Construct Background (All-Cause) Survival from a US-CDC Life-Table

Uses age- and sex-specific annual death rates from a life-table to build a cumulative background survival curve, then interpolates it onto a user- supplied time grid. The resulting curve is multiplied against a relative (disease-specific) survival curve inside run_tumour_analysis to obtain net (all-cause) survival.

Usage

make_background_surv(lifetable, mean_age, rate_col, time_grid_years)

Arguments

lifetable: A data frame containing the life-table. Must include an Age column (integer ages 0, 1, 2, …) and at least one numeric column whose name is supplied via rate_col. The bundled lifetable_seer dataset is the canonical input.
mean_age: Numeric scalar. The mean (or median) age of the study cohort. The life-table is sub-set to rows where Age >= floor(mean_age).
rate_col: Character scalar. Name of the column in lifetable that contains the annual death rates to use (e.g. "btrate_LR" or "btrate_DR" after sex-mixing has been applied).
time_grid_years: Numeric vector of time points (in years) onto which the cumulative survival is interpolated.

Value

A tibble with two columns:

time: Time in years (same as time_grid_years).
surv: Background survival probability at each time point.

Details

The cumulative background survival at integer year $t$ (starting from floor(mean_age)) is: $$B(t) = \prod_{j=0}^{t-1} \bigl(1 - q_j\bigr),$$ where $q_j$ is the annual death rate at age $j + \lfloor\text{mean age}\rfloor$. Non-integer time points are linearly interpolated; times beyond the last life-table row use flat extrapolation (rule = 2 in approx).

Examples

data(lifetable_seer)

# Add a sex-mixed rate column (60% male cohort)
lt <- lifetable_seer
lt$btrate_mix <- lt$Males * 0.60 + lt$Females * 0.40

grid <- seq(0, 39, by = 1)   # 39-year horizon from age 61
B <- make_background_surv(lt, mean_age = 61, rate_col = "btrate_mix",
                          time_grid_years = grid)
head(B)
#> # A tibble: 6 × 2
#>    time  surv
#>   <dbl> <dbl>
#> 1     0 1    
#> 2     1 0.990
#> 3     2 0.978
#> 4     3 0.967
#> 5     4 0.954
#> 6     5 0.941