## Sample size calculator

Get a quick estimation of the number of subjects for your clinical trial using the simple and intuitive calculator. This tool can be used for parallel two arms trials with a continuous outcome (such as blood pressure, mean change of visual analogue scale, etc.). This calculator uses an approximation to the Normal distribution and is suitable only for relatively large sample sizes.**Note that most online calculators (including this one) can be used only for illustrative purposes.**

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Treatment Difference

Reference better

Study drug better

Noninferiority established

Noninferiority

not established

Superiority established

Superiority

not established

*Possible scenarios of observed treatment differences. Plot elements are located schematically.*

According to Chow et al. (Sample Size Calculations in Clinical Research, 2^{nd} ed., 2008), the problem of testing non-inferiority and superiority can be unified by the following hypotheses:

H_{0}: ε ≤ Δ versus H_{a}: ε > Δ,

where Δ is the superiority or non-inferiority margin. When Δ > 0, the rejection of the null hypothesis indicates the superiority of the test drug over the control. When Δ < 0, the rejection of the null hypothesis indicates the non-inferiority of the test drug against the control. ε = μ_{T} − μ_{R} is the expected difference between the mean response of a test drug (μ_{T}) and a reference drug / placebo (μ_{R}). In case of non-inferiority study design treatment difference ε is assumed to be equal to zero.

Calculation of the sample size (N) per group is based on the formula:

N = 2 * (Z_{1-α} + Z_{β})^{2} * σ^{2} / (ε – Δ)^{2}

Z is the percentile of the standard normal distribution.