A function to define a parametric proportional hazards model where the baseline hazard is modelled by a basis spline. This function returns an object inheriting class 'basehazardspec', list of functions 'distinfo', 'basehazard', 'gradbasehazard', 'hessbasehazard', 'cumbasehazard', 'gradcumbasehazard', 'hesscumbasehazard' and 'densityquantile'
BsplineHaz(times, knots = quantile(times), degree = 3, MLinits = NULL)an object inheriting class 'basehazardspec'
vector of survival times (both censored and uncensored)
vector of knots in ascending order, must include minimum and maximum values of 'times'
degree of the spline basis, default is 3
optional starting values for the non-spatial maximisation routine using optim. Note that we are working with the log of the parameters. Default is -10 for each parameter.
The distinfo function is used to provide basic distribution specific information to other spatsurv functions. The user is required
to provide the following information in the returned list: npars, the number of parameters in this distribution; parnames,
the names of the parameters; trans, the transformation scale on which the priors will be provided; itrans, the inverse
transformation function that will be applied to the parameters before the hazard, and other functions are evaluated; jacobian,
the derivative of the inverse transformation function with respect to each of the parameters; and hessian, the second derivatives
of the inverse transformation function with respect to each of the parameters -- note that currently the package spatsurv
only allows the use of functions where the parameters are transformed independently.
The basehazard function is used to evaluate the baseline hazard function for the distribution of interest. It returns a
function that accepts as input a vector of times, t and returns a vector.
The gradbasehazard function is used to evaluate the gradient of the baseline hazard function with respect to the parameters,
this typically returns a vector. It returns a function that accepts as input a vector of times, t, and returns a matrix.
The hessbasehazard function is used to evaluate the Hessian of the baseline hazard function. It returns a function that accepts
as input a vector of times, t and returns a list of hessian matrices corresponding to each t.
The cumbasehazard function is used to evaluate the cumulative baseline hazard function for the distribution of interest.
It returns a function that accepts as input a vector of times, t and returns a vector.
The gradcumbasehazard function is used to evaluate the gradient of the cumulative baseline hazard function with respect
to the parameters, this typically returns a vector. It returns a function that accepts as input a vector of times, t, and returns a matrix.
The hesscumbasehazard function is used to evaluate the Hessian of the cumulative baseline hazard function. It returns a
function that accepts as input a vector of times, t and returns a list of hessian matrices corresponding to each t.
The densityquantile function is used to return quantiles of the density function. This is NOT REQUIRED for running the MCMC,
merely for us in post-processing with the predict function where type is 'densityquantile'. In the case of the Weibull
model for the baseline hazard, it can be shown that the q-th quantile is:
exponentialHaz, gompertzHaz, makehamHaz, weibullHaz