## CI for Transformed data Unbalanced study [General Statistics]

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

In your case:

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

» 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

Just a reminder: don’t try evaluations in M$-Excel; the

See

http://www.practicalstats.com/xlsstats/excelstats.html

http://www.mis.coventry.ac.uk/~nhunt/pottel.pdf

I would heartly recommend two textbooks:

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

*n*_{1}

and *n*_{2}

, respectively, where *n* = *n*_{1} + *n*_{2}

.In your case:

*n*_{1} = 17

*n*_{2} = 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:

**S-C Chow and J-p Liu**

*Design and Analysis of Bioavailability and Bioequivalence Studies*

Marcel Dekker, New York, 2^{nd}Ed. (2000)

**D Hauschke, VW Steinijans and I Pigeot**

*Bioequivalence Studies in Drug Development*

Wiley, Chichester (2007)

—

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

*Dif-tor heh smusma*🖖_{}Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### Complete thread:

- Confidence Interval for Transformed data Unbalanced study usfda_emea 2007-03-06 14:39 [General Statistics]
- 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 from ISC in FDA approach d_labes 2017-03-05 12:18
- s2wR != mse, FDA != EMA VStus 2017-03-04 21:41
- s2wR != mse, FDA != EMA Helmut 2017-03-06 13:40

- s2wR != mse, FDA != EMA ElMaestro 2017-03-04 19:13

- s2wR != mse, FDA != EMA d_labes 2017-03-04 14:49

- RSABE ⇒ ABEL VStus 2017-03-03 15:31

- RSABE ⇒ ABEL Helmut 2017-03-03 13:34

- LSM limbo Helmut 2014-07-31 02:54

- CI for Transformed data Unbalanced study Helmut 2007-03-07 12:04

- CI for Transformed data Unbalanced studyHelmut 2007-03-06 16:46