Prior kernels of the binomial normalized power prior

Computes, on the rate lattice, the normalized power prior integrated over the power parameter, as a function of the target control rate and of the risk difference, together with the same kernel weighted by the power parameter and by its square.

Usage

binomial_npp_prior_kernels(
  n_control_source,
  n_successes_control_source,
  n_treatment_source,
  n_successes_treatment_source,
  gamma_rule,
  n_lattice = 1000L,
  n_log_likelihood_points = 20001L
)

Arguments

n_control_source, n_successes_control_source

Source control arm.

n_treatment_source, n_successes_treatment_source

Source treatment arm.

gamma_rule

Quadrature rule for the prior of the power parameter, as returned by npp_gamma_rule(): a single node of weight one gives the conditional power prior with that power parameter.

n_lattice

Number of lattice points N on the rates.

n_log_likelihood_points

Number of points on which the weight functions of the source log likelihood are tabulated before interpolation.

Value

A list with n_lattice, the rates, and the N x (2N - 1) matrices kernel, kernel_gamma and kernel_gamma_squared, indexed by the target control rate and the risk difference k / N, k = -(N - 1), ..., N - 1. They are zero where the target treatment rate would leave \([0, 1]\).