Transcript Biologically-Based Risk Estimation for Radiation

Biologically-Based Risk
Estimation for Radiation-Induced
Chronic Myeloid Leukemia
Radiation Carcinogenesis: Applying
Basic Science to Epidemiological
Estimates of Low-Dose Risks
Overview

Bayesian methods and CML

Linear-Quadratic-Exponential model

Likelihood and prior data sets

Baseline LQE estimate of CML risk

Improved risk estimates based on BCR-to-ABL
distances and CML target cell numbers

Net lifetime CML risk: Can it have a U-shaped
low dose response?
Bayesian Methods
Priors+ likelihood estimates  posteriors
 Posterior information equals prior plus
likelihood information
 Posterior means are information-weighted
averages of prior and likelihood means
 Posteriors are normal if the prior and likelihood
estimates are normal
 Priors act as soft constraints on the parameters
 Priors and structures come from the same data

Chronic Myeloid Leukemia

CML is homogeneous, prevalent, radiationinduced, and caused by BCR-ABL

The a2 intron of ABL is unusually large

Leukemic endpoints have rapid kinetics

White blood cells need fewer stages

Linear CML risk is not biologically-based

Linear-quadratic-exponential CML risk does have
a biological basis
Linear Risk Model
Using the BCR-ABL to CML
waiting time density
and the linear model
mi  (e
3 2
t
k t e
w(t ) 
2
c1  kai
we maximized
the log-likelihood
 kt t
2 c2 kt ti
i i
 Dt e
) Pi
 O log(m )  m
i
i
i
i
Linear-Quadratic-Exponential Model
The LQE model is
mi  [e
c1  kai
 ( Di 
where


D 
2
i
n

2 c2  k t t i
i
Dni )t e
]Pi e
 ( k Di   k D2i  kn Dni )
NP(ba | T )w(ti )  ti2ec2 kt ti
Di and Dni are the gamma and neutron doses in gray
N is the number of CML target cells per adult
P(ba|T) is the probability of BCR-ABL given a translocation
This is a one-stage model of carcinogenesis.
Likelihood Data
 CML is practically absent in Nagasaki
 High dose HF waiting times are too long
 HM data is consistent with prior expectations
Table 1: Hiroshima CML cases by age, sex and dose in sieverts.
D  0.2 Sv
Males
aage
0.2 Sv D  1 Sv
Females
tsxc
Males
agea
O (E)b
1-10
0 (0.02)
0 (0.01)
0 (0.00)
10-20
0 (0.15)
0 (0.09)
1 (0.02)
20-30
0 (0.38)
1 (0.28)
30-40
1 (0.71)
23
40-51
1 (1.32)
50-60
O (E)
tsx
O (E)
1 Sv D
Females
tsx
O (E)
Males
tsx
O (E)
Females
tsx
O (E)
tsx
0 (0.00)
0 (0.00)
8
0 (0.01)
2 (0.00)
10
0 (0.00)
1 (0.05)
14
0 (0.05)
1 (0.01)
6
0 (0.01)
0 (0.64)
2 (0.11)
12
0 (0.10)
2 (0.03)
7
2 (0.02)
18
18
0 (1.29)
1 (0.17)
33
1 (0.20)
11
2 (0.05)
7
1 (0.04)
23
3 (1.83)
24
1 (2.06)
23
2 (0.26)
15
4 (0.33)
9
0 (0.08)
60-70
3 (2.18)
22
4 (2.57)
27
1 (0.33)
11
4 (0.41)
19
1 (0.09)
70
4 (3.76)
34
4 (4.44)
32
0 (0.56)
1 (0.69)
38
total
12 (10.4)
8 (1.50)
10 (1.8)
10 (11)
14
0 (0.00)
0 (0.07)
14
1 (0.08)
28
0 (0.11)
1 (0.09)
28
8 (0.38)
5 (0.32)
at diagnosis
= observed cases (E = expected background cases based on U.S. incidence rates)
ctsx = average of the times since exposure for the cases
bO
Prior Data: Sources
 C1 and k:
SEER data
 kt : Patients irradiated for BGD
 k, k and kn : CAFC and MRA assays
 / and n/: Lymphocyte dicentric yields
 C2 : Depends on , kt, N, and P(ba|T)
• N: SEER and translocation age structure data
• P(ba|T): BCR and ABL intron sizes, the genome size
Parameter Estimates
point estimate (95% confidence interval)
parameter
LQE Prior
LQE Likelihood
LQE Posterior
c1
-13.04 (-13.21, -12.87)
-12.6338 (-14.69,-10.58)
-13.0340 (-13.20, -12.87)
k (yr-1)
0.042 (0.0395, 0.0445)
0.0395 (0.0063, 0.073)
0.0422 (0.040, 0.045)
kt (yr-1)
0.377 (0.014, 0.740)
0.4220 (0.220, 0.630)
0.3858 (0.218, 0.554)
c2
-10.47 (-16.06, -4.81)
-9.5505 (-11.41, -7.69)
-9.7287 (-11.28, -8.174)
k (Gy-1)
0.290 (0.251, 0.329)
0.3044 (0.034, 0.643)
0.2900 (0.251, 0.329)
k (Gy-2)
0.068 (0.054, 0.082)
0.0238 (-0.098, 0.146)
0.0673 (0.054, 0.081)
CML Risk Estimates
The lifetime excess CML risk in the limit of low -ray doses

R
t
0
2
e
c2  k t t
2e c2
dt 
kt3
yields

Linear model
• R = 0.0075 Gy-1 and Q = 0.0158 Gy-1

LQE posterior model
• R = 0.0022 Gy-1 and Q = 0.0042 Gy-1
CML Target Cell Numbers

A comparison of age responses for CML
and total translocations suggests a CML
target cell number of 2x108

1012 nucleated marrow cells per adult
and one LTC-IC per 105 marrow cells
suggests 107 CML target cells

P(ba|T) = 2TablTbcr/2 may not hold
BCR-to-ABL 2D distances in lymphocytes
Kozubek et al. (1999) Chromosoma 108: 426-435
Theory of Dual Radiation Action

P(ba | D)  2TBCRTABLY D 
2
0
t D (r )
2
S
(
r
)
g
(
r
)
dr


D


D
ba
ba
ba
 4r 2
P(ba|D) = probability of a BCR-ABL translocation per G0/G1 cell given a dose D
tD(r)dr = expected energy at r given an ionization event at the origin
t D (r )  t (r )   4r 2 D =
intra-track component + inter-track component
Sba(r) = the BCR-to-ABL distance probability density
g(r) = probability that two DSBs misrejoin if they are created r units apart
Y = 0.0058 DSBs per Mb per Gy;  = mass density
TBCR = 5.8 kbp; TABL = 300 kbp
Estimation of g(r)

2
 d
r2
r3
r5
S0 (r )  3 3  (9 / 4) 4  (3 / 16) 6
R
R
R
g (r )  p0e( r / r0 )
S0 (r ) ( r / r0 )
1 ( p0G )

t
(
r
)
e
dr

4 6.25 0
4r 2
2

S0 (r ) ( r / r0 )
1 ( p0G )
 dx 
t
(
r
)
e
dr
x
4 6.25 0
4r 2

1
 d  ( p0G 2 )  S0 (r )e ( r / r0 ) dr
4
0
d in [.01, .025], dx in [.04, .05], d in [.05, .06]
R = 3.7 um  r0 = 0.24 m, p0 = 0.06
G=35 DSB/Gy per cell
6.25 kev/um3 = 1 Gy
m  [e
c1  ka

 ( D 
R   t e
2 c2  k t t
0
ba
ba
D 
2
 ban
 ba
2 c2 kt t
Dn )t e
2ec2
dt  3  N ba
kt

 ( k D   k D2  kn Dn )
]Pe
N
R
 ba
Dependence of R and N on the choice of fixed LQE parameters ba/ba and ban/ba
BA/BA
.055/.0107
.055/.022
.45/3.64
.45/3.64
.45/3.64
.45/3.64
.45/3.64
a
BAn/BA
.8/.0107
.8/.022
.8/.022
3.8/.022
(1/3).8/.022
10.8/.022
(1/10).8/.022
In parentheses are the 95% CI.
R (Gy-1)
.0022 (.0012, .0039)a
.0039 (.0020, .0073)
.0094 (.0051, .0176)
.0056 (.0029, .0106)
.0116 (.0065, .0216)
.0027 (.0014, .0052)
.0128 (.0072, .0237)
8
6.1x10
5.2x108
7.6x106
4.5x106
9.4x106
2.2x106
1.0x107
N
(3.3x108, 1.1x109)
(2.7x108, 9.8x108)
(4.1x106, 1.4x107)
(2.3x106, 8.6x106)
(5.3x106, 1.7x107)
(4.2x106, 1.1x106)
(5.8x106, 1.9x107)
Dead-Band Control of HSC levels
 Transplant doses of 10, 100, and 1000 CRU
=> CRU levels 1-20% or 15-60% normal
Blood (1996) 88: 2852-2858
 Broad variation in human HSC levels
Stem Cells (1995) 13: 512-516
 Low levels of HSCs in BMT patients
Blood (1998) 91: 1959-1965
Figure 3: Hypersensitivity ratios in the literature (left panel) and the log-survival dose
response for T98G human glioma cells (right panel). Figures from Joiner, M.C., Marples,
B., Lambin, P., Short, S.C. and Turesson, I., Low-dose hypersensitivity: current status
and possible mechanisms. Int J Radiat Oncol Biol Phys (2001) 49: 379-389.
Net Lifetime CML Risk
The net lifetime excess risk of CML is
yT
R   [  (a | x, D)   (a)] S (a | x)da
x

yT


c  ka
2
2 c k ( a x )
 ([e 1  ( D  baba D  baban Dn )(a  x) e 2 t ]e
 ( k D   k D2  kn Dn )
 e c1  ka )  S (a | x)da
x
Letting Dn = 0 while D  0
yT
R0  D  [(a  x) 2 ec2 kt ( a  x )   ks ec1  ka ]  S (a | x)da.
x
We solved R0 = 0 for ks as a function of exposure age x.
Conclusions

Bayesian methods provide a natural framework
for biologically based risk estimation

BCR-to-ABL distance data and knowledge of CML
target cell numbers can be useful in a biologically
based approach to CML risk estimation

Low dose hypersensitivity to killing might lead to a
U-shaped low dose response if there is a deadband in the control of target cell numbers
Acknowledgments
Rainer Sachs
 David Hoel
 NIH and DOE
