calc_predictive {ppseq}

Calculate a single posterior predictive probability

Description

This function is meant to be used in the context of a clinical trial with a binary endpoint. The goal is to calculate the posterior predictive probability of success at the end of a trial, given the data available at an interim analysis. For the two-sample case the number of events observed at interim analysis, the sample size at interim analysis, and the total planned sample size are denoted y0, n0, and N0 in the standard-of-care arm and y1, n1, and N1 in the experimental arm. For the one-sample case, the number of events observed at interim analysis, the sample size at interim analysis, and the total planned sample size are denoted y, n, and N.

Usage

calc_predictive(
  y,
  n,
  p0,
  N,
  direction = "greater",
  delta = NULL,
  prior = c(0.5, 0.5),
  S = 5000,
  theta = 0.95
)

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.

N

the total planned sample size at the end of the trial. Vector of length two c(N0, N1) for the two-sample case; integer N for the one-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

theta

The target posterior probability. e.g. Efficacy decision if P(p1 > p0) > theta for the two-sample case with greater direction. Default is 0.95.

Value

Returns the numeric posterior predictive probability

Examples

set.seed(123)

# Setting S = 100 for speed, in practice you would want a much larger sample

# One-sample case 
calc_predictive(
  y = 14, 
  n = 50, 
  p0 = 0.2, 
  N = 100, 
  S = 100
  )

# Two-sample case 
calc_predictive(
  y = c(7, 12), 
  n = c(50, 50), 
  p0 = NULL, 
  N = c(100, 100),
  delta = 0,
  S = 100
  )