RERF Report No. 5-14

Paper published in the Journal of Clinical Epidemiology§“Interaction between a Single Exposure and Age in Cohort-based Hazard Rate
Models Impacted the Statistical Distribution of Age at Onset”
Shizue Izumi, Ritsu Sakata, Michiko Yamada, John B Cologne
J Clin Epidemiol: 2016 (March); 71:43-50(doi: 10.1016/j.jclinepi.2015.10.004)
Study Findings
This research showed that the standard practice of assessing interaction between age andexposure to infer risk modification (how the magnitude of risk depends on other factors related
to age that are not directly measured) also impacts the statistical distribution of age at onset ofthe outcome. The implication is that two phenomena—effect modification by unmeasured
variables correlated with age, and distribution of onset-age among exposed persons—are both
affected by a single interaction parameter in the statistical analysis model. Hence, there isconfounding of that parameter by two effects that cannot be distinguished without furtherinformation. We therefore recommend that either 1) additional data on specific age-related
effect modifiers be obtained and included as covariates in the analysis or 2) biologicalinformation about the effect of exposure on the onset-age distribution be incorporated into theanalysis model.
Explanation
This methodological research was carried out to elucidate the particular form of exposureby-age interaction reported by Sakata et al. in their analysis of radiation effects on age atmenopause in the RERF Life Span Study (LSS) (Radiation Research 2011; 176:787–795). In anadditive (excess absolute rate) model, they reported that radiation risk was modified by a loglinear function of (log of age)-squared. Because biological considerations predict that some, but
not all, exposed women may experience accelerated onset of menopause, we sought to assess
how the reported age modifier impacted the onset-age distribution.
1. Study purpose
Interaction between exposure and various age-time scales is commonly studied inepidemiologic risk analyses. Age at exposure, time since exposure, and age at risk (or attainedage, the advancing age throughout follow-up) are frequently tested for interaction with radiationdose in follow-up studies of risk. The primary motivation for examining such interactions is thatunderlying, but unmeasured, biological factors that are correlated with these age-time scales
may be modifying the radiation risk. Because the actual modifying factors are not measured, theinteractions are assessed using the age-time scales as surrogates. For example, risk for exposure
may be modified by growth leading to carcinogenic promotion; hence, there may be an age-atexposure effect on risk. Aging may lead to genomic instability, allowing past mutations to beexpressed; hence there may be an effect of advancing age on risk. Carcinogenesis is known to
be a multi-stage process, so that accumulation of multiple exposures may increase risk; hence,
there may be a time-since-exposure effect. However, because age is the underlying time scale
used for comparing rates between exposed and non-exposed persons, it is apparent that if
increased risk is not constant with age, some statistical interaction between age and exposure
may be required to adequately capture the effect of exposure on the age at onset. We therefore
undertook to study how exposure-by-age interaction impacts the statistical distribution of age atonset.
2. Study methods
Based on the data of Sakata et al. (2011), we performed statistical analyses using various
forms of exposure-by-age interaction for both additive (excess absolute rate) and multiplicative1

RERF Report No. 5-14(excess relative risk) models. We noted that the menopause onset-age distribution in nonexposed women could be approximated by a normal distribution. We then derived the resulting
onset-age distributions among exposed women using statistical theory that relates the risk andsurvival functions to the density function (distribution of onset age).
3. Study results
We discovered that the form of interaction between exposure and age, including the basicmodel (whether a relative or absolute risk model) has a substantial impact on the estimateddistribution of age at onset of outcome among exposed persons. For the type of onset-age
distribution seen with menopause, an interaction between radiation dose and the square of log
age, after dividing by age 50, on the absolute risk scale was most consistent with what would beexpected from biological and clinical considerations. In other words, risk was stochastic,
meaning that some exposed women experienced early menopause whereas other exposed
women did not, such that the distribution of onset age spread out towards younger ages. Otherforms of age modification, such as using the log of age (rather than the square of log of age) or
no modification at all, or using age modification with a relative risk model, produced unnatural
shapes of onset-age distribution. Most notably, no age modification with an additive (excessabsolute rate) model led to the conclusion that risk of menopause increases with radiation
exposure at all ages, including ages prior to menarche, which is implausible.
Study SignificanceOur study has implications for analyses of RERF data in general, because the onset-age
distributions of chronic diseases, such as cancer and cardiovascular disease, in older age adults
have similar constraints in that the risk is low or nonexistent in the very young. It is common
practice in RERF risk analyses to include interactions with age to assess how risk varies withage as a surrogate for underlying physiological or biological processes that are correlated withage but which are not measured. The implication is that, because interaction with age may benecessary to correctly specify the underlying onset-age distribution and only a single interaction
model can be used, researchers should be aware of these competing needs and consider
carefully how their fitted models are interpreted in terms of the onset-age distribution,
something that is rarely done in risk analyses.

The Radiation Effects Research Foundation has studied A-bomb survivors and their offspring in
Hiroshima and Nagasaki for more than 60 years. RERF’s research achievements are considered theprincipal scientific basis for radiation risk assessment by the United Nations Scientific Committee on theEffects of Atomic Radiation (UNSCEAR) and for recommendations regarding radiation protection
standards by the International Commission on Radiological Protection (ICRP). RERF expresses its
profound gratitude to the A-bomb survivors and survivors’ offspring for their cooperation in our studies.
§Journal of Clinical Epidemiology is an online, open access, and internationally peer-reviewed
journal. The journal aims to promote the quality of clinical epidemiologic and health service
studies.(Impact factor in 2014: 3.417)

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