Biologically-Based Risk Biologically-Based Risk Estimation for Radiation-Estimation for Radiation-Induced Chronic Myeloid Induced Chronic Myeloid LeukemiaLeukemia

Radiation Carcinogenesis: Radiation Carcinogenesis: Applying Basic Science to Applying Basic Science to Epidemiological Estimates of Epidemiological Estimates of Low-Dose RisksLow-Dose Risks

OverviewOverview

Bayesian methods and CML Bayesian methods and CML Linear-Quadratic-Exponential modelLinear-Quadratic-Exponential model Likelihood and prior data setsLikelihood and prior data sets Baseline LQE estimate of CML risk Baseline LQE estimate of CML risk Improved risk estimates based on Improved risk estimates based on

BCR-to-ABL distances and CML target BCR-to-ABL distances and CML target cell numberscell numbers

Net lifetime CML risk: Can it have a U-Net lifetime CML risk: Can it have a U-shaped low dose response?shaped low dose response?

Bayesian MethodsBayesian Methods

Priors+ likelihood estimates Priors+ likelihood estimates posteriors posteriors Posterior information equals prior plus Posterior information equals prior plus

likelihood informationlikelihood information Posterior means are information-weighted Posterior means are information-weighted

averages of prior and likelihood meansaverages of prior and likelihood means Posteriors are normal if the prior and Posteriors are normal if the prior and

likelihood estimates are normallikelihood estimates are normal Priors act as soft constraints on the Priors act as soft constraints on the

parametersparameters Priors and structures come from the same dataPriors and structures come from the same data

Chronic Myeloid LeukemiaChronic Myeloid Leukemia

CML is homogeneous, prevalent, CML is homogeneous, prevalent, radiation-induced, and caused by BCR-ABLradiation-induced, and caused by BCR-ABL

The a2 intron of ABL is unusually largeThe a2 intron of ABL is unusually large

Leukemic endpoints have rapid kineticsLeukemic endpoints have rapid kinetics

White blood cells need fewer stagesWhite blood cells need fewer stages

Linear CML risk is not biologically-basedLinear CML risk is not biologically-based

Linear-quadratic-exponential CML risk Linear-quadratic-exponential CML risk does have a biological basisdoes have a biological basis

Linear Risk ModelLinear Risk Model

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Using the Using the BCRBCR--ABLABL to CML to CMLwaiting time densitywaiting time density

and the linear modeland the linear model

Linear-Quadratic-Exponential Linear-Quadratic-Exponential ModelModel

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The LQE model isThe LQE model is

DDii and and DDni ni are the gamma and neutron doses in grayare the gamma and neutron doses in grayNN is the number of CML target cells per adult is the number of CML target cells per adult PP((ba|Tba|T)) is the probability of is the probability of BCRBCR--ABLABL given a translocation given a translocation

This is a one-stage model of carcinogenesis.This is a one-stage model of carcinogenesis.

wherewhere

Likelihood DataLikelihood Data

CML is practically absent in NagasakiCML is practically absent in Nagasaki

High dose HF waiting times are too High dose HF waiting times are too longlong

HM data is consistent with prior HM data is consistent with prior expectationsexpectations

Table 1: Hiroshima CML cases by age, sex and dose in sieverts.

D 0.2 Sv 0.2 Sv D 1 Sv 1 Sv D

Males Females Males Females Males Females

agea O (E)b tsxc O (E) tsx O (E) tsx O (E) tsx O (E) tsx O (E) tsx

1-10 0 (0.02) 0 (0.01) 0 (0.00) 0 (0.00) 0 (0.00) 0 (0.00)

10-20 0 (0.15) 0 (0.09) 1 (0.02) 8 0 (0.01) 2 (0.00) 10 0 (0.00)

20-30 0 (0.38) 1 (0.28) 14 1 (0.05) 14 0 (0.05) 1 (0.01) 6 0 (0.01)

30-40 1 (0.71) 23 0 (0.64) 2 (0.11) 12 0 (0.10) 2 (0.03) 7 2 (0.02) 18

40-51 1 (1.32) 18 0 (1.29) 1 (0.17) 33 1 (0.20) 11 2 (0.05) 7 1 (0.04) 23

50-60 3 (1.83) 24 1 (2.06) 23 2 (0.26) 15 4 (0.33) 9 0 (0.08) 0 (0.07)

60-70 3 (2.18) 22 4 (2.57) 27 1 (0.33) 11 4 (0.41) 19 1 (0.09) 14 1 (0.08) 28

70 4 (3.76) 34 4 (4.44) 32 0 (0.56) 1 (0.69) 38 0 (0.11) 1 (0.09) 28

total 12 (10.4) 10 (11) 8 (1.50) 10 (1.8) 8 (0.38) 5 (0.32)

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

Prior Data: SourcesPrior Data: Sources

CC11 and k: SEER data and k: SEER data

kktt : Patients irradiated for BGD : Patients irradiated for BGD

kk, , k k and and kn kn : CAFC and MRA assays: CAFC and MRA assays

// and and nn//: Lymphocyte dicentric yields: Lymphocyte dicentric yields

CC22 : Depends on : Depends on , k, ktt, N, and P(ba|T), N, and P(ba|T)• N: SEER and translocation age structure dataN: SEER and translocation age structure data

• P(ba|T): BCR and ABL intron sizes, the genome size P(ba|T): BCR and ABL intron sizes, the genome size

Parameter EstimatesParameter 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 EstimatesCML Risk Estimates

Linear model Linear model

• RR = 0.0075 Gy = 0.0075 Gy-1 -1 and Qand Q = 0.0158 Gy = 0.0158 Gy-1 -1

LQE posterior modelLQE posterior model

• RR = 0.0022 Gy = 0.0022 Gy-1 -1 and Qand Q = 0.0042 Gy = 0.0042 Gy-1-1

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The lifetime excess CML risk in the limit of low The lifetime excess CML risk in the limit of low -ray doses-ray doses

yieldsyields

CML Target Cell NumbersCML Target Cell Numbers

A comparison of age responses for A comparison of age responses for CML and total translocations CML and total translocations suggests a CML target cell number suggests a CML target cell number of 2x10of 2x1088

10101212 nucleated marrow cells per nucleated marrow cells per adult and one LTC-IC per 10adult and one LTC-IC per 1055 marrow cells suggests 10marrow cells suggests 1077 CML CML target cells target cells

P(ba|T) = 2TP(ba|T) = 2TablablTTbcrbcr//2 2 may not holdmay not hold

BCR-to-ABL 2D distances in lymphocytes

Kozubek et al. (1999) Chromosoma 108: 426-435

Theory of Dual Radiation Theory of Dual Radiation ActionAction

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 = 0.0058 DSBs per Mb per Gy; = mass density

TBCR = 5.8 kbp; TABL = 300 kbp

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6.25 kev/um3 = 1 GyR = 3.7 um r0 = 0.24 m, p0 = 0.06

d in [.01, .025], dx in [.04, .05], d in [.05, .06]

Dependence of R and N on the choice of fixed LQE parameters ba/ba and ban/ba

BA/BA

BAn/BA R (Gy-1) N

.055/.0107 .8/.0107 .0022 (.0012, .0039)a 6.1x108 (3.3x108, 1.1x109) .055/.022 .8/.022 .0039 (.0020, .0073) 5.2x108 (2.7x108, 9.8x108) .45/3.64 .8/.022 .0094 (.0051, .0176) 7.6x106 (4.1x106, 1.4x107) .45/3.64 3.8/.022 .0056 (.0029, .0106) 4.5x106 (2.3x106, 8.6x106) .45/3.64 (1/3).8/.022 .0116 (.0065, .0216) 9.4x106 (5.3x106, 1.7x107) .45/3.64 10.8/.022 .0027 (.0014, .0052) 2.2x106 (4.2x106, 1.1x106) .45/3.64 (1/10).8/.022 .0128 (.0072, .0237) 1.0x107 (5.8x106, 1.9x107)

aIn parentheses are the 95% CI.

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Dead-Band Control of HSC Dead-Band Control of HSC levelslevels

Transplant doses of 10, 100, and Transplant doses of 10, 100, and 1000 CRU => CRU levels 1-20% or 1000 CRU => CRU levels 1-20% or 15-60% normal 15-60% normal BloodBlood (1996) 88: (1996) 88: 2852-28582852-2858

Broad variation in human HSC levels Broad variation in human HSC levels Stem CellsStem Cells (1995) 13: 512-516 (1995) 13: 512-516

Low levels of HSCs in BMT patients Low levels of HSCs in BMT patients BloodBlood (1998) 91: 1959-1965 (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 RiskNet Lifetime CML Risk

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Letting Letting DDnn = 0 while = 0 while DD 0 0

We solved RWe solved R0 0 = 0 for = 0 for kkss as a function of exposure age x. as a function of exposure age x.

ConclusionsConclusions

Bayesian methods provide a natural framework Bayesian methods provide a natural framework for biologically based risk estimationfor biologically based risk estimation

BCR-to-ABL distance data and knowledge of BCR-to-ABL distance data and knowledge of CML target cell numbers can be useful in a CML target cell numbers can be useful in a biologically based approach to CML risk biologically based approach to CML risk estimationestimation

Low dose hypersensitivity to killing might lead to Low dose hypersensitivity to killing might lead to a U-shaped low dose response if there is a dead-a U-shaped low dose response if there is a dead-band in the control of target cell numbers band in the control of target cell numbers

AcknowledgmentsAcknowledgments

Rainer SachsRainer Sachs David HoelDavid Hoel NIH and DOENIH and DOE