libaiyi
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China,
2018-06-19 06:15
(890 d 10:30 ago)

Posting: # 18918
Views: 5,133
 

 Test statistic about Tmax [Nonparametrics]

Dears,

I have one question about Tmax. In a 2*2 cross-over BE study. If we want to test the Tmax betweent different treatments. Which test statistic should be used? Wilcoxon signed rank test or Wilcoxon rank sum test?

And it is also make me puzzled that the results from SAS and Winnonlin are different (Both are Hodges-Lehmann). Would you please help me to figure the reason out? Many thanks.


Edit: Category changed; see also this post #1[Helmut]
Helmut
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Vienna, Austria,
2018-06-19 09:54
(890 d 06:52 ago)

@ libaiyi
Posting: # 18920
Views: 4,724
 

 Wilcoxon signed rank test

Hi libaiyi,

» […] In a 2*2 cross-over BE study. If we want to test the Tmax betweent different treatments. Which test statistic should be used? Wilcoxon signed rank test or Wilcoxon rank sum test?

The former (aka Wilcoxon T test).
The latter (aka Mann–Whitney U test, Mann–Whitney–Wilcoxon test, Wilcoxon–Mann–Whitney test) is for independent samples (parallel design).

» And it is also make me puzzled that the results from SAS and Winnonlin are different (Both are Hodges-Lehmann).

The test gives you only a p value.1 The point estimate (Hodges-Lehmann: x̃ of Walsh averages) and its CI (Moses) are other pieces of magic.2

» Would you please help me to figure the reason out?

Try Detlew’s example with tied data:
subject period sequence treatment  t
  1       1       TR       T      2.0
  1       2       TR       R      2.0
  2       1       RT       R      1.5
  2       2       RT       T      3.0
  3       1       TR       T      2.0
  3       2       TR       R      2.0
  4       1       RT       R      2.0
  4       2       RT       T      2.0
  5       1       TR       T      3.0
  5       2       TR       R      2.0
  6       1       RT       R      3.0
  6       2       RT       T      2.0
  7       1       TR       T      1.5
  7       2       TR       R      2.0
  8       1       RT       R      3.0
  8       2       RT       T      2.0
  9       1       TR       T      2.0
  9       2       TR       R      3.0
 10       1       RT       R      2.0
 10       2       RT       T      1.5
 11       1       TR       T      1.5
 11       2       TR       R      2.0
 12       1       RT       R      2.0
 12       2       RT       T      3.0
 13       1       TR       T      1.5
 13       2       TR       R      3.0
 14       1       RT       R      3.0
 14       2       RT       T      3.0


In Phoenix 8.0 / Crossover object:

T–R    : -0.25
~90% CI: -0.75, +0.25

In R / package coin with some additional coding:

  HL exact       : -0.25  interval midpoint: -0.25
  HL asymptotic  : -0.25  interval midpoint: -0.25
Confidence intervals (CI)
  Exact (90.21%) : -0.75, +0.25
Asymptotic (≥90%): -0.75, +0.25

Both agree with what Detlew got in SAS’ NPAR1WAY (after dividing by two!).
Which setup are you using in SAS?


  1. Koch GG. The Use of None-Parametric Methods in the Statistical Analysis of the Two-Period Change-Over Design. Biometrics. 1972;28(2):577-84. doi:10.2307/2556170.
  2. Hauschke D, Steinijans VW, Diletti E. A distribution-free procedure for the statistical analysis of bioequivalence studies. Int J Clin Pharm Ther Toxicol. 1990;28(2):72–8. PMID 2307548.

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d_labes
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Berlin, Germany,
2018-06-19 11:25
(890 d 05:20 ago)

(edited by d_labes on 2018-06-19 11:36)
@ Helmut
Posting: # 18921
Views: 4,684
 

 Wilcoxon-Mann-Whitney!

Dear Helmut,

» » […] In a 2*2 cross-over BE study. If we want to test the Tmax betweent different treatments. Which test statistic should be used? Wilcoxon signed rank test or Wilcoxon rank sum test?
»
» The former (aka Wilcoxon T test).
» The latter (aka Mann–Whitney U test, Mann–Whitney–Wilcoxon test, Wilcoxon–Mann–Whitney test) is for independent samples (parallel design).

Here you err!

The Wilcoxon signed rank test1 can only applied if you neglect period effects. It tests the within-subject treatment differences against zero and is therefore a non-parametric analogon of the paired Student t-test.

To account for period effects you have to apply the Wilcoxon–Mann–Whitney test2 with sequence as grouping factor if you evaluate a 2x2 cross-over design. This test is sometimes also called Hauschke test. Guess why :cool:.
In case of a parallel design the grouping factor is of course the treatment, as you correctly stated.

The cited example you quote uses the correct test.
And I suppose Phoenix 8.0 / Crossover object does the same


1 V. W. Steinijans and E. Diletti
"Statistical Analysis of Bioavailability Studies: Parametric and Nonparametric Confidence Intervals"
Eur J Clin Pharmacol (1983) 24:127-136

2 D. HAUSCHKE, V. W. STEINIJANS and E. DILETTI
"A distribution-free procedure for the statistical analysis of bioequivalence studies"
International Journal of Clinical Pharmacology, Therapy and Toxicology,
Vol. 28 No. 2 -1990 (72-78) / Vol.30, Suppl. No. 1 -1992 (pp,S37-43)

Regards,

Detlew
Helmut
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Vienna, Austria,
2018-06-19 14:38
(890 d 02:07 ago)

@ d_labes
Posting: # 18922
Views: 4,523
 

 Wilcoxon-Mann-Whitney!

Dear Detlew,

» Here you err!

Not the first and not the last time. I stand corrected!

» To account for period effects you have to apply the Wilcoxon–Mann–Whitney test with sequence as grouping factor if you evaluate a 2x2 cross-over design. This test is sometimes also called Hauschke test. Guess why :cool:.

Right. Part of the title of Steinijans & Hauschke* says it all. ;-)
  • Unlike the nonparametric confidence interval according to Steinijans and Diletti [1983], the non­parametric approach by Hauschke et al. [1990] is no longer limited by the assumption of equal period effects. Although, according to our vast experience, unequal period effects are extremely rare, they may result in a biased point estimate and an unnecessarily wide confidence interval if the procedure assuming equal period effects is applied incorrectly. To avoid this, the nonparametric procedure by Steinijans and Diletti [1983] should generally be replaced by that of Hauschke et al. [1990].



  • Steinijans VW, Hauschke D. Update on the statistical analysis of bioequivalence studies. Int J Clin Pharm Ther Toxicol. 1990;28(3):105–10. PMID 2318545.
    Int J Clin Pharmacol Ther Toxicol. 1992;30(Suppl 1):S45-50. PMID 1601531.

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Helmut Schütz
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d_labes
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Berlin, Germany,
2018-06-19 15:10
(890 d 01:36 ago)

(edited by d_labes on 2018-06-19 15:22)
@ Helmut
Posting: # 18923
Views: 4,480
 

 Wilcoxon-Mann-Whitney PMID

Dear Helmut,

» » Here you err!
»
» Not the first and not the last time...

Seems so :-D.
The first PMID of the reference directs to another paper.
Last number odd in the link.
(link=https://www.ncbi.nlm.nih.gov/pubmed/23185451)PMID 2318545(/link).


THX! Corrected in my OP. [Helmut]

Regards,

Detlew
libaiyi
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China,
2018-06-20 06:20
(889 d 10:26 ago)

@ Helmut
Posting: # 18927
Views: 4,428
 

 choice of result

Hi, Helmut

Thanks for the response. I find out that the output of Winnonlin is the same as SAS when I consider the p value of Kruskal-Wallis test in SAS output. But I also find out that the p value in R result is the same as the p value in exact test in SAS output. So, which p value should I take as the decision standard for the test?

Thanks in advance. :flower:
Helmut
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Vienna, Austria,
2018-06-20 09:24
(889 d 07:22 ago)

@ libaiyi
Posting: # 18928
Views: 4,465
 

 No significance testing in BE

Hi libaiyi,

no idea about SAS.

Phoenix:
Test                   T_stat    p_value 
Treatment|(SEQ1=SEQ2)    46    0.39727171


My R-code:
Expectation   : 52.5
Statistic     : 46
Exact         : Z = -0.84650388, p-value = 0.41491841
Asymptotic    : Z = -0.84650388, p-value = 0.39727171


» So, which p value should I take as the decision standard for the test?

Generally I prefer an exact test over an asymptotic one.
Significance testing is of historic interest in BE only (was abandoned decades ago). You should pre-specify an interval which you consider to be not relevant from a clinical perspective. For tmax of a pain-killer it might be just ±20 minutes but for a modified release product which is only used in steady state even a couple of hours. At the end assess whether the CI of the difference lies within the interval as usual.

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