Bioequivalence and Bioavailability Forum

CV vs. sigma [RSABE / ABEL]

posted by Helmut  – Vienna, Austria, 2010-11-09 21:11 (5709 d 18:03 ago) – Posting: # 6125
Views: 17,638

Dear Angus!

❝ The reason for the confusion is we do not know the calculation that is being made by Pharsight. Consequently we do not know conceptually it is incorrect or if there is an error in it.

1. Right.
   
2. I would say both.
   
3. Five more hours have passed. I'm still waiting for a response at the Extranet (it's a bright day across the pond, isn't it?)...

❝ I had difficulty getting the same number you got so I must not be interpreting your equation correctly.

❝   exp(+log(1.25)*sigmaRef/0.25)

❝

❝ For sigma = 0.30 I get 1.3221 for above calculation (when exp(+log(1.25) is used. Am I misunderstanding the parenthesis used? [...]

Don’t know, but let's see how to get this right. I didn’t check your parentheses business, but mainly you mixed up CVWR with sigmaWR, in other words you plugged in CVWR, whereas a conversion to sigmaWR is required first. See one of my lectures (slides 34pp): sigmaWR=sqrt(ln(CVWR²+1)).
For example (including all intermediate steps):
CVWR: 0.30
CVWR²: 0.09
CVWR²+1: 1.09
ln(CVWR²+1): 0.86178
sqrt(ln(CVWR²+1)): 0.29356 (Hurrah, that’s sigma_WR!)
ln(1.25): 0.22314 (Aha – the usual suspect: upper limit in log-scale.)
ln(1.25)*sigmaWR/0.25: 0.26202 (Scaled limit in log scale; note FDA’s magic 0.25…)
exp(±ln(1.25)*sigmaWR/0.25): 0.7695-1.2996 (Welcome back to the linear world.)

A word about the magic 0.25 in FDA’s method. Note that this value does not correspond to a theoretical start of switching of CVWR 25%, but corresponds to a CVWR=sqrt(exp(0.25²)-1)) 25.396% (sigmaWR 0.25). That’s the CV where the dashed lines in my plots intersect the conventional limits. If I recall it right, this value was chosen for convenience (if you are masochistic, follow the links here). Haidar et al. suggested 0.25 in their paper without any justification.

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


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Science Quotes

Complete thread:

• reference scaled bioequivalence AngusMcLean 2010-11-07 14:55 
  • reference scaled bioequivalence Helmut 2010-11-07 16:08
    • reference scaled bioequivalence AngusMcLean 2010-11-08 22:22
      • RSABE: FDA vs. EMA Helmut 2010-11-09 02:13
        • Farside CV relabelling d_labes 2010-11-09 10:42
          • Farside CV relabelling Helmut 2010-11-09 15:10
            • Laszlo's constant d_labes 2010-11-09 16:46
          • Farside CV relabelling AngusMcLean 2010-11-09 17:12
            • Widened calculations step by step d_labes 2010-11-09 19:48
              • Widened calculations step by step AngusMcLean 2010-11-09 20:46
                • ln vs. log Helmut 2010-11-09 22:07
                • ln on US calculators! d_labes 2010-11-10 08:31
                  • Spreadsheet addiction Helmut 2010-11-10 13:42
            • CV vs. sigmaHelmut 2010-11-09 20:11
              • CV vs. sigma AngusMcLean 2010-11-09 20:57
                • log(e) vs. log(10) Helmut 2010-11-09 21:31
              • slide 15 of the Pharsight presentation SDavis 2010-11-19 18:02
        • one more ref. for the ref. list of RSABE yjlee168 2010-11-30 07:16
          • Great! Helmut 2010-11-30 15:44