In radiation risk assessment based on follow-up data, estimation of the excess relative cancer rate involves evaluation of effect-modification by time-related factors such as age at exposure, time since exposure, and attained age. Because these variables are collinear, the regression coefficients purportedly measuring effect-modification of the radiation-related excess relative rate by time and age factors generally differ from the individual effects of these factors. For example, depending on whether it is an age-at-exposure/attained-age effect-modification model or an age-at-exposure/time-since-exposure model which is used, the regression coefficient for the effect of changes in age at exposure on the excess relative rate per Gray measures the combined effects of changes in both age at exposure and time since exposure, or of age at exposure and attained age, respectively, rather than the individual effect of changes in age at exposure, which is of interest for scientific purposes. Such insights should be integrated when reporting and interpreting estimates for time-related risk modification in cohort studies of radiation-exposed populations. Cancer incidence data for the Life Span Study of atomic-bomb survivors are used for illustration in parallel to theory. In summary, model coefficients for time-since-exposure, age-at-exposure, and attained-age effects on radiation-induced cancer risks among atomic-bomb survivors and in other cohort studies estimate combined effects (estimable combined effects are explicated). An appropriate unequivocal display of results for effect-modification is suggested. Goodness of fit appears unreliable for sorting out the most significant effect-modifiers. For example, a model including only one of the effect-modifiers may provide a fit similar to a model including the other two effect-modifiers, even when only the latter are actually related to effect-modification. Also, due to collinearity between these effect-modifier variables, all three models with two of the effect-modifiers necessarily show equivalent fits.