AAPM Summer School – Vancouver 2011
Evidence‐based accuracy requirements in radiation oncology – tumor focus
Søren M Bentzen, Ph.D., D.Sc.
Departments of Human Oncology; Medical Physics; Biostatistics and Medical Informatics,
University of Wisconsin Carbone Cancer Center, Madison, Wisconsin, USA
bentzen@humonc.wisc.edu
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Evolution of RT Data Collection Required for
Advanced Technology Clinical Trials
Prior to 3DOG/
RTOG 9406
3DOG/RTOG 9406
to present
2010+ Protocols
• Data objects (typical
patient accrual digital data
set ~ 100 MB)
• Film, paper
forms (CRFs).
• Postal
 Thanks to Jim Purdy
– Volumetric, digital images
(planning CT)
– Contours (TV, OAR)
– 3D dose distributions
(fractionation)
– Treatment plans
– DVHs
– Treatment verif. images
• Participants mostly
submit data digitally
3
• Additional data objects
needed for 2010 trials
–
–
–
Diagnostic imaging studies
(pre- & post, MRI, MRS,
PET/CT,…)
Treatment verif. images
(planar, kV CBCT, MV CT,
Calypso,…)
Treat. plans (parameters for
dose recalc.
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Precision and accuracy: the target analogy
Not precise, NOT ACCURATE
[in metrology the blue darts would be seen as “accurate” = unbiased]
Precise (i.e. reproducible), but biased = NOT ACCURATE
Precise AND
unbiased = ACCURATE
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Mean Squared
Error:
Root Mean
Squared Error:
Probability density
Statistics of radiation delivery
precision, 
bias
0
Deviation from planned dose [%]
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Probability density
Comparing radiation dose deliveries
Root
Mean
Square
Errors
0.32%
2.04%
1.50%
Deviation from planned dose [%]
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Dosimetric precision in vivo
Entrance and exit
Si diode measurements
in 11 patients with
HNSCC
x = -0.5%
SD = 4.3%
 Leunens,…, van der Schueren, R&O 25: 242 (1992)
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DISCLAIMER
"I guess I should warn you that if I turn out to be particularly clear, you've probably misunderstood me.“
Alan Greenspan at his 1988 confirmation hearings
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The normalized dose‐response gradient
Response probability
P(D)
P
D
Dose (Gy)
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Steepness of DR curves for HNSCC
3.0
2.5
Larynx
Head&Neck
Supraglottic
Pharynx
Neck nodes
2.0
1.5
1.0
0.5
0.0
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 Bentzen R&O 32: 1 (1994)
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Steepness of normal‐tissue dose‐response curves
7
6
5
4
3
2
1
0
50
fixed dose/F
fixed no. F
Influenced by dose inhomogeneity (?)
HNSCC
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 Bentzen R&O 32: 1 (1994)
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Sensori‐neural hearing loss
In c id e n c e o f h e a rin g lo s s (% )
50 = 0.70 with 95% CI (0.22; 1.18)
100
80
60
40
20
0
0
20
40
60
80
Total dose (Gy)
 Honore et al. R&O 65: 9 (2002)
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Sensori‐neural hearing loss
In c id e n c e o f h e a rin g lo s s (% )
50 = 3.4 with 95% CI (0.3; 6.5)
100
Adjusting for
patient’s age
and pre-RT
hearing level
80
60
40
49 y.o.
43 dB pre‐RT hearing level
20
0
0
20
40
60
80
Total dose (Gy)
 Honore et al. R&O 65: 9 (2002)
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50 vs. local ‐value
•  varies with position on the dose‐
response curve, i.e. with the response level.
Local steepness, x
50%
• The curve is still parameterized in terms of D50 and 50
• However, in most situations the local ‐value should be applied
Response level, x
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‐value for dose‐per‐fraction escalation
 At a reference dose per fraction of dr the relationship between N and d is
EXAMPLE:
Assume / = 2 Gy dr = 2 Gy N = 1.5d
dr = 6 Gy N = 1.75d
 Two asymptotic results are
 Bentzen Acta Oncol 44: 825 (2005)
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2
2
 D2   pop
  F2   pop
  2f / N
Uncertainty components
The delivered dose can be decomposed as:
Dˆ  DP  b  
Effect of BIAS on outcome
where DP is the planned (intended or acceptable to the physician) dose,
b is the bias, and  is a random error
The variance of  is
  
2
2
course

2
Fx

2
course
 / N
2
fx
where course is the patient-to-patient variability that does not vary
between fractions, f is the fraction-to-fraction variability, N is the
number of fractions
 Bentzen, IAEA report (in preparation)
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Estimating the clinical effect of imprecision
The expectation value of P(D) in the presence of variability in dose is
The change in P(D) due to imprecision in dose delivery is
The Taylor expansion of P(D) is
The first order term cancels out in the convolution integral due to the symmetry of the p.d.f.
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Second derivative of dose‐response function
 Logistic dose‐response curve: D50=60 Gy, 50=1.8
P’’(D)
P(D)21%
= MAXIMUM INCREASE IN NTCP
Dose, D
MAXIMUM LOSS OF TCP =
P(D)79%
 Bentzen, IAEA report (in preparation)
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Loss of TCP with reduced precision
Around TCP=79%
Loss of TCP, %
50=3
50=2
50=1
0
Precision, x
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Increase in NTCP with reduced precision
Increase in NTCP, %
Around NTCP=21%
50=6
50=4
50=2
0
Precision, x
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So, what’s the accuracy target then?
Tumor control
• GOAL: lack of accuracy results in <5% loss of tumor control probability
• ASSUMPTION: 50,N=3
Local steepness, x
• What is  at the 80% level where the precision requirement is tightest?
50%
50=3
80=2.1
Response level, x
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So, what’s the accuracy target then?
Tumor control
• GOAL: lack of accuracy results in <5% loss of tumor control probability
• ASSUMPTION: 50,N=3
• What is  at the 80% level where the precision requirement is tightest?
• Answer: 80,N2.1
• Accepting a maximum loss due to bias of 3% bias 1.5%
• This caps the loss due to imprecision at 2%
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Loss of TCP with reduced precision
NOTE: These curves refer to 50 NOT the local 
Loss of TCP, %
50=3
50=2
50=1
0
Precision, x
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So, what’s the accuracy target then?
Tumor control
• GOAL: lack of accuracy results in <5% loss of tumor control probability
• ASSUMPTION: 50,N=3
• What is  at the 80% level where the precision requirement is tightest?
• Answer: 80,N2.1
• Accepting a maximum loss due to bias of 3% bias 1.5%
• This caps the loss due to imprecision at 2%  5%
• If treatment is delivered in, say, 30F this could be split as •
course 4.5%
•
Fx 2.2% fx 12% /SMB 09/11
So, what if we gave 15 Gy x 3 instead?
Tumor control
• GOAL: lack of accuracy results in <5% loss of tumor control probability
• ASSUMPTION: tumor / = 8 Gy, 50,d = 2.5 50,N=3=4.1
• At the 80% level where the precision requirement is tightest 80,N2.9
• Accepting a maximum loss due to bias of 3% bias 1%
• This caps the loss due to imprecision at 2%  3.9%
• As treatment is delivered in 3F this now yields course 3.5%
Fx 1.7% fx 3.0% /SMB 09/11
So, what about the NT accuracy target?
NTCP
• GOAL: lack of accuracy results in <5% increase in NTCP
• ASSUMPTION: 50,N=4
• At the 20% level where the precision requirement is tightest 20,N2.3
• Accepting a maximum loss due to bias of 3% bias 1.3%
• This caps the loss due to imprecision at 2%  4%
• If treatment is delivered in, say, 30F this could be split as course 3.5%
Fx 1.9% fx 10.6% /SMB 09/11
Special consideration – subclinical breast cancer
LOCAL CONTROL
Clinical outcome data from
1487 patients in the two 13F
test arms of the START A trial
Lancet Oncol 9: 331 (2008)
CHANGE IN
BREAST
APPEARANCE
eff = 0.2
30 = 1.7
13F
…without adjusting for age, chemotherapy, tamoxifen, breast size, and surgical deficit
 Yarnold, Bentzen et al. IJROBP 79:1 (2011)
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Target moved
(or dose distribution moved)
Fraction of dose missed, D
Missing a fraction of Dp to a fractional volume
3%
1%
5%
2%
Fraction of volume missed, V
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TAKEHOME MESSAGE:
IF YOU MAKE MISTAKES,
MAKE SURE TO MAKE THEM RANDOMLY!
3
1
2
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EPILOGUE: Accuracy in a (humbling) perspective
% of patients who lost >3 Gy due to poor compliance
80
70
73 75
OVERALL:
dose=9%
64
60
AT THE PATIENT LEVEL!!!
%
50
41 44
40
*
30
28
*
20
23
27
16
*
10
4
0
22811
22851
Conventional
22791
Altered
PMH
CHART
Altered + Miso
 Khalil et al. IJROBP 55: 568 (2003)
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EPILOGUE: Accuracy in a (humbling) perspective
Co‐factors in the expression of RT effects
Endpoint
Risk factor
OR
Ref.
D*
Various
Connective tissue disease
2.0
Hoelscher
4.9 Gy
Telangiectasia of the skin
Moist desquamation during RT
3.0
Bentzen
7.8 Gy
Radiological lung fibrosis
Tamoxifen during RT
3.2
Bentzen
8.3 Gy
Pneumonitis
Non‐smokers/smokers
4.2
Liao
10.2 Gy
Sensori‐neural hearing loss
5 years increment in patient’s age
10
Honore
16.4 Gy
12
Cosset
17.7 Gy
Gastrointestinal injury RT Previous laparotomy
for Hodgkin’s Disease
*50=3, D=70 Gy, p0=10%
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EPILOGUE: Accuracy in a (humbling) perspective
Variation in Mean Equivalent Lung Dose
 18 patients with NSCLC receiving chemo‐RT
 Average MELD=10.2 Gy
 CVMELD=42%
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Thanks to Fridtjof Nüsslin, Jan-Willem Leer, Jacques Bernier &
Jake van Dyk for inspiring discussions on aspects of this topic
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Influence of dosimetric variation on 50
 Pettersen et al. R&O 86: 195 (2008)
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Inflation of sample size needed in RCT
1.15
3.0
1.50
50,biol
1.05
2.0
1.30
1.20
1.80
1.10
dose
 Bentzen (in preparation)
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Intermediate/high risk prostate cancer
 Diez, Vogelius, Bentzen IJROBP 77: 1066 (2010)
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Local control (%)
Dose‐response stratified for in vitro radiosensitivity
Biologic dose (Gy)
 Bentzen IJRB 61: 417 (1991)
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When is dose delivery precise enough?
Distribution of delivered dose
CV(%)
D5 (Gy)
TCP
10
68.73
50.0
5
71.76
62.9
0.02
2
72.85
67.2
0.01
1
73.01
67.9
0.1
73.07
68.1
0.05
0.04
0.03
60
50
80
60
100
70
D5
120
80
 Bentzen, IJROBP 58: 320 (2004)
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