binom_sample_size {adaptDiag}

Calculate the minimum number of samples required for a one-sided exact binomial test

Description

Calculate the minimum number of samples required for a one-sided exact binomial test to distinguish between two success probabilities with specified alpha and power.

Usage

binom_sample_size(alpha = 0.05, power = 0.9, p0 = 0.9, p1 = 0.95)

Arguments

alpha

scalar. The desired false positive rate (probability of incorrectly rejecting the null). Must be be between 0 and 1. Default value is alpha = 0.05.

power

scalar. The the minimum probability of correctly rejects the null when the alternate is true.

p0

scalar. The expected proportion of successes under the null.

p1

scalar. The proportion of successes under the alternate hypothesis.

Details

This is a one-sided function, such that p_0 < p_1. It determines the minimum sample size to evaluate the hypothesis test:

H_0: \, p_1 \le p_0, \, vs.

H_1: \, p_1 > p_0

Value

A list containing the required sample size and the number of successful trials required.

References

Chow S-C, Shao J, Wang H, Lokhnygina Y. (2017) Sample Size Calculations in Clinical Research, Boca Raton, FL: CRC Press.

Examples

# The minimum number of reference positive cases required to demonstrate
# the true sensitivity is >0.7, assuming that the true value is 0.824, with
# 90% power is

binom_sample_size(alpha = 0.05, power = 0.9, p0 = 0.7, p1 = 0.824)

# With a sample size of n = 104, if the true prevalence is 0.2, we would
# require a sample size of at least n = 520 randomly sampled subjects to
# have adequate power to demonstrate the sensitivity of the new test.

# The minimum number of reference negative cases required to demonstrate
# the true specificity is >0.9, assuming that the true value is 0.963, with
# 90% power is

binom_sample_size(alpha = 0.05, power = 0.9, p0 = 0.9, p1 = 0.963)

# The proposed total sample size of n = 520 would be sufficient to
# demonstrate both endpoint goals are met.