Aarhus and the A-Bomb Survivor Studies

Donald A. Pierce

RERF Hiroshima

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Connections: Aarhus Biostats and RERF

• M. Vaeth has been instrumental at both places

• Both places owe much to a “Golden Age” in biostatistics starting in about 1975

• My “sideline” theoretical work: likelihood asymptotics due to Barndorff-Nielsen, Aarhus Theoretical Statistics

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Golden Age for Biostatistics: 1975 to ????

• Generalized linear models: regression using likelihood rather than least squares, frequency data

• Developments in survival analysis: relative risk (Cox) regression

• Case control methods: relation to the above, improved understanding, extensions

• Developments for clinical trials: use of survival analysis methods

• Analysis of longitudinal data: sequential/clustered observations

• Advances in computing: individual computers and statistical software

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Relevance to RERF and Aarhus Biostatistics

• This Golden Age had much to do with successes at RERF since 1980 and no doubt a lot to do with formation/success of Aarhus Biostatistics

• Intriguing and rich connections between analysis of survival times and regression analysis of Poisson data ---- cross-tabulations of cases and person-years

• These connections are central to effectively utilizing the RERF data: cohort of 100,000, followed up for 50 years, with a wide range of radiation doses

• Radiation risk for cancer at a given dose is not a “number” but a pattern depending on exposure age, time since exposure, attained age, and sex

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Overview of RERF Radiation and Cancer Study

• By 1980 RERF methods were oriented to testing for radiation effects rather than description of them

• Effects for leukemia were fairly clear, but what to expect for other cancers was almost totally unknown

• Would there be much effect at all? How long would it last? It turns out that a brief radiation exposure increases cancer risk for all remaining lifetime

• Has mechanistic implications regarding radiation and cancer; and probably for carcinogenesis in general

• Cancer arises largely from somatic mutations and radiation adds to these ---- effect of exposures at every age is highly informative regarding this

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Survival analysis and case-PY tabulations

• Data are fundamentally times of cancer incidence, for individuals exposed at various ages and to a wide range of doses

• Analysis best aims at directly estimating cancer rates, rather than alternative focus on response times

• Data are used in terms of detailed cross-tabulations of cases and PY, according to categories of dose, exposure age, sex, time since exposure, and attained age

• Imprecise rate estimates {cases/PY} for thousands of tabular cells, are then smoothed through regression models using the above covariables

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Advantages of cross-tabulation approach

• Dealing with 100,000 persons and 10,000 cancer cases, while giving careful attention to age-time variations in risk

• Dealing with departures from proportional hazards formulation: infeasible to use standard Cox regression with age-dependent covariables

• The initial cross-tabulation effectively carries out the heavy calculations once and for all, reducing inhibitions to extensive exploratory analysis

• Direct analysis from the outset of rates, rather than response times, has conceptual advantages and allows for focus on excess risk

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After considerable development, late1980’s view of solid cancer relative risk

ERR / 100 mSv (Sex avg)

0%

10%

20%

35 45 55 65 75 85

Age (at risk)

Agex 5

Agex 15

Agex 30

Agex 55

ERR, excess relative risk, is the % increase in age-specific cancer rate

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Current improved understanding

ERR / 100mSv (Sex avg)

0%

10%

20%

30%

35 45 55 65 75 85

Age (at risk)

Agex 5

Agex 15

Agex 30

Agex 55

Much of “exposure-age” effect was attained age variation. Related to stochastics of accumulation of mutations.

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Age-time patterns of excess rates

30 40 50 60 70 80 90

0

10

20

30

40

50

Ages at exposure: 10, 30, 50

LSS R12 Fig. 2

10

3050

Males Females

Cas

es /

10K

PY

-Sv

Age

Novel methods, clarifying the age increase and modest sex effect (factor of 2 in ERR)

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Description of dose response:sex-avg ERR at age 60

Interesting methodological issues

-0.1

0.1

0.3

0.5

0.7

0.9

0 0.5 1 1.5 2

Dose (Sv)

Ex

ce

ss

Re

lati

ve

Ris

k

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Overall Statistical Developments at RERF

• The above involved major developments in approach and software

• Epicure: Poisson and binomial regression, direct analysis of survival times, case-control studies

• Rich general class of risk models, fitting either RR or absolute rates, profile likelihood calculation, etc.

• Includes capabilities for making complex {case, PY} tables

• Methodology and software essential to RERF study and used elsewhere for radiation epidemiology and other purposes

• Will now consider some more specific developments central to the needs

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Some more specific developments

• Allowing for dose-estimation errors (with Vaeth)– Involves neglected issues regarding covariate errors

• Simultaneous analysis for specific types of cancer– Allowing for parameters in common and distinctive

• Issues specific to low-dose risks – Bias related to comparison group

• Theoretical stochastic analysis of accumulation of mutations (with Vaeth)– Clarifies age patterns in relative risk

• Joint effect of smoking and radiation– Additive vs multiplicative effects

• Effects of selection of cohort by survival (with Vaeth)– “Radiation-resistant survivors”: controversial issue

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Dose estimation errors

• Elaborate Dosimetry System estimates based on survivor location and shielding

• Reasonable to assume unbiased estimation, i.e.

E(estimated dose | true dose) = true dose

• Surprisingly to many, this does not mean that

E( true | estimated) = estimated

• Partly because estimation does not aim to use

information provided by survival of the person

• Need to adjust dose estimates to allow for the

apparent cohort distribution of true doses

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RERF “survivor” dose estimates

• We explicitly estimate distribution of true doses, then the joint distribution of (true, estimated), finally arriving at a representation

E(true | estimate) = g(estimate) X estimate

• These are called “survivor” dose estimates, used for all purposes at RERF

• The “cohort-specific” issues in this are general (not restricted to where survival is an issue), and are widely neglected in dealing with covariate errors

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Adjustment factor for typical assumptions:35% CV for each of

“estimative” and “grouping” errors

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

0 1 2 3 4 5 6

Dose Estimate (Sv)

Ad

just

men

t F

acto

r

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Idealized stochastic modeling of radiation and cancer

• Cancer is largely due to accumulation of somatic mutations in stem cells

• Radiation can cause such mutations• This allows for idealized stochastic modeling of the

age-time patterns of radiation risk• Results agree remarkably well with what is seen in

the data• In particular, this can explain the decrease in RR with

increasing age• Aim is to provide guidance for challenging descriptive

analyses

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. . tumor. ... .... .... .

age of person

(h

istor

y-1)

(h

istor

y-2)

(h

istor

y-3)

(hist

ory-

4)

Exposure rate d(a)

During exposure period, whatever are currently in effect in the various cells are increased to

Action in a given cell without exposure

'r s

[1 ( )]r d a

Mathematical model for cancer and mutagenic exposure

Without exposure, very general age-homogeneous Markov process (no assumption about number of mutations)

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Consequences of idealized model

Markov states may depend arbitrarily on mutational status of the cell: allows, e.g. for “mutator phenotypes” and selective growth advantage

Cancer rates following dose D should have form

Since fairly generally it is found that

this suggests that one might expect

essentially as seen in our data

0( ) ( )d da a D

0 ( )pa a

( )( ; ) (1 / ) 1 /

pp

p

a DRR a d D a p D a

a

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Risks during exposure (for other applications)

• Main result becomes

• Final term is a Jacobian in the mathematics, but also corresponds to effect of exposure causing the final-required mutation

• Approximating as before, leading term in RR is

• The extra term is important in applications: miners exposed to radon, and effect of smoking on lung cancer

0( ) ( ) 1 ( )D a a D a d a

0 ( )a

; ( ) 1 ( ) / 1 ( )RR a d p D a a d a

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Effect of stopping smoking: Datafrom (another) major epidemiological study

Fit of our RR Model to the PointsInsensitive to choice of p

So really requires only the one parameter beta

0

5

10

15

20

25

45 50 55 60 65 70 75 80

Age

Re

lati

ve

Ris

k (

to n

ev

er

sm

ok

ers

)

Current

Stop 35

Stop 45

Stop 52.5

Stop 57.5

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Conclusions

• Considerable statistical development at RERF in past 20 years

• Methods and pressing issues should be of interest to many biostatisticians

• Close connections in two respects to Aarhus Biostatistics

– Personal interactions

– Golden age for biostatistics