Derivatives of phase cumulative and instantaneous hazard w.r.t. shape params

Computes \(\Phi_j(t)\), \(\phi_j(t)\), and their derivatives with respect to t_half, nu, and m using central finite differences on hzr_decompos(). The log_t_half derivative is obtained via the chain rule: \(d\Phi/d(\log t_{1/2}) = t_{1/2} \cdot d\Phi/dt_{1/2}\).

Usage

.hzr_phase_derivatives(
  time,
  t_half,
  nu,
  m,
  type = c("cdf", "hazard", "constant")
)

Arguments

time

Numeric vector of positive times.

t_half

Positive scalar half-life.

nu

Numeric scalar time exponent.

m

Numeric scalar shape exponent.

type

Phase type: "cdf", "hazard", or "constant".

Value

Named list:

Phi

Cumulative hazard contribution \(\Phi(t)\).

phi

Instantaneous hazard contribution \(\phi(t) = d\Phi/dt\).

dPhi_dlog_thalf

\(d\Phi / d(\log t_{1/2})\).

dPhi_dnu

\(d\Phi / d\nu\).

dPhi_dm

\(d\Phi / dm\).

dphi_dlog_thalf

\(d\phi / d(\log t_{1/2})\).

dphi_dnu

\(d\phi / d\nu\).

dphi_dm

\(d\phi / dm\).