# Clinical trial study hypothesis

I am having a two armed clinical trial where I would like to measure the difference between restricted mean survival times for placebo and treatment arms.

If the difference is atleast "5" units, I will conclude that the treatment is effective.

So, my question is what should be my hypothesis like ?

I am thinking that a superiority trial would be fine, with hypothesis,

H0:mu1=mu2 vs H1:mu1>mu2

But if so, how would I measure the significance of 5 units superiority of the treatment ?

Any suggestions would be extremely helpful.

• This is unclear. The hypothesis you state is clearly one to test the superiority of treatment 1. However, you say you'll reject the null if the RMSE in group 1 is 5 or more greater than the control/placebo group 2. This sounds like a boundary, not a margin. Is the null hypothesis that you are actually trying to test, "H0: mu1 <= mu2 + 5"? Commented Mar 8, 2022 at 23:49
• Yes Sir, I would like to know if the treatment is atleast 5 units more or not than placebo. But then, what trial should it fall under ? Superiority ?
– OJS
Commented Mar 8, 2022 at 23:58
• @AdamO Actually Sir, the trial is devised in such a way that the treatment is clinically significant if its mean survival is atleast 3 units more than placebo. So in such case if we formulate a superiority trail hypothesis as in H0:mu1=mu2 vs H1:mu1>mu2, and we get a statistically significant difference of say 2units, should we then conclude that the mean difference is statistically significant but not clinically (as its not atleast 3 units). Please guide me if I am taking the right way..
– OJS
Commented Mar 9, 2022 at 11:17

Your initial hypothesis formulation, $$H_0: \mu_1 = \mu_2$$ vs. $$H_1: \mu_1 > \mu_2$$, is a standard setup for a superiority trial. However, you're interested in determining not just if the treatment is superior, but if it is superior by a clinically significant margin. Given your goal, to detect a clinically significant difference in restricted mean survival time (RMST) between treatment and control arms, the hypothesis should incorporate a pre-specified superiority margin, denoted as $$\Delta_S$$ and it's interpretation should be similar to non-inferiority trials where we would have a non-inferiority margin.

The null hypothesis would state that the new intervention's effect is not superior to the control intervention by more than a pre-specified margin $$\Delta_S$$. This can be written as: $$H_0: \mu_1 - \mu_2 \leq \Delta_S$$

The alternative hypothesis would assert that the new intervention is superior to the control by more than $$\Delta_S$$ units: $$H_1: \mu_1 - \mu_2 > \Delta_S$$

If the test intervention lies to the right of the no difference margin but is within the $$\Delta_S$$, it would not be considered clinically superior, so in your case, the lower boundary of the confidence interval should be beyond the superiority margin as shown in the figure (Shafiq & Malhotra, 2015)

Statistical Significance and Clinical Relevance

• Statistical Significance: If the lower boundary of the confidence interval for the difference in RMST between treatment and control ($$\mu_1 - \mu_2$$) exceeds $$\Delta_S$$, the result would be considered statistically significant.
• Clinical Significance: The magnitude of $$\Delta_S$$ should be determined by the minimal clinically important difference (MCID), which is the smallest difference in RMST that is considered meaningful from a clinical perspective.

I would like to know if the treatment is at least 5 units more or not than placebo. But then, what trial should it fall under ? Superiority ?

The trial still falls under the category of a superiority trial. The key difference is that you're not just testing for any difference but for a difference that exceeds a specific clinical threshold ($$\Delta_S$$)

References:

Shafiq, N., & Malhotra, S. (2015). Superiority trials: raising the bar of null hypothesis statistical testing. BMJ Evidence-Based Medicine, 20(5), 154-155. https://ebm.bmj.com/content/20/5/154