# sampleSizePhase2BinaryTest: Compute sample size for a Phase 2 study of a binary test In biostatUZH: Misc Tools of the Department of Biostatistics, EBPI, University of Zurich

## Description

Compute sample size for a Phase 2 study of a binary test using either normal approximation or via simulation. In simulations, the function goes through a grid of sample sizes and computes empirically the power for the given alternatives FPF1 and TPF1. The test decision is based on a rectangular confidence region using one-sided confidence limits for these two binomial parameters where the confidence intervals are either computed according to Wilson's method or exact as Clopper-Pearson intervals. The chosen sample sizes are the smallest numbers of cases and controls where the power is above power for all subsequent combinations. It may happen that the desired power is reached for even smaller numbers of cases and controls but that for larger numbers we find power below the desired limit. This phenomena can be attributed to the discrete nature of the problem and is well-known from the similar setup for one binomial proportion.

## Usage

 1 2 3 4 5 sampleSizePhase2BinaryTest(FPF0 = 0.2, TPF0 = 0.75, FPF1 = 0.05, TPF1 = 0.9, alpha = 0.05, power = 0.9) sampleSizePhase2BinaryTestSimulated(FPF0, TPF0, FPF1, TPF1, alpha = 0.05, power = 0.9, M = 5000, range = 15, print = TRUE, type = c("wilson", "exact")[2]) 

## Arguments

 FPF0 Minimally acceptable value for the false positive fraction. TPF0 Minimally acceptable value for the true positive fraction. FPF1 Desirable value for the false positive fraction. TPF1 Desirable value for the true positive fraction. alpha Significance level. power Desired power, i.e. 1 - probability of type II error. M Number of diagnostic tests to be simulated for the alternative. range Starting from the normally approximated sample size wald.n a range of wald.n\pmrange is went through to compute power. print If TRUE progress is indicated through simulations. type Confidence interval to be used: either Wilson or the exact by Clopper and Pearson.

## Value

A list with the entries

 n.cases Number of cases necessary to achieve prescribed power based on wald test. n.controls Number of cases necessary to achieve prescribed power based on wald test.

for sampleSizePhase2BinaryTest and entries

 wald.n.cases Number of cases necessary to achieve prescribed power based on wald test. wald.n.controls Number of cases necessary to achieve prescribed power based on wald test. simul.n.cases Number of cases necessary to achieve prescribed power based on simulations. simul.n.controls Number of controls necessary to achieve prescribed power based on simulations. simul.power Actual power that is achieved in simulations. alphastar Confidence level for the two univariate confidence intervals for FPF and TPF, equals 1 - √{1 - α}. simul.powers Computed powers for all the number of cases/controls combinations in simulations.

## Author(s)

Kaspar Rufibach
[email protected]

## References

Pepe, M.S. (2003) The statistical evaluation of medical tests for classification and prediction. Oxford: Oxford University Press.

The function sampleSizePhase2BinaryTestSimulated depends on sampleSizePhase2BinaryTest, wilson, and clopperPearson.
 1 2 3 4 5 6 ## Example 8.1 in Pepe (2001): ## "The Statistical Evaluation Medical Tests for Classification and Prediction" sampleSizePhase2BinaryTest(FPF0 = 0.2, TPF0 = 0.75, FPF1 = 0.05, TPF1 = 0.9, alpha = 0.1, power = 0.9) sampleSizePhase2BinaryTestSimulated(FPF0 = 0.2, TPF0 = 0.75, FPF1 = 0.05, TPF1 = 0.9, alpha = 0.1, power = 0.9, M = 1000, range = 15, print = TRUE)