exp_hazards function

Exponential hazard, cumulative hazard and inverse cumulative hazard

Exponential hazard, cumulative hazard and inverse cumulative hazard

Functions which return the hazard, cumulative hazard and inverse cumulative hazard at time t for an exponential distribution with parameter λ\lambda and true hazard ratio μ\mu.

haz_exp(t, lambda, mu = log(1))

chaz_exp(t, lambda, mu = log(1))

inv_chaz_exp(t, lambda, mu = log(1))

Arguments

  • t: time of evaluation.
  • lambda: parameter of the exponential distribution.
  • mu: (optional) true excess hazard rate μ\mu.

Returns

Value of specified function at time tt.

Details

The hazard function of an exponential distribution is given by:

h(t∣λ,μ)=λe\muh(t∣λ,μ)=λeμ h(t| \lambda, \mu) = \lambda e^\muh(t|\lambda, \mu) = \lambda e^\mu

The cumulative hazard (with true hazard ratio μ\mu) is given by:

H(t∣λ,μ)=λte\muH(t∣λ,μ)=λ∗t∗exp(μ) H(t| \lambda, \mu) = \lambda t e^\muH(t|\lambda, \mu) = \lambda * t * exp(\mu)

The inverse cumulative hazard (with true hazard ratio μ\mu) by:

H−1(t∣λ,μ)=tλeμH(−1)(t∣λ,μ)=t/(λexp(μ)) H^{-1}(t| \lambda, \mu) = \frac{t}{\lambda e^\mu}H^(-1)(t|\lambda, \mu) = t/(\lambda exp(\mu))
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