Returns the function H0(tau) for the chosen baseline. Under the memoryless baseline it is elapsed exposure itself; the Weibull, log-logistic and Gompertz baselines let the hazard rise or fall with how long the individual has already been exposed. Shape and scale arrive as per-draw vectors, and elapsed time may be a vector or a matrix whose rows are draws.
Arguments
- baseline
A character string, a key of h0_catalogue:
"mem","weibull","llogis"or"gompertz".
Value
A function of (tau, shape, scale) giving the cumulative baseline hazard.
What shape and scale mean depends on the baseline:
"mem": both are ignored."weibull"and"llogis":shapeis k andscaleis s."gompertz":shapeis the rate constant gamma andscaleis ignored.
Details
For the Gompertz baseline the first argument is the rate constant gamma and the
second is ignored. A negative gamma is a valid value and means a hazard that
falls the longer the individual has been exposed. The cumulative hazard then levels
off: it rises towards 1/|gamma| but never reaches it, instead of growing without
limit. Survival therefore never drops to zero, and the model predicts that some
individuals never fail (a cure fraction, in survival-analysis terms). H0inv_of()
gives the time by which a chosen fraction of individuals has failed; when that
fraction is never reached it returns NaN for the time, rather than a large
number standing in for "never".
Examples
# The memoryless baseline is elapsed exposure itself.
H0_of("mem")(tau = c(10, 30, 60), shape = 1, scale = 1)
#> [1] 10 30 60
# A Weibull baseline with shape 2 and scale 60: H0(tau) = (tau / 60)^2.
H0_of("weibull")(tau = 30, shape = 2, scale = 60)
#> [1] 0.25