Comparing two groups for equivalence / non-inferiority


First post - newbie here.

I work in medicine and currently working on a project that involves comparing the outcomes of two groups of patients which have received different types of care.

I am hypothesizing that there is no difference between the two groups when it comes to certain measured outcomes (e.g. death, complications, etc).

My question is: how do I go about statistically showing this? I know that a student's t-test would not be the right test because it attempts to disprove the null hypothesis, which in this case I am trying to prove. How would the results be presented (p value? CI? none of the above?)

Any help is appreciated!


Omega Contributor
Well you need to decide if you want to say they are equivalent or one is not inferior to the other. Sounds like the former in your case.

Now based on clinical relevance and signicance you need to select a comfort level you would be willing to say they may still be the same (e.g, within +/-5 mmHg when comparing comparing blood pressure treatments). If you had a continuous outcome the test is similar to a ttest if you have binary outcomes you just need to search the web to get the formula for the righth test, most are named after the people who came up with them (Farrington Manning sp?).
hlsmith is right - You need to decide how close can be considered near enough to be the same as no difference. But what to do then?
One approach is to make a 95% confidence interval for the observed difference. This CI should should lie completely within the allowable limits. Environmental statisticians have improved on this slightly by using two one sided tests TOST. Using this TOST approach you effectively only need a 90% CI inside the limits. This approach will give you a p value, as well.
Another approach, if you haven't collected your data yet, is to do a power analysis first to find the sample size needed so that a "not significant" verdict means that the true difference is unlikely to be greater than that you have allowed yourself.
If you have collected your data already, a simple p value is not enough. A verdict of "no sig diff" simply means "I don't know if there is a difference or not". In this case, you could present a 95% confidence interval and say "I don't know if there is a difference or not, but if there is one I'm reasonably sure that it is less than ..." then let the reader decide for themselves.
cheers, kat