Joshua
☆

India,
2012-01-17 07:59
(4084 d 21:04 ago)

Posting: # 7953
Views: 13,116

## Tmax in Partial Replicate Design [Nonparametrics]

Dear All,

Greetings

Can anyone kindly guide on how to do the non-parametric analysis for tmax for a two treatment, three period, three sequence (partial replicate) design.

Regards,
Joshua.

Edit: Category changed. [Helmut]

Joshua.
Helmut
★★★

Vienna, Austria,
2012-01-17 12:34
(4084 d 16:30 ago)

@ Joshua
Posting: # 7954
Views: 12,019

## Good question!

Dear Joshua!

❝ Can anyone kindly guide on how to do the non-parametric analysis for tmax for a two treatment, three period, three sequence (partial replicate) design.

Good point. Since tmax is not required for the FDA, I guess you are referring to the EMA’s GL?

A statistical evaluation of tmax 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 tmax and its variability between test and reference product.

The EMA hates nonparametrics – which is manifested in the first sentence. ‘No apparent difference in median tmax 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.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
Joshua
☆

India,
2012-01-20 12:54
(4081 d 16:09 ago)

@ Helmut
Posting: # 7974
Views: 11,852

## Good question!

Dear Helmut,

Thank you so much for your reply. I was actually referring to the USFDA.

Joshua.
Helmut
★★★

Vienna, Austria,
2012-01-20 13:56
(4081 d 15:08 ago)

@ Joshua
Posting: # 7978
Views: 11,873

## Early exposure (+scaling?)

Dear Joshua!

❝ Thank you so much for your reply. I was actually referring to the USFDA.

IMHO FDA never asked for tmax. 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.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
d_labes
★★★

Berlin, Germany,
2012-01-20 12:12
(4081 d 16:52 ago)

@ Joshua
Posting: # 7972
Views: 13,211

## Tmax in Partial replicate design

Dear Joshua, dear All!

❝ Can anyone kindly guide on how to do the non-parametric analysis for tmax for a two treatment, three period, three sequence (partial replicate) design.

Beside Helmut's answer there may be some reasons to do an non-parametric analysis of tmax, among them:
• The world is sometimes greater then North America and Europe
(Myself got a deficiency letter from a small country in Asia requesting a p-value for differences in tmax)
• Not satisfied with the in the discussion section of the report
• Scientific credibility
• Fun in developing/programming ambitious analysis methods

To my knowledge there is no explicit method described for calculating non-parametric 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 T-R for each subject and do a Wilcoxon signed rank test with these intra-subject 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 p-value 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 intra-subject 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 intra-subject contrasts and their expectation (assuming only treatment, period and subject effects for the sake of simplicity).
Let Yijkl the tmax value of subject i in sequence j having administered treatment k in period l.
Sequence   Contrast             Expectation 1  TRR   YiT1-0.5(YiR2+YiR3)  µ(T-R) + p1-0.5(p2+p3) 2  RTR   YiT2-0.5(YiR1+YiR3)  µ(T-R) + p2-0.5(p1+p3) 3  RRT   YiT3-0.5(YiR1+YiR2)  µ(T-R) + p3-0.5(p1+p3) (index j omitted)
Homework: Show that the mean of the expectations over sequences is µ(T-R). 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 3-period 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), 712-719.

which can be found online here.

The al-Gore-Rhythm proceeds as following (cook book manner):
1. Calculate a 'mean' function for the values in each period. This function has expectation pl+µ where µ is the mean over treatment effects, pl is the period effect of period l. 'Align' the tmax values by subtracting the corresponding period 'mean'. Note that the period effects vanish by this operation but the aligned values are lowered by µ.
2. Use the aligned values to calculate the intra-subject contrasts to estimate µ(T-R) as above. Note that µ cancels out by this step.
3. Use the intra-subject contrasts to perform a Wilcoxon signed rank test with calculation of CIs based on it.
This algorithm and related ones are sometimes called Aligned-rank test.
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 Hodges-Lehmann point estimator (median of the order statistics, the pairwise Walsh averages of the intra-subject differences).

Hope this make sense for you.
BTW: Can post some R code upon request. But is a little bit lengthy.

Regards,

Detlew
Joshua
☆

India,
2012-01-20 13:09
(4081 d 15:54 ago)

@ d_labes
Posting: # 7976
Views: 11,864

## Tmax in Partial replicate design

Dear D_Labes,

Thank you so much for the elaborate response .

Method 1:

❝ Calculate the differences T-R for each subject and do a Wilcoxon signed rank test with these intra-subject 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
★★★

Berlin, Germany,
2012-01-20 13:55
(4081 d 15:08 ago)

@ Joshua
Posting: # 7977
Views: 11,853

## Intra-subject contrast (difference)

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
☆

India,
2012-01-20 14:01
(4081 d 15:03 ago)

@ d_labes
Posting: # 7979
Views: 11,826

## Intra-subject contrast (difference)

Dear D_Labes,

That was a silly question indeed. Anyways thanks a ton for your reply. Was bit confused earlier . Now its clear

Joshua.
Astea
★★

Russia,
2023-02-14 19:44
(38 d 09:20 ago)

@ d_labes
Posting: # 23465
Views: 320

## Wilcoxon for 2x2x4. "Not many things easier than that"?

Dear Smart People!
Could you please advise me how to extend Wilcoxon test for 4-period replicate study properly?
1. Do we need to use means of two periods of T's and R's? If yes, why do we need arithmetic means, why don't we need neither medians nor harmonic means nor so on?
2. How does Phoenix perform this calculation in Crossover object? According to guideline it is used only for 2x2 design, but it also works for 2x2x4 somehow.
Below is my suggested code (first two periods coincide with the example from the post). For this data Phoenix gave p=0.6863 - does it make any sense?
 data<-c("Subject Sequence P1 P2 P3 P4 1 TRTR 2.0 2.0 3.0 3.0 2 RTRT 1.5 3.0 1.5 3.0 3 TRTR 2.0 2.0 2.0 3.0 4 RTRT 2.0 2.0 1.5 2.0 5 TRTR 3.0 2.0 2.0 1.5 6 RTRT 3.0 2.0 2.0 3.0 7 TRTR 1.5 2.0 1.5 2.0 8 RTRT 3.0 2.0 2.0 2.0 9 TRTR 2.0 3.0 1.5 3.0 10 RTRT 2.0 1.5 2.0 2.0 11 TRTR 1.5 2.0 2.0 2.0 12 RTRT 2.0 3.0 3.0 2.0 13 TRTR 1.5 3.0 3.0 2.0 14 RTRT 3.0 3.0 1.5 2.0") tc <- textConnection(data) PKt  <- read.table(tc, header=TRUE, strip.white=TRUE, as.is=TRUE) close(tc)   PKt$pdiff <- PKt$P1+PKt$P3-PKt$P2-PKt$P4 library(coin) PKt$Sequence <- as.factor(PKt$Sequence) t1 <- wilcox_test(pdiff ~ Sequence, data=PKt, conf.int=TRUE, conf.level=0.9, distribution="exact") print(t1) #p=0.4353 t2 <- wilcox_test(pdiff ~ Sequence, data=PKt, conf.int=TRUE, conf.level=0.9, distribution="asymptotic") print(t2) #p=0.3983  "Being in minority, even a minority of one, did not make you mad" mittyri ★★ Russia, 2017-01-04 00:24 (2271 d 04:39 ago) @ d_labes Posting: # 16925 Views: 8,735 ## Tmax in Partial replicate design Dear Detlew, Could you please enlighten my pea-sized brain: Method 1: ❝ Calculate the differences T-R for each subject and do a Wilcoxon signed rank test with these intra-subject differences For each subject we got one difference (contrast). How to perform the test using only one value for each subject? Thanks in advance! Kind regards, Mittyri d_labes ★★★ Berlin, Germany, 2017-01-04 11:21 (2270 d 17:43 ago) @ mittyri Posting: # 16927 Views: 8,828 ## ISC and Wilcoxon signed rank test Dear mittyri, ❝ Could you please enlighten my pea-sized brain: ❝ ❝ Method 1: ❝ ❝ Calculate the differences T-R for each subject and do a Wilcoxon signed rank test with these intra-subject differences ❝ For each subject we got one difference (contrast). How to perform the test using only one value for each subject? Don't get your point. May be you are confused by my writing ❝ ❝ Calculate the differences T-R for each subject Sorry. But I'm not an English man (but only "een Balina, wa"). One difference for each subject, calculated as above described and analyzed by a Wilcoxon signed rank test (non-parametric analogue of a paired t-test) using of course the intra-subject contrasts of all subjects under study. Let's take a hypothetical example, 8 subjects, ISC already calculated:  subj <- c(1, 2, 3, 4, 5, 6, 7, 8) isc <- c(0, 0.5, -0.5, 0.25, 0.0, 1.0, -0.25, -1.0) tr <- wilcox.test(isc, conf.int = T, conf.level = 0.9, exact=F) tr$estimate is the point estimate of T-R, tr\$conf.int its 90% confidence interval.

exact=F is to avoid warnings
cannot compute exact p-value with ties cannot compute exact p-value with zeroes

If you are interested in an exact solution wich can handle ties and zero's see package exactRankTests or coin.

Regards,

Detlew
mittyri
★★

Russia,
2017-01-04 15:17
(2270 d 13:46 ago)

@ d_labes
Posting: # 16930
Views: 8,932

## ISC and Wilcoxon signed rank test in coin package

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
★★★

Berlin, Germany,
2017-01-04 17:09
(2270 d 11:55 ago)

@ mittyri
Posting: # 16931
Views: 8,870

## ISC and Wilcoxon signed rank test in coin package

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.

Regards,

Detlew
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