Calculate a single posterior probability — calc

This function is meant to be used in the context of a clinical trial with a binary endpoint. For the two-sample case, the total number of events in the standard-of-care arm is y0 and the total number of events in the experimental arm is y1. The function samples from the posterior beta distribution based on the data and the prior beta hyperparameters, and returns the posterior probability that p1 is greater than (or less than) p0 given the data. The one-sample case is also available, in which a target p0 must be specified and the function returns the posterior probability that p is greater than (or less than) p0 given the data.

Usage

calc_posterior(
  y,
  n,
  p0,
  direction = "greater",
  delta = NULL,
  prior = c(0.5, 0.5),
  S = 5000
)

Arguments

y: number of events observed so far. Vector of length two c(y0, y1) for the two-sample case; integer y for the one-sample case.
n: sample size observed so far. Vector of length two c(n0, n1) for the two-sample case; integer n for the one-sample case.
p0: the target value to compare to in the one-sample case. Set to NULL for the two-sample case.
direction: "greater" (default) if interest is in P(p1 > p0) in the two-sample case or P(p > p0) in the one-sample case; "less" if interest is in P(p1 < p0) for the two-sample case or P(p < p0) for the one-sample case.
delta: clinically meaningful difference between groups. Typically 0 for the two-sample case. NULL for one-sample case (default).
prior: vector of length two containing hyperparameters of the prior beta distribution. c(0.5, 0.5) is default, for the Beta(0.5, 0.5) distribution.
S: number of samples, default is 5000

Value

Returns the numeric posterior probability

Examples


set.seed(123)

# One-sample case
calc_posterior(
  y = 27, 
  n = 100, 
  p0 = 0.2
  )
#> [1] 0.9558

# Two-sample case
calc_posterior(
  y = c(14, 23), 
  n = c(100, 100), 
  p0 = NULL, 
  delta = 0
  )
#> [1] 0.9508