randombadger
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UK,
2011-05-31 22:26
(4684 d 21:21 ago)

Posting: # 7040
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 Hodges Lehmann CI for a 2 Treat/3 Period Design [Nonparametrics]

Hi,

I have a 3 period, 2 treatment crossover (TRR, RTT) design and I've been asked to construct CI's for Tmax. Since the data is not normal, I plan to construct Hodges Lehmann CI's.

From reading Shein-Chung Chow, Jen-pei Liu. Design and Analysis of Bioavailability and Bioequivalence Studies Third Edition, it would appear I should calculate the pairwise calculations using the following formula:

Dik=1/4(2Yi1k - Yi2k - Yi3k) where i= number of differences & k= number of sequences.

Usually, Dik=Yi1 - Yi2

However, from looking at the SAS online help section, I cannot see a way of stipulating this using PROC NPAR1WAY. Do you have any suggestions?

Thanks!


Edit: Category changed. [Helmut]
Helmut
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Vienna, Austria,
2011-05-31 23:06
(4684 d 20:42 ago)

@ randombadger
Posting: # 7041
Views: 7,549
 

 CI for a 2 Treat/3 Period Design

Dear Randombadger!

To late over here to dig into Chow & Liu. I’m not gifted with [image], but have a look at this thread.

<nitpicking>
The point estimate is calculated according to HL – whereas AFAIK the CI according to Moses. ;-)
</nitpicking>

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d_labes
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Berlin, Germany,
2011-06-01 11:09
(4684 d 08:38 ago)

@ randombadger
Posting: # 7043
Views: 7,669
 

 Hodges Lehmann CI for a 2 Treat/3 Period Design

Dear randombadger,

❝ I have a 3 period, 2 treatment crossover (TRR, RTT) design and I've been asked to construct CI's for Tmax. Since the data is not normal, I plan to construct Hodges Lehmann CI's.


If this is for the EMA forget it. "... A non-parametric analysis is not acceptable. ..." (page 15 of the EMA guidance) :angry:.

❝ From reading Shein-Chung Chow, Jen-pei Liu ...


Where is your problem?
Calculate the Dik as you have given for each subject.
They estimate 0.5*(T-R) in case of the sequence TRR and -0.5*(T-R) in case of sequence RTT within a subject. If you construct the difference of sequence group TRR versus RTT you will get an estimate of T-R and the corresponding CI.

Thus just feed the Dik into Proc NPAR1WAY and use sequence group as grouping factor (aka class):

... Proc Transpose and datastep to calculate Dik ...

Proc NPAR1Way data=DikData HL alpha=0.1;
  class sequence;
  var Dik;
  exact HL;
run;


BTW: The HL option is only available since SAS 9.
You must code the sequences as 1=TRR and 2=RTT to get the right sign.
If you use TRR and RTT as character SAS will calculate R-T and thus you have to change the sign of the point estimate and the CI.

BTW2: This method is applicable for all higher order designs with 2 sequences. Only the formulas for the period differences Dik have to adapted to the design. You can write generalized code if you calculate the so-called basic estimator for each subject, i.e.

basicest = mean(T's) - mean(R's)

multiply by 1/2 and take a negative sign in case that the sequence starts with R to get the Dik.

For more than 2 sequences consider an application/adaption of the method given in

Susan A. Willavize, Elizabeth A. Morgenthien
"Nonparametric confidence intervals for Tmax in sequence-stratified crossover studies"
Pharmaceut. Statist. 2008 Jan-Mar;7(1):9-19

Although this paper describes a 3x3 crossover with 6 sequences the method can easily adapted to higher order designs where the sequence groups can be matched to contain the same combination of period effects.
Not covered is the partial replicate design (TRR/RTR/RRT).

Hope this helps.

Regards,

Detlew
randombadger
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UK,
2011-06-01 21:32
(4683 d 22:15 ago)

@ d_labes
Posting: # 7052
Views: 7,439
 

 Hodges Lehmann CI for a 2 Treat/3 Period Design

Dear d_labes,
Thanks for your advice. Unfortunately, I do not have SAS v9.2 but found the "Calculating the point estimate and confidence interval of Hodges-Lehmann's median using SAS® software" by Lingling Han so will derive the long way.

RB


Edit: Paper linked. [Helmut]
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