Summarises the prior for the constant hazard implied by a particular prior on the hazard scale parameter and spline specification.

Summarises the prior for the constant hazard implied by a particular prior on the hazard scale parameter and M-spline specification, when the spline coefficients are fixed to define a constant hazard using mspline_constant_coefs.

Usage

prior_haz_const(
  mspline,
  prior_hscale = p_normal(0, 20),
  nsim = 10000,
  quantiles = c(0.025, 0.5, 0.975)
)

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.

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.

nsim

Number of simulations to draw

quantiles

Quantiles used to summarise the implied prior distributions of the simulated quantities.

See also

p_meansurv, mspline_constant_coefs