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Generate and/or plot a sample from the prior distribution of M-spline hazard curves

Source: R/priors.R
prior_sample_hazard.Rd

Generates and/or plots the hazard curves (as functions of time) implied by a prior mean for the spline coefficients (a constant hazard by default) and particular priors for the baseline log hazard and smoothness standard deviation.

Usage

prior_sample_hazard(
  knots = NULL,
  df = 10,
  degree = 3,
  bsmooth = TRUE,
  coefs_mean = NULL,
  prior_hsd = p_gamma(2, 1),
  prior_hscale = NULL,
  smooth_model = "exchangeable",
  prior_loghr = NULL,
  formula = NULL,
  cure = NULL,
  nonprop = NULL,
  newdata = NULL,
  newdata0 = NULL,
  prior_hrsd = NULL,
  tmin = 0,
  tmax = 10,
  nsim = 10
)

plot_prior_hazard(
  knots = NULL,
  df = 10,
  degree = 3,
  bsmooth = TRUE,
  coefs_mean = NULL,
  prior_hsd = p_gamma(2, 1),
  prior_hscale = p_normal(0, 20),
  smooth_model = "exchangeable",
  prior_loghr = NULL,
  formula = NULL,
  cure = NULL,
  nonprop = NULL,
  newdata = NULL,
  prior_hrsd = p_gamma(2, 1),
  tmin = 0,
  tmax = NULL,
  nsim = 10
)

Arguments

knots

Vector of knot locations. If not supplied, df has to be specified. One of two rules is then used to choose the knot locations. If bknots is specified, a set of equally spaced knots between zero and bknots is used. Otherwise if obstimes is supplied, the knots are chosen as equally spaced quantiles of obstimes.

The number of knots (excluding zero) is df - degree + 1 if bsmooth is TRUE, or df - degree - 1 otherwise.

df

Desired number of basis terms, or "degrees of freedom" in the spline. If knots is not supplied, the number of knots is then chosen to satisfy this.

degree

Spline polynomial degree. Can only be changed from the default of 3 if bsmooth is FALSE.

bsmooth

If TRUE then the function is constrained to also have zero derivative and second derivative at the boundary.

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 survival formula in standard R formula syntax, with a call to Surv() on the left hand side.

Covariates included on the right hand side of the formula with be modelled with proportional hazards, or if nonprop is TRUE then a non-proportional hazards is used.

If data is omitted, so that the model is being fitted to external aggregate data alone, without individual data, then the formula should not include a Surv() call. The left-hand side of the formula will then be empty, and the right hand side specifies the covariates as usual. For example, formula = ~1 if there are no covariates.

cure

If TRUE, a mixture cure model is used, where the "uncured" survival is defined by the M-spline model, and the cure probability is estimated.

nonprop

Non-proportional hazards model specification. This is achieved by modelling the spline basis coefficients in terms of the covariates. See the methods vignette for more details.

If TRUE, then all covariates are modelled with non-proportional hazards, using the same model formula as formula.

If this is a formula, then this is assumed to define a model for the dependence of the basis coefficients on the covariates.

IF this is NULL or FALSE (the default) then any covariates are modelled with proportional hazards.

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.

tmin

Minimum plotting time. Defaults to zero.

tmax

Maximum plotting time. Defaults to the highest knot.

nsim

Number of simulations to draw