Imph ★ 20220607 18:56 (681 d 16:43 ago) Posting: # 23044 Views: 1,760 

Hello, I struggle to define the nonparametric statistical analysis methodology of tmax. Should I use the MannWhitneyWilcoxon test and then calculate the confidence interval based on the HodgesLehmann estimator or choose one of the two? Another question If I may: how to define the bioequivalence limits for the tmax in this case? Best regards. 
Helmut ★★★ Vienna, Austria, 20220607 19:32 (681 d 16:08 ago) @ Imph Posting: # 23045 Views: 1,472 

Hi Imph, ❝ Should I use the MannWhitneyWilcoxon test and then calculate the confidence interval based on the HodgesLehmann estimator or choose one of the two? Cave: The MannWhitneyWilcoxon test^{1} is for independent samples (parallel groups). If you deal with crossover designs or paired samples you want the Wilcoxon signedrank test.^{2} If you specify the hypotheses as usual,$$\small{\eqalign{ H_0:\Delta&=0\\ H_{\textrm{a}}:\Delta&\neq0}}$$ you get one pvalue (twosided test, of course). IMHO, that’s not useful because you will be trapped like in the approach for BE used in the early 1980s (before Donald Schuirmann’s TOST entered the stage).
❝ Another question If I may: how to define the bioequivalence limits for the tmax in this case? You may. Only (‼) if t_{max} is clinically relevant (rapid onset of effect, safety issues) you should prespecify limits. Otherwise, simply report the HodgesLehmann estimate and the ≈90% confidence interval. How to set the limits is the million dollar question. For a painkiller they might be pretty narrow (say, ±30 minutes).^{3} For a drug used in management of chronic pain – which means multiple doses – the limits might be pretty wide. Now for the 10^{7}$ question: How to deal with a drug with multiple indications? When ibuprofen is used as a painkiller, narrow limits. What about fever? Difference less relevant. Two limits, must pass both? Gimme a break! Furthermore, the distribution of t_{max} is not symmetric (skewed to the right). Perhaps it would make sense to set asymmetric limits, say, –25 min to +40 min… More details in this article.
— Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
Imph ★ 20220613 12:30 (675 d 23:10 ago) @ Helmut Posting: # 23055 Views: 1,444 

Hello, Thank you very much for your explanations. Best regards. 