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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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
11.
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
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
13.
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
14.
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
16.
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
17.
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
18.
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
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
22.
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
23.
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
33.
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
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
35.
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
36.
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
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
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
75.
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
76.
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
79.
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
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
83.
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
84.
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
85.
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
86.
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
87.
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
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
89.
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
90.
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
91.
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
92.
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
93.
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
94.
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
95.
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
97.
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
98.
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
99.
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
100.
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
101.
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
103.
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
104.
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
105.
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
106.
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
107.
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
108.
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
109.
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
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
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
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