Bioequivalence and Bioavailability Forum

Hi Ken,

❝ […] I have gone through the paper on Weighted least square linear regression (Almeida et al., 2002)…

That’s an excellent paper, IMHO.

❝ … and example plus calculation given by Helmut.

❝

❝ I would like to know how the values of 1/x and 1/x² were calculated. The x is the input as given in the first column (1,2,4,8,16) ?? I could not get the data as presented in the table.

x is the independent variable (in bioanalytics concentration) and y the dependent (observed) one – in BA the response (analyte/IS-ratio, peak height/area, whatsoever). The weights are not given in the table, they are simply 1/x or 1/x². Sorry for the confusion caused. The table entries are the back-calculated x-values based on the intercept/slope of the respective models given below. All calculations were done in full precision, therefore you will see some slight differences.
One example: With a response of 3.7 back-calculated values are (3.7-1.4250)/2.0185=1.13 (unweighted), (3.7-1.6109)/1.9876=1.05 (weight=1/x), and (3.7-1.7133)/1.9537=1.02 (w=1/x²). Bias is given as % relative error or 100(estimated-true)/true, e.g., 100×(1.13-1)/1=+13.0%.

❝ Kindly let me know the program in R-software that can be used to perform this calculation.

I’m not in the office right now; I will post some tomorrow.

❝ […] Also sorry to Helmut for using his example without permission.

No problem. All my posts are open-source .