Bioequivalence and Bioavailability Forum

CI for Transformed data Unbalanced study [General Statistics]

posted by Helmut – Vienna, Austria, 2007-03-07 13:04 (6680 d 10:37 ago) – Posting: # 565
Views: 32,039

Dear USFDA_EMEA!

❝ ❝ Let's call Xt the LSM of the test, and Xr the LSM of the reference (log-scale).

❝

❝ Can you help me with the formula for LSM (I wish to do a manual calculation, for verification purposes) and a brief explaination about why this method is used for unbalanced study?

The calculation is not different from a balanced study.

I’ll give you an example for the reference:
Calculate the (arithmetic) mean of log-transformed values in sequence 1 (if seq 1 = RT from period 1) as
Xr1 = sum ( Xr1 … n1 ) / n1

Calculate the (arithmetic) mean of log-transformed values in sequence 2 (if seq 2 = TR from period 2) as
Xr2 = sum ( Xr1 … n2 ) / n2

LSM for the reference is the arithmetic mean of Xr1 and

Xr2

Xr = ( Xr1 + Xr2 ) / 2 )

The difference Xt – Xr is also called MLE (the Maximum Likelihood Estimator) of the true difference Mu(t) – Mu(r), which is slightly biased according to the degree of ‘unbalancedness’.
A better estimate of the true difference is MVUE (the Minimum Variance Unbiased Estimator), however, its calculation is a little bit tricky (involves the Γ-distribution).
For details see Chow & Liu’s book.

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Helmut Schütz

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Complete thread:

Confidence Interval for Transformed data Unbalanced study usfda_emea 2007-03-06 14:39 [General Statistics]
- CI for Transformed data Unbalanced study Helmut 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 studyHelmut 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

CI for Transformed data Unbalanced study [General Sta­tis­tics]

Complete thread:

CI for Transformed data Unbalanced study [General Statistics]