Bioequivalence and Bioavailability Forum

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) .

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

Where is your problem?
Calculate the D_ik 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 D_ik 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 D_ik 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 D_ik.

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.