Binomial data distribution

Implements the normal approximation for a test on rates. The reponse rate in the control group, r_C, has to be specified by rate_control. The null hypothesis is: r_E ≤ r_C, where r_E denotes the response rate in the invervention group. It is tested against the alternative r_E > r_C. The test statistic is given as X₁ = √n (r_E - r_C) / √(2 r₀ (1-r₀)), where r₀ denotes the mean between r_E and r_C in the two-armed case, and r_E in the one-armed case.#' All priors have to be defined for the rate difference r_E - r_C.

Usage

Binomial(rate_control, two_armed = TRUE)

# S4 method for class 'Binomial'
quantile(x, probs, n, theta, ...)

# S4 method for class 'Binomial,numeric'
simulate(object, nsim, n, theta, seed = NULL, ...)

Arguments

rate_control

assumed response rate in control group

two_armed

logical indicating if a two-armed trial is regarded

x

outcome

probs

vector of probabilities

n

sample size

theta

distribution parameter

...

further optional arguments

object

object of class Binomial

nsim

number of simulation runs

seed

random seed

Details

Note that simulate for class Binomial simulates the normal approximation of the test statistic.

Slots

rate_control

cf. parameter 'rate_control'

See also

see probability_density_function and cumulative_distribution_function to evaluate the pdf and the cdf, respectively.

Examples

datadist <- Binomial(rate_control = 0.2, two_armed = FALSE)