sample size calc for one-sample non-inferiority test

[Naoko Kozuki]

Hi-

I am trying to calculate the sample size to test for non-inferiority of a recovery rate from a new treatment protocol, against a currently accepted recovery rate cut-off of 75% (to clarify, this is NOT a trial, just testing to see if recovery rate is non-inferior to existing standard). We'll state for the time being that a recovery rate as low as 65% will be considered non-inferior. I came across the sampsi command, and wanted to see if this is the right thing to be doing:

sampsi 0.75 0.65, onesample

Thank you.

Naoko

[Bruce Weaver]

Hello Naoko. I believe that tests of non-inferiority are one-sided tests, so you probably want to add the onesided option to your sampsi command.

. sampsi 0.75 0.65, onesample onesided

Estimated sample size for one-sample comparison of proportion
  to hypothesized value

Test Ho: p = 0.7500, where p is the proportion in the population

Assumptions:

         alpha =   0.0500  (one-sided)
         power =   0.9000
 alternative p =   0.6500

Estimated required sample size:

             n =      176

I get a pretty similar result (n = 180) using PASS.

PASS 15.0.1 23/05/2017 11:19:17 AM 1

Non-Inferiority Tests for One Proportion

Numeric Results for Testing Non-Inferiority of One Proportion using the Exact Test
Higher Proportions are Better
Alternative Hypothesis: One-Sided (H0: P ≤ P0 vs. H1: P > P0)

Baseline Non-Inf. Actual
Proportion Difference Difference Target Actual Reject H0
Power* n PB d0 d1 Alpha Alpha* If R ≥
0.90018 180 0.7500 -0.1000 0.0000 0.0500 0.0489 128

* Power and actual alpha were computed using binomial enumeration of all possible outcomes.

Summary Statements
A sample size of 180 achieves 90.018% power to detect a non-inferiority difference (P0-PB) of -0.1000 using a one-sided exact test with a target significance level of 0.0500. The actual significance level achieved by this test is 0.0489. These results assume a baseline proportion (PB) of 0.7500 and that the actual difference (P1-PB) is 0.0000.

Report Definitions
Power is the probability of rejecting the null hypothesis when it is false. It should be close to one.
n is the size of the sample drawn from the population. To conserve resources, it should be as small as
possible.
PB is the baseline or standard value of the proportion.
d0 = P0-PB is the distance below PB that is still considered non-inferior.
d1 = P1-PB is the value of the difference at which the power is calculated.
Alpha (significance level) is the probability of rejecting the null hypothesis when it is true. It should be small.
Target Alpha is the significance level that the study design is meant to achieve.
Actual Alpha is the significance level that is actually achieved by the design.
Reject H0 If... gives the critical value(s) for the test.

References
Blackwelder, W.C. 1998. 'Equivalence Trials.' In Encyclopedia of Biostatistics, John Wiley and Sons. New York.
Volume 2, 1367-1372.
Chow, S. C., Shao, J., and Wang, H. 2008. Sample Size Calculations in Clinical Research, Second Edition.
Chapman & Hall/CRC. Boca Raton, Florida.
Fleiss, J. L., Levin, B., and Paik, M.C. 2003. Statistical Methods for Rates and Proportions. Third Edition.
John Wiley & Sons. New York.

HTH.

[Naoko Kozuki]

Thank you, Bruce. Good point re: the one-sided test.