Draws a sample from the joint prior distribution of the parameters
governing a survextrap model for given covariates. This is used,
for example, in `prior_sample_hazard`

, to visualise the
prior distribution around hazard curves implied by a particular
M-spline model and parameter priors.

## Usage

```
prior_sample(
mspline,
coefs_mean = NULL,
prior_hsd = p_gamma(2, 1),
prior_hscale,
smooth_model = "exchangeable",
prior_loghr = NULL,
formula = NULL,
cure = NULL,
nonprop = NULL,
newdata = NULL,
newdata0 = NULL,
prior_hrsd = NULL,
prior_cure = NULL,
prior_logor_cure = NULL,
nsim = 100
)
```

## Arguments

- mspline
A list of control parameters defining the spline model.

`knots`

: Spline knots. If this is not supplied, then the number of knots is taken from`df`

, and their location is taken from equally-spaced quantiles of the observed event times in the individual-level data.`add_knots`

: This is intended to be used when there are`external`

data included in the model. External data are typically outside the time period covered by the individual data.`add_knots`

would then be chosen to span the time period covered by the external data, so that the hazard trajectory can vary over that time.If there are external data, and both

`knots`

and`add_knots`

are omitted, then a default set of knots is chosen to span both the individual and external data, by taking the quantiles of a vector defined by concatenating the individual-level event times with the`start`

and`stop`

times in the external data.`df`

: Degrees of freedom, i.e. the number of parameters (or basis terms) intended to result from choosing knots based on quantiles of the data. The total number of parameters will then be`df`

plus the number of additional knots specified in`add_knots`

.`df`

defaults to 10. This does not necessarily overfit, because the function is smoothed through the prior.`degree`

: Polynomial degree used for the basis function. The default is 3, giving a cubic. This can only be changed from 3 if`bsmooth`

is`FALSE`

.`bsmooth`

: If`TRUE`

(on by default) the spline is smoother at the highest knot, by defining the derivative and second derivative at this point to be zero.- coefs_mean
Spline basis coefficients that define the prior mean for the hazard function. By default, these are set to values that define a constant hazard function (see

`mspline_constant_coefs`

). They are normalised to sum to 1 internally (if they do not already).- prior_hsd
Gamma prior for the standard deviation that controls the variability over time (or smoothness) of the hazard function. This should be a call to

`p_gamma()`

. The default is`p_gamma(2,1)`

. See`prior_haz_sd`

for a way to calibrate this to represent a meaningful belief.- prior_hscale
Prior for the baseline log hazard scale parameter (

`alpha`

or`log(eta)`

). This should be a call to a prior constructor function, such as`p_normal(0,1)`

or`p_t(0,2,2)`

. Supported prior distribution families are normal (parameters mean and SD) and t distributions (parameters location, scale and degrees of freedom). The default is a normal distribution with mean 0 and standard deviation 20.Note that

`eta`

is not in itself a hazard, but it is proportional to the hazard (see the vignette for the full model specification)."Baseline" is defined by the continuous covariates taking a value of zero and factor covariates taking their reference level. To use a different baseline, the data should be transformed appropriately beforehand, so that a value of zero has a different meaning. For continuous covariates, it helps for both computation and interpretation to define the value of zero to denote a typical value in the data, e.g. the mean.

- smooth_model
The default

`"exchangeable"`

uses independent logistic priors on the multinomial-logit spline coefficients, conditionally on a common smoothing variance parameter.The alternative,

`"random_walk"`

, specifies a second-order random walk for the multinomial-logit spline coefficients, based on logistic distributions with a common smoothing variance. See the methods vignette for full details.In non-proportional hazards models, setting

`smooth_model`

also determines whether an exchangeable or random walk model is used for the non-proportionality parameters (\(\delta\)).- prior_loghr
Priors for log hazard ratios. This should be a call to

`p_normal()`

or`p_t()`

. A list of calls can also be provided, to give different priors to different coefficients, where the name of each list component matches the name of the coefficient, e.g.`list("age45-59" = p_normal(0,1), "age60+" = p_t(0,2,3))`

The default is

`p_normal(0,2.5)`

for all coefficients.- formula
A model formula with no response, defining the covariates on the hazard scale.

- cure
A model formula with no response, giving any covariates on the cure proportion.

- nonprop
A model formula with no response, defining any covariates affecting the spline basis coefficients, which gives a nonproportional hazards model.

- newdata
A data frame with one row, containing variables in the model formulae. Samples will then be drawn, for any covariate-dependent parameters, with covariates set to the values given here.

- newdata0
A data frame with one row, containing "reference" values of variables in the model formulae. The hazard ratio between the hazards at

`newdata`

and`newdata0`

will be returned.- prior_hrsd
Prior for the standard deviation parameters that smooth the non-proportionality effects over time in non-proportional hazards models. This should be a call to

`p_gamma()`

or a list of calls to`p_gamma()`

with one component per covariate, as in`prior_loghr`

. See`prior_hr_sd`

for a way to calibrate this to represent a meaningful belief.- prior_cure
Prior for the baseline cure probability. This should be a call to

`p_beta()`

. The default is a uniform prior,`p_beta(1,1)`

. Baseline is defined by the mean of continuous covariates and the reference level of factor covariates.- prior_logor_cure
Priors for log odds ratios on cure probabilities. This should be a call to

`p_normal()`

or`p_t()`

. The default is`p_normal(0,2.5)`

.- nsim
Number of simulations to draw

## Value

`prior_sample_hazard`

returns a data frame of the
samples, and `plot_prior_hazard`

generates a plot. No
customisation options are provided for the plot function, which
is just intended as a quick check.

A list with components:

`alpha`

: Baseline log hazard scale parameter (`log(eta)`

in the notation of the manual). For models with covariates, this is at the covariate values supplied in `X`

, or at zero if `X`

is not supplied.

`hscale`

: Baseline hazard scale parameter (`eta`

).

`coefs`

: Spline coefficients. For non-proportional hazards model with covariates, these are returned at the suppled value of `X`

, or at values of zero if `X`

is not supplied.

`beta`

: Multinomial logit-transformed spline coefficients.

`hsd`

: Smoothing standard deviation for spline coefficients.

If `X0`

is supplied, then `alpha0`

, `hscale0`

, `beta0`

, `coefs0`

are also returned, representing reference covariate values.

`pcure`

is returned in cure models (the cure probability).