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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.

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    $\begingroup$ 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"? $\endgroup$
    – AdamO
    Commented Mar 8, 2022 at 23:49
  • $\begingroup$ 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 ? $\endgroup$
    – OJS
    Commented Mar 8, 2022 at 23:58
  • $\begingroup$ @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.. $\endgroup$
    – OJS
    Commented Mar 9, 2022 at 11:17

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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) enter image description here

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

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