Sample size calculator non inferiority

This calculator is useful for the types of tests known as non-inferiority and superiority tests. Whether the null hypothesis represents 'non-inferiority' or 'superiority' depends on the context and whether the non-inferiority/superiority margin, $\delta$, is positive or negative. In this setting, we wish to test whether the proportion in group 'A', $p_A$, is non-inferior/superior to the proportion in group 'B', $p_B$. We collect a sample from both groups, and thus will conduct a two-sample test. The idea is that statistically significant differences between the proportions may not be of interest unless the difference is greater than a threshold, $\delta$. This is particularly popular in clinical studies, where the margin is chosen based on clinical judgement and subject-domain knowledge. The hypotheses to test are $H_0:p_A-p_B\le\delta$ $H_1:p_A-p_B>\delta$ where $\delta$ is the superiority or non-inferiority margin and the ratio between the sample sizes of the two groups is $$\kappa=\frac$$

Formulas

$\kappa=n_A/n_B$ is the matching ratio
$\Phi$ is the standard Normaldistribution function
$\Phi^$ is the standard Normalquantile function
$\alpha$ is Type I error
$\beta$ is Type II error, meaning $1-\beta$ is power
$\delta$ is the testing margin

R Code

R code to implement these functions:

pA=0.85 pB=0.65 delta=-0.10 kappa=1 alpha=0.05 beta=0.20 (nB=(pA*(1-pA)/kappa+pB*(1-pB))*((qnorm(1-alpha)+qnorm(1-beta))/(pA-pB-delta))^2) ceiling(nB) # 25 z=(pA-pB-delta)/sqrt(pA*(1-pA)/nB/kappa+pB*(1-pB)/nB) (Power=pnorm(z-qnorm(1-alpha))+pnorm(-z-qnorm(1-alpha)))

References

Chow S, Shao J, Wang H. 2008. Sample Size Calculations in Clinical Research. 2nd Ed. Chapman & Hall/CRC Biostatistics Series. page 90.