Bioequivalence and Bioavailability Forum • The unknown x

The unknown x [RSABE / ABEL]

posted by jdetlor – 2010-09-28 19:22 (5739 d 03:53 ago) – Posting: # 5943
Views: 41,147

Dear d_labes and all

❝ Does anyone know what this ominous x in the code is and where it comes from :confused: .

❝

❝ "[snip] -----

❝ From the dataset IGLM2 (or IOUT2), calculate the following:

❝ IGLM2: pointest=exp(estimate);

❝ x=estimate**2-stderr**2;

❝ boundx=(max((abs(LowerCL)),(abs(UpperCL))))**2;

❝ [/snip] -----".

❝

❝ See on page 5 or 8 of the FDA Progesterone DRAFT guidance.

I saw this and thought I'd post my opinion.

I believe the calculated x value represents the 'true' value of squared difference ((Y_T-Y_R)²)). If we simply square the log difference, we actually have
(Y_T-Y_R)²)) + sigma_d²
(As shown here)

Approximation I from the Howe paper referenced in the Progesterone guidance requires the first moment for each part of the reference-scaled criterion (labeled as x and y in the FDA SAS code), thus the variability must be subtracted to obtain this first moment for the squared difference.

This issue can also be highlighted through a simulation where random full (or partial) replicate results of the log difference are squared. Averaging over all simulations, the estimate of the squared log difference is the squared 'true' log difference (as specified in the input simulation parameters) plus the twice the intra-subject variability. In this case it is the variance of the log difference and not the squared standard error of the log difference because we are simulating the overall distribution of the log difference.

—
J. Detlor

Complete thread:

Reference scaled BE - FDA (and FARTSSIE update) ddubins 2010-04-26 20:28 [RSABE / ABEL]
- Reference scaled ABE - FDA d_labes 2010-04-27 08:58
  - Reference scaled ABE - FDA ElMaestro 2010-04-27 13:39
    - Factor 2 is unbiased d_labes 2010-04-27 14:30
    - Biased bonus from MoM d_labes 2010-05-04 12:10
      - Biased bonus from MoM ElMaestro 2010-05-04 12:54
        
        Mixed MoM d_labes 2010-05-04 14:40
        
        Mixed MoM ElMaestro 2010-05-04 15:08
        
        R and G, CSH and UN d_labes 2010-05-05 10:42
        
        A sailor gets confused ElMaestro 2010-05-05 11:49
        
        Confused V/Z matratzen and tips d_labes 2010-05-05 14:49
        
        superb post! ElMaestro 2010-05-05 21:32
        
        Gambling with UN d_labes 2010-05-06 11:00
        
        Mixed MoM yjlee168 2010-05-05 09:12
- Reference scaled BE - FDA (and FARTSSIE update) KR 2010-04-27 13:14
- Reference scaled BE - EMA Helmut 2010-04-27 14:58
  - Reference scaled BE - EMA ddubins 2010-04-27 17:52
    - Partial replicate design and FDA ABE code d_labes 2010-04-28 09:47
    - Reference scaled BE - EMA Helmut 2010-04-28 14:46
    - Switching - null sWR d_labes 2010-05-04 14:04
- The unknown x d_labes 2010-05-06 13:26
  - The unknown xjdetlor 2010-09-28 17:22
    - Unknown x corrected? d_labes 2010-10-01 12:14
      - Unknown x corrected? Qilex 2016-09-21 12:25
        
        Official unknown x d_labes 2016-09-21 13:22