Instantaneous hazard contribution from a single phase

Computes \(\phi_j(t) = d\Phi_j/dt\) for one phase – the derivative of the cumulative hazard contribution returned by hzr_phase_cumhaz().

Usage

hzr_phase_hazard(
  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 instantaneous hazard contributions \(\phi(t)\), same length as time.

Details

• "cdf": \(\phi(t) = g(t)\) (density).

• "hazard": \(\phi(t) = h(t) = g(t)/(1-G(t))\).

• "constant": \(\phi(t) = 1\).

See also

hzr_decompos() for the underlying parametric family, hzr_phase_cumhaz() for the cumulative version.

Examples

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