Sample Size Estimation for Superiority Hypothesis in ANCOVA (HELP!)

[Gianfranco Di Gennaro]

Dear all,
thanks in advance.

I have a question regarding sample size estimation. I have previously estimated sample sizes for equivalence and non-inferiority, but I have never dealt with such a specific superiority hypothesis. I have a feeling that the solution is simple, but I just can't see it.

I have two treatment groups (Experimental vs. Control), and the outcome is the VAS score (lower is better). I expect the post-treatment difference to be at least -20 VAS points in favor of the experimental treatment.

Thus, my null hypothesis is:

H0:meanEXP−meanCTRL>−20

while my alternative hypothesis is:

HA:meanEXP−meanCTRL≤−20

I would like to know how to estimate the required sample size for this type of hypothesis.

Additional information: I plan to use ANCOVA as the statistical test.

If I use sampsi (or power twomeans) with a code like:

sampsi 20 0, sd(20) r01(0.5) pre(1) post(1) alpha(0.05) power(0.9)

the null hypothesis tested is actually H0:meanEXP=meanCTRL, which is completely different from what I need to demonstrate.

How can I correctly estimate the required sample size for my superiority hypothesis using ANCOVA in Stata?

Thank you again for your help!

[Joseph Coveney]

. . . the null hypothesis tested is actually H0:meanEXP=meanCTRL, which is completely different from what I need to demonstrate.

How can I correctly estimate the required sample size for my superiority hypothesis . . .?

Add the onesided option to the command line.

sampsi 20 0, sd(20) r01(0.5) pre(1) post(1) alpha(0.05) power(0.9) onesided

[Gianfranco Di Gennaro]

Dear Joseph Coveney ,
thank you very much for your help.

However, there is one thing I do not understand.
I enter

onesided

, and that's ok.
In this way, I test my hypothesis that my treatment is superior (and not simply different from the control arm).

However, in this command, the two means that I enter (20 and 0 in my post, but in reality, there's a mistake: it should be written as -20 and 0, or 40 and 60, if I wanted to use the absolute values of VAS for the minimally clinically important difference) represent the difference I intend to demonstrate, but STATA does not recognize them as my margin of superiority.

Basically, let's say I want to demonstrate a margin of superiority of -20. I should use the formula that can be found in any paper or book dealing with sample size calculation for superiority with continuous outcomes:



At that point, I should have a stata code in which I insert val:

• the two expected means (say 30 VAS points in the experimental group, and 65 VAS points in the control group)
• mysuperiority margin (-20 VAS points)

I just did not understand how to write these denominator values in a STATA command (

sampsi

or

power twomeans

or

power repeated

, ecc).

Thank you so much, your help is precious.

[Joseph Coveney]

. . . I wanted to use the absolute values of VAS for the minimally clinically important difference) . . . , but STATA does not recognize them as my margin of superiority.

. . . I should have a stata code in which I insert val:

• the two expected means (say 30 VAS points in the experimental group, and 65 VAS points in the control group)
• mysuperiority margin (-20 VAS points)

OK, I understand now.

In the sample-size / power commands, you set up the null difference (margin of superiority) and expected difference in for the two means to be tested.

As an example, the case shown here, Page 10, is for a superiority sample size for two-sample t-test with a null difference of 0.001 and an expected difference of 2.3 with an SD of 4.5. It uses SAS's PROC POWER to get a (fractional) sample size of 48.07 for 80% power. For Stata's power twomeans, you put the superiority margin / null difference (0.001) in for m1 and the expected difference (2.3) in for m2.

power twomeans 0.001 2.3, sd(4.5) nfractional power(0.8) onesided

and it will yield the n per group of 48.07. (Ditto for the example on the following two pages at that link where the authors change the superiority margin to 0.1 and get a sample size of 52.43; Stata gets 52.4239.)

With your situation, with its -20 margin and smaller-is-better, I'd probably get lost in all of the double negatives, but you can take a look at the table of how to set up the two means for Superiority–Smaller-is-better and Superiority–Larger-is-better in the table at the SAS Usage Note here (it's cited in passing in the link above), and follow that for what to fill in with sampsi or power repeated.

It should be fairly easy just to implement that formula in Mata, too.

[Gianfranco Di Gennaro]

Thank you so much Joseph Coveney ! I appreciate your help and thanks for your time!