Bioequivalence and Bioavailability Forum

CI for Transformed data Unbalanced study [General Sta­tis­tics]

posted by Helmut  – Vienna, Austria, 2007-03-06 17:46 (7038 d 17:02 ago) – Posting: # 560
Views: 35,165

Dear USFDA_EMEA!

I guess that’s not your real name

❝ I am looking for help on estimation of 90% confidence interval for log transformed data of AUC (0-inf) for a bioequivalence study. This study involved two-way crossover, two-period, two-sequence design with a total of 33 subjects completing the study. Each sequence had Period I TR=16 and RT=17, and in Period II TR=17 and RT=16; thus, total of 33 completed the study.

OK, the number of subjects in each sequence is n1 and n2, respectively, where n = n1 + n2.
In your case:

n1 = 17
n2 = 16
n  = 33

The assignment of sequence 1 to RT follows the literature, but is only a convention (if you want you may call TR sequence 1 as long as you keep this convention through all calculations…)

❝ In order to estimate the 90% confidence interval, can some one help me with the formula and a worked out example for the ease of understanding. OR Guide me to a site where this can be found.

Let’s see. Which formula are you using right now?
If you have something like 1/n in it, for unbalanced data you have to replace it by 1/n1 + 1/n2.

❝ I believe least-squares mean estimate for each formulation needs to be used to form the difference, together with the standard error. However, in lack of exact formula i am seeking the help of experts out there.

Yes, you are on the right track!
Let's call Xt the LSM of the test, and Xr the LSM of the reference (log-scale). sigma-w is the within- (or intra-) subject standard deviation (sqrt(MSE) from your ANOVA), t(1-alpha,n1+n2-2) is the 0.95 quantile of the central t-distribution with n1+n2-2 degrees of freedom. Then the upper/lower 90% confidence limits (log scale) are given by
Xt - Xr ± t(1-alpha,n1+n2-2) × sqrt(MSE) × sqrt[ 1/2 × (1/n1 + (1/n2) ]

Just a reminder: don’t try evaluations in M$-Excel; the t-quantile (TINV) is implemented in a rather queer way: in order to get the correct value for t(1-alpha,n1+n2-2), you would have to use TINV(2 × alpha, n1+n2-2)!
See
http://www.practicalstats.com/xlsstats/excelstats.html
http://www.mis.coventry.ac.uk/~nhunt/pottel.pdf

I would heartly recommend two textbooks:

1. S-C Chow and J-p Liu
   Design and Analysis of Bioavailability and Bioequivalence Studies
   Marcel Dekker, New York, 2^nd Ed. (2000)
   
2. D Hauschke, VW Steinijans and I Pigeot
   Bioequivalence Studies in Drug Development
   Wiley, Chichester (2007)

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


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Complete thread:

• Confidence Interval for Transformed data Unbalanced study usfda_emea 2007-03-06 14:39 
  • CI for Transformed data Unbalanced studyHelmut 2007-03-06 16:46
    • CI for Transformed data Unbalanced study drshiv 2007-03-06 18:49
    • CI for Transformed data Unbalanced study usfda_emea 2007-03-07 06:21
      • CI for Transformed data Unbalanced study Helmut 2007-03-07 12:04
        • CI for Transformed data Unbalanced study usfda_emea 2007-03-07 12:34
        • CI for Transformed data Unbalanced study Ohlbe 2014-07-30 15:04
          • LSM limbo Helmut 2014-07-31 02:54
            • LSM limbo Ohlbe 2014-07-31 09:47
            • 90% CI limbo VStus 2017-03-01 14:07
              • RSABE ⇒ ABEL Helmut 2017-03-03 13:34
                • RSABE ⇒ ABEL VStus 2017-03-03 15:31
                  • s2wR != mse, FDA != EMA d_labes 2017-03-04 14:49
                    • s2wR != mse, FDA != EMA ElMaestro 2017-03-04 19:13
                      • s2wR from ISC in FDA approach d_labes 2017-03-05 12:18
                        • s2wR from ISC in FDA approach ElMaestro 2017-03-05 13:50
                    • s2wR != mse, FDA != EMA VStus 2017-03-04 21:41
                      • s2wR != mse, FDA != EMA Helmut 2017-03-06 13:40