Description Usage Arguments Details Value See Also

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'

1 | ```
BsplineHaz(times, knots = quantile(times), degree = 3, MLinits = NULL)
``` |

`times` |
vector of survival times (both censored and uncensored) |

`knots` |
vector of knots in ascending order, must include minimum and maximum values of 'times' |

`degree` |
degree of the spline basis, default is 3 |

`MLinits` |
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:

an object inheriting class 'basehazardspec'

exponentialHaz, gompertzHaz, makehamHaz, weibullHaz

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