Using gEUD to model volume effects for pneumonitis in prospective data from 4 Non-Small Cell Lung Cancer (NSCLC) dose-escalation trials

1. Using gEUD to model volume effects for
pneumonitis in prospective data from 4 Non-Small
Cell Lung Cancer (NSCLC) dose-escalation trials
E. Williams1 , J. Belderbos2 , W.R. Bosch3 , F. Kong4 , J.V. Lebesque2 ,
F. Liu5 , K.E. Rosenzweig6 , W.L. Straube3 , R.K. Ten Haken4 , A. Jackson1
1
Memorial Sloan-Kettering Cancer Center, New York, NY
The Netherlands Cancer Institute, Amsterdam, Netherlands
3
Washington University School of Medicine, St. Louis, MO
4
University of Michigan, Ann Arbor, MI
5
New York Medical College, Valhalla, NY
6
Mount Sinai School of Medicine, New York, NY
2
April 11, 2013

2. Overview
Goal: To model the dependence of radiation pneumonitis (RP) on
generalized equivalent uniform dose (gEUD), in prospective data from
four dose-escalation trials
Radiation Pneumonitis
What is it?
From DVH to gEUD to NTCP
A short history of acronyms
The data
Who, what and where
Methods
Dataset combination and analysis
Results and Conclusions
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
1 / 12

3. Overview
Goal: To model the dependence of radiation pneumonitis (RP) on
generalized equivalent uniform dose (gEUD), in prospective data from
four dose-escalation trials
Radiation Pneumonitis
What is it?
From DVH to gEUD to NTCP
A short history of acronyms
The data
Who, what and where
Methods
Dataset combination and analysis
Results and Conclusions
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
1 / 12

4. Overview
Goal: To model the dependence of radiation pneumonitis (RP) on
generalized equivalent uniform dose (gEUD), in prospective data from
four dose-escalation trials
Radiation Pneumonitis
What is it?
From DVH to gEUD to NTCP
A short history of acronyms
The data
Who, what and where
Methods
Dataset combination and analysis
Results and Conclusions
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
1 / 12

5. Overview
Goal: To model the dependence of radiation pneumonitis (RP) on
generalized equivalent uniform dose (gEUD), in prospective data from
four dose-escalation trials
Radiation Pneumonitis
What is it?
From DVH to gEUD to NTCP
A short history of acronyms
The data
Who, what and where
Methods
Dataset combination and analysis
Results and Conclusions
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
1 / 12

6. Overview
Goal: To model the dependence of radiation pneumonitis (RP) on
generalized equivalent uniform dose (gEUD), in prospective data from
four dose-escalation trials
Radiation Pneumonitis
What is it?
From DVH to gEUD to NTCP
A short history of acronyms
The data
Who, what and where
Methods
Dataset combination and analysis
Results and Conclusions
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
1 / 12

7. Overview
Goal: To model the dependence of radiation pneumonitis (RP) on
generalized equivalent uniform dose (gEUD), in prospective data from
four dose-escalation trials
Radiation Pneumonitis
What is it?
From DVH to gEUD to NTCP
A short history of acronyms
The data
Who, what and where
Methods
Dataset combination and analysis
Results and Conclusions
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
1 / 12

8. Overview
Goal: To model the dependence of radiation pneumonitis (RP) on
generalized equivalent uniform dose (gEUD), in prospective data from
four dose-escalation trials
Radiation Pneumonitis
What is it?
From DVH to gEUD to NTCP
A short history of acronyms
The data
Who, what and where
Methods
Dataset combination and analysis
Results and Conclusions
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
1 / 12

9. Radiation Pneumonitis (RP)
Lung damage from ionizing radiation is generally divided into:
Early (acute) inflammatory damage: radiation pneumonitis
Late chronic scarring: radiation fibrosis
In the treatment of NSCLC, RP is often dose limiting
complication
RP in this study was defined as requiring steroids or worse
toxicity before 6 months from end of treatment
Toxicity grades: ≥ RTOG RP grade 3 or ≥ SWOG RP grade 2
Incidence of RP for Cancer of the Lung
RP
Incidence
Def. of
RP
27/461 (6%)
25/191 (13%)
14/84 (17%)
17/106 (16%)
10/78 (13%)
RTOG≥Gd 3
RTOG≥Gd 3
SWOG≥Gd 2
SWOG≥Gd 2
RTOG≥Gd 3
Study
Byhardt 1998 1
Inoue 2001 2
Rancati 2003 3
Seppenwoolde 2004 4
Yorke 2005 5
Chest radiographs before (L) and after (R) treatment of
NSCLC in the left lung (arrow). Post-tx shows faint areas
of increased opacity (RP) within field
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
2 / 12

10. Overview
Goal: To model the dependence of radiation pneumonitis (RP) on
generalized equivalent uniform dose (gEUD), in prospective data from
four dose-escalation trials
Radiation Pneumonitis
What is it?
From DVH to gEUD to NTCP
A short history of acronyms
The data
Who, what and where
Methods
Dataset combination and analysis
Results and Conclusions
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
2 / 12

11. From DVH to NTCP
Normal Tissue Complication Proability (NTCP) models attempt to reduce
complicated dosimetric and anatomic information into a single risk measure
(e.g. probability of complication)
DVH-reduction models estimate complication probability under uniform
irradition from nonuniform dose distributions
→
??
→
??
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
3 / 12

12. From DVH to NTCP
Normal Tissue Complication Proability (NTCP) models attempt to reduce
complicated dosimetric and anatomic information into a single risk measure
(e.g. probability of complication)
DVH-reduction models estimate complication probability under uniform
irradition from nonuniform dose distributions
→
Mean
Dose
→
Marks, IJROBP 76:2010
QUANTEC: Radiation Dose-Volume Effects in the Lung
E. Williams (MSKCC)
Pooled RP gEUD Analysis
Dmean
April 11, 2013
3 / 12

13. From DVH to NTCP
Normal Tissue Complication Proability (NTCP) models attempt to reduce
complicated dosimetric and anatomic information into a single risk measure
(e.g. probability of complication)
DVH-reduction models estimate complication probability under uniform
irradition from nonuniform dose distributions
����������
→
VD
→
Marks, IJROBP 76:2010
QUANTEC: Radiation Dose-Volume Effects in the Lung
E. Williams (MSKCC)
Pooled RP gEUD Analysis
VD
April 11, 2013
3 / 12

14. From DVH to NTCP
Normal Tissue Complication Proability (NTCP) models attempt to reduce
complicated dosimetric and anatomic information into a single risk measure
(e.g. probability of complication)
DVH-reduction models estimate complication probability under uniform
irradition from nonuniform dose distributions
→
gEUD
→
gEUD
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
3 / 12

15. From DVH to NTCP
Normal Tissue Complication Proability (NTCP) models attempt to reduce
complicated dosimetric and anatomic information into a single risk measure
(e.g. probability of complication)
DVH-reduction models estimate complication probability under uniform
irradition from nonuniform dose distributions
→
gEUD
→
gEUD
Generalized Equivalent Uniform Dose:
gEU D(a) = (
E. Williams (MSKCC)
1/a
a
i (di ) νi )
(Lyman Model with n = 1/a)
Pooled RP gEUD Analysis
April 11, 2013
3 / 12

16. From DVH to NTCP
Normal Tissue Complication Proability (NTCP) models attempt to reduce
complicated dosimetric and anatomic information into a single risk measure
(e.g. probability of complication)
DVH-reduction models estimate complication probability under uniform
irradition from nonuniform dose distributions
→
gEUD
→
gEUD
Generalized Equivalent Uniform Dose:
gEU D(a) = (
1/a
a
i (di ) νi )
(Lyman Model with n = 1/a)
Lyman-Kutcher-Burman (LKB) model describes dose-response for uniform
irradiation (gEUD) with a two-parameter (T D50 , m) probit function:
P =
E. Williams (MSKCC)
√1
2π
2
t
e−x /2 dx,
−∞
t=
gEU D(a)−T D50
m×T D50
Pooled RP gEUD Analysis
April 11, 2013
3 / 12

17. Generalized Equivalent Uniform Dose
gEU D(a) = (
1/a
a
i (di ) νi )
Reduces DVH to a single biologically relevant index, accounting for
dose heterogeneity (partial organ uniform irradiation)
Represents the uniform dose which yields the same complication rate
as the delivered dose distribution
’Volume parameter’ a reflects volumetric dose-response of
tissue
Value of a
gEU D
Description
High (a → ∞)
Low (a → 0)
a=1
∼ Max dose
∼ Min dose
= Mean dose
Series organs
Parallel organs
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
4 / 12

18. Generalized Equivalent Uniform Dose
gEU D(a) = (
1/a
a
i (di ) νi )
Reduces DVH to a single biologically relevant index, accounting for
dose heterogeneity (partial organ uniform irradiation)
Represents the uniform dose which yields the same complication rate
as the delivered dose distribution
’Volume parameter’ a reflects volumetric dose-response of
tissue
Value of a
gEU D
Description
High (a → ∞)
Low (a → 0)
a=1
∼ Max dose
∼ Min dose
= Mean dose
Series organs
Parallel organs
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
4 / 12

19. Generalized Equivalent Uniform Dose
gEU D(a) = (
1/a
a
i (di ) νi )
Reduces DVH to a single biologically relevant index, accounting for
dose heterogeneity (partial organ uniform irradiation)
Represents the uniform dose which yields the same complication rate
as the delivered dose distribution
’Volume parameter’ a reflects volumetric dose-response of
tissue
Value of a
gEU D
Description
High (a → ∞)
Low (a → 0)
a=1
∼ Max dose
∼ Min dose
= Mean dose
Series organs
Parallel organs
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
4 / 12

20. Overview
Goal: To model the dependence of radiation pneumonitis (RP) on
generalized equivalent uniform dose (gEUD), in prospective data from
four dose-escalation trials
Radiation Pneumonitis
What is it?
From DVH to gEUD to NTCP
A short history of acronyms
The data
Who, what and where
Methods
Dataset combination and analysis
Results and Conclusions
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
5 / 12

21. The data
RP data pooled from four prospective dose-escalation trials:
→ Small number of events in individual datasets, combining
multi-institutional data increases statistical power
Institute
Memorial Sloan-Kettering
Cancer Center (MSK)
Netherlands Cancer
Institute (NKI)
Radiation Therapy Onc.
Group 93-11 (RTOG)
University of
Michigan (UMich)
Total
#
Patients
RP
Incidence
RP
Grade
78
13% (10/78)
RTOG ≥ 3
Cancer 103;2005 6
86
16% (14/86)
SWOG ≥ 2
IJROBP 66;2006 7
113
8% (9/113)
RTOG ≥ 3
IJROBP 61;2005 8
80
20% (16/80)
SWOG ≥ 2
IJROBP 65;2006 9
357
14% (49/357)
Protocol
RP prospectively scored and primary end point in each trial
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
6 / 12

22. The data
RP data pooled from four prospective dose-escalation trials:
→ Small number of events in individual datasets, combining
multi-institutional data increases statistical power
Institute
Memorial Sloan-Kettering
Cancer Center (MSK)
Netherlands Cancer
Institute (NKI)
Radiation Therapy Onc.
Group 93-11 (RTOG)
University of
Michigan (UMich)
Total
#
Patients
RP
Incidence
RP
Grade
78
13% (10/78)
RTOG ≥ 3
Cancer 103;2005 6
86
16% (14/86)
SWOG ≥ 2
IJROBP 66;2006 7
113
8% (9/113)
RTOG ≥ 3
IJROBP 61;2005 8
80
20% (16/80)
SWOG ≥ 2
IJROBP 65;2006 9
357
14% (49/357)
Protocol
RP prospectively scored and primary end point in each trial
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
6 / 12

23. The data
RP data pooled from four prospective dose-escalation trials:
→ Small number of events in individual datasets, combining
multi-institutional data increases statistical power
Institute
Memorial Sloan-Kettering
Cancer Center (MSK)
Netherlands Cancer
Institute (NKI)
Radiation Therapy Onc.
Group 93-11 (RTOG)
University of
Michigan (UMich)
Total
#
Patients
RP
Incidence
RP
Grade
78
13% (10/78)
RTOG ≥ 3
Cancer 103;2005 6
86
16% (14/86)
SWOG ≥ 2
IJROBP 66;2006 7
113
8% (9/113)
RTOG ≥ 3
IJROBP 61;2005 8
80
20% (16/80)
SWOG ≥ 2
IJROBP 65;2006 9
357
14% (49/357)
Protocol
RP prospectively scored and primary end point in each trial
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
6 / 12

24. The data
RP data pooled from four prospective dose-escalation trials:
→ Small number of events in individual datasets, combining
multi-institutional data increases statistical power
Institute
Memorial Sloan-Kettering
Cancer Center (MSK)
Netherlands Cancer
Institute (NKI)
Radiation Therapy Onc.
Group 93-11 (RTOG)
University of
Michigan (UMich)
Total
#
Patients
RP
Incidence
RP
Grade
78
13% (10/78)
RTOG ≥ 3
Cancer 103;2005 6
86
16% (14/86)
SWOG ≥ 2
IJROBP 66;2006 7
113
8% (9/113)
RTOG ≥ 3
IJROBP 61;2005 8
80
20% (16/80)
SWOG ≥ 2
IJROBP 65;2006 9
357
14% (49/357)
Protocol
RP prospectively scored and primary end point in each trial
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
6 / 12

25. The data
RP data pooled from four prospective dose-escalation trials:
→ Small number of events in individual datasets, combining
multi-institutional data increases statistical power
Institute
Memorial Sloan-Kettering
Cancer Center (MSK)
Netherlands Cancer
Institute (NKI)
Radiation Therapy Onc.
Group 93-11 (RTOG)
University of
Michigan (UMich)
Total
#
Patients
RP
Incidence
RP
Grade
78
13% (10/78)
RTOG ≥ 3
Cancer 103;2005 6
86
16% (14/86)
SWOG ≥ 2
IJROBP 66;2006 7
113
8% (9/113)
RTOG ≥ 3
IJROBP 61;2005 8
80
20% (16/80)
SWOG ≥ 2
IJROBP 65;2006 9
357
14% (49/357)
Protocol
RP prospectively scored and primary end point in each trial
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
6 / 12

26. The data
RP data pooled from four prospective dose-escalation trials:
→ Small number of events in individual datasets, combining
multi-institutional data increases statistical power
Institute
Memorial Sloan-Kettering
Cancer Center (MSK)
Netherlands Cancer
Institute (NKI)
Radiation Therapy Onc.
Group 93-11 (RTOG)
University of
Michigan (UMich)
Total
#
Patients
RP
Incidence
RP
Grade
78
13% (10/78)
RTOG ≥ 3
Cancer 103;2005 6
86
16% (14/86)
SWOG ≥ 2
IJROBP 66;2006 7
113
8% (9/113)
RTOG ≥ 3
IJROBP 61;2005 8
80
20% (16/80)
SWOG ≥ 2
IJROBP 65;2006 9
357
14% (49/357)
Protocol
RP prospectively scored and primary end point in each trial
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
6 / 12

27. Overview
Goal: To model the dependence of radiation pneumonitis (RP) on
generalized equivalent uniform dose (gEUD), in prospective data from
four dose-escalation trials
Radiation Pneumonitis
What is it?
From DVH to gEUD to NTCP
A short history of acronyms
The data
Who, what and where
Methods
Dataset combination and analysis
Results and Conclusions
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
7 / 12

28. Methods
Radiation pneumonitis defined as toxicity scored ≥ RTOG Grade 3
or ≥ SWOG Grade 2, within 6 months of RT
→ Treatment with steroids and/or oxygen
Same lung definition for DVHs from each study: excluding GTV
Institute
MSK
NKI
RTOG
UMich
Treated Doses [Gy]
Fraction Size [Gy]
57.6 − 90.0
60.7 − 94.5
70.9 − 90.3
63.0 − 103
1.8 − 2.0
2.25
2.15
2.10
Linear quadratic correction to doses in 2 Gy fractions using α/β = 3 Gy
LKB maximum likelihood fits for −1 ≤ log10 (a) ≤ 1 in 0.1 steps
→ Primary interest: volume paramater (a) wrt lung tissue complication
architecture (parallel/serial)
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
8 / 12

29. Overview
Goal: To model the dependence of radiation pneumonitis (RP) on
generalized equivalent uniform dose (gEUD), in prospective data from
four dose-escalation trials
Radiation Pneumonitis
What is it?
From DVH to gEUD to NTCP
A short history of acronyms
The data
Who, what and where
Methods
Dataset combination and analysis
Results and Conclusions
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
9 / 12

30. Results and Conclusions
← parallel
E. Williams (MSKCC)
Pooled RP gEUD Analysis
serial →
April 11, 2013
10 / 12

31. Results and Conclusions
← parallel
E. Williams (MSKCC)
Pooled RP gEUD Analysis
serial →
April 11, 2013
10 / 12

32. Results and Conclusions
← parallel
E. Williams (MSKCC)
Pooled RP gEUD Analysis
serial →
April 11, 2013
10 / 12

33. Results and Conclusions
← parallel
E. Williams (MSKCC)
Pooled RP gEUD Analysis
serial →
April 11, 2013
10 / 12

34. Results and Conclusions
← parallel
E. Williams (MSKCC)
Pooled RP gEUD Analysis
serial →
April 11, 2013
10 / 12

35. Results and Conclusions
← parallel
E. Williams (MSKCC)
Pooled RP gEUD Analysis
serial →
April 11, 2013
10 / 12

36. Results and Conclusions
0
10
−0.34
−2
10
p−value
−0.36
−0.38
−4
10
−6
10
−0.4
−8
10
−0.42
−10
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
10
−1
−0.8
−0.6
−0.4
−0.2
log10(a)
0
0.2
0.4
0.6
0.8
1
log10(a)
MSK + NKI + RTOG + UMich
1
log (a) = −1
10
RP rate observed
log likelihood per degree of freedom
LKB model fits: Combined data
0.8
p−val: 1.5e−08
0.6
0.4
0.2
0
0
10
20
30
40
50
60
70
80
90
gEUD [Gy]
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
11 / 12

37. Results and Conclusions
0
10
−0.34
−2
10
p−value
−0.36
−0.38
−4
10
−6
10
−0.4
−8
10
−0.42
−10
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
10
−1
−0.8
−0.6
−0.4
−0.2
log10(a)
0
0.2
0.4
0.6
0.8
1
log10(a)
MSK + NKI + RTOG + UMich
1
log10(a) = −0.2
RP rate observed
log likelihood per degree of freedom
LKB model best fit: Combined data
0.8
p−val: 1.7e−09
0.6
0.4
0.2
0
0
10
20
30
40
50
60
70
80
90
gEUD [Gy]
TD50 [95% CI]
m [95% CI]
19 Gy [14.7 − 24.3 Gy]
E. Williams (MSKCC)
a [95% CI]
0.4 [0.30 − 0.52]
0.63 [0.32 − 1.02]
Pooled RP gEUD Analysis
April 11, 2013
11 / 12

38. Results and Conclusions
Represents the largest gEUD study on prospective pneumonitis
data to date
The LKB model ’volume parameter’, a, was determined to be
0.63 (n = 1.6) with a 95% confidence interval between 0.32 and
1.02
Values of a < 1 suggest parallel tissue architecture; mean lung
dose (a = 1) has not been excluded
Observed heterogeneity between datasets in fit results motivates
future work
→ e.g. incidental irradiation of the heart 10
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

39. Backup

40. References I
[1] Byhardt RW, Scott C, Sause WT, et al. Response, toxicity, failure patterns, and survival in five radiation therapy oncology
group (rtog) trials of sequential and/or concurrent chemotherapy and radiotherapy for locally advanced
non-small-cell-carcinoma of the lung. Int J Radiat Oncol Biol Phys, 42:469–78, 1998.
[2] Inoue A, Kunitoh H, Saijo N, et al. Radiation pneumonitis in lung cancer patients: A retrospective study of risk factors an
dthe long-term prognosis. Int J Radiat Oncol Biol Phys, 49:649–55, 2001.
[3] Rancati T, Ceresoli GL, Cattaneo GM, et al. Factors predicting radiation pneumonitis in lung cancer patients: A
retrospective study. Radiother Oncol, 67:275–83, 2003.
[4] Seppenwoolde Y, De JK, Lebesque JV, et al. Regional differences in lung radiosensitivity after radiotherapy for
non-small-cell-lung cancer. Int J Radiat Oncol Biol Phys, 60:748–58, 2004.
[5] Yorke ED, Jackson A, Ling C, et al. Correlation of dosimetric factors and radiation pneumonitis for non-small-cell lung
cancer patients in a recently completed dose escalation study. Int J Radiat Oncol Biol Phys, 63:672–682, 2005.
[6] Rosenzweig KE, Fox J, et al. Results of a phase i dose-escalation study using three-dimensional conformal radiotherapy in
the treatment of inoperable nonsmall cell lung carcinoma. Cancer, 103:2118–27, 2005.
[7] Belderbos JS, Heemsbergen W, Lebesque JV, et al. Final results of a phase i/ii dose escalation trial in non-small-cell lung
cancer using three-dimensional conformal radiotherapy. Int J Radiat Oncol Biol Phys, 66:126–34, 2006.
[8] Bradley J, Graham MV, and Emami B. Toxicity and outcome results of rtog 9311: A phase i/ii dose-escalation study using
three-dimensional conformal radiotherapy in patients with inoperable non-small-cell lung carcinoma. Int J Radiat Oncol
Biol Phys, 61:318–28, 2005.
[9] Kong FM, Hayman J, Ten Haken RK, et al. Final toxicity results of a radiation-dose escalation study in patients with
non-small-cell lung cancer (nsclc): Predictors for radiation pneumonitis and fibrosis. Int J Radiat Oncol Biol Phys,
65:1075–86, 2006.
[10] Huang EX, Hope AJ, Bradley JD, and Deasy J. Heart irradiation as a risk factor for radiation pneumonitis. Acta
Oncologica, 50:51–60, 2011.
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

41. LKB Results
MSKCC
RTOG
Average gEUDs
Average gEUDs
1
1
Avg. with comp
Central 68%
Avg. no comp
Central 68%
−1
−0.5
−0.5
10
0
0.5
log10(a)
0
0.5
log (a)
Avg. with comp
Central 68%
Avg. no comp
Central 68%
−1
1
−1
−0.5
1
−1
−0.5
0
0
0.5
0.5
1
0
10
20
30
40
50
60
70
1
80
0
10
20
30
gEUD [Gy]
UMich
60
70
80
Average gEUDs
1
Avg. with comp
Central 68%
Avg. no comp
Central 68%
−1
Avg. with comp
Central 68%
Avg. no comp
Central 68%
−1
−0.5
−0.5
0
0.5
log10(a)
0
0.5
10
50
NKI
Average gEUDs
1
log (a)
40
gEUD [Gy]
1
−1
−0.5
1
−1
−0.5
0
0
0.5
0.5
1
0
10
20
30
40
50
60
70
80
1
0
10
gEUD [Gy]
E. Williams (MSKCC)
20
30
40
50
60
70
80
gEUD [Gy]
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

42. LKB Results
MSKCC
RTOG
Probability that RPS rate ≥ 20%
0.9
0.8
0.7
0.6
0.5
0.4
log10(a)
log10(a)
Probability that RPS rate ≥ 20%
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
−0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.3
0.2
0.1
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
−0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
gEUD [Gy]
gEUD [Gy]
UMich
NKI
Probability that RPS rate ≥ 20%
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
log10(a)
log10(a)
Probability that RPS rate ≥ 20%
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
−0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
−0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
5
gEUD [Gy]
E. Williams (MSKCC)
10
15
20
25
30
35
40
45
50
55
60
65
70
gEUD [Gy]
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

43. LKB Results
Combined: MSK + NKI + RTOG + UMich
log10(a)
Probability that RPS rate ≥ 20%
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
−0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
gEUD [Gy]
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

44. LKB Results
MSKCC
RTOG
Low 68% CL on RP rate
0.5
0.45
0.4
0.35
0.25
0.2
10
0.3
log (a)
log10(a)
Low 68% CL on RP rate
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
−0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.15
0.1
0.05
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
0
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
−0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
gEUD [Gy]
UMich
NKI
Low 68% CL on RP rate
0.5
0.45
0.4
0.35
0.25
0.2
0.15
0.1
0.05
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
0
10
0.3
log (a)
log10(a)
Low 68% CL on RP rate
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
−0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
−0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
5
10
gEUD [Gy]
E. Williams (MSKCC)
0
gEUD [Gy]
15
20
25
30
35
40
45
50
55
60
65
70
0
gEUD [Gy]
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

45. LKB Results
Combined: MSK + NKI + RTOG + UMich
log10(a)
Low 68% CL on RP rate
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
−0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
0
gEUD [Gy]
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

46. LKB Results
LKB model fits (zoom)
MSK
0.6
RTOG
log10(a) = 1
0.6
p−val: 0.01
RP rate observed
RP rate observed
p−val: 0.11
0.5
0.4
0.3
0.2
0.1
0
0
log10(a) = 1
0.5
0.4
0.3
0.2
0.1
10
20
30
40
50
60
70
0
0
80
20
40
gEUD
UMich
0.6
0.6
100
log10(a) = 1
p−val: 0.87
RP rate observed
p−val: 0.82
RP rate observed
80
NKI
log10(a) = 1
0.5
0.4
0.3
0.2
0.1
0
0
60
gEUD
0.5
0.4
0.3
0.2
0.1
10
20
30
40
50
60
70
80
90
0
0
10
gEUD
E. Williams (MSKCC)
20
30
40
50
60
70
80
gEUD
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

47. LKB Results
LKB model fits
MSK
RTOG
1
1
log10(a) = 1
0.6
0.4
0.2
0
0
p−val: 0.01
0.8
RP rate observed
RP rate observed
log10(a) = 1
p−val: 0.11
0.8
0.6
0.4
0.2
10
20
30
40
50
60
70
80
0
0
90
10
20
30
gEUD
40
50
60
UMich
90
1
log10(a) = 1
log10(a) = 1
p−val: 0.82
p−val: 0.87
0.8
RP rate observed
0.8
RP rate observed
80
NKI
1
0.6
0.4
0.2
0
0
70
gEUD
0.6
0.4
0.2
10
20
30
40
50
60
70
80
90
0
0
10
gEUD
E. Williams (MSKCC)
20
30
40
50
60
70
80
90
gEUD
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

48. LKB Results
LKB p-values
LKB Log-likelihoods
0
−0.2
10
−1
10
−2
10
−0.3
−3
10
−4
10
−0.35
p−value
log likelihood per degree of freedom
−0.25
−0.4
−5
10
−6
10
−7
10
−0.45
−8
10
−0.5
−9
10
MSK
−0.55
−1
−0.8
MSK
−10
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
10
1
log (a)
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
log10(a)
10
MSK
T D50
(Q p-value, I 2 [95%CIs])
m
a
(Q p-value, I 2 [95%CIs])
(Q p-value, I 2 [95%CIs])
(0.75, 0 [0 − 0.01])
(0.08, 0.60 [0.35 − 0.83])
(< 0.01, 0.98 [0.24 − 1])
(0.13, 0.57 [0.34 − 0.79])
(< 0.01, 0.89 [0.40 − 0.1])
(< 0.01, 0.85 [0.33 − 1])
(0.33, 0 [0 − 0.01])
(0.06, 0.65 [0.3 − 1])
(0.02, 0.70 [0.46 − 0.93])
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

49. LKB Results
LKB p-values
LKB Log-likelihoods
0
−0.2
10
−1
10
−2
10
−0.3
−3
10
−4
10
−0.35
p−value
log likelihood per degree of freedom
−0.25
−0.4
−5
10
−6
10
−7
10
−0.45
−8
10
−0.5
−9
10
MSK
NKI
−0.55
−1
−0.8
MSK
NKI
−10
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
10
1
log (a)
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
log10(a)
10
MSK+NKI
T D50
(Q p-value, I 2 [95%CIs])
m
a
(Q p-value, I 2 [95%CIs])
(Q p-value, I 2 [95%CIs])
(0.75, 0 [0 − 0.01])
(0.08, 0.60 [0.35 − 0.83])
(< 0.01, 0.98 [0.24 − 1])
(0.13, 0.57 [0.34 − 0.79])
(< 0.01, 0.89 [0.40 − 0.1])
(< 0.01, 0.85 [0.33 − 1])
(0.33, 0 [0 − 0.01])
(0.06, 0.65 [0.3 − 1])
(0.02, 0.70 [0.46 − 0.93])
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

50. LKB Results
LKB p-values
LKB Log-likelihoods
0
−0.2
10
−1
10
−2
10
−0.3
−3
10
−4
10
−0.35
p−value
log likelihood per degree of freedom
−0.25
−0.4
−5
10
−6
10
−7
10
−0.45
−8
10
−0.5
−0.55
−1
MSK
NKI
UMich
−0.8
−0.6
MSK
NKI
UMich
−9
10
−10
−0.4
−0.2
0
0.2
0.4
0.6
0.8
10
1
log (a)
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
log10(a)
10
MSK+NKI+UMich
T D50
(Q p-value, I 2 [95%CIs])
m
a
(Q p-value, I 2 [95%CIs])
(Q p-value, I 2 [95%CIs])
(0.75, 0 [0 − 0.01])
(0.08, 0.60 [0.35 − 0.83])
(< 0.01, 0.98 [0.24 − 1])
(0.13, 0.57 [0.34 − 0.79])
(< 0.01, 0.89 [0.40 − 0.1])
(< 0.01, 0.85 [0.33 − 1])
(0.33, 0 [0 − 0.01])
(0.06, 0.65 [0.3 − 1])
(0.02, 0.70 [0.46 − 0.93])
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

51. LKB Results
LKB p-values
LKB Log-likelihoods
0
−0.2
10
−1
10
−2
10
−0.3
−3
10
−4
10
−0.35
p−value
log likelihood per degree of freedom
−0.25
−0.4
−5
10
−6
10
−7
10
−0.45
−0.5
−0.55
−1
−8
10
MSK
NKI
UMich
RTOG
−0.8
−0.6
MSK
NKI
UMich
RTOG
−9
10
−10
−0.4
−0.2
0
0.2
0.4
0.6
0.8
10
1
log (a)
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
log10(a)
10
MSK+NKI+UMich+RTOG
T D50
(Q p-value, I 2 [95%CIs])
m
a
(Q p-value, I 2 [95%CIs])
(Q p-value, I 2 [95%CIs])
(0.75, 0 [0 − 0.01])
(0.08, 0.60 [0.35 − 0.83])
(< 0.01, 0.98 [0.24 − 1])
(0.13, 0.57 [0.34 − 0.79])
(< 0.01, 0.89 [0.40 − 0.1])
(< 0.01, 0.85 [0.33 − 1])
(0.33, 0 [0 − 0.01])
(0.06, 0.65 [0.3 − 1])
(0.02, 0.70 [0.46 − 0.93])
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

52. LKB Results
LKB p-values
LKB Log-likelihoods
0
−0.2
10
−1
10
−2
10
−0.3
−3
10
−4
10
−0.35
p−value
log likelihood per degree of freedom
−0.25
−0.4
−5
10
−6
10
−7
10
−0.45
−0.5
−0.55
−1
MSK
NKI
UMich
RTOG
COMB
−0.8
−0.6
MSK
NKI
UMich
RTOG
COMB
−8
10
−9
10
−10
−0.4
−0.2
0
0.2
0.4
0.6
0.8
10
1
log (a)
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
log10(a)
10
MSK+NKI+UMich+RTOG
T D50
(Q p-value, I 2 [95%CIs])
m
a
(Q p-value, I 2 [95%CIs])
(Q p-value, I 2 [95%CIs])
(0.75, 0 [0 − 0.01])
(0.08, 0.60 [0.35 − 0.83])
(< 0.01, 0.98 [0.24 − 1])
(0.13, 0.57 [0.34 − 0.79])
(< 0.01, 0.89 [0.40 − 0.1])
(< 0.01, 0.85 [0.33 − 1])
(0.33, 0 [0 − 0.01])
(0.06, 0.65 [0.3 − 1])
(0.02, 0.70 [0.46 − 0.93])
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

53. History of gEUD
What to expect?
Fitting institutional datasets to find best values of three parameters:
Volume parameter, a (= 1/n)
50% complication tolerance dose, TD50
Cohort radiosensitivity slope parameter, m
Consensus based lung tolerance parameters (Emami et al., 1991)
combined with a fit to clinical data (Burman et al., 1991) resulted
LKB parameter values:
n = 1/a = 0.87,
T D50 = 24.5 Gy,
m = 0.18
Since then:
Marks, IJROBP 76:2010
QUANTEC: Radiation Dose-Volume Effects in the Lung
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

54. log(a) log-likelihood
Logistic Regression
LKB Model
Dashed line: 68% CL
Solid line: 95% CL
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

55. log(a) p-values
Logistic Regression
E. Williams (MSKCC)
LKB
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

56. gEUD Rank-Sum p-values
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

57. LKB Model consistency
Data
MSK + NKI
TD50
m
a
Q
0.1024
2.305
0.9412
I2
[95% CL]
0.749
0.129
0.332
0
0.566
0
[0 - 0]
[0.343 - 0.789]
[0 - 0.008]
Q p-value
MSK + NKI + RTOG
TD50
m
a
88.79
20.09
9.756
< 0.001
< 0.001
0.008
0.977
0.900
0.795
[0.728 - 1]
[0.328 - 1]
[0.69 - 0.9]
MSK + NKI + UMich
TD50
m
a
4.951
18.39
5.762
0.084
< 0.001
0.056
0.596
0.891
0.653
[0.362 - 0.831]
[0.402 - 1]
[0.3 - 1]
< 0.001
< 0.001
0.020
0.977
0.852
0.695
[0.239 - 1]
[0.325 - 1]
[0.457 -0.934]
MSK + NKI +
UMich + RTOG
TD50
m
a
E. Williams (MSKCC)
130.8
20.23
9.85
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

58. Logistic Regression ROC Curves
ROC for classification by logistic regression
1
0.9
True positive rate (Sensitivity)
0.8
0.7
0.6
0.5
MSK
AUC: 0.715
NKI
AUC: 0.658
RTOG
AUC: 0.797
UMich
AUC: 0.914
MSK+NKI+RTOG+UMich
AUC: 0.753
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False positive rate (1−Specificity)
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

59. gEUDs
MSK
RTOG
80
EUD [Gy]
EUD [Gy]
80
60
40
20
0
60
40
20
Censored
0
Complication
Censored
NKI
UMich
80
EUD [Gy]
EUD [Gy]
80
60
40
20
0
Complication
60
40
20
Censored
E. Williams (MSKCC)
Complication
0
Pooled RP gEUD Analysis
Censored
Complication
April 11, 2013
12 / 12

60. Combined gEUDs
MSK + NKI + RTOG + UMich
90
80
70
EUD [Gy]
60
50
40
30
20
10
0
E. Williams (MSKCC)
Censored
Pooled RP gEUD Analysis
Complication
April 11, 2013
12 / 12

61. Combined gEUD response (zoom)
Comb
Log10(a) = 1
0.6
p−val: 0.791
RP rate observed
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
60
70
80
90
100
gEUD
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12

62. Combined gEUD response
1
0.9
Comb
Log10(a) = 1
0.8
p−val: 0.791
RP rate observed
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
60
70
80
90
gEUD
E. Williams (MSKCC)
Pooled RP gEUD Analysis
April 11, 2013
12 / 12