population_LAR: Population-averaged Lifetime Attributable Risk

Compute population-averaged lifetime attributable risk (LAR) due to radiation exposure, aggregating over a population age distribution and sex-specific baseline rates. The function combines user-specified excess risk models (ERR/EAR) with site-specific baseline incidence/mortality and all-cause mortality to produce age-category summaries and overall totals, with uncertainty from Monte Carlo sampling.

Usage

population_LAR(
  dsGy,
  reference,
  riskmodel,
  agex = 1:8 * 10 - 5,
  PER = 10000,
  nmc = 10000
)

Arguments

dsGy

Numeric scalar. Radiation dose in Gy (or Sv if your model is parameterized accordingly). Must be nonnegative.

reference

List describing the target reference population, with components:

baseline — data frame of site-specific baseline incidence or mortality rates (per person-year) over ages 1–100, with columns age, male, female.
mortality — data frame of all-cause mortality (same structure/age grid).
agedist — data frame or vector with the population age distribution used to average risks across ages (e.g., by single year or grouped ages).

All three components must refer to the same region/population and share consistent sex coding.

riskmodel

List defining the radiation risk model. Typically contains sublists for ERR and/or EAR:

err / ear — each is a list with:
- para — numeric vector of model parameters;
- var — parameter variance–covariance matrix (for multi-parameter models), or ci — confidence bounds for one-parameter models;
- f — function of the form f(beta, data, lag) returning age-specific excess risk given parameters and data (dose, ages, sex).

See package examples (e.g., LSS_mortality$allsolid$L, LSS_incidence$leukaemia$LQ).

agex

Numeric vector of ages at exposure (midpoints for grouped categories). Default is 1:8 * 10 - 5 (i.e., 5, 15, …, 75) representing 0–10, 10–20, …, 70–80.

PER

Integer scaling factor for reporting results per PER persons. Default 10000 (i.e., cases per 10,000 persons).

nmc

Integer Monte Carlo sample size for uncertainty propagation. Default 10000.

Value

A list with components for each transfer model present (typically $err and $ear). Each component is a data frame with one row per exposure age category (rows named by agex) plus an all row, and columns:

male, male_lo, male_up
female, female_lo, female_up
all, all_lo, all_up

Values are LAR per PER persons.

Details

Let agedist denote the population age distribution (by single-year or grouped ages) and baseline/mortality denote site-specific baseline rates and all-cause mortality for the same region/population and sex coding. For each age-at-exposure category in agex, population_LAR() evaluates LAR under the supplied risk model(s) and then averages across the age structure, returning sex-specific estimates and an all-sex average. Uncertainty is obtained by drawing model parameters either from a variance–covariance matrix (var) or, in one-parameter models, from 95% confidence bounds (ci) when provided.

Results are reported per PER persons (default: per 10,000). The default agex = 1:8 * 10 - 5 corresponds to midpoint ages 5, 15, …, 75, i.e., exposure categories 0–10, 10–20, …, 70–80 years, which should match the categories of agedist.

Units & Alignment

Doses must be in Gy (or consistent with your model). Ensure baseline and mortality share the same age grid (typically 1–100) and sex coding, and that agedist corresponds to the same population.

Examples

set.seed(100)
# Default package data: LSS-derived models and WHO-like regional rates
# Example 1: All solid cancer mortality, Region 1, dose = 0.1 Gy
ref1 <- list(
  baseline  = Mortality[[1]]$allsolid,   # site-specific baseline mortality
  mortality = Mortality[[1]]$allcause,   # all-cause mortality
  agedist   = agedist_rgn[[1]]           # population age distribution
)
mod1 <- LSS_mortality$allsolid$L         # linear ERR model (LSS)
out1 <- population_LAR(dsGy = 0.1, reference = ref1, riskmodel = mod1)
out1$err   # per 10,000 persons by default
#>          male   male_lo   male_up     female  female_lo female_up        all
#> 5   130.37052 83.684260 203.04478 221.901462 145.741428 338.04836 175.529433
#> 15   92.10210 63.056550 131.64627 156.473982 114.794414 214.09618 123.449312
#> 25   65.42755 45.114384  91.52862 110.051941  85.437062 143.21353  87.395346
#> 35   46.41875 30.530566  68.26803  76.956627  57.227143 103.48037  61.729352
#> 45   32.54654 19.564183  52.98648  51.984849  35.094862  77.12590  42.443120
#> 55   21.22069 11.404601  38.98402  33.086807  19.583245  55.58879  27.321900
#> 65   12.22755  5.847979  25.35129  18.738471   9.682757  35.86489  15.754229
#> 75    5.77911  2.450553  13.67047   8.481243   3.835635  18.60684   7.335593
#> all  52.81522 36.466146  73.98011  83.455376  64.177472 109.88703  68.485470
#>         all_lo    all_up
#> 5   120.542859 259.25148
#> 15   95.165421 164.04028
#> 25   70.012219 110.64680
#> 35   46.722220  81.66375
#> 45   28.712903  62.47583
#> 55   16.167233  46.05064
#> 65    8.134999  30.36719
#> 75    3.280844  16.19603
#> all  54.678094  87.25822

# Example 2: Leukaemia incidence, Region 4, dose = 0.1 Gy, LQ model
ref2 <- list(
  baseline  = Incidence[[4]]$leukaemia,
  mortality = Mortality[[4]]$allcause,
  agedist   = agedist_rgn[[4]]
)
mod2 <- LSS_incidence$leukaemia$LQ
out2 <- population_LAR(dsGy = 0.1, reference = ref2, riskmodel = mod2, PER = 10000, nmc = 10000)
out2$err
#>          male    male_lo  male_up    female  female_lo female_up       all
#> 5   16.887526 0.09510633 71.64065 12.803411 0.07139758  52.82134 14.948397
#> 15   8.101229 0.03876649 20.11160  6.519586 0.03078176  15.82578  7.351688
#> 25   6.343635 0.03221517 13.38227  5.493388 0.02795455  11.57930  5.934571
#> 35   6.222154 0.02525119 12.92559  5.466720 0.02237215  11.48464  5.852195
#> 45   6.521093 0.02523791 14.57651  5.490056 0.02127415  12.34995  6.011522
#> 55   6.806484 0.02594877 17.28338  5.358925 0.02039229  13.58449  6.084538
#> 65   6.629825 0.02477937 19.66861  4.865219 0.01810706  14.22901  5.720060
#> 75   5.538629 0.02033106 19.23206  3.817298 0.01393391  12.94007  4.608737
#> all  8.807671 0.04953417 22.81574  6.954832 0.03980346  17.48186  7.897506
#>         all_lo   all_up
#> 5   0.08377032 62.67576
#> 15  0.03496200 18.09759
#> 25  0.03018724 12.51534
#> 35  0.02384939 12.21162
#> 45  0.02328657 13.48848
#> 55  0.02317223 15.43496
#> 65  0.02134263 16.86451
#> 75  0.01687491 15.83090
#> all 0.04477201 20.19862