From Higgs to the Hospital: Normal Tissue Complication Probability Modeling in Radiation Therapy
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Transcript of From Higgs to the Hospital: Normal Tissue Complication Probability Modeling in Radiation Therapy
From Higgs to the Hospital: Normal TissueComplication Probability Modeling in Radiation
Therapy
Eric Williams
Memorial Sloan-Kettering Cancer CenterNew York, NY
January 17, 2014
Overview
• IntroductionWhat does the Higgs have to do with it?
• The α, β, γ’s of Radiation in MedicineDiscovery and modern use
• Normal Tissue Complication Probability ModelingNTCP → DVH → NTD: A short history of acronyms
• Radiation induced Chest-Wall PainA retrospective analysis
• Radiation Therapy & Global HealthA digression
• ConclusionsSeriously though, whats the deal with the Higgs?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 1 / 29
Overview
• IntroductionWhat does the Higgs have to do with it?
• The α, β, γ’s of Radiation in MedicineDiscovery and modern use
• Normal Tissue Complication Probability ModelingNTCP → DVH → NTD: A short history of acronyms
• Radiation induced Chest-Wall PainA retrospective analysis
• Radiation Therapy & Global HealthA digression
• ConclusionsSeriously though, whats the deal with the Higgs?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 1 / 29
Overview
• IntroductionWhat does the Higgs have to do with it?
• The α, β, γ’s of Radiation in MedicineDiscovery and modern use
• Normal Tissue Complication Probability ModelingNTCP → DVH → NTD: A short history of acronyms
• Radiation induced Chest-Wall PainA retrospective analysis
• Radiation Therapy & Global HealthA digression
• ConclusionsSeriously though, whats the deal with the Higgs?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 1 / 29
Overview
• IntroductionWhat does the Higgs have to do with it?
• The α, β, γ’s of Radiation in MedicineDiscovery and modern use
• Normal Tissue Complication ProbabilityModelingNTCP → DVH → NTD: A short history of acronyms
• Radiation induced Chest-Wall PainA retrospective analysis
• Radiation Therapy & Global HealthA digression
• ConclusionsSeriously though, whats the deal with the Higgs?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 1 / 29
Overview
• IntroductionWhat does the Higgs have to do with it?
• The α, β, γ’s of Radiation in MedicineDiscovery and modern use
• Normal Tissue Complication Probability ModelingNTCP → DVH → NTD: A short history of acronyms
• Radiation induced Chest-Wall PainA retrospective analysis
• Radiation Therapy & Global HealthA digression
• ConclusionsSeriously though, whats the deal with the Higgs?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 1 / 29
Overview
• IntroductionWhat does the Higgs have to do with it?
• The α, β, γ’s of Radiation in MedicineDiscovery and modern use
• Normal Tissue Complication Probability ModelingNTCP → DVH → NTD: A short history of acronyms
• Radiation induced Chest-Wall PainA retrospective analysis
• Radiation Therapy & Global HealthA digression
• ConclusionsSeriously though, whats the deal with the Higgs?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 1 / 29
Overview
• IntroductionWhat does the Higgs have to do with it?
• The α, β, γ’s of Radiation in MedicineDiscovery and modern use
• Normal Tissue Complication Probability ModelingNTCP → DVH → NTD: A short history of acronyms
• Radiation induced Chest-Wall PainA retrospective analysis
• Radiation Therapy & Global HealthA digression
• ConclusionsSeriously though, whats the deal with the Higgs?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 1 / 29
Overview
• IntroductionWhat does the Higgs have to do with it?
• The α, β, γ’s of Radiation in MedicineDiscovery and modern use
• Normal Tissue Complication Probability ModelingNTCP → DVH → NTD: A short history of acronyms
• Radiation induced Chest-Wall PainA retrospective analysis
• Radiation Therapy & Global HealthA digression
• ConclusionsSeriously though, whats the deal with the Higgs?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 1 / 29
Introduction
From Higgs:
↓
To Health:
↓
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 2 / 29
Overview
• IntroductionWhat does the Higgs have to do with it?
• The α, β, γ’s of Radiation in MedicineDiscovery and modern use
• Normal Tissue Complication Probability ModelingNTCP → DVH → NTD: A short history of acronyms
• Radiation induced Chest-Wall PainA retrospective analysis
• Radiation Therapy & Global HealthA digression
• ConclusionsSeriously though, whats the deal with the Higgs?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 2 / 29
Radiation in Medicine – Discovery
• Radiation (x-rays) discovered by Wilhelm Roentgen(1895) while Henri Becquerel concurrently discoveredradioactivity (uranium)
• Following, Marie Curie pioneered research inradioactivity with radium and polonium
• Potential to medicine quickly realized (Figure 1)
• Within a month, radiographs were underproduction
• Within 6 months, they were used in battle tolocate bullets in soldiers
Figure 1: The firstx-ray of BerthaRoentgen’s hand.• Dangers of radiation also quick to surface:
“If one leaves a small glass ampulla with several centigramsof radium salt in ones pocket for a few hours, one will feelabsolutely nothing. But in 15 days afterwards redness willappear on the epidermis, and then a sore, which will be verydifficult to heal. A more prolonged action could lead toparalysis and death.”– Pierre Curie, Nobel lecture 1903
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 3 / 29
Radiation in Medicine – Discovery
• Radiation (x-rays) discovered by Wilhelm Roentgen(1895) while Henri Becquerel concurrently discoveredradioactivity (uranium)
• Following, Marie Curie pioneered research inradioactivity with radium and polonium
• Potential to medicine quickly realized (Figure 1)
• Within a month, radiographs were underproduction
• Within 6 months, they were used in battle tolocate bullets in soldiers
Figure 1: The firstx-ray of BerthaRoentgen’s hand.• Dangers of radiation also quick to surface:
“If one leaves a small glass ampulla with several centigramsof radium salt in ones pocket for a few hours, one will feelabsolutely nothing. But in 15 days afterwards redness willappear on the epidermis, and then a sore, which will be verydifficult to heal. A more prolonged action could lead toparalysis and death.”– Pierre Curie, Nobel lecture 1903
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 3 / 29
Radiation in Medicine – Discovery
• Radiation (x-rays) discovered by Wilhelm Roentgen(1895) while Henri Becquerel concurrently discoveredradioactivity (uranium)
• Following, Marie Curie pioneered research inradioactivity with radium and polonium
• Potential to medicine quickly realized (Figure 1)
• Within a month, radiographs were underproduction
• Within 6 months, they were used in battle tolocate bullets in soldiers
Figure 1: The firstx-ray of BerthaRoentgen’s hand.• Dangers of radiation also quick to surface:
“If one leaves a small glass ampulla with several centigramsof radium salt in ones pocket for a few hours, one will feelabsolutely nothing. But in 15 days afterwards redness willappear on the epidermis, and then a sore, which will be verydifficult to heal. A more prolonged action could lead toparalysis and death.”– Pierre Curie, Nobel lecture 1903
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 3 / 29
Radiation in Medicine – Modern Use
• Diagnostic tools:• X-ray images → computed tomography (CT )• Positron Emission Tomography (PET )• Magnetic Resonance Imaging (MRI )
Eleckta Linear Accelerator• Therapeutic tools:• 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
Radiation in Medicine – Modern Use
• Diagnostic tools:• X-ray images → computed tomography (CT )• Positron Emission Tomography (PET )• Magnetic Resonance Imaging (MRI )
Eleckta Linear Accelerator• Therapeutic tools:• 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
Radiation in Medicine – Modern Use
• Diagnostic tools:• X-ray images → computed tomography (CT )• Positron Emission Tomography (PET )• Magnetic Resonance Imaging (MRI )
Eleckta Linear Accelerator• Therapeutic tools:• 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
Overview
• IntroductionWhat does the Higgs have to do with it?
• The α, β, γ’s of Radiation in MedicineDiscovery and modern use
• Normal Tissue Complication ProbabilityModelingNTCP → DVH → NTD: A short history of acronyms
• Radiation induced Chest-Wall PainA retrospective analysis
• Radiation Therapy & Global HealthA digression
• ConclusionsSeriously though, whats the deal with the Higgs?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 4 / 29
NTCP Modeling: Purpose
A key challenge in radiotherapy is maximizing radiation doses to cancercells while minimizing damage to surrounding healthy (normal) tissue
Successful tumor control depends principally on the total dosedelivered, but tolerances of surrounding normal tissues limit this dose.3
Goal: To model Normal Tissue Complication Probability (NTCP), basedon clinical and dosimetric predictors, to reduce future toxicities and allowhigher doses to the target for greater tumor control.
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 5 / 29
NTCP Modeling: Dose-Volume Histograms
To obtain useful predictors, need to simplify complicated 3Ddosimetric and anatomic information from treatment plans:
Lung Treatment Plan
→Dose-Volume Histogram
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 6 / 29
NTCP Modeling: Dose-Volume Histograms
Dose-volume histograms (DVH)
• DVHs summarize dose-volume information for a particularstructure (e.g. tumor, or organ)
• A point on the DVH represents: The volume (V) of the givenstructure 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
NTCP Modeling: Dose-Volume Histograms
Dose-volume histograms (DVH)
• DVHs summarize dose-volume information for a particularstructure (e.g. tumor, or organ)
• A point on the DVH represents: The volume (V) of the givenstructure 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
NTCP Modeling: Dose-Volume Histograms
Dose-volume histograms (DVH)
• DVHs summarize dose-volume information for a particularstructure (e.g. tumor, or organ)
• A point on the DVH represents: The volume (V) of the givenstructure 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
NTCP Modeling: Model Building
• NTCP models use these DVH reduction values (e.g. VD) aspredictive parameters to produce a single measure: probability ofcomplication
→ ??? →
???
Common NTCPindependent 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)
Common NTCPcomplication probability models
• Logistic Regression
• ROC Analysis
• Cox Proportional Hazards
• Logrank + Kaplan-Meier
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 8 / 29
NTCP Modeling: Model Building
• NTCP models use these DVH reduction values (e.g. VD) aspredictive parameters to produce a single measure: probability ofcomplication
→ VD,i →
VD
Common NTCPindependent 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)
Common NTCPcomplication probability models
• Logistic Regression
• ROC Analysis
• Cox Proportional Hazards
• Logrank + Kaplan-Meier
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 8 / 29
NTCP Modeling: Model Building
• NTCP models use these DVH reduction values (e.g. VD) aspredictive parameters to produce a single measure: probability ofcomplication
→ MeanDosei →
Dmean
Common NTCPindependent 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)
Common NTCPcomplication probability models
• Logistic Regression
• ROC Analysis
• Cox Proportional Hazards
• Logrank + Kaplan-Meier
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 8 / 29
NTCP Modeling: Model Building
• NTCP models use these DVH reduction values (e.g. VD) aspredictive parameters to produce a single measure: probability ofcomplication
→ F(Di, Vi, ...)→
F(D,V, ...)
Common NTCPindependent 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)
Common NTCPcomplication probability models
• Logistic Regression
• ROC Analysis
• Cox Proportional Hazards
• Logrank + Kaplan-Meier
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 8 / 29
NTCP Modeling: Model Building
• NTCP models use these DVH reduction values (e.g. VD) aspredictive parameters to produce a single measure: probability ofcomplication
→ ??? →
???
Common NTCPindependent 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)
Common NTCPcomplication probability models
• Logistic Regression
• ROC Analysis
• Cox Proportional Hazards
• Logrank + Kaplan-Meier
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 8 / 29
NTCP Modeling: Model Building
• NTCP models use these DVH reduction values (e.g. VD) aspredictive parameters to produce a single measure: probability ofcomplication
→ ??? →
0 10 20 30 40 50 600
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
gEUD [Gy]
Com
plic
ation p
robabili
ty
log10
(a) = 0.6
p−val: 1.33e−04
Common NTCPindependent 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)
Common NTCPcomplication probability models
• Logistic Regression
• ROC Analysis
• Cox Proportional Hazards
• Logrank + Kaplan-Meier
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 8 / 29
NTCP Modeling: Model Building
• NTCP models use these DVH reduction values (e.g. VD) aspredictive parameters to produce a single measure: probability ofcomplication
→ ??? →
Common NTCPindependent 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)
Common NTCPcomplication probability models
• Logistic Regression
• ROC Analysis
• Cox Proportional Hazards
• Logrank + Kaplan-Meier
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 8 / 29
NTCP Modeling: Model Building
• NTCP models use these DVH reduction values (e.g. VD) aspredictive parameters to produce a single measure: probability ofcomplication
→ ??? →
Common NTCPindependent 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)
Common NTCPcomplication probability models
• Logistic Regression
• ROC Analysis
• Cox Proportional Hazards
• Logrank + Kaplan-Meier
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 8 / 29
NTCP Modeling: Model Building
• NTCP models use these DVH reduction values (e.g. VD) aspredictive parameters to produce a single measure: probability ofcomplication
→ ??? →
Common NTCPindependent 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)
Common NTCPcomplication probability models
• Logistic Regression
• ROC Analysis
• Cox Proportional Hazards
• Logrank + Kaplan-Meier
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 8 / 29
Overview
• IntroductionWhat does the Higgs have to do with it?
• The α, β, γ’s of Radiation in MedicineDiscovery and modern use
• Normal Tissue Complication Probability ModelingNTCP → DVH → NTD: A short history of acronyms
• Radiation induced Chest-Wall PainA retrospective analysis
• Radiation Therapy & Global HealthA digression
• ConclusionsSeriously though, whats the deal with the Higgs?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 8 / 29
SBRT Induced Chest-Wall Pain: Purpose
Chest-wall pain (CWP) is among the most common adverse effectsof 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 incidenceof CWP using dose/volume and clinical parameters.
Prescriptive→ Derive clinically implementabledose/volume guidelines (thresholds) to be imposed infuture treatments.
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 9 / 29
SBRT Induced Chest-Wall Pain: Purpose
Chest-wall pain (CWP) is among the most common adverse effectsof 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 incidenceof CWP using dose/volume and clinical parameters.
Prescriptive→ Derive clinically implementabledose/volume guidelines (thresholds) to be imposed infuture treatments.
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 9 / 29
SBRT Induced Chest-Wall Pain: Purpose
Chest-wall pain (CWP) is among the most common adverse effectsof 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 incidenceof CWP using dose/volume and clinical parameters.
Prescriptive→ Derive clinically implementabledose/volume guidelines (thresholds) to be imposed infuture treatments.
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 9 / 29
SBRT Induced Chest-Wall Pain: Patient Cohort
Patient and Tumor Characteristics• 316 lung tumors in 295 patients treated between 2006-2012 wereretrospectively analyzed
N Percent (%)
Median age 77 (49− 95)yMedian KPS 70 (50− 100)Tumor
Primary NSCLC 285 90.2Oligometastatic 13 4.1Recurrent 18 5.7
Doses x Num Fx.18− 20 Gy × 3 113 35.812 Gy × 4 114 36.19− 10 Gy × 5 62 19.6Other 27 8.5
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 10 / 29
SBRT Induced Chest-Wall Pain: Chest-wall definition
Definition of chest wall (CW)
Chest wall contoured for each patient:
• 2cm expansion of the lung inrind around ipsilateral lung
• 4 CT slices (0.8 cm) aboveand below the tumor
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 11 / 29
SBRT Induced Chest-Wall Pain: Outcome Definition
Definition of Chest-Wall Piain (CWP)
CWP Grade Description
Grade 1 Mild pain, not interfering with functionGrade 2 Moderate pain interfering with function but not ADLs,
requiring NSAIDs/TylenolGrade 3 Severe pain interfering with ADLs, requiring narcotics,
or needing intervention
CTCAE v4.0 with specifications
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 12 / 29
SBRT Induced Chest-Wall Pain: Outcome Definition
Definition of Chest-Wall Piain (CWP)
CWP Grade Description
Grade 1 Mild pain, not interfering with functionGrade 2 Moderate pain interfering with function but not
ADLs, requiring NSAIDs/TylenolGrade 3 Severe pain interfering with ADLs, requiring
narcotics, or needing intervention
CTCAE v4.0 with specifications
CWP outcome studied ≥ 2 Grade.
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 12 / 29
SBRT Induced Chest-Wall Pain: Modeling
Actuarial analysis necessary due to inherent latency of chest-wall pain
0 1 2 3 4 5 60
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Years
Inic
idence o
f gra
de >
= 2
Chestw
all
Pain
Median onset time: 0.61 yr
• 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 methodused to assess correlation of risk factors to CWP
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 13 / 29
SBRT Induced Chest-Wall Pain: Univariate Results
Variable Coef. Std. Err lnL CPH p-value
→
V39Gy 0.0207 0.0032 −320.30 1.1× 10−10
→
V30Gy 0.0129 0.0022 −322.65 7.8× 10−10
→
Presc. Dose (Tx) 0.0008 0.0002 −329.76 6.8× 10−5
→
Dose/Fx 0.001 0.0003 −331.90 7.5× 10−4
→
Num. of Fx −0.47 0.18 −333.85 7.5× 10−3
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→
BMI 0.04 0.02 −335.32 0.031
Predictors not significant in univariate CPH: KPS, Sex, Age
Variable beta se lnL p-value
KPS -0.02 0.01 -337.06 0.25Sex -0.18 0.26 -337.45 0.48Age -0.01 0.01 -337.68 0.83
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 14 / 29
SBRT Induced Chest-Wall Pain: Univariate Results
Variable Coef. Std. Err lnL CPH p-value
→ V39Gy 0.0207 0.0032 −320.30 1.1× 10−10
→ V30Gy 0.0129 0.0022 −322.65 7.8× 10−10
→
Presc. Dose (Tx) 0.0008 0.0002 −329.76 6.8× 10−5
→
Dose/Fx 0.001 0.0003 −331.90 7.5× 10−4
→
Num. of Fx −0.47 0.18 −333.85 7.5× 10−3
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→
BMI 0.04 0.02 −335.32 0.031
• VD is a common dose-volume metric utilized by planners in theclinic, 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
SBRT Induced Chest-Wall Pain: Univariate Results
Variable Coef. Std. Err lnL CPH p-value
→ V39Gy 0.0207 0.0032 −320.30 1.1× 10−10
→ V30Gy 0.0129 0.0022 −322.65 7.8× 10−10
→
Presc. Dose (Tx) 0.0008 0.0002 −329.76 6.8× 10−5
→
Dose/Fx 0.001 0.0003 −331.90 7.5× 10−4
→
Num. of Fx −0.47 0.18 −333.85 7.5× 10−3
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→
BMI 0.04 0.02 −335.32 0.031
• Since goal of study is produce clinically implementable prescriptivemodels, 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 Gy is chosen as variable of interest over V39 Gy
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 14 / 29
SBRT Induced Chest-Wall Pain: Univariate Results
Variable Coef. Std. Err lnL CPH p-value
→
V39Gy 0.0207 0.0032 −320.30 1.1× 10−10
→ V30Gy 0.0129 0.0022 −322.65 7.8× 10−10
→
Presc. Dose (Tx) 0.0008 0.0002 −329.76 6.8× 10−5
→
Dose/Fx 0.001 0.0003 −331.90 7.5× 10−4
→
Num. of Fx −0.47 0.18 −333.85 7.5× 10−3
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→
BMI 0.04 0.02 −335.32 0.031
0 10 20 30 40 50 60−340
−335
−330
−325
−320
(VD
) Dose [Gy]
CP
H log−
likelih
ood
Low 68% CI
Low 95% CI
Max LogL = −320.3 at D
39 Gy
0 10 20 30 40 50 6010
−10
10−8
10−6
10−4
10−2
100
(VD
) Dose [Gy]
CP
H p
−valu
e
Min p−val = 1.1e−10 at V39 Gy
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 14 / 29
SBRT Induced Chest-Wall Pain: Univariate Results
Variable Coef. Std. Err lnL CPH p-value
→
V39Gy 0.0207 0.0032 −320.30 1.1× 10−10
→ V30Gy 0.0129 0.0022 −322.65 7.8× 10−10
→
Presc. Dose (Tx) 0.0008 0.0002 −329.76 6.8× 10−5
→
Dose/Fx 0.001 0.0003 −331.90 7.5× 10−4
→
Num. of Fx −0.47 0.18 −333.85 7.5× 10−3
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→
BMI 0.04 0.02 −335.32 0.031
V30threshold
SensitivityTP
TP+FN
SpecificityTN
TN+FP
30cc 0.891 0.29450cc 0.828 0.52470cc 0.656 0.0726
AUC = 0.73 [0.66− 0.81 (95%CI)]
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 14 / 29
SBRT Induced Chest-Wall Pain: Univariate Results
Variable Coef. Std. Err lnL CPH p-value
→
V39Gy 0.0207 0.0032 −320.30 1.1× 10−10
→ V30Gy 0.0129 0.0022 −322.65 7.8× 10−10
→
Presc. Dose (Tx) 0.0008 0.0002 −329.76 6.8× 10−5
→
Dose/Fx 0.001 0.0003 −331.90 7.5× 10−4
→
Num. of Fx −0.47 0.18 −333.85 7.5× 10−3
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→
BMI 0.04 0.02 −335.32 0.031
• V30Gy splits at 30cc, 50cc,70cc all significant
• Recommend: V30Gy ≤ 50cc
• Greater protection than70cc
• More achievable than30cc
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 14 / 29
SBRT Induced Chest-Wall Pain: Univariate Results
Variable Coef. Std. Err lnL CPH p-value
→
V39Gy 0.0207 0.0032 −320.30 1.1× 10−10
→ V30Gy 0.0129 0.0022 −322.65 7.8× 10−10
→
Presc. Dose (Tx) 0.0008 0.0002 −329.76 6.8× 10−5
→
Dose/Fx 0.001 0.0003 −331.90 7.5× 10−4
→
Num. of Fx −0.47 0.18 −333.85 7.5× 10−3
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→
BMI 0.04 0.02 −335.32 0.031
• V30Gy splits at 30cc, 50cc,70cc all significant
• Recommend: V30Gy ≤ 50cc
• Greater protection than70cc
• More achievable than30cc
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 14 / 29
SBRT Induced Chest-Wall Pain: Univariate Results
Variable Coef. Std. Err lnL CPH p-value
→
V39Gy 0.0207 0.0032 −320.30 1.1× 10−10
→
V30Gy 0.0129 0.0022 −322.65 7.8× 10−10
→ Presc. Dose (Tx) 0.0008 0.0002 −329.76 6.8× 10−5
→ Dose/Fx 0.001 0.0003 −331.90 7.5× 10−4
→ Num. of Fx −0.47 0.18 −333.85 7.5× 10−3
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→
BMI 0.04 0.02 −335.32 0.031
But we’ve forgotten something!
Number Dose per Prescriptionof Fractions Fraction (Gy) Dose (Gy)
3 18− 20 54− 604 12 605 9− 10 45− 50
What is a ‘fraction’ and how does it effect treatment?E. Williams (MSKCC) Higgs → Hospital January 17, 2014 14 / 29
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
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
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 onthe fractionation regime (how much dose per fraction)!
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 15 / 29
SBRT Induced Chest-Wall Pain: Fractionation Effects
How does this effect this study?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 16 / 29
SBRT Induced Chest-Wall Pain: Fractionation Effects
How does this effect this study?
Cohort has various SBRTfractionation schemes! →
Number Dose per Prescriptionof Fractions Fraction (Gy) Dose (Gy)
3 18− 20 54− 604 12 605 9− 10 45− 50
Problem: If tissues respond differently to different fractionationschemes (see above), how can we infer dose-responses relationship ina mixed cohort?Solution: Linear-Quadratic Model!2 Proposed as solution to thisproblem for conventional radiotherapy in the 80s
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 16 / 29
SBRT Induced Chest-Wall Pain: Fractionation Effects
How does this effect this study?
Cohort has various SBRTfractionation schemes! →
Number Dose per Prescriptionof Fractions Fraction (Gy) Dose (Gy)
3 18− 20 54− 604 12 605 9− 10 45− 50
Problem: If tissues respond differently to different fractionationschemes (see above), how can we infer dose-responses relationship ina mixed cohort?Solution: Linear-Quadratic Model!2 Proposed as solution to thisproblem for conventional radiotherapy in the 80s
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 16 / 29
SBRT Induced Chest-Wall Pain: Fractionation Effects
How does this effect this study?
Cohort has various SBRTfractionation schemes! →
Number Dose per Prescriptionof Fractions Fraction (Gy) Dose (Gy)
3 18− 20 54− 604 12 605 9− 10 45− 50
Problem: If tissues respond differently to different fractionationschemes (see above), how can we infer dose-responses relationship ina mixed cohort?Solution: Linear-Quadratic Model!2 Proposed as solution to thisproblem 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
SBRT Induced Chest-Wall Pain: LQ Model
The LQ Model accounts for the effect of fractionation on cell-killingthrough a single, tissue dependent, parameter α/β (for moredetailed explanation see [Hall 2012])
→ Normalized Total Dose (NTD), replaces ‘physical’ dose, andallows for comparison between different fractionation schemes:
NTDα/β = (nd)×
(αβ + dαβ + 2
)n− number of fractions
d− dose per fraction
Using NTD results in models that are easily implementable in theclinic (important). Therefore it would be of much interest if LQformalism can be applied to predictive models in SBRT cohorts...
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 17 / 29
SBRT Induced Chest Wall Pain: LQ ModelQuestion: Does using LQ model NTD instead of ‘physical’ dose improve ourNTCP models?
Method: Compare VD CPH models (previous results) to models usingVNTDα/β for a range of α/β
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 18 / 29
SBRT Induced Chest Wall Pain: LQ ModelQuestion: Does using LQ model NTD instead of ‘physical’ dose improve ourNTCP models?
Method: Compare VD CPH models (previous results) to models usingVNTDα/β for a range of α/β
0 50 100 150 200
−334
−332
−330
−328
−326
−324
−322
−320
−318
VD
[Gy]
Lo
g−
like
liho
od
, C
ox m
od
el
Max ln(L) at V39
0 2 4 6 8 10 12 14 16 18 20 22 24−321.5
−321
−320.5
−320
−319.5
−319
Log−
likelih
ood for
best V
NT
D C
ox M
odel
α/β [Gy]
Physical DoseBest fit ln(L) = −320.3
Answer:
Yes, using NTD with any α/β value < 17.7 Gy results in a better SBRTCWP VNTD model than physical dose!
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 18 / 29
SBRT Induced Chest Wall Pain: LQ ModelQuestion: Does using LQ model NTD instead of ‘physical’ dose improve ourNTCP models?
Method: Compare VD CPH models (previous results) to models usingVNTDα/β for a range of α/β
0 50 100 150 200
−334
−332
−330
−328
−326
−324
−322
−320
−318
VD
[Gy]
Lo
g−
like
liho
od
, C
ox m
od
el
0 2 4 6 8 10 12 14 16 18 20 22 24−318.8
−318.7
−318.6
−318.5
−318.4
−318.3
−318.2
−318.1
−318
−317.9
−317.8
Physical DoseBest fit ln(L) = −320.3
NTD DoseBest fit ln(L) = −317.87
at α/β = 2.1
α/β [Gy]
Log−
likelih
ood for
best V
NT
D C
PH
M
Low 68% CI
Answer:
Yes, using NTD with any α/β value < 17.7 Gy results in a better SBRTCWP VNTD model than physical dose!
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 18 / 29
SBRT Induced Chest Wall Pain: LQ ModelQuestion: Does using LQ model NTD instead of ‘physical’ dose improve ourNTCP models?
Method: Compare VD CPH models (previous results) to models usingVNTDα/β for a range of α/β
0 50 100 150 200
−334
−332
−330
−328
−326
−324
−322
−320
−318
VD
[Gy]
Lo
g−
like
liho
od
, C
ox m
od
el
0 2 4 6 8 10 12 14 16 18 20 22 24−318.8
−318.7
−318.6
−318.5
−318.4
−318.3
−318.2
−318.1
−318
−317.9
−317.8
Physical DoseBest fit ln(L) = −320.3
NTD DoseBest fit ln(L) = −317.87
at α/β = 2.1
α/β [Gy]
Log−
likelih
ood for
best V
NT
D C
PH
M
Low 68% CI
Answer: Yes, using NTD with any α/β value < 17.7 Gy results in a better SBRTCWP VNTD model than physical dose!
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 18 / 29
SBRT Induced Chest Wall Pain: LQ ModelQuestion: Does using LQ model NTD instead of ‘physical’ dose improve ourNTCP models?
Method: Compare VD CPH models (previous results) to models usingVNTDα/β for a range of α/β
0 50 100 150 200
−334
−332
−330
−328
−326
−324
−322
−320
−318
VD
[Gy]
Lo
g−
like
liho
od
, C
ox m
od
el
0 2 4 6 8 10 12 14 16 18 20 22 24−318.8
−318.7
−318.6
−318.5
−318.4
−318.3
−318.2
−318.1
−318
−317.9
−317.8
Physical DoseBest fit ln(L) = −320.3
NTD DoseBest fit ln(L) = −317.87
at α/β = 2.1
α/β [Gy]
Log−
likelih
ood for
best V
NT
D C
PH
M
Low 68% CI
Answer: Yes, using NTD with any α/β value < 17.7 Gy results in a better SBRTCWP VNTD model than physical dose!
Best fit VNTD model at α/β = 2.1 Gy → V99Gy2.1
(Gyα/β normalized dose units)
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 18 / 29
SBRT Induced Chest-Wall Pain: CPH Model Results
Variable Coef. Std. Err lnL CPH p-value
→ V99Gy2.1 0.0175 0.0035 −317.87 4.3× 10−12
→
V30Gyphys0.0129 0.0022 −322.65 7.8× 10−10
→
Presc. Dose (Tx) 0.0008 0.0002 −329.76 6.8× 10−5
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→
BMI 0.04 0.02 −335.32 0.031
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 19 / 29
SBRT Induced Chest-Wall Pain: CPH Model Results
Variable Coef. Std. Err lnL CPH p-value
→ V99Gy2.1 0.0175 0.0035 −317.87 4.3× 10−12
→
V30Gyphys0.0129 0.0022 −322.65 7.8× 10−10
→ Presc. Dose (Tx) 0.0008 0.0002 −329.76 6.8× 10−5
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→
BMI 0.04 0.02 −335.32 0.031
Model: V99Gy2.1 + Tx
CPH p-value lnL AIC
V99Gy2.1 1.1× 10−7-317.7 639.4
Tx 0.58
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
SBRT Induced Chest-Wall Pain: CPH Model Results
Variable Coef. Std. Err lnL CPH p-value
→ V99Gy2.1 0.0175 0.0035 −317.87 4.3× 10−12
→
V30Gyphys0.0129 0.0022 −322.65 7.8× 10−10
→
Presc. Dose (Tx) 0.0008 0.0002 −329.76 6.8× 10−5
→ Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→
BMI 0.04 0.02 −335.32 0.031
Model: V99Gy2.1 + cm2cw
CPH p-value lnL AIC
V99Gy2.1 4.3× 10−7-317.4 638.8
cm2cw 0.33
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 19 / 29
SBRT Induced Chest-Wall Pain: CPH Model Results
Variable Coef. Std. Err lnL CPH p-value
→ V99Gy2.1 0.0175 0.0035 −317.87 4.3× 10−12
→
V30Gyphys0.0129 0.0022 −322.65 7.8× 10−10
→
Presc. Dose (Tx) 0.0008 0.0002 −329.76 6.8× 10−5
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→ BMI 0.04 0.02 −335.32 0.031
Model: V99Gy2.1+BMI
CPH p-value lnL AIC
V99Gy2.1 3.6× 10−10-315.7 635.3
BMI 0.035
Valid bi-variate CPH model!
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 19 / 29
SBRT Induced Chest-Wall Pain: CPH Model Results
Variable Coef. Std. Err lnL CPH p-value
→ V99Gy2.1 0.0175 0.0035 −317.87 4.3× 10−12
→
V30Gyphys0.0129 0.0022 −322.65 7.8× 10−10
→
Presc. Dose (Tx) 0.0008 0.0002 −329.76 6.8× 10−5
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→ BMI 0.04 0.02 −335.32 0.031
Two significant CPH NTCP models:
V99Gy2.1
CPH p-value lnL AIC
V99Gy2.14.3× 10−12 −317.87 637.7
V99Gy2.1+BMI
CPH p-value lnL AIC
V99Gy2.13.6× 10−10
−315.7 635.3BMI 0.035
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 19 / 29
SBRT Induced Chest-Wall Pain: CPH Model Results
Variable Coef. Std. Err lnL CPH p-value
→ V99Gy2.1 0.0175 0.0035 −317.87 4.3× 10−12
→
V30Gyphys0.0129 0.0022 −322.65 7.8× 10−10
→
Presc. Dose (Tx) 0.0008 0.0002 −329.76 6.8× 10−5
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→ BMI 0.04 0.02 −335.32 0.031
Two significant CPH NTCP models:
V99Gy2.1
CPH p-value lnL AIC
V99Gy2.14.3× 10−12 −317.87 637.7
V99Gy2.1+BMI
CPH p-value lnL AIC
V99Gy2.13.6× 10−10
−315.7 635.3BMI 0.035
Bivariate model preferred by AICE. Williams (MSKCC) Higgs → Hospital January 17, 2014 19 / 29
SBRT Induced Chest-Wall Pain: KM + Logrank results
V99Gy2.1
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 p = 2.1e − 06
HR = 4.06
Years
Pro
babili
ty o
f C
W P
ain
V99 < 31.6ccV99 ≥ 31.6cc
V99Gy2.1+BMI
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 p = 3.2e − 06
HR = 3.84
Years
Pro
babili
ty o
f C
W P
ain
βV99Gy2.1× V99Gy2.1 + βBMI × BMI < 1.64
βV99Gy2.1× V99Gy2.1 + βBMI × BMI ≥ 1.64
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 20 / 29
SBRT Induced Chest-Wall Pain: KM + Logrank results
V99Gy2.1
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 p = 2.1e − 06
HR = 4.06
Years
Pro
babili
ty o
f C
W P
ain
V99 < 31.6ccV99 ≥ 31.6cc
V99Gy2.1+BMI
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 p = 3.2e − 06
HR = 3.84
Years
Pro
babili
ty o
f C
W P
ain
βV99Gy2.1× V99Gy2.1 + βBMI × BMI < 1.64
βV99Gy2.1× V99Gy2.1 + βBMI × BMI ≥ 1.64
How do oncologists/medical physcists/planners implementthese results?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 20 / 29
SBRT Induced Chest-Wall Pain: Clinic Implementation
LQ Model results lends to convenient clinicalinterpretation and implementation:
NTDα/β = Dphys ×(
αβ+
DphysNfx
αβ+2
)Dphys - physical dose used and understood by
physicians/planners
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 21 / 29
SBRT Induced Chest-Wall Pain: Clinic Implementation
LQ Model results lends to convenient clinicalinterpretation and implementation:
NTDα/β = Dphys ×(
αβ+
DphysNfx
αβ+2
)Dphys - physical dose used and understood by
physicians/planners
∴ D2phys +(αβ ·Nfx)×Dphys +(−Nfx ·NTDα/β ·(αβ +2)) = 0
→ can solve for Dphys in terms of fraction number (Nfx)←
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 21 / 29
SBRT Induced Chest-Wall Pain: Clinic Implementation
LQ Model results lends to convenient clinicalinterpretation and implementation:
NTDα/β = Dphys ×(
αβ+
DphysNfx
αβ+2
)Dphys - physical dose used and understood by
physicians/planners
∴ D2phys +(αβ ·Nfx)×Dphys +(−Nfx ·NTDα/β ·(αβ +2)) = 0
→ 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
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 atleast 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 limitsgiven in table:
Number of VDFractions Threshold
3 V32Gy < 31.6cc4 V36Gy < 31.6cc5 V40Gy < 31.6cc
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 22 / 29
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 atleast 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 limitsgiven in table:
Number of VDFractions Threshold
3 V32Gy < 31.6cc4 V36Gy < 31.6cc5 V40Gy < 31.6cc
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 22 / 29
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 atleast 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 limitsgiven in table:
Number of VDFractions Threshold
3 V32Gy < 31.6cc4 V36Gy < 31.6cc5 V40Gy < 31.6cc
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 22 / 29
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 atleast 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 limitsgiven in table:
Oncologists, planners and radiationtherapists are more fluent in ‘physical’
dose than ‘LQ-model’ dose!
Number of VDFractions Threshold
3 V32Gy < 31.6cc4 V36Gy < 31.6cc5 V40Gy < 31.6cc
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 22 / 29
SBRT Induced Chest-Wall Pain: Clincal Results
Model: V99Gy2.1
Nfx = 3
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 p = 7.5e − 03
HR = 2.65
Years
Pro
babili
ty o
f C
W P
ain
V99 < 57.3ccV99 ≥ 57.3cc
Nfx = 4
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 p = 2.8e − 02
HR = 2.91
Years
Pro
babili
ty o
f C
W P
ain
V99 < 28.8ccV99 ≥ 28.8cc
Nfx = 5
0 0.5 1 1.5 2 2.5 3 3.5 40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 p = 2.4e − 02
HR = 4.34
Years
Pro
babili
ty o
f C
W P
ain
V99 < 0.716ccV99 ≥ 0.716cc
Model: V99Gy2.1+BMI
Nfx = 3
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 p = 8.4e − 05
HR = 4.36
Years
Pro
ba
bili
ty o
f C
W P
ain
βV99Gy2.1× V99Gy2.1 + βBMI × BMI < 2.1
βV99Gy2.1× V99Gy2.1 + βBMI × BMI ≥ 2.1
Nfx = 4
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 p = 8.0e − 02
HR = 2.27
Years
Pro
ba
bili
ty o
f C
W P
ain
βV99Gy2.1× V99Gy2.1 + βBMI × BMI < 1.91
βV99Gy2.1× V99Gy2.1 + βBMI × BMI ≥ 1.91
Nfx = 5
0 0.5 1 1.5 2 2.5 3 3.5 40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 p = 1.3e − 01
HR = 3.22
YearsP
rob
ab
ility
of
CW
Pa
in
βV99Gy2.1× V99Gy2.1 + βBMI × BMI < 0.338
βV99Gy2.1× V99Gy2.1 + βBMI × BMI ≥ 0.338
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 23 / 29
Overview
• IntroductionWhat does the Higgs have to do with it?
• The α, β, γ’s of Radiation in MedicineDiscovery and modern use
• Normal Tissue Complication Probability ModelingNTCP → DVH → NTD: A short history of acronyms
• Radiation induced Chest-Wall PainA retrospective analysis
• Radiation Therapy & Global HealthA digression
• ConclusionsSeriously though, whats the deal with the Higgs?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 23 / 29
Radiation Therapy & Global Health - A DigressionHalf 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
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
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 devicesince 1884
• No computer/calculatornecessary
• Can be used to display mostmultivariate predictive models
• Hypothetical ‘atlas ofnomogram health outcomes’
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 25 / 29
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 devicesince 1884
• No computer/calculatornecessary
• Can be used to display mostmultivariate predictive models
• Hypothetical ‘atlas ofnomogram health outcomes’
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 25 / 29
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 devicesince 1884
• No computer/calculatornecessary
• Can be used to display mostmultivariate predictive models
• Hypothetical ‘atlas ofnomogram health outcomes’
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 25 / 29
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 devicesince 1884
• No computer/calculatornecessary
• Can be used to display mostmultivariate predictive models
• Hypothetical ‘atlas ofnomogram health outcomes’
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 25 / 29
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 devicesince 1884
• No computer/calculatornecessary
• Can be used to display mostmultivariate predictive models
• Hypothetical ‘atlas ofnomogram health outcomes’
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 25 / 29
Overview
• IntroductionWhat does the Higgs have to do with it?
• The α, β, γ’s of Radiation in MedicineDiscovery and modern use
• Normal Tissue Complication Probability ModelingNTCP → DVH → NTD: A short history of acronyms
• Radiation induced Chest-Wall PainA retrospective analysis
• Radiation Therapy & Global HealthA digression
• ConclusionsSeriously though, whats the deal with the Higgs?
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 25 / 29
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 toreduce 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 intuitivemultivariate probability calculations
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 26 / 29
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 toreduce 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 intuitivemultivariate probability calculations
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 26 / 29
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 toreduce 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 intuitivemultivariate probability calculations
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 26 / 29
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 toreduce 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 intuitivemultivariate probability calculations
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 26 / 29
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 toreduce 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 intuitivemultivariate probability calculations
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 26 / 29
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 toreduce 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 intuitivemultivariate probability calculations
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 26 / 29
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 toreduce 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 intuitivemultivariate probability calculations
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 26 / 29
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 toreduce 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 intuitivemultivariate probability calculations
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 26 / 29
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 centrallung tumors
• Modeling pulmonary toxicity in a large cohort of central lung tumorstreated with SBRT
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 27 / 29
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 centrallung tumors
• Modeling pulmonary toxicity in a large cohort of central lung tumorstreated with SBRT
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 27 / 29
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 centrallung tumors
• Modeling pulmonary toxicity in a large cohort of central lung tumorstreated with SBRT
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 27 / 29
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 centrallung tumors
• Modeling pulmonary toxicity in a large cohort of central lung tumorstreated with SBRT
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 27 / 29
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 centrallung tumors
• Modeling pulmonary toxicity in a large cohort of central lung tumorstreated with SBRT
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 27 / 29
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 centrallung tumors
• Modeling pulmonary toxicity in a large cohort of central lung tumorstreated with SBRT
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 27 / 29
Conclusions (III/IV): Particle Physics - Lessons Learned
‘Big data’ analytics and modeling experience acquired at CERN:
• Conducted a search for exotic theoretical particle - Extra-dimensionalWarped 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 ofDisease
• Managing large scale data analysis projects from inception tocompletion
• Extensive experience working in large research organizations withdiverse colleagues
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 28 / 29
Conclusions (III/IV): Particle Physics - Lessons Learned
‘Big data’ analytics and modeling experience acquired at CERN:
• Conducted a search for exotic theoretical particle - Extra-dimensionalWarped 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 ofDisease
• Managing large scale data analysis projects from inception tocompletion
• Extensive experience working in large research organizations withdiverse colleagues
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 28 / 29
Conclusions (III/IV): Particle Physics - Lessons Learned
‘Big data’ analytics and modeling experience acquired at CERN:
• Conducted a search for exotic theoretical particle - Extra-dimensionalWarped 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 ofDisease
• Managing large scale data analysis projects from inception tocompletion
• Extensive experience working in large research organizations withdiverse colleagues
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 28 / 29
Conclusions (III/IV): Particle Physics - Lessons Learned
‘Big data’ analytics and modeling experience acquired at CERN:
• Conducted a search for exotic theoretical particle - Extra-dimensionalWarped 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 ofDisease
• Managing large scale data analysis projects from inception tocompletion
• Extensive experience working in large research organizations withdiverse colleagues
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 28 / 29
Conclusions (III/IV): Particle Physics - Lessons Learned
‘Big data’ analytics and modeling experience acquired at CERN:
• Conducted a search for exotic theoretical particle - Extra-dimensionalWarped 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 ofDisease
• Managing large scale data analysis projects from inception tocompletion
• Extensive experience working in large research organizations withdiverse colleagues
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 28 / 29
Conclusions (III/IV): Particle Physics - Lessons Learned
‘Big data’ analytics and modeling experience acquired at CERN:
• Conducted a search for exotic theoretical particle - Extra-dimensionalWarped 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 ofDisease
• Managing large scale data analysis projects from inception tocompletion
• Extensive experience working in large research organizations withdiverse colleagues
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 28 / 29
Conclusions (III/IV): Particle Physics - Lessons Learned
‘Big data’ analytics and modeling experience acquired at CERN:
• Conducted a search for exotic theoretical particle - Extra-dimensionalWarped 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 ofDisease
• Managing large scale data analysis projects from inception tocompletion
• Extensive experience working in large research organizations withdiverse colleagues
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 28 / 29
Conclusions (III/IV): Particle Physics - Lessons Learned
‘Big data’ analytics and modeling experience acquired at CERN:
• Conducted a search for exotic theoretical particle - Extra-dimensionalWarped 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 ofDisease
• Managing large scale data analysis projects from inception tocompletion
• Extensive experience working in large research organizations withdiverse colleagues
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 28 / 29
Conclusions (IV/IV)
Finally, I am excited for the opportunity to transfer the skills I’ve acquiredat 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
Conclusions (IV/IV)
Finally, I am excited for the opportunity to transfer the skills I’ve acquiredat 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
Backups
References I
[1] IMV Medical Information Division. “Physician Characteristics andDistribution in the U.S.” In: 2003 SROA Benchmarking (2010).
[2] Fowler FJ. “The linear-quadratic model and progress inradiotherapy”. In: BR. J. Radiol. 62 (1989), pp. 679–694.
[3] Barnett GC, West CML, Dunning AM, et al. “Normal tissue reactionsto 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 TissueComplicatoin Probability Models in the Clinic”. In: Int. J. RadiationOncology Biol. Phys. 76 (2010), S10–S19.
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
Karnofsky performance status (KPS)
In medicine (oncology and other fields), performance status is an attemptto 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 requiredintensity of palliative care. It is also used in oncological randomizedcontrolled trials as a measure of quality of life.
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
CWP: Linear-Quadratic Model
Modeling fractionation: Linear-Quadratic Model
• LQ model describes cell-survival curvesassuming two components of cell killing
1) ∝ dose (single-strand DNA breaks)2) ∝ dose2 (double-strand DNA breaks)
• Cell survival then modeled:
S = e−αD−βD2
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
CWP: Linear-Quadratic Model
Modeling fractionation: Linear-Quadratic Model
• LQ model describes cell-survival curvesassuming two components of cell killing
1) ∝ dose (single-strand DNA breaks)2) ∝ dose2 (double-strand DNA breaks)
• Cell survival then modeled:
S = e−αD−βD2
From this cell-survival model, we can derive a Normalized Total Dose(NTD) useful to compare two different fractionation schemes:
NTD = (nd)× (1 + dα/β )/(1 +
2α/β )
n - number of fractionsd - dose per fraction
→ α/β is a free, tissue dependent, parameter→ Given α/β, NTD replaces dose and allows comparison betweendifferent fractionation schemes
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
CWP: Linear-Quadratic Model
Modeling fractionation: Linear-Quadratic Model
• LQ model describes cell-survival curvesassuming two components of cell killing
1) ∝ dose (single-strand DNA breaks)2) ∝ dose2 (double-strand DNA breaks)
• Cell survival then modeled:
S = e−αD−βD2
From this cell-survival model, we can derive a Normalized Total Dose(NTD) useful to compare two different fractionation schemes:
NTD = (nd)× (1 + dα/β )/(1 +
2α/β )
n - number of fractionsd - dose per fraction
→ α/β is a free, tissue dependent, parameter→ Given α/β, NTD replaces dose and allows comparison betweendifferent fractionation schemes
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
CWP: CPH Univariate Backup
Variable beta se lnL CPH p-value
→ D83cc 0.0766 0.0136 −323.30 1.7× 10−8
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→
BMI 0.04 0.02 −335.32 0.031
0 200 400 600 800 1000−338
−336
−334
−332
−330
−328
−326
−324
−322
(DV) Volume [cc]
CP
H log−
likelih
ood
Low 68% CI
Low 95% CIMax LogL = −323.3 at D
83 cc
0 200 400 600 800 100010
−8
10−6
10−4
10−2
100
(DV) Volume [cc]
CP
H p
−valu
e
Min p−val = 1.7e−08 at D83 cc
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
CWP: CPH Univariate Backup
Variable beta se lnL CPH p-value
→ D83cc 0.0766 0.0136 −323.30 1.7× 10−8
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→
BMI 0.04 0.02 −335.32 0.031
DV and VD correlated due to DVH constraints (R(V39Gy, D83cc) = 0.86)
(VD
) Dose [Gy]
(DV)
Volu
me [cc]
R(VD
,DV) Correlations
20 40 60
200
400
600
800
1000
0.2
0.4
0.6
0.8
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
CWP: CPH Univariate Backup
Variable beta se lnL CPH p-value
→
D83cc 0.0766 0.0136 −323.30 1.7× 10−8
→ Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→
BMI 0.04 0.02 −335.32 0.031
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
CWP: CPH Univariate Backup
Variable beta se lnL CPH p-value
→
D83cc 0.0766 0.0136 −323.30 1.7× 10−8
→
Dist. GTV to CW −0.52 0.18 −330.17 1.4× 10−3
→ BMI 0.04 0.02 −335.32 0.031
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
CWP: ROC Curves V30Gy
AUC: area under curve =probability that random positiveinstance will be assigned correctly
AUC S.E. 95% CI
0.73 0.038 0.66 - 0.81
Standardized AUC (σAUC): 6.02p-value: 8.7×10−10
TP : True Positive: # complications above cutFP : False Positive: # censor above cutTN : True Negative: # censor below cutFN : False Negative: # complications below cut
V30
Threshold TP/FP FN/TN
30cc 57/178 7/7450cc 53/120 11/13270cc 42/69 22/183
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
CWP: ROC Curves V30Gy
V30
Threshold
SenstivityTP
TP+FN
SpecificityTN
TN+FP
EfficiencyTP+TN
TP+TN+FP+TN
30cc 0.891 0.294 0.41550cc 0.828 0.524 0.58570cc 0.656 0.726 0.712
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
CWP: Average DVHs (2cm and 3cm defs)
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
Universal Survival Curve
Survival Curves
• The linear quadratic (LQ) model approximates clonogenic survivaldata with truncated power series expansion of natural log of survivingproportion S, → lnS = −α · d− β · d2
• LQ model overestimates the effect of radiation on clonogenicity in thehigh doses commonly used in SBRT
• The multitarget model (MTM) provides another description ofclonogenic survival, assuming n targets need to be hit to disruptclonogenicity
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 andthe multitarget model asymptote for high-dose range
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
Universal Survival Curve
• Universal Survival Curve (USC) described by:
lnS =
{−(α · d+ β · d2) if d ≤ DT
− 1D0d+
DqD0
if d ≥ DT
}
• 4 independent params (α, β,D0, and Dq) constrainted to 3 whenasymptotic 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
DT =2 ·Dq
1− α ·D0E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
CWP: Model Comparisons
LQ and USC models: α/β = 3 Gy
Best Model Logistic RegressionModel Parameters Log-likelihood/df AIC
LQ gEUD log10(a) = 1.1 −0.467 295.30LQ DMAX log10(a) = ∞ −0.469 296.53Phys gEUD log10(a) = 1.3 −0.459 290.25Phys DMAX log10(a) = ∞ −0.461 291.51
log10(a) = 0.6USC gEUD α ·D0 = 0.22 −0.453 290.22
Dq = 6.4 GyDT = 16.4 Gy
log10(a) = ∞α ·D0 = 0.13
USC DMAX Dq = 6.6 Gy −0.461 295.34DT = 15.2 Gy
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
CWP Logistic Regression Model Responses
LQ gEUD, AIC= 295.3
0 50 100 150 200 250 300 350 400 4500
0.1
0.2
0.3
0.4
0.5
0.6
gEUDLQ
log10
(a) =1
Com
plic
ation r
ate
observ
ed
LQ DMAX, AIC= 296.53
0 100 200 300 400 500 6000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Max BED Dose [Gy]
CW
P p
robabili
ty
Phys gEUD, AIC= 290.25
0 10 20 30 40 50 600
0.1
0.2
0.3
0.4
0.5
0.6
gEUDPHYS
log10
(a) =1.3C
om
plic
atio
n r
ate
ob
se
rve
d
Phys DMAX, AIC= 291.51
0 10 20 30 40 50 60 700
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Max PHYS
CW
P p
rob
ab
ility
USC gEUD, AIC= 290.22
0 20 40 60 80 100 120 140 160 180 2000
0.1
0.2
0.3
0.4
0.5
0.6
gEUDUSC
log10
(a) =0.6
Co
mp
lica
tio
n r
ate
ob
se
rve
d
USC DMAX, AIC= 295.34
0 50 100 150 200 250 300 350 4000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
USC Dmax [Gy]
CW
P p
robabili
ty
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
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
)
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−0.495
−0.49
−0.485
−0.48
−0.475
−0.47
−0.465
−0.46
log10
(a)
Log−
likelih
ood / d
f
Max log-likelihood/df = −0.467
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1294
296
298
300
302
304
306
308
310
312
314
log10
(a)
AIC
Min AIC(n paramLQ = 1) = 295.33
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
LQ Model: Chest-wall pain
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 110
−6
10−5
10−4
10−3
10−2
10−1
log10
(a)
p−
valu
e
Min p-value at log10(a) = 1p = 1.1× 10−6
0 50 100 150 200 250 300 350 400 4500
0.1
0.2
0.3
0.4
0.5
0.6
gEUDLQ
log10
(a) =1
Com
plic
ation r
ate
observ
ed
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
Universal Survival Curve: Chest-wall pain• gEUD analysis with −1 < log10(a) < 1
• BEDUSC model with three parameters: α/β, α ·D0 and Dq
BEDUSC =
{D
(1 + d
α/β
)if d ≤ DT
1α·D0
(D − n ·Dq) if d ≥ DT
}
• αβ= 3 Gy, (α ·D0) = 0.01 : 0.01 : 0.5, Dq = 0.2 : 0.2 : 7.6 Gy
Dq [Gy]
α⋅ D
0
1 2 3 4 5 6 7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Lo
g−
like
liho
od
/df
−0.5
−0.495
−0.49
−0.485
−0.48
−0.475
−0.47
−0.465
−0.46
−0.455
Max llhd/df = −0.453 at Dq = 6.4 Gy, α ·D0 = 0.22
log10(a) = 0.6
Dq [Gy]
α⋅ D
0
1 2 3 4 5 6 7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
AIC
295
300
305
310
315
320
Min AIC = 290.23 at Dq = 6.4 Gy, α ·D0 = 0.22
log10(a) = 0.6, llhd = −0.453
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
Universal Survival Curve: Chest-wall pain
Dq [Gy]
α⋅ D
0
1 2 3 4 5 6 7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
DT
10
20
30
40
50
60
Dq [Gy]
α⋅ D
0
1 2 3 4 5 6 7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
P−
va
lue
0.01
0.02
0.03
0.04
0.05
0.06
Dq [Gy]
α⋅ D
0
1 2 3 4 5 6 7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Best lo
g10(a
)
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
Universal Survival Curve: Chest-wall pain
Dq [Gy]
α⋅ D
0
1 2 3 4 5 6 7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Lo
g−
like
liho
od
/df
−0.5
−0.495
−0.49
−0.485
−0.48
−0.475
−0.47
−0.465
−0.46
−0.455
0 1 2 3 4 5 6 7 8−0.461
−0.46
−0.459
−0.458
−0.457
−0.456
−0.455
−0.454
−0.453
−0.452
−0.451
Dq [Gy]
Ma
x L
og
−lik
elih
oo
d/d
f
0 0.1 0.2 0.3 0.4 0.5−0.46
−0.459
−0.458
−0.457
−0.456
−0.455
−0.454
−0.453
−0.452
−0.451
α⋅ D0 [Gy]
Max L
og−
likelih
ood/d
f
0 5 10 15 20 25 30−0.468
−0.466
−0.464
−0.462
−0.46
−0.458
−0.456
−0.454
−0.452
−0.45
DT [Gy]
Max L
og−
likelih
ood/d
f
68% CI
95% CI
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
Universal Survival Curve: Chest-wall pain
Dq [Gy]
α⋅ D
0
1 2 3 4 5 6 7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Fra
ctio
n F
ull
CW
LQ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Dq [Gy]
α⋅ D
0
1 2 3 4 5 6 7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Fra
ctio
n L
Q B
ins
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
• “Fraction Full CW LQ” - Fraction ofpatients with all dose bins ≤ DT (calc asBEDLQ)
• “Fraction LQ Bins” - Fraction of all dosebins with ≤ DT (calc as BEDLQ)
0 5 10 15 20 25 30 350
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
DT [Gy]
Fra
ction L
Q
Fraction Full CW LQ
Fraction Bins LQ
• Steps in Fraction Full CW LQ, patientfractionation schemes?
• At best fit:
• Frac LQ bins = 0.947• Frac Full LQ = 0.703
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29
Universal Survival Curve: CWP
LQ model
0 50 100 150 200 250 300 350 400 4500
0.1
0.2
0.3
0.4
0.5
0.6
gEUDLQ
log10
(a) =1
Com
plic
ation r
ate
observ
ed
Max llhd/df = −0.467p = 1.1× 10−6, log10(a) = 1
AIC = 295.33
USC model
0 20 40 60 80 100 120 140 160 180 2000
0.1
0.2
0.3
0.4
0.5
0.6
gEUDUSC
log10
(a) =0.6
Com
plic
ation r
ate
observ
ed
Max llhd/df = −0.453p = 1.8× 10−7, log10(a) = 0.6
AIC = 290.2Dq = 6.4 Gy, α ·D0 = 0.22
DT = 16.4 Gy
E. Williams (MSKCC) Higgs → Hospital January 17, 2014 29 / 29