Bioequivalence and Bioavailability Forum

Dear Vishal!

❝ In Bio Analytical phase we plotting linear curve aplying weighting factor (e.g 1/A or 1/A2) & Get equation in y=mx+c Format.

If your model is y=mx+c, your weighting factors probably are 1/x or 1/x².

❝ I want to calculate unknown concentration in excel sheet but i dont know how to apply weighting factor in Excelsheet.

OK, a little bit of terminology first. What we are interested in is calibration, which in statistical terms is called “inverse regression”. Most literature is dealing with true “regression”, which after getting the parameters of the model (if it’s linear: slope and intercept), gives predictions of y for a given x.
In inverse regression we want to make predictions of x from y. So once your model’s parameters are established, back-calculation (irrespective of the weighting scheme) is always
x = (y – intercept) / slope.

Example:
model: y = 1.0000 + 2.0000 * x + error
 ┌────┬──────┬───────┬────────┬───────┬────────┬───────┬────────┐
 │ x  │  y   │  w=1  │  bias  │ w=1/x │  bias  │ w=1/x²│  bias  │
 ├────┼──────┼───────┼────────┼───────┼────────┼───────┼────────┤
 │  1 │  3.7 │  1.13 │ 13.0%  │  1.05 │  5.00% │  1.02 │  2.00% │
 │  2 │  5.6 │  2.07 │  3.50% │  2.01 │  0.50% │  1.99 │ -0.50% │
 │  4 │  9.4 │  3.95 │ -1.25% │  3.92 │ -2.00% │  3.93 │ -1.75% │
 │  8 │ 17   │  7.72 │ -3.50% │  7.74 │ -3.25% │  7.82 │ -2.25% │
 │ 16 │ 34   │ 16.1  │  0.63% │ 16.3  │  1.88% │ 16.5  │  3.13% │
 ├────┴──────┼───────┴────────┼───────┴────────┼───────┴────────┤
 │ intercept │ 1.4250 (+42.5%)│ 1.6109 (+61.1%)│ 1.7133 (+71.3%)│
 │     slope │ 2.0185 (+0.93%)│ 1.9876 (-0.62%)│ 1.9537 (-2.31%)│
 └───────────┴────────────────┴────────────────┴────────────────┘

Lesson learned from the example: although unweighted linear regression gives the best estimates of slope and intercept in terms of bias, 1/x² is the best weighting scheme in terms of bias of back-calculated responses (inverse regression).

❝ Let me know if any other software available for this calculation.

Excel is an expensive toy I would only recommend for home-based statistics (remember: you have to validate it – good luck with Excel).
All statistical software packages can do the job.
WinNonlin, Stata, NCSS, Statistica, SPSS, Minitab, Systat, S-Plus, SAS, or my personal favorite R (freeware),…