Absolute risk (Euler approximation) for a cause under piecewise-constant hazards — pch_absolute_risk

Computes the cumulative incidence function using the first-order Euler (discrete) approximation: $$F_j(t) \approx \sum S(t_{k-1}) \lambda_{j,k} \Delta t_k$$ Grouped by id, this returns the cumulative incidence at the end of each interval.

Usage

pch_absolute_risk_euler(
  id,
  dt,
  haz,
  cause_idx,
  one_based = TRUE,
  na_is_zero = FALSE
)

Arguments

id: Integer vector. Sorted by id then time.
dt: Numeric vector of interval lengths.
haz: Numeric matrix (n x C) of cause-specific hazards per interval.
cause_idx: Integer. Index of the cause of interest (1-based by default).
one_based: Logical. If TRUE, cause_idx is 1-based. If FALSE, 0-based.
na_is_zero: Logical. If TRUE, treat NA/Inf hazards as zero.

Value

Numeric vector of cumulative incidence values (Euler approximation) at the end of each interval.

Examples

id <- c(1L, 1L, 2L, 2L)
dt <- c(1, 1, 1, 1)
haz <- rbind(
  c(0.10, 0.05),
  c(0.20, 0.10),
  c(0.05, 0.02),
  c(0.10, 0.03)
)
pch_absolute_risk_euler(id = id, dt = dt, haz = haz, cause_idx = 1)
#> [1] 0.1000000 0.2721416 0.0500000 0.1432394