Bioequivalence and Bioavailability Forum • Misunderstanding

Misunderstanding [🇷 for BE/BA]

posted by Helmut – Vienna, Austria, 2016-11-09 16:29 (3494 d 02:42 ago) – Posting: # 16793
Views: 27,091

Dear Ben,

❝ We should bear in mind that when we back transform to the original scale we end up with asymmetry with respect to +/-.

This is exactly the idea – reflecting the distributional properties of the data:

[image]

length of upper / lower whiskers:

0.826 0.950 0.859 0.730 0.528 0.411 0.329 0.273 0.228 0.179 0.111  0.0566

0.607 0.735 0.693 0.607 0.454 0.358 0.286 0.232 0.185 0.137 0.0758 0.0337

❝ Therefore, it is IMHO not appropriate to do +/- back transformed standard deviation. Symmetry is however obtained with respect to * and /. So the error bars should be such that lower end = gMean / gSD and upper end = gMean * gSD, where gSD = exp(standard deviation from log-transformed values).

❝ [Mathematical rationale: exp(m - s) = exp(m)/exp(s) = gMean / gSD and exp(m + s) = exp(m) * exp(s) = gMean * gSD), where m and s are mean and sd on log scale, respectively]

Can’t agree more. I did not express myself clearly. Blue your method and red the one* I meant. Of course they are equivalent.

x <- c(1, 2, 4) log.x <- log(x) mean.log <- mean(log.x) SD.log <- sd(log.x) gMean <- exp(mean.log) gSD <- exp(SD.log) BL.lohi <- c(gMean / gSD, gMean * gSD) HS.lohi <- exp(mean.log + c(-1, +1) * SD.log) unique(BL.lohi == HS.lohi) # [1] TRUE

Also used in Phoenix/WinNonlin.
──────────────
Recipe for novices setting up the plot. I assume a table with at least the following columns: subject, scheduled, time, concentration. It is important to have a column with scheduled times. You must not use the actual times.
Descriptive Stats:
  Mappings
    concentration ⦿ Summary
    scheduled ⦿ Sort
  Options
    ☑ Number of SD     1
Execute. Results > Output Data > Results [right click] Send To > Plotting > XY Plot
XY Plot:
Mappings
    scheduled ⦿ X
    GeometricMean ⦿ Y
    GEOLowerSD Error Bars ⦿ Lower
    GEOUpperSD Error Bars ⦿ Upper
Options
    Graphs > GeometricMean vs scheduled > Error Bars > Content
    Change the User Calculation Type Relative to Absolute

—
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Helmut Schütz

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Complete thread:

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        Geometric means ± SD nobody 2016-01-27 15:20
        
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        Money makes the world go ’round nobody 2016-01-27 16:31
        
        Fixed or random effect kumarnaidu 2016-11-04 14:05
        
        PROC GLM fixes Subject mittyri 2016-11-04 23:00
        
        PROC GLM fixes Subject kumarnaidu 2016-11-05 05:22
        
        PROC GLM fixes Subject mittyri 2016-11-05 10:13
        
        PROC GLM fixes Subject kumarnaidu 2016-11-07 06:24
        
        PROC GLM fixes Subject mittyri 2016-11-07 11:57
        
        PROC GLM fixes Subject kumarnaidu 2016-11-07 12:42
        
        Geometric means ± SD Ben 2016-11-08 21:20
        
        MisunderstandingHelmut 2016-11-09 15:29
        
        Misunderstanding Ben 2016-11-14 19:40
        
        RTFM Helmut 2016-11-14 21:50