varinderkb
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2009-12-15 16:44
(6031 d 21:43 ago)

Posting: # 4480
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 Weibull [Dissolution / BCS / IVIVC]

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hi
please anyone can guide me how to calculate alpha and beta parameters of Weibull from a given in-vitro data using Excel.

Edit: Category changed. [Helmut]
 
Helmut
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Vienna, Austria,
2009-12-15 20:54
(6031 d 17:33 ago)

@ varinderkb
Posting: # 4481
Views: 8,210
 

 Weibull

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Dear Varinder!
  • Time points in column A
  • Cumulative % dissolved in Column B
  • C1: =1-EXP(-F$1*A1^G$1), copy the formula down to all cells containing values in column A (these are the estimated values of the cumulative Weibull-distribution)
  • D1: =(C1-B1)^2, copy the formula down to all cells containing values in column A (these are the squared residuals)
  • E1: =SUM(D:D) (this is the sum of squared residuals we want to minimize)
  • F1: 1 (starting value for alpha)
  • G1: 1 (starting value for beta)
  • Fire up the Solver Add-in
  • Set Cell: $E$1
  • Equal To: [•] Min
  • By Changing Target Cells: $F$1:$G$1
  • Subject to the Constraints: Remove all constraints (if any).
  • Options...
  • [X] Assume Non-Negative
  • OK
  • Solve
Remark: alpha and beta of the cumulative Weibull-distribution are positive real numbers (>0), therefore the constraints.

Example (Excel 2000 on XP Pro SP3 and Vista Pro SP2):
  t    Qc     fit
  0    0      0
  0.5  0.209  0.204
  1    0.536  0.547
  1.5  0.818  0.806
  2    0.933  0.936
  2.5  0.974  0.983
gives alpha 0.7908, beta 1.796, and an SSQ of 0.000388691.
BTW, Excel is a terrible piece of software - especially the solver-routine. Consider opting for real software.
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varinderkb
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2009-12-16 15:06
(6030 d 23:21 ago)

@ Helmut
Posting: # 4482
Views: 8,257
 

 Weibull

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Hi
Thanks for quick and kind response

with regards
Varinder Kumar :-)
 
ElMaestro
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Denmark,
2009-12-16 17:25
(6030 d 21:03 ago)

@ Helmut
Posting: # 4483
Views: 8,188
 

 Weibull

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Hi HS,

"Since neither measured nor estimated dissolution percentage should assume negative values there might be a constraint on the error distribution that speaks against using minimisation of sums of squares for estimation of alpha and beta. The applicant should qualify...." :-P:-P:-P

OK, sorry, could not help it. I am unfortunately too unfamiliar with dissolution (or the Excel solver) but do you have a ref. to a work using the equation you have fitted the data to?

❝ BTW, Excel is (...) real software.


Yeah, I love it too.

Merry Xmas.
EM.
 
Helmut
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Vienna, Austria,
2009-12-16 19:13
(6030 d 19:15 ago)

@ ElMaestro
Posting: # 4484
Views: 8,273
 

 Weibull & and beyond

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Dear ElMaestro!

❝ "Since neither measured nor estimated dissolution percentage should assume negative values there might be a constraint on the error distribution that speaks against using minimisation of sums of squares for estimation of alpha and beta. The applicant should qualify...." :-P:-P:-P


Wonderful! Do you quote from your memory? The style sounds familiar to me (aka ‘old sock’). Next time I fit PK-data to a multiexponential model, I will not state that I use constraints (≥0 for coefficients and ≤0 for exponents). ;-)

❝ I am unfortunately too unfamiliar with dissolution (or the Excel solver) but do you have a ref. to a work using the equation you have fitted the data to?


The equation is the CDF of the Weibull-distribution.
Other empirical models in dissolution are the CDF of the exponential (\(\small{y=1-\exp (-\alpha\cdot x)}\), where \(\small{\alpha >0}\)), Higuchi (\(\small{y=\alpha\cdot \sqrt{x}}\)), Korsmeyer–Peppas (\(\small{y=\alpha\cdot \exp (1/\beta)}\)), …
Reference? Hhm, dissolution is not my cup of tea. But have a look at Dissolution Technologies (back issues).

❝ ❝ BTW, Excel is (...) real software.


Yes, Sir!

I’m also unfamiliar with Excel’s solver…
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ElMaestro
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Denmark,
2009-12-16 19:48
(6030 d 18:40 ago)

@ Helmut
Posting: # 4485
Views: 8,110
 

 the lingo

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Dear HS,

❝ Wonderful! Do you quote from your memory? The style sounds familiar (...)


You know I speak Flemish and I talk dirty. In addition, I have over the years picked up a little bit of the regulatory syntax. This was just an improvisation.

I think I will need to read some more about dissolution. It seems it is becoming more and more important in a quantitative way, due to biowaivers and ivivc's. To me all this is pretty obscure. But now I am going off topic, so will stop here and start reading.

EM.
 
Helmut
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Vienna, Austria,
2009-12-16 20:10
(6030 d 18:18 ago)

@ ElMaestro
Posting: # 4486
Views: 8,097
 

 Dissolution

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Dear ElMaestro!

❝ To me all this is pretty obscure.


Dazed and confused? If you have some spare money (haha) consider attending one of Jean-Michel’s workshops.
—
Dif-tor heh smusma 🖖🏼 Довге життя Україна! [image]
Helmut Schütz
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