1. Biologically-Based Risk Estimation for Radiation-Induced Chronic Myeloid Leukemia
Radiation Carcinogenesis: Applying Basic Science to Epidemiological Estimates of Low-Dose Risks

2. 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?

3. 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

4. Chronic Myeloid Leukemia
CML is homogeneous, prevalent, radiation-induced, 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

6. Linear Risk Model Using the BCR-ABL to CML waiting time density
and the linear model
we maximized
the log-likelihood

7. Linear-Quadratic-Exponential Model
The LQE model is
where
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.

8. Likelihood Data CML is practically absent in Nagasaki
High dose HF waiting times are too long
HM data is consistent with prior expectations

9. aage at diagnosis
bO = observed cases (E = expected background cases based on U.S. incidence rates)
ctsx = average of the times since exposure for the cases

10. 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

13. Parameter Estimates

14. CML Risk Estimates
The lifetime excess CML risk in the limit of low -ray doses
yields
Linear model
R = Gy-1 and Q = Gy-1
LQE posterior model
R = Gy-1 and Q = Gy-1

15. 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

16. BCR-to-ABL 2D distances in lymphocytes
Kozubek et al. (1999) Chromosoma 108:

17. Theory of Dual Radiation Action
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
= 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 = DSBs per Mb per Gy;  = mass density
TBCR = 5.8 kbp; TABL = 300 kbp

18. Estimation of g(r)
d in [.01, .025], dx in [.04, .05], d in [.05, .06]
G=35 DSB/Gy per cell
6.25 kev/um3 = 1 Gy
R = 3.7 um  r0 = 0.24 m, p0 = 0.06

19. 

20. 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:
Broad variation in human HSC levels Stem Cells (1995) 13:
Low levels of HSCs in BMT patients Blood (1998) 91:

21. 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:

22. Net Lifetime CML Risk The net lifetime excess risk of CML is
Letting Dn = 0 while D  0
We solved R0 = 0 for ks as a function of exposure age x.

25. 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 dead-band in the control of target cell numbers

26. Acknowledgments
Rainer Sachs
David Hoel
NIH and DOE