# Sample Size Calculator: Two Crossover-Sample Means

Hypothesis: One-Sided Non-Inferiority / Superiority

Data Input: (Help) (Example)

 Input Results α β Allowable difference n Population variance δ

Note:

 Variables Descriptions α One-sided significance level 1-β Power of the test Allowable difference Acceptable mean difference between sample two and sample one (µ2-µ1) Population variance Population variance δ δ>0, the superiority margin or δ<0, the non-inferiority margin n Sample size of each group

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Application: This procedure computes sample size for non-inferiority and superiority tests in 2×2 cross-over designs in which the outcome is a continuous normal random variable. A non-inferiority test tests that the treatment mean is not worse than the reference mean by more than a small equivalence margin. The actual direction of the hypothesis depends on the response variable being studied. A superiority test tests that the treatment mean is better than reference mean by more than a small equivalence margin. The actual direction of the hypothesis depends on the response variable being studied. The following hypotheses are usually considered: .

Procedure:

1. Enter

a)      value of α, the probability of type I error

b)      value of β, the probability of type II error

c)      value of allowable difference

d)     value of population variance

e)      value of δ>0, the superiority margin or value of δ<0, the non-inferiority margin.

1. Click the button “Calculate” to obtain result sample size of each group n.

Formula:                                                                                                             (*)

Notations:

α:               The probability of type I error (significance level) is the probability of rejecting the true null hypothesis.

β:               The probability of type II error (1 – power of the test) is the probability of failing to reject the false null hypothesis.

δ:               Clinically meaningful difference. The largest change from the reference value (baseline) that is considered to be trivial.

μ2 – μ1:      The true difference between the two mean values at which the power is calculated.

Population variance:   The within mean square error from the ANOVA table used to analyze the Cross-Over design.

Examples

Example 1: Suppose you want to consider the sample size of a balanced, cross-over design that will be analyzed the t-test approach. Thus when the non-inferiority margin is δ=-0.05, the true difference between the means under H0 is assumed to be 0, with population variance  of 0.01 and the significance level of α=0.05 given. We have the sample size to achieve 80% power for both values of at β=0.2 is n=13.

Reference: Chow, Shao and Wang, Sample Size Calculations In Clinical Research, Taylor & Francis, NY. (2003) Pages 63-68.

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