Author:J. Anthony Parker, MD PhD (J.A.Parker@IEEE.org ) Dates:2010/08/13: First version

2010/09/07: LAR-upper-age-limit and dLAR/dy options added

Source:The source program file is, Cancer_RateTP.java. This plugin uses five tables, located in a directory named, plugins/cancerRate or plugins/NucMed/cancerRate, or in resource named, /cancerRate or /NucMed/cancerRate. Four files, which give incidence and mortality cancer-rates, are named, IncidenceMan.txt, IncidenceWoman.txt, MortalityMan.txt, and MortalityWoman.txt. A file, SurvivalAll.txt, gives all-cause survival rates and expected-years-of-life-remaining. TableFormat.txt explains the format of the tables. These files are included in Cancer_RateTP.jar, NucMed_TP.jar, tp_collection.jar and tp_collectionFiji.jar; they do notneed to be downloaded separately.

Installation:Download Cancer_RateTP.jar, and restart ImageJ or Fiji. (Alternately, download only one of collections - NucMed.jar, tp_collection.jar, or tp_collectionFiji.jar described in NucMed and Nuclear Medicine Collection.) Installation with "about" or key down on start: shows about message. Installation with "tables" or key down on start: shows BEIR tables 12.1, 12.2, and 12.3.

Description:: This ImageJ PlugIn calculates the radiation-induced cancer-incidence-rate, the cancer-mortality-rate, the lifetime-attributable-risk (LAR), the years-of-life-lost, and the LAR-per-year for a given effective-dose as a function of the exposure-age, attained-age, time-since-exposure, effective-dose, or LAR-upper-age-limit using the Biological Effectiveness of Ionizing Radiation (BEIR) VII formulae.Purpose

This plugin is intended to demonstrate how changes in the BEIR VII parameters affect the calculation of cancer risks and rates. Thus, the user may change any of the parameters. This plugin has not been debugged and has not be checked against validated calculations, so it should not be be used to calculate actual cancer rates. Since I am not an expert any corrections are welcome.

BEIR VII has paramaters for category, "all-solid" cancers; however, BEIR VII uses the sum of site-specific solid-cancers to estimate all-solid cancer-risk. In contrast, this plugin only provides a calculation using the "all-solid" parameters. The BEIR VII uncertainty calculations are based on 1) statistics of all of the paramaters used in a calculation, 2) uncertainty in DDREF, and 3) uncertainty in weighting factor for relative and absolute cancer-rates. In contrast, this plugin only includes uncertainty for statistics of one or all parameters.

:UsageThe plotting capabilities of this plugin are primitive. However, a table can be produced that can be saved and imported to more elegant plotting applications. This plugin does not consider non-uniform exposure. But again, the tables for individual cancers can be imported to a spreadsheet and then combined to account for non-uniform exposures. Similarly, years-of-life-affected, the baseline expected-years-of-life-remaining at the age of cancer-incidence, is not particularly interesting; however, years-of-life-lost minus years-of-life-affected is the years of life after cancer diagnosis, i.e. quality of life could be affected during this period.

- Not all user entered values are needed for a particular calculation.
- The cancer category called, all-solid, refers to all cancers except for leukemia, thyroid, and non-melanoma skin cancer.
- Most user entered values are remembered between calls. To revert to the default values, quit ImageJ or Fiji.
- Selecting a cancer selects the default paramaters which will be used during calculation. If a parameter is changed by the user, then the cancer category changes to either "non-BEIR solid-equation" or "non-BEIR leukemia-equation".
- For lifetime-attributable-risk, LAR, plots versus exposure-age give the integral from exposure-age to LAR-upper-age-limit. Plots versus attained-age give the integral from attained-age to LAR-upper-age-limit. Plots versus time-since-exposure give the integral from exposure-age plus time-since-exposure to LAR-upper-age-limit. LAR values with LAR-upper-age-limit other than 100 are non-standard.
- Plotting LAR values versus LAR-upper-limit (with attained-age equal to the lower limit) is the compliment of plotting versus attained-age.
- dLAR/dy shows the excess cancer incidence- or death-rate per year of attained-age.
- Since incidence and mortality cancer-rates, all-cause survival, and expected-years-of-life-remaining tables, may have data per 5 years or per decade, the plugin has an option for smoothing the target-population tables.

Ninety-five percent confidence intervals for individual parameters can be included. The confidence interval called, "all", will use all of the intervals simultaneously. Note that simultaneously selecting more than one 95% interval is not valid statistically and will produce extreme results.

is defined as the excess probability of developing (or dying from) the first radiation induced cancer including the probability of developing (or dying from) that cancer at an earlier age. The risk does not take into account the reduction in risk due to death at an earlier age from other radiation induced causes; however, below 1 Sv, this reduction is small.Cancer-risk

is defined as the risk per year,Cancer-ratei.e. rate = Δrisk/year. There are two cancer-ratemodels, excess-relative-risk(sic),ERR, and excess-absolute-risk(sic),EAR. The ERR model assumes the cancer-rate depends on the baseline cancer-rate. The EAR model assumes cancer-rate is independent of baseline cancer-rate. The terminology, "relative-risk", is consistent with statistical use, although "relative-rate" would have been more consistent with BEIR VII definitions.

: Solid-tissue cancer-rates for both ERR and EAR use the following linear, no-threshold model:Solid-tissue cancer-rate formula

D β_{sex}e^{γ e*}(a/60)^{η}

where D is the effective-dose in Sv, a is the attained-age in years, and η is the attained-age-exponent. For ERR, the dose-parameter, β_{sex}, is given in units of Sv^{-1}. For EAR, β_{sex}is given in units of (10,000 patient-years-Sv)^{-1}. γ is the per-decade-exposure-age factor.

where e is the exposure-age in years. For thyroid and breast cancer (e-30)/10 is used for all exposure-ages.

e* =(e-30)/10,e <= 300,e > 30

: Leukemia caner-rates for both ERR and EAR use the following linear-quadratic, no-threshold model:Leukemia cancer-rate formula

(D' + θ D'^{2}) β_{sex}e^{γ e*}(t/25)^{δ + φ e*}

where D' is the bone-marrow-dose, θ is the degree-of-curvature, t is the time-since-exposure, δ is dependence on time-since-exposure, and φ is dependence of exposure-age on time-since-exposure.

: BEIR VII has separate parameters for incidence and mortality for "all-solid" cancer. However since records on individual cancer-mortality is not thought to be reliable, BEIR VII only has cancer-incidence parameters for site-specific cancers. Mortality-rate data for leukemia is thought to be more reliable than the incidence-rate data and the mortality data spans a longer date range. Thus, mortality data was used to derive the paramaters for leukemia; however, the paramaters are given in terms of incidence. (In at atom-bomb-population, the incidence and mortality of leukemia was nearly equal.) In summary, BEIR VII provides incidence paramaters in all cases, and also provides mortality parameters for the category, "all-solid" cancer.BEIR VII paramaters

: The EAR and ERR values from the atom-bomb-population need to be "transported" to the target-population. Transport is relatively simple for the following cases:Transport

ERR_{target}= ERR_{atom-bomb}/ DDREF

where ERR

EAR_{target}= EAR_{atom-bomb}/ DDREF(1)_{target}and EAR_{target}are the target-population ERR and EAR; ERR_{atom-bomb}and EAR_{atom-bomb}are the atom-bomb-population ERR and EAR; and DDREF is the dose and dose-rate reduction factor. DDREF adjust for unaccounted differences between the atom-bomb and the target-population dose and dose-rate.

Since it is assumed that the mortality-to-incidence ratio is the same for the radiation-induced and non-radiation-induced cancer, the target-population EAR based on the atom-bomb-population ERR can be calculated as:

where λ

EAR_{target}= ERR_{atom-bomb}x λ_{target}/ DDREF(2)_{target}is the target-population baseline cancer-incidence or cancer-mortality rate as appropriate. Similarly:

ERR_{target}= EAR_{atom-bomb}/ (λ_{target}x DDREF)

Chronic lymphocytic leukemia, CLL, is not thought to be radiation sensitive. Ideally, baseline non-CLL leukemia incidence and mortality rates should be used for the target-population; however, default tables supplied with this plugin include CLL.

The traget-population mortality-rate can be obtained from the target-population incidence-rate by multiplying by the target-population baseline mortality-to-incidence ratio:

EAR_{target-mortality}= EAR_{target-incidence}x (λ_{target-mortality}/λ_{target-incidence})

substituting from above:

where EAR

EAR_{target-mortality}= EAR_{atom-bomb-incidence}x (λ_{target-mortality}/λ_{target-incidence}) / DDREF(3)_{atom-bomb-incidence}is the atom-bomb-population incidence EAR. Similarly:

ERR_{target-mortality}= ERR_{atom-bomb-incidence}x (λ_{target-mortality}/λ_{target-incidence}) / DDREF

: The target-population EAR incidence or mortality, EARWeighted average EAR_{target}_{target}, is calculated from either the atom-bomb-population ERR or EAR using equations, 1, 2, and 3. BEIR VII uses a weighted average of the calculations based on atom-bomb-population ERR or EAR. The weighted average on a logarithmic scale is obtained as follows:

wEAR_{target}= exp{ w x ln[EAR_{target}(ERR_{atom-bomb})] + (1-w) x ln[EAR_{target}(EAR_{atom-bomb})] }

where EAR_{target}(ERR_{atom-bomb}) is the target-population EAR based on the atom-bomb-population ERR, and EAR_{target}(EAR_{atom-bomb}) is the target-population EAR based on the atom-bomb-population EAR. In BEIR VII, w is equal to 1 for thyroid, 0 for breast, 0.3 for lung, and 0.7 for other cancers. The same weights are used for incidence and mortality.

: lifetime-attributable-risk, LAR, is the sum from (the exposure-age plus latency) to (LAR-upper-limit) of (the yearly target-population wEAR) multiplied by (the probability of surviving to attained-age, a, given survival to exposure-age, e):Lifetime-attributable-risk

LAR = Σ wEAR_{target}x survival(a)/survival(e)

The latency is 2 years for leukemia and 5 years for other cancers. Data in the atom-bomb population was not collected until year 5 after exposure; the leukemia rate from 2 to 5 years after exposure is assumed to be equal to the rate 5 years after collection. LAR-upper-limit is defined to be 100.

Note: LAR is given in units of (100,000 patient x 0.1 Sv)^{-1}. β is in units of (10,000 patient-years x Sv)^{-1}, but mathematically the difference in number of patients cancels the difference in dose.

: Years-of-life-lost is calculated with the same summation as LAR, but with an extra term for expected-years-of-life-remaining. In combination with incidence (as opposed to mortality) this calculation gives years-of-life-affected.Years-of-life-lost

: Calculation of target-population LAR using atom-bomb-population relative-rates require taget-population cancer-rate versus age tables, IncidenceMan.txt, IncidenceWoman.txt, MortalityMan.txt, or MortalityWoman.txt. (The tables are also need when calculating target-population ERR using atom-bomb-population EAR andTablesvice versa.) Calculation of LAR also requires target-population overall survival-rates in SurvivalAll.txt. Calculation of years-of-life-lost also requires expected-years-of-life-remaining in SurvivalAll.txt.

These tables are included in the .jar files (see TableFormat.txt -- currently SEER 2000-2005 and CDC 2006 data). To see the effects of differences in target-population cancer-rates and mortality-rates, the user needs to supply different tables. The plugin looks for tables in plugins/cancerRate/ and plugins/NucMed/cancerRate/ before using default tables in the .jar files.