Sample Size Calculator: One-Sample Proportion

Hypothesis: One-Sided Non-Inferiority / Superiority

Data Input: (Help) (Example)

 

Input

 

Results

α

 

 

 

β

 

 

θ

 

N

θ0

 

 

 

δ

 

 

 

 

Note:

Variables

Descriptions

α

One-sided significance level

1-β

Power of the test

θ

Expected success proportion of sample

θ0

Known success proportion

δ

True difference of mean response rates, δ>0, the superiority margin or value of δ<0, the non-inferiority margin

N

Sample size

Help Aids Top

 

Application: To test non-inferiority and superiority that unified by the following hypotheses:

Here δ is the non-inferiority (δ<0) or superiority margin (δ>0).

 

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 θ, a true mean response rate of a test drug

d)     value of θ0, a reference response rate

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

  1. Click the button “Calculate” to obtain result sample size 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.

 

θ-θ0:          The difference between the true mean response rates of a test drug (θ) and a reference value (θ0).

 

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

 

Examples

 

Example 1: We want to show that the majority of patients whose change in bone density after treatment is at least as good as the reference value, say, θ0=30%. If we assume that a difference of 10% in responder rate is considered of no clinical significance, say, δ=-10%, to test for non-inferiority. Also the true response rate is θ=50%. According to (*), at α=0.05, the required sample size for having an 80% power (i.e., β=0.2) is N=18.

 

 

Reference:

  1. Casagrande, Pike and Smith (1978), Biometrics 34: 483-486.
  2. Chow, Shao and Wang, Sample Size Calculations In Clinical Research, Taylor & Francis, NY. (2003) Pages 83-84.
  3. Flesis J.L., Statistical Methods for Rates and Proportions (2nd edition). Wiley: New York, 1981.

 

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