Dear all,
assume there are two groups, Control and Experimental. Non-Inferiority
(NI) of E to C is in many cases concluded if ln(HR)+q_0.975*SE (the
upper 95% CI limit for ln(HR) with HR being the hazard ratio of E vs C)
is below ln(m), where m>1 is the non-inferiority margin.
Essentially, this is a one-sided test problem of H0: ln(HR) >= ln(m)
against H1: ln(HR) < ln(m) and thus I wonder whether there is a p-value
for that? The NI criterion I could rewrite as [ln(HR) - ln(m)]/SE <
(-1)*q_0.975 and then one way to define the p-value is as p =
Phi([ln(HR) - ln(m)]/SE ), i.e., the probability to see an even more
extreme result than that of the study (Phi being the cdf of the standard
normal). Another way: Find an alpha such that the upper limit of the
2-sided 1-alpha CI equals ln(m), leading to the same result.
My concern is the normal distribution, as I need the distribution of
ln(HR) under the "null hypothesis" that the two groups differ by the
margin m.
Has anybody ever come across a similar problem for time dependent
endpoints? I would be grateful for any thoughts the member of the list
may have and I'll gladly summarize responses to anybody who would be
interested in them. In that case, pls let me know.
Thanks a lot to all in advance.
Kind regards
Markus
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