Cumulative hazard contribution from a single phase

Computes \(\Phi_j(t)\) for one phase in the additive model \(H(t|x) = \sum_j \mu_j(x) \Phi_j(t)\).

Usage

hzr_phase_cumhaz(
  time,
  t_half = 1,
  nu = 1,
  m = 0,
  type = c("cdf", "hazard", "constant")
)

Arguments

time

Numeric vector of times (> 0).

t_half

Half-life parameter (> 0).

nu

Time exponent.

m

Shape parameter.

type

Phase type: "cdf" (early – uses \(G(t)\)), "hazard" (late – uses cumulative hazard from \(h(t)\)), or "constant" (flat rate – \(\Phi = t\)).

Value

Numeric vector of cumulative hazard contributions \(\Phi(t)\), same length as time.

Details

• "cdf": \(\Phi(t) = G(t)\). Bounded \([0, 1]\). Models early risk that resolves over time.

• "hazard": \(\Phi(t) = -\log(1 - G(t))\). Monotone increasing. Models late or aging risk. This is the cumulative hazard derived from the hazard function \(h(t)\), since \(\int_0^t h(s)\,ds = -\log(1 - G(t))\).

• "constant": \(\Phi(t) = t\). Ignores t_half, nu, m. Equivalent to exponential (constant hazard rate).

See also

hzr_decompos() for the underlying parametric family, hzr_phase_hazard() for the instantaneous hazard contribution.

Examples

t_grid <- seq(0.1, 10, by = 0.1)
phi_early <- hzr_phase_cumhaz(t_grid, t_half = 2, nu = 2, m = 0,
                               type = "cdf")
phi_late  <- hzr_phase_cumhaz(t_grid, t_half = 5, nu = 1, m = 0,
                               type = "hazard")
phi_const <- hzr_phase_cumhaz(t_grid, type = "constant")