 0.0008 −0.52 0.04 0.0035 0.0022 0.0002 0.18 0.02 −317.87 −322.65 −329.76 −330.17 −335.32 4.3 × 10−12 7.8 × 10−10 6.8 × 10−5 1.4 × 10−3 0.031 Two signiﬁcant CPH NTCP models: V99Gy2.1 V99Gy2.1 +BMI CPH p-value V99Gy2.1 ln L AIC 4.3 × 10−12 −317.87 637.7 CPH p-value V99Gy2.1 BMI ln L AIC 3.6 × 10−10 0.035 −315.7 635.3 Bivariate model preferred by AIC E. Williams (MSKCC) Higgs → Hospital January 17, 2014 19 / 29

69. SBRT Induced Chest-Wall Pain: KM + Logrank results V99Gy2.1 +BMI V99Gy2.1 0.8 p = 2.1e − 06 HR = 4.06 V99 < 31.6cc V99 ≥ 31.6cc 0.7 Probability of CW Pain 0.7 Probability of CW Pain 0.8 0.6 0.5 0.4 0.3 0.2 p = 3.2e − 06 HR = 3.84 βV99Gy2.1 × V99Gy2.1 + βBM I × BMI < 1.64 βV99Gy2.1 × V99Gy2.1 + βBM I × BMI ≥ 1.64 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0 0 1 2 3 Years E. Williams (MSKCC) 4 5 6 0 0 Higgs → Hospital 1 2 3 4 5 6 Years January 17, 2014 20 / 29

70. SBRT Induced Chest-Wall Pain: KM + Logrank results V99Gy2.1 +BMI V99Gy2.1 0.8 p = 2.1e − 06 HR = 4.06 V99 < 31.6cc V99 ≥ 31.6cc 0.7 Probability of CW Pain 0.7 Probability of CW Pain 0.8 0.6 0.5 0.4 0.3 0.2 p = 3.2e − 06 HR = 3.84 βV99Gy2.1 × V99Gy2.1 + βBM I × BMI < 1.64 βV99Gy2.1 × V99Gy2.1 + βBM I × BMI ≥ 1.64 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0 0 1 2 3 Years 4 5 6 0 0 1 2 3 4 5 6 Years How do oncologists/medical physcists/planners implement these results? E. Williams (MSKCC) Higgs → Hospital January 17, 2014 20 / 29

71. SBRT Induced Chest-Wall Pain: Clinic Implementation LQ Model results lends to convenient clinical interpretation and implementation: N T Dα/β = Dphys × α Dphys β + Nfx α β +2 Dphys - physical dose used and understood by physicians/planners E. Williams (MSKCC) Higgs → Hospital January 17, 2014 21 / 29

72. SBRT Induced Chest-Wall Pain: Clinic Implementation LQ Model results lends to convenient clinical interpretation and implementation: N T Dα/β = Dphys × α Dphys β + Nfx α β +2 Dphys - physical dose used and understood by physicians/planners 2 ∴ Dphys +( α · Nfx ) × Dphys +(−Nfx · N T Dα/β · ( α +2)) = 0 β β → can solve for Dphys in terms of fraction number (Nfx )← E. Williams (MSKCC) Higgs → Hospital January 17, 2014 21 / 29

73. SBRT Induced Chest-Wall Pain: Clinic Implementation LQ Model results lends to convenient clinical interpretation and implementation: N T Dα/β = Dphys × α Dphys β + Nfx α β +2 Dphys - physical dose used and understood by physicians/planners 2 ∴ Dphys +( α · Nfx ) × Dphys +(−Nfx · N T Dα/β · ( α +2)) = 0 β β → can solve for Dphys in terms of fraction number (Nfx )← Why is this helpful in communicating results? CWP V99Gy2.1 as an example → E. Williams (MSKCC) Higgs → Hospital January 17, 2014 21 / 29

74. SBRT Induced Chest-Wall Pain: Clinic Implementation Example: Presenting CPH V99Gy2.1 results to the MD - 2 scenarios: “To reduce the risk of post-SBRT chest-wall pain...” ‘LQ-model’ speak: Try to keep CW volume receiving at least 99 Gy of normalized total dose with α/β = 2.1 Gy to less than 31.6cc → V99Gy2.1 < 31.6cc ← ‘Physical’ dose model speak: Try to keep CW dose-volume limits given in table: E. Williams (MSKCC) Higgs → Hospital Number of Fractions VD Threshold 3 4 5 V32Gy < 31.6cc V36Gy < 31.6cc V40Gy < 31.6cc January 17, 2014 22 / 29

77. SBRT Induced Chest-Wall Pain: Clinic Implementation Example: Presenting CPH V99Gy2.1 results to the MD - 2 scenarios: “To reduce the risk of post-SBRT chest-wall pain...” ‘LQ-model’ speak: Try to keep CW volume receiving at least 99 Gy of normalized total dose with α/β = 2.1 Gy to less than 31.6cc → V99Gy2.1 < 31.6cc ← ‘Physical’ dose model speak: Try to keep CW dose-volume limits given in table: Oncologists, planners and radiation therapists are more ﬂuent in ‘physical’ dose than ‘LQ-model’ dose! E. Williams (MSKCC) Higgs → Hospital Number of Fractions VD Threshold 3 4 5 V32Gy < 31.6cc V36Gy < 31.6cc V40Gy < 31.6cc January 17, 2014 22 / 29

78. SBRT Induced Chest-Wall Pain: Clincal Results Model: V99Gy2.1 Nfx = 3 Nfx = 4 p = 7.5e − 03 HR = 2.65 0.8 V99 < 57.3cc V99 ≥ 57.3cc 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 Nfx = 5 p = 2.8e − 02 HR = 2.91 0.8 V99 < 28.8cc V99 ≥ 28.8cc 0.7 Probability of CW Pain Probability of CW Pain 0.7 Probability of CW Pain 0.8 0.6 0.5 0.4 0.3 0.2 0.1 1 2 3 Years 4 5 0 0 6 p = 2.4e − 02 HR = 4.34 V99 < 0.716cc V99 ≥ 0.716cc 0.6 0.5 0.4 0.3 0.2 0.1 1 2 3 Years 4 5 0 0 6 0.5 1 1.5 2 Years 2.5 3 3.5 4 Model: V99Gy2.1 +BMI Nfx = 3 Nfx = 4 0.8 βV99Gy2.1 × V99Gy2.1 + βBM I × BMI < 2.1 βV99Gy2.1 × V99Gy2.1 + βBM I × BMI ≥ 2.1 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 p = 8.0e − 02 HR = 2.27 Nfx = 5 0.8 βV99Gy2.1 × V99Gy2.1 + βBM I × BMI < 1.91 βV99Gy2.1 × V99Gy2.1 + βBM I × BMI ≥ 1.91 0.7 Probability of CW Pain Probability of CW Pain 0.7 p = 8.4e − 05 HR = 4.36 Probability of CW Pain 0.8 0.6 0.5 0.4 0.3 0.2 0.1 1 2 3 4 Years E. Williams (MSKCC) 5 6 0 0 p = 1.3e − 01 HR = 3.22 βV99Gy2.1 × V99Gy2.1 + βBM I × BMI < 0.338 βV99Gy2.1 × V99Gy2.1 + βBM I × BMI ≥ 0.338 0.6 0.5 0.4 0.3 0.2 0.1 1 2 3 4 Years Higgs → Hospital 5 6 0 0 0.5 1 1.5 2 2.5 3 3.5 4 Years January 17, 2014 23 / 29

80. Radiation Therapy & Global Health - A Digression Half of the 10 million cancer diagnoses/yr (not counting melanomas of the skin) occur in developing countries where the cancer incidence is increasing dramatically4 Over 25 countries have no radiotherapy services available E. Williams (MSKCC) Higgs → Hospital January 17, 2014 24 / 29

81. Radiation Therapy & Global Health - A Digression Assertion: Normal tissue toxicities should be avoided at all costs, regardless of the technological capabilities of the institute. Question: How can these results be communicated in a global context? E. Williams (MSKCC) Higgs → Hospital January 17, 2014 25 / 29

82. Radiation Therapy & Global Health - A Digression Assertion: Normal tissue toxicities should be avoided at all costs, regardless of the technological capabilities of the institute. Question: How can these results be communicated in a global context? ‘Solution’: Nomograms • Graphical calculating device since 1884 • No computer/calculator necessary • Can be used to display most multivariate predictive models • Hypothetical ‘atlas of nomogram health outcomes’ E. Williams (MSKCC) Higgs → Hospital January 17, 2014 25 / 29

88. Conclusions (I/IV): NTCP Modeling - Lessons Learned Normal Tissue Complication Probability Modeling conclusions: • Normal tissue toxicities are dose limiting and often lethal • NTCP models parameterize clinical and dose-volume metrics to reduce toxicity and increase dose to target • Radiation induced chest-wall pain post-SBRT: • LQ-model dose superior to physical dose predicting CWP • Improved VD CW thresholds (implemented at MSKCC), potentially reducing future complications • VD +BMI model best predicts ≥ 2 Grade CWP • Nomograms provide quick, practical and intuitive multivariate probability calculations E. Williams (MSKCC) Higgs → Hospital January 17, 2014 26 / 29

96. Conclusions (II/IV): Medical Physics - Lessons Learned Conducted multiple health outcomes studies while at MSKCC: • Chest-wall pain in thoracic SBRT: • Modeling of predictive parameters • Eﬃcacy of linear-quadratic dose correction in model building • Modeling radiation pneumonitis: • on generalized equivalent uniform dose in a pooled cohort • due to regional lung sensitivities in NSCLC radiation treatments • after incidental irradiation of the heart • Incidence of brachial plexopathy after high-dose SBRT • Dosimetric predictors of esophageal toxicity after SBRT for central lung tumors • Modeling pulmonary toxicity in a large cohort of central lung tumors treated with SBRT E. Williams (MSKCC) Higgs → Hospital January 17, 2014 27 / 29

102. Conclusions (III/IV): Particle Physics - Lessons Learned ‘Big data’ analytics and modeling experience acquired at CERN: • Conducted a search for exotic theoretical particle - Extra-dimensional Warped Randall-Sundrum Graviton (spoiler: I didn’t ﬁnd it) • Huge data: 3TB of ‘clean’ data • Quantiﬁcation of discovery (or lack there of) • Tools: Machine learning (e.g. boosted decision trees), Monte-Carlo simulation, Bayesian/Frequentist models, etc... • Complete parameterization of systematic uncertainties→ crucial for generating and communicating estimates for the Global Burden of Disease • Managing large scale data analysis projects from inception to completion • Extensive experience working in large research organizations with diverse colleagues E. Williams (MSKCC) Higgs → Hospital January 17, 2014 28 / 29

110. Conclusions (IV/IV) Finally, I am excited for the opportunity to transfer the skills I’ve acquired at the CERN and Memorial Sloan-Kettering Cancer Center to address the greatest challenges in Global Health E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29

111. Conclusions (IV/IV) Finally, I am excited for the opportunity to transfer the skills I’ve acquired at the CERN and Memorial Sloan-Kettering Cancer Center to address the greatest challenges in Global Health Thank you! E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29

112. Backups

113. References I [1] IMV Medical Information Division. “Physician Characteristics and Distribution in the U.S.” In: 2003 SROA Benchmarking (2010). [2] Fowler FJ. “The linear-quadratic model and progress in radiotherapy”. In: BR. J. Radiol. 62 (1989), pp. 679–694. [3] Barnett GC, West CML, Dunning AM, et al. “Normal tissue reactions to radiotherapy: towards tailoring treatment dose by genotype”. In: Nature Reviews Cancer 9 (2009), pp. 134–142. [4] IAEA. A Silent Crisis: Cancer Treatment in Developing Countries. 2006. [5] Marks LB, Yorke ED, and Deasy JO. “Use of Normal Tissue Complicatoin Probability Models in the Clinic”. In: Int. J. Radiation Oncology Biol. Phys. 76 (2010), S10–S19. E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29

114. Karnofsky performance status (KPS) In medicine (oncology and other ﬁelds), performance status is an attempt to quantify cancer patients’ general well-being and activities of daily life. This measure is used to determine whether they can receive chemotherapy, whether dose adjustment is necessary, and as a measure for the required intensity of palliative care. It is also used in oncological randomized controlled trials as a measure of quality of life. E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29

115. CWP: Linear-Quadratic Model Modeling fractionation: Linear-Quadratic Model • LQ model describes cell-survival curves assuming two components of cell killing 1) ∝ dose (single-strand DNA breaks) 2) ∝ dose2 (double-strand DNA breaks) • Cell survival then modeled: S = e−αD−βD E. Williams (MSKCC) 2 Higgs → Hospital January 17, 2014 29 / 29

116. CWP: Linear-Quadratic Model Modeling fractionation: Linear-Quadratic Model • LQ model describes cell-survival curves assuming two components of cell killing 1) ∝ dose (single-strand DNA breaks) 2) ∝ dose2 (double-strand DNA breaks) • Cell survival then modeled: S = e−αD−βD 2 From this cell-survival model, we can derive a Normalized Total Dose (NTD) useful to compare two diﬀerent fractionation schemes: N T D = (nd) × (1 + d α/β )/(1 + 2 α/β ) n - number of fractions d - dose per fraction → α/β is a free, tissue dependent, parameter → Given α/β, NTD replaces dose and allows comparison between diﬀerent fractionation schemes E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29

117. CWP: Linear-Quadratic Model Modeling fractionation: Linear-Quadratic Model • LQ model describes cell-survival curves assuming two components of cell killing 1) ∝ dose (single-strand DNA breaks) 2) ∝ dose2 (double-strand DNA breaks) • Cell survival then modeled: S = e−αD−βD 2 From this cell-survival model, we can derive a Normalized Total Dose (NTD) useful to compare two diﬀerent fractionation schemes: N T D = (nd) × (1 + d α/β )/(1 + 2 α/β ) n - number of fractions d - dose per fraction → α/β is a free, tissue dependent, parameter → Given α/β, NTD replaces dose and allows comparison between diﬀerent fractionation schemes E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29

118. CWP: CPH Univariate Backup Variable → beta D83cc Dist. GTV to CW BMI se ln L 0.0766 −0.52 0.04 0.0136 0.18 0.02 −323.30 −330.17 −335.32 0 −326 −328 −330 −332 −2 CPH p−value Low 68% CI Low 95% CI Max LogL = −323.3 at D83 cc −324 CPH log−likelihood 1.7 × 10−8 1.4 × 10−3 0.031 10 −322 10 −4 10 −6 10 −334 −336 −338 0 CPH p-value Min p−val = 1.7e−08 at D83 cc −8 200 400 600 800 1000 10 0 400 600 800 1000 (DV) Volume [cc] (DV) Volume [cc] E. Williams (MSKCC) 200 Higgs → Hospital January 17, 2014 29 / 29

119. CWP: CPH Univariate Backup Variable → D83cc Dist. GTV to CW BMI beta se ln L 0.0766 −0.52 0.04 0.0136 0.18 0.02 CPH p-value −323.30 −330.17 −335.32 1.7 × 10−8 1.4 × 10−3 0.031 DV and VD correlated due to DVH constraints (R(V39Gy , D83cc ) = 0.86) R(VD,DV) Correlations (DV) Volume [cc] 1000 0.8 800 0.6 600 0.4 400 0.2 200 20 40 60 (VD) Dose [Gy] E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29

120. CWP: CPH Univariate Backup Variable → D83cc Dist. GTV to CW BMI E. Williams (MSKCC) beta se ln L 0.0766 −0.52 0.04 0.0136 0.18 0.02 −323.30 −330.17 −335.32 Higgs → Hospital CPH p-value 1.7 × 10−8 1.4 × 10−3 0.031 January 17, 2014 29 / 29

121. CWP: CPH Univariate Backup Variable → D83cc Dist. GTV to CW BMI E. Williams (MSKCC) beta se ln L 0.0766 −0.52 0.04 0.0136 0.18 0.02 −323.30 −330.17 −335.32 Higgs → Hospital CPH p-value 1.7 × 10−8 1.4 × 10−3 0.031 January 17, 2014 29 / 29

122. CWP: ROC Curves V30Gy AU C: area under curve = probability that random positive instance will be assigned correctly AU C S.E. 95% CI 0.73 0.038 0.66 - 0.81 Standardized AUC (σAU C ): 6.02 p-value: 8.7×10−10 T P : True Positive: # complications above cut F P : False Positive: # censor above cut T N : True Negative: # censor below cut F N : False Negative: # complications below cut V30 Threshold Higgs → Hospital F N/T N 30cc 50cc 70cc E. Williams (MSKCC) T P/F P 57/178 53/120 42/69 7/74 11/132 22/183 January 17, 2014 29 / 29

123. CWP: ROC Curves V30Gy V30 Threshold Senstivity Speciﬁcity Eﬃciency TP T P +F N TN T N +F P T P +T N T P +T N +F P +T N 30cc 50cc 70cc 0.891 0.828 0.656 0.294 0.524 0.726 0.415 0.585 0.712 E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29

124. CWP: Average DVHs (2cm and 3cm defs) E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29

125. Universal Survival Curve

126. Survival Curves • The linear quadratic (LQ) model approximates clonogenic survival data with truncated power series expansion of natural log of surviving proportion S, → ln S = −α · d − β · d2 • LQ model overestimates the effect of radiation on clonogenicity in the high doses commonly used in SBRT • The multitarget model (MTM) provides another description of clonogenic survival, assuming n targets need to be hit to disrupt clonogenicity S = e−d/d1 · 1 − (1 − e−d/D0 )n • d1 and D0 are the parameters that determine the initial (first log kill) and final “slopes” of survival curve • Fits empirical data well, especially in the high-dose range → Universal Survival Curve hybridizes LQ model for low-dose range and the multitarget model asymptote for high-dose range E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29

127. Universal Survival Curve • Universal Survival Curve (USC) described by: ln S = −(α · d + β · d2 ) if d ≤ DT D 1 − D0 d + Dq if d ≥ DT 0 • 4 independent params (α, β, D0 , and Dq ) constrainted to 3 when asymptotic line of MTM is tangential to LQ model parabola at DT • β as dependent variable allows params. to be obtained by measured curve β= (1 − α · D0 )2 4D0 · Dq • Transition dose, DT , calculated as a function of three remaining USC params 2 · Dq DT = 1 − α · D0 E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29

128. CWP: Model Comparisons LQ and USC models: α/β = 3 Gy Model LQ gEUD LQ DMAX Phys gEUD Phys DMAX USC gEUD USC DMAX E. Williams (MSKCC) Best Model Parameters log10 (a) log10 (a) log10 (a) log10 (a) log10 (a) α · D0 Dq DT log10 (a) α · D0 Dq DT = = = = = = = = = = = = Logistic Regression Log-likelihood/df AIC −0.467 −0.469 −0.459 −0.461 295.30 296.53 290.25 291.51 −0.453 290.22 −0.461 295.34 1.1 ∞ 1.3 ∞ 0.6 0.22 6.4 Gy 16.4 Gy ∞ 0.13 6.6 Gy 15.2 Gy Higgs → Hospital January 17, 2014 29 / 29

129. CWP Logistic Regression Model Responses LQ gEUD, AIC= 295.3 Phys gEUD, AIC= 290.25 0.5 0.4 0.3 0.2 0.1 0.5 0.4 0.3 0.2 0.1 50 100 150 200 250 300 350 400 0 0 450 gEUDLQ log10(a) =1 0.3 0.2 10 20 30 40 50 0 0 60 CWP probability 0.4 0.3 0.2 0.3 400 500 E. Williams (MSKCC) 600 120 140 160 180 200 0 0 0.4 0.3 0.2 0.1 0.1 Max BED Dose [Gy] 100 0.5 0.4 0.2 0.1 80 0.6 0.5 0.5 300 60 0.7 0.6 200 40 USC DMAX , AIC= 295.34 0.7 0.6 100 20 gEUDUSC log10(a) =0.6 Phys DMAX , AIC= 291.51 0.7 CWP probability 0.4 gEUDPHYS log10(a) =1.3 LQ DMAX , AIC= 296.53 0 0 0.5 0.1 CWP probability 0 0 0.6 Complication rate observed 0.6 Complication rate observed Complication rate observed 0.6 USC gEUD, AIC= 290.22 10 20 30 40 50 Max PHYS Higgs → Hospital 60 70 0 0 50 100 150 200 250 300 350 400 USC Dmax [Gy] January 17, 2014 29 / 29

130. LQ Model: Chest-wall pain • gEUD analysis with −1 < log10 (a) < 1 • BEDLQ model with single parameter α/β → BEDLQ = D 1 + d α/β 314 −0.46 312 −0.465 310 308 306 −0.475 AIC Log−likelihood / df −0.47 −0.48 304 302 300 −0.485 298 −0.49 −0.495 −1 296 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 294 −1 Max log-likelihood/df = −0.467 E. Williams (MSKCC) −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 log10(a) log10(a) Min AIC(n paramLQ = 1) = 295.33 Higgs → Hospital January 17, 2014 29 / 29

131. LQ Model: Chest-wall pain −1 10 0.6 −2 Complication rate observed 10 p−value −3 10 −4 10 −5 10 0.5 0.4 0.3 0.2 0.1 −6 10 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 0 0 log10(a) 50 100 150 200 250 300 350 400 450 gEUDLQ log10(a) =1 Min p-value at log10 (a) = 1 p = 1.1 × 10−6 E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29

132. Universal Survival Curve: Chest-wall pain • gEUD analysis with −1 < log10 (a) < 1 • BEDU SC model with three parameters: α/β, α · D0 and Dq BEDU SC = • α β D 1+ 1 α·D0 d α/β if d ≤ DT (D − n · Dq ) if d ≥ DT = 3 Gy, (α · D0 ) = 0.01 : 0.01 : 0.5, Dq = 0.2 : 0.2 : 7.6 Gy 320 −0.455 0.7 −0.46 0.7 0.6 315 0.5 310 0.6 0.4 −0.475 −0.48 0.3 −0.485 0.2 −0.49 0.1 −0.495 0.4 305 AIC −0.47 α⋅ D0 α⋅ D 0 0.5 Log−likelihood/df −0.465 0.3 300 0.2 295 0.1 −0.5 1 2 3 4 5 6 1 7 Dq [Gy] 2 3 4 5 6 7 Dq [Gy] Max llhd/df = −0.453 at Dq = 6.4 Gy, α · D0 = 0.22 Min AIC = 290.23 at Dq = 6.4 Gy, α · D0 = 0.22 log10 (a) = 0.6 log10 (a) = 0.6, llhd = −0.453 E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29

133. Universal Survival Curve: Chest-wall pain 60 0.7 50 0.6 40 0.4 30 DT α⋅ D 0 0.5 0.3 20 0.2 10 1 0.7 1 2 3 4 5 6 0.8 7 0.6 0.6 Dq [Gy] 0.7 0.4 0.5 0.06 α⋅ D0 0.2 0.6 0.05 0.5 P−value α⋅ D0 0.03 0 −0.2 0.3 0.04 0.4 0.4 −0.4 0.2 −0.6 0.3 0.02 Best log10(a) 0.1 0.1 −0.8 0.2 0.01 0.1 1 2 3 4 5 6 7 −1 D [Gy] q 1 2 3 4 5 6 7 Dq [Gy] E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29

134. Universal Survival Curve: Chest-wall pain −0.451 −0.455 0.7 −0.452 −0.46 0.6 −0.47 0.4 −0.475 −0.48 0.3 −0.485 0.2 −0.49 0.1 Log−likelihood/df α⋅ D0 0.5 Max Log−likelihood/df −0.453 −0.465 −0.495 2 3 4 5 6 −0.455 −0.456 −0.457 −0.458 −0.459 −0.5 1 −0.454 −0.46 0 7 0.1 0.2 Dq [Gy] 0.4 0.5 −0.45 −0.452 −0.452 −0.453 −0.454 Max Log−likelihood/df −0.451 Max Log−likelihood/df 0.3 α⋅ D0 [Gy] −0.454 −0.455 −0.456 −0.457 −0.458 −0.458 −0.46 −0.462 −0.464 −0.459 −0.466 −0.46 −0.461 0 68% CI 95% CI −0.456 1 2 3 4 Dq [Gy] E. Williams (MSKCC) 5 6 7 8 −0.468 0 Higgs → Hospital 5 10 15 DT [Gy] 20 January 17, 2014 25 30 29 / 29

135. Universal Survival Curve: Chest-wall pain • “Fraction Full CW LQ” - Fraction of 1 0.7 0.7 0.5 0 0.6 0.4 0.5 0.4 0.3 0.3 0.2 Fraction Full CW LQ 0.8 0.6 α⋅ D patients with all dose bins ≤ DT (calc as BEDLQ ) 0.9 • “Fraction LQ Bins” - Fraction of all dose bins with ≤ DT (calc as BEDLQ ) 1 0.9 0.8 0.2 0.1 0.7 1 2 3 4 5 6 7 Fraction LQ 0.1 0 Dq [Gy] 1 0.7 α⋅ D 0 0.6 0.4 0.5 0.3 0.4 0.2 0.1 Fraction LQ Bins 0.5 0.4 0.2 0.8 0.7 Fraction Full CW LQ Fraction Bins LQ 0.5 0.3 0.9 0.6 0.6 0 0 5 10 15 20 25 30 35 D [Gy] T • Steps in Fraction Full CW LQ, patient 0.3 0.2 fractionation schemes? • At best ﬁt: 0.1 0.1 1 2 3 4 5 6 7 Dq [Gy] E. Williams (MSKCC) Higgs → Hospital • Frac LQ bins = 0.947 • Frac Full LQ = 0.703 January 17, 2014 29 / 29

136. Universal Survival Curve: CWP LQ model USC model 0.6 Complication rate observed Complication rate observed 0.6 0.5 0.4 0.3 0.2 0.1 0.5 0.4 0.3 0.2 0.1 0 0 50 100 150 200 250 300 350 gEUDLQ log10(a) =1 400 450 0 0 40 60 80 100 120 140 160 180 200 gEUDUSC log10(a) =0.6 Max llhd/df = −0.467 p = 1.1 × 10−6 , log10 (a) = 1 AIC = 295.33 E. Williams (MSKCC) 20 Max llhd/df = −0.453 p = 1.8 × 10−7 , log10 (a) = 0.6 AIC = 290.2 Dq = 6.4 Gy, α · D0 = 0.22 DT = 16.4 Gy Higgs → Hospital January 17, 2014 29 / 29

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