find_beta_params {adaptr}

Find beta distribution parameters from thresholds

Description

Helper function to find a beta distribution with parameters corresponding to the fewest possible patients with events/non-events and a specified event proportion. Used in the Advanced example vignette (vignette("Advanced-example", "adaptr")) to derive beta prior distributions for use in beta-binomial conjugate models, based on a belief that the true event probability lies within a specified percentile-based interval (defaults to ⁠95%⁠). May similarly be used by users to derive other beta priors.

Usage

find_beta_params(
  theta = NULL,
  boundary_target = NULL,
  boundary = "lower",
  interval_width = 0.95,
  n_dec = 0,
  max_n = 10000
)

Arguments

theta

single numeric ⁠> 0⁠ and ⁠< 1⁠, expected true event probability.

boundary_target

single numeric ⁠> 0⁠ and ⁠< 1⁠, target lower or upper boundary of the interval.

boundary

single character string, either "lower" (default) or "upper", used to select which boundary to use when finding appropriate parameters for the beta distribution.

interval_width

width of the credible interval whose lower/upper boundary should be used (see boundary_target); must be ⁠> 0⁠ and ⁠< 1⁠; defaults to 0.95.

n_dec

single non-negative integer; the returned parameters are rounded to this number of decimals. Defaults to 0, in which case the parameters will correspond to whole number of patients.

max_n

single integer ⁠> 0⁠ (default 10000), the maximum total sum of the parameters, corresponding to the maximum total number of patients that will be considered by the function when finding the optimal parameter values. Corresponds to the maximum number of patients contributing information to a beta prior; more than the default number of patients are unlikely to be used in a beta prior.

Value

A single-row data.frame with five columns: the two shape parameters of the beta distribution (alpha, beta), rounded according to n_dec, and the actual lower and upper boundaries of the interval and the median (with appropriate names, e.g. p2.5, p50, and p97.5 for a ⁠95%⁠ interval), when using those rounded values.