Joshua Junior India, 20120117 06:59 Posting: # 7953 Views: 7,674 

Dear All, Greetings Can anyone kindly guide on how to do the nonparametric analysis for t_{max} for a two treatment, three period, three sequence (partial replicate) design. Thanks a ton in advance. Regards, Joshua. Edit: Category changed. [Helmut] — Joshua. 
Helmut Hero Vienna, Austria, 20120117 11:34 @ Joshua Posting: # 7954 Views: 6,980 

Dear Joshua! » Can anyone kindly guide on how to do the nonparametric analysis for t_{max} for a two treatment, three period, three sequence (partial replicate) design. Good point. Since t_{max} is not required for the FDA, I guess you are referring to EMA’s GL? A statistical evaluation of t_{max} is not required. However, if rapid release is claimed to be clinically relevant and of importance for onset of action or is related to adverse events, there should be no apparent difference in median t_{max} and its variability between test and reference product. The EMA hates nonparametrics – which is manifested in the first sentence. ‘No apparent difference in median t_{max}’ without statistics boils down to in the discussion section of the report. How can we assess the variabilities? I would go with reporting the products’ IQRs followed by . In a partial replicate I would mean the two administrations of the reference.— Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
Joshua Junior India, 20120120 11:54 @ Helmut Posting: # 7974 Views: 6,889 

Dear Helmut, Thank you so much for your reply. I was actually referring to the USFDA. — Joshua. 
Helmut Hero Vienna, Austria, 20120120 12:56 @ Joshua Posting: # 7978 Views: 6,895 

Dear Joshua! » Thank you so much for your reply. I was actually referring to the USFDA. IMHO FDA never asked for t_{max}. If clinically relevant ‘early exposure’ should be assessed (Guidance 2003, Section III.A.8.a.): […] the guidance recommends use of partial AUC as an early exposure measure. We recommend that the partial area be truncated at the population median of Tmax values for the reference formulation. We also recommend that at least two quantifiable samples be collected before the expected peak time to allow adequate estimation of the partial area. — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
d_labes Hero Berlin, Germany, 20120120 11:12 @ Joshua Posting: # 7972 Views: 7,931 

Dear Joshua, dear All! » Can anyone kindly guide on how to do the nonparametric analysis for t_{max} for a two treatment, three period, three sequence (partial replicate) design. Beside Helmut's answer there may be some reasons to do an nonparametric analysis of tmax, among them:
To my knowledge there is no explicit method described for calculating nonparametric CIs in case of a partial replicate design in the literature out there. But from the known literature (known by the small brain of mine, for me as agnostic lazy reader) I would suggest two methods. Method 1: Calculate the differences TR for each subject and do a Wilcoxon signed rank test with these intrasubject differences, including confidence intervals based on that test. Implementation should not so hard in R because wilcox.test() implementing the asymptotic variant is contained in the basic installation, package stats . For exact calculations considering also ties see package exactRankTests . In SAS^{®} itself out of the box there is no implementation of the CIs based on Wilcoxon signed rank test, only the test statistic and pvalue can be acquired from Proc Univariate . Additional expensive software Proc StatXact is needed to do it. Else you have to roll your own. And this may be hard for the uninitiated . But see here.This method of course assumes that no period effects occur (see the expectations of the intrasubject differences below). If period effects are present, the CI's calculated are wider then with taking the period effects into account. But I wouldn't dare too much about that. First: Usually there are no equivalence limits constrained upon tmax. Thus wider intervals are of no consequences. Second: In balanced partial replicate designs (equal number of subjects in the sequence groups) the period effects cancel out. To see this lets look at the intrasubject contrasts and their expectation (assuming only treatment, period and subject effects for the sake of simplicity). Let Y_{ijkl} the tmax value of subject i in sequence j having administered treatment k in period l. Sequence Contrast Expectation Homework: Show that the mean of the expectations over sequences is µ(TR). One subject per sequence . Method 2: Not satisfied with the neglection of period effects? Then borrow the ideas from: Oehrvik J. "Nonparametric Methods in Crossover Trials" Biometrical Journal, 40, Issue 7, pages 771–789, November 1998 to get rid of the period effects. This method (but only the test statistics and elaborated for a 3period crossover with 3 treatments) is also described in: Mary E. Putt and Vernon M. Chinchilli "Nonparametric Approaches to the Analysis of Crossover Studies" Statist. Sci. Volume 19, Number 4 (2004), 712719. which can be found online here. The alGoreRhythm proceeds as following (cook book manner):
The 'mean' function could be the ordinary mean, but more robust (and more in the spirit of nonparametrics) would be the median or, as Oehrvik proposed, the HodgesLehmann point estimator (median of the order statistics, the pairwise Walsh averages of the intrasubject differences). Hope this make sense for you. BTW: Can post some R code upon request. But is a little bit lengthy. — Regards, Detlew 
Joshua Junior India, 20120120 12:09 @ d_labes Posting: # 7976 Views: 6,878 

Dear D_Labes, Thank you so much for the elaborate response . » Method 1: » » Calculate the differences TR for each subject and do a Wilcoxon signed rank test with these intrasubject differences, including confidence intervals based on that test. Could you please explain me on how to calculate the difference for the treatments for each subject when the sequence is in TRR form and then go for the non parametric analysis. Your references were very much useful. Thanks for your consideration on sending the 'R' code also. Thank you. — Joshua. 
d_labes Hero Berlin, Germany, 20120120 12:55 @ Joshua Posting: # 7977 Views: 6,925 

Dear Joshua, » Could you please explain me on how to calculate the difference for the treatments for each subject when the sequence is in TRR form and then go for the non parametric analysis. Should I really explain this? Not many things easier than that. Take the value of tmax from the period where the subject is under treatment T(est) and subtract the mean of the two values where the subject receives R(eference). — Regards, Detlew 
Joshua Junior India, 20120120 13:01 @ d_labes Posting: # 7979 Views: 6,851 

Dear D_Labes, That was a silly question indeed. Anyways thanks a ton for your reply. Was bit confused earlier . Now its clear — Joshua. 
mittyri Senior Russia, 20170103 23:24 @ d_labes Posting: # 16925 Views: 3,801 

Dear Detlew, Could you please enlighten my peasized brain: » Method 1: » Calculate the differences TR for each subject and do a Wilcoxon signed rank test with these intrasubject differences For each subject we got one difference (contrast). How to perform the test using only one value for each subject? Thanks in advance! — Kind regards, Mittyri 
d_labes Hero Berlin, Germany, 20170104 10:21 @ mittyri Posting: # 16927 Views: 3,870 

Dear mittyri, » Could you please enlighten my peasized brain: » » » Method 1: » » Calculate the differences TR for each subject and do a Wilcoxon signed rank test with these intrasubject differences » For each subject we got one difference (contrast). How to perform the test using only one value for each subject? Don't get your point. May be you are confused by my writing » » Calculate the differences TR for each subject Sorry. But I'm not an English man (but only "een Balina, wa"). One difference for each subject, calculated as above described and analyzed by a Wilcoxon signed rank test (nonparametric analogue of a paired ttest) using of course the intrasubject contrasts of all subjects under study. Let's take a hypothetical example, 8 subjects, ISC already calculated:
subj < c(1, 2, 3, 4, 5, 6, 7, 8) tr$estimate is the point estimate of TR, tr$conf.int its 90% confidence interval.exact=F is to avoid warnings cannot compute exact pvalue with ties If you are interested in an exact solution wich can handle ties and zero's see package exactRankTests or coin .— Regards, Detlew 
mittyri Senior Russia, 20170104 14:17 @ d_labes Posting: # 16930 Views: 3,776 

Thank you very much Detlew! I think the problem is not in your writing level, but in my reading/understanding level » If you are interested in an exact solution wich can handle ties and zero's see package exactRankTests or coin .Yes, I tried to do that in coin package, but I need a formula "of the form y ~ x  block where y is a numeric variable, x is a factor and block is an optional factor for stratification" What is x in this case? PS: exactRankTests works fine! — Kind regards, Mittyri 
d_labes Hero Berlin, Germany, 20170104 16:09 @ mittyri Posting: # 16931 Views: 3,746 

Dear mittyri, » I think the problem is not in your writing level, but in my reading/understanding level Don't hide your light under a bushel . » Yes, I tried to do that in coin package, but I need a formula "of the form y ~ x  block where y is a numeric variable, x is a factor and block is an optional factor for stratification" » What is x in this case? Was a long time ago that I dealt with coin. Has definitely a steep learning curve. May be this link helps. — Regards, Detlew 