title: Interaction between a single exposure and age in cohort-based hazard rate models impacted the statistical distribution of age at onset.
abstract: OBJECTIVE
  Statistical interaction between a single, instantaneous exposure and attained age (age during follow-up; attained age = age at exposure + time since exposure) is used in risk analyses to assess potential effect modification by unmeasured factors correlated with age. However, the impact of such interaction on the statistical distribution of age-at-onset of outcome (disease or death) is infrequently assessed. We therefore explored the impact of such interaction on the shape of the onset-age distribution.
  
  
  METHODS
  We use for illustration age-at-onset of radiation-related early menopause in a cohort of female Japanese Atomic Bomb Survivors. The statistical distribution of age-at-onset was derived from a parametric hazard rate model fit to the data, assuming an underlying Gaussian onset-age distribution among nonexposed women.
  
  
  RESULTS
  Commonly used forms of exposure-by-age (attained age) interaction led to unnatural estimates of the age-specific rate function and unreasonable estimates of the onset-age distribution among exposed women, including positive risk of menopause before menarche.
  
  
  CONCLUSIONS
  We recommend that researchers examine the distribution of age-at-onset and exposure-age interaction when conducting risk analyses. To distinguish this from potential etiologic interaction between exposure and unmeasured factors represented by age as a surrogate, richer models or additional data may be required.
authors.affiliation: Faculty of Engineering, Department of Computer Science and Intelligent Systems, Oita University, 700 Dannoharu, Oita 870-1192, Japan.
authors.forename: Shizue
authors.initials: S
authors.lastname: Izumi
authors.affiliation: Department of Epidemiology, Radiation Effects Research Foundation, 5-2 Hijiyama Park, Minami-ku, Hiroshima 732-0815, Japan.
authors.forename: Ritsu
authors.initials: R
authors.lastname: Sakata
authors.affiliation: Department of Clinical Studies, Radiation Effects Research Foundation, 5-2 Hijiyama Park, Minami-ku, Hiroshima 732-0815, Japan.
authors.forename: Michiko
authors.initials: M
authors.lastname: Yamada
authors.affiliation: Department of Statistics, Radiation Effects Research Foundation, 5-2 Hijiyama Park, Minami-ku, Hiroshima 732-0815, Japan. Electronic address: jcologne@rerf.jp.
authors.forename: John
authors.initials: J
authors.lastname: Cologne
mesh_terms: D017677:Age Distribution; D017668:Age of Onset; D015331:Cohort Studies; D005260:Female; D006801:Humans; D007564:Japan; D008572:Menarche / Q000528:radiation effects*; D008593:Menopause / Q000528:radiation effects*; D008875:Middle Aged; D054043:Nuclear Weapons; D016016:Proportional Hazards Models; D018788:Radioactive Hazard Release / Q000706:statistics & numerical data*; D012307:Risk Factors; D017741:Survivors / Q000706:statistics & numerical data*
keywords: Cohort study; Effect modification; Excess absolute rate; Menopause; Onset-age distribution; Risk analysis