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# Null Hypothesis Formulation: Purpose and Errors

Null Hypothesis Formulation: Purpose and Errors
13.7
So let’s compare the superior to non-inferiority and I listed the equivalents here just for completeness sake but very rarely or equivalence trials done. Primarily for generics and vaccine batches is done but for the most part its non-inferiority that is done. And so you shouldn’t a researcher or as the reader, you shouldn’t use the word equivalence in a non-inferiority trial that should be saved for actual equivalent studies Now you’re right recall and superior already studies the null hypothesis says there is no difference. Now pretty much everything with non-inferiority is going to be the opposite of that.
52.5
So once you understand what a superiority study is designed to do and what it tells you then it’s just the opposite for a non-inferiority study. So you can see for them then instead of saying there is no difference, you can say there is a difference and there’s a couple other ways that it can also be stated as the study treatment is not non inferior or both treatments are not equally effective. And so you then either approve or disapprove of that. So you can see with the superiority remember there were potentially two outcomes and the third was inconclusive. We had two treatments a was better than B. B was better than A or there was no difference.
89.1
And remember that does not imply that it’s non inferior or equivalent because it’s not possible to show that. So that’s what you’ll shown a non-inferiority trial you’re either gonna say that A is noninferior to treatment B and this is usually called therapeutic equivalence or you’re gonna say that they’re not. And saying that they’re not does not mean the one treatment it’s inferior to the other one. So you could get potentially two possible outcomes from a superiority that are beneficial or you can make a conclusion about not inferiority. It’s just the one. Either it’s non inferior and not is inconclusive just like no difference is inconclusive in a superiority trial.
126.7
So my colleagues and I came up with this facts assessment to be able to have a stepwise approach to be able to look at a non-inferiority trial to make sure you’re assessing the things that you need to. So you’re going to formulate the null hypothesis from an non-inferiority standpoint, you’re going to assess the NI margin for appropriateness then going to compare the ITT and PP results translate the CI results graphically and this will help you then to maybe go back if you’re having difficulty with MOA’s and see how these are graphed very similarly And then summarize the clinical relevance of the results which is what we do with all trials.
167.1
Alright so formulate the null hypothesis, the null hypothesis just like with superiority studies should be based on the primary endpoint or if there’s more than one endpoint you have more than one hypothesis. It should also include the study duration because again shorter duration longer duration would depend on the effectiveness of it. And then there’s going to be something that you haven’t seen before in superiority studies called the NI margin or threshold. It’s also called Delta and listed by Greek letters. Now for non-inferiority only one-sided CIs is necessary but often times 2 is there, and 2 is needed for equivalence to make sure that that the treatments are as similar as possible.
208
So as I already mentioned the null hypothesis for a non-inferiority study says that there is A difference and you would list that out between study group with the dose and control group with the dose in the primary outcome by a pre-specified one-sided NI margin over the study duration. Now remember again that the null hypothesis for NI studies is the opposite, instead of no difference it’s a difference. So just remember that pretty much everything in non-inferiority is reversed, just like you can see that the Superman on the right side has his S reversed.
246.1
So the purpose in a NIi trial is to reject the null hypothesis and I gave you an example below of a null hypothesis statement in a clinical trial. You note that the null hypothesis again is there’s a statement of that there is a difference and you can see what it’s listed there as and you need to make sure that when a null hypothesis is listed in a non-inferiority trial that it includes both a Delta and an alpha value, so in this case with non-inferiority studies, pretty much they have to provide the null hypothesis to give you the Delta and the Alpha whereas you might recall in superiority studies they don’t always provide that information about the null hypothesis you need to formulate it from the objective but in NI trials they usually provide it because they need to give you the Delta.
296.8
All right so then let’s just look at the different types of errors just to show you how they vary between superiority and non-inferiority trials. So you might remember that superiority there’s there’s two ways to be right; two ways to be wrong same thing with non-inferiority. So there’s a false positive and a false negative the both of them but they mean something different. Type one error and superiority is saying the treatments are superior when possibly they are not. whereas a non-authority stating non inferior when possibly they are not.
328.2
So again you can see that that’s the one that the researchers are going to be most concerned about because you don’t want to say a treatment is not inferior when possibly it’s not. So you don’t want to say it’s as good when it may not be. So a type two error in both cases are false negative in a superiority trial it is saying it’s not superior to control one possibly it is. And a false negative is stating a new treatment is not not inferior to control one possibly it is not inferior.

Prof. Mary Ferrill gives a clear illustration of how to analyze an Non-Inferiority (NI) trial.

To begin with, we have to learn the differences between superiority and non-inferiority.

In addition, there are five stepwise approaches to analyze NI clinical trials. We should formulate the null hypothesis, assess the NI margin, compare the ITT and PP results, translate the CI results graphically, and finally summarize the clinical relevance of the results.

When formulating NI trials, we should notice NI margin or threshold, which is also called Delta and listed by Greek letters.

NOTE: The null hypothesis for a non-inferiority study says that there is a difference, and the null statement for NI studies is opposite of what is formulated for a superiority trial.

Therefore, the purpose in a NI trial is to reject the null hypothesis. If you are confused with this idea, please watch the example in this video or leave your question below.

Ultimately, we should know how to distinguish type I and type II errors from the final table in this video.