Fig 1.
Excess relative risk of solid cancers as a function of dose in atomic bomb survivors.
Reprinted with permission from figure 3 of “Studies of the mortality of atomic bomb survivors, Report 14, 1950–2003: an overview of cancer and noncancer diseases.” [8]. Estimated excess relative risk (ERR—equal to relative risk minus one) of solid cancer development vs. mean total colon dose for atomic bomb survivors. These estimates represent the risk of solid cancer development by age 70 to a person exposed at 30 years of age after controlling for the influence of gender and city (Hiroshima vs. Nagasaki) using models specified by Ozasa and others [8]. Black points represent central estimates for each exposure group. Vertical bars represent 95% confidence intervals. Linear (L) and linear-quadratic (LQ) dose response models were both fit to the data and appear as labeled. A linear-quadratic model fit to doses below 2 Gy is shown as well (LQ (<2Gy)). The apparent quadratic component of ERR increase with dose is most pronounced for exposures less than 2 Gy. This curvature is presumably a consequence of the relatively lower than expected solid cancer development risks in the dose range 0.3–0.7 Gy for which neither Ozasa and others nor earlier reports offer an explanation.
Fig 2.
Two possible dose response models based on linear-quadratic model (A) and linear/linear model (B).
A schematic representation of a linear-quadratic dose response model, like the one used in the BEIR VII report (A), is shown above an idealized representation of the results of this analysis (B). Each panel shows dose (x-axis) vs. risk (y-axis) in which risk represents the excess risk of carcinogenesis or organism mortality. Black lines represent the response to acute exposures. Red lines represent the response to protracted exposures. Both are applicable to exposures less 1.5 Sv or 2.0 Sv, the maximum doses considered in the BEIR VII report and this one. While the linear-quadratic model predicts that protracted dose-response can be estimated based on the curvature of acute dose response our results show that this is not the case. Also, while the linear-quadratic model predicts that responses to low dose exposure are collinear with responses to protracted exposures, our observations are inconclusive.
Fig 3.
BEIR VII DDREFLSS estimates from 3 data sources.
Reprinted with permission from figures 10–2, 10B-2, and 10B-3 of “Health risks from exposure to low levels of ionizing radiation: BEIR VII phase 2” [2]. Linear-quadratic models used for DDREFLSS evaluation fit to three data sources, (A) excess risk of carcinogenesis in atomic bomb survivors, (B) risk of tumor development in various animal studies, and (C) inverse mean lifespan in two animal studies. All panels show dose (x-axis) vs. various measurements of risk (y-axis). Best-fit linear-quadratic models are shown for each model. The LSS carcinogenesis data shows best-fit models with various curvatures. Animal carcinogenesis data shows best-fit models for each panel individually (solid black lines) and the consensus curvature across all panels (dashed lines). The animal mortality data shows the single best-fit model with both acute (linear-quadratic) and protracted (linear) projections. Only animal mortality data included both acute, “A”, and protracted, “C”, exposures. Above each panel, DDREFLSS estimates derived from the corresponding data source are shown with 95% credible intervals in parenthesis. These estimates were combined (using Bayesian update) to form BEIR VII's central estimate, DDREFLSS ~ 1.5 (1.1, 2.3).
Table 1.
Data selection by inclusion criteria.
Fig 4.
Kaplan-Meier survival curves based on individual animal data show the percent of surviving animals vs. age for each treatment group of the expanded animal data set used in this analysis. The color of each curve indicates total dose, from dark blue (unexposed controls) to light blue (up to 1.5 Gy). A solid line indicates acute exposures. A dashed line indicates fractionated exposures. A vertical gray line indicates age at first exposure. Treatments are stratified by sex, strain, type of radiation, and age at first exposure as labeled. The strata are presented in order of total number of animals included, so that the 1st strata on the top left has the most animals, 6977, and the 16th strata on the bottom right has the least, 126. This same ordering is maintained in all subsequent figures, as are the strata identifiers (e.g. strata labeled #2 always shows data from female B6CF1 ANL animals, 114 days old at the time of first exposure). Please note that the bottom row contains data from studies that investigated the effects of radiation exposure on very young (pre-natal and neonatal) and very old mice. In addition, note that the uppermost leftmost stratum contains data used in the original BEIR VII analysis. This is only the acute exposure data from that analysis, as the data from protracted exposures was not available for individual mice.
Fig 5.
BEIR VII model applied to expanded animal data set.
The relationship between inverse mean lifespan, y-axis, and dose, x-axis is shown grouped by analysis strata. Strata are organized and labeled as in Fig 4. The y-axis maintains a constant scale, 0.0001 days per tick with a different baseline for each stratum. Single points indicate results for each treatment group with standard error bars as indicated. Acute exposures and quadratic dose response estimates are shown in black, protracted exposures and linear dose response estimates are shown in red. Please note that protracted exposure data was available in only few cases—strata 2, 3, 4, and 6. DDREFLSS estimates from each stratum analyzed independently are listed in each facet label with 95% credible intervals in parentheses. These are also shown in S3 Table. The central DDREFLSS estimated from the full data set is infinite with a 95% confidence interval from 2.9 to infinity (see Table 2).
Fig 6.
BEIR VII model applied to acute exposures only.
Identical to Fig 5, except that data are restricted to animals that received only acute radiation exposures. Protracted extrapolations, estimated from the linear term of acute exposures, are still shown (red lines). Notably, protracted extrapolations are very similar to acute risk estimates because these dose-responses are nearly linear with only a minimal quadratic curvature. This analysis is similar to BEIR VII's estimates of DDREFLSS based on atomic bomb survivors and animal carcinogenesis data that only included acute exposure data as well (Fig 3).
Fig 7.
BEIR VII model applied only to protracted-acute comparisons.
Similar to Fig 5, except that data are restricted to strata that received both acute and protracted exposures. Also, in contrast to Fig 5, fits based on acute data alone (the same as those in Fig 6) are shown as dotted lines for comparison. Note that the real risk of protracted exposure is substantially lower than the risk projected based on acute data. Also, note stratum 4 has two protracted exposures at 1.0 Gy corresponding to two different fractionation patterns as described in S2 Table.
Table 2.
DDREFLSS estimates for various models.
Table 3.
DDREFLSS estimate from the original BEIR VII report.
Fig 8.
The same DDREF estimate, 2 in this example, can be obtained when (A) acute exposures appear more damaging than protracted exposures or when (B) acute exposures appear more beneficial than protracted exposures.