Bioequivalence and Bioavailability Forum

Dear Pavan!

❝ In another data set the R² values of both linear and quadratic

❝ are equal (ie 0.9954) in this situation,

❝

❝ How we can identify the best fit?

R2 (coefficient of determination) and R (coefficient of correlation) are ineffectual decision tools. To identify the best model first prepare a residual plot (x: calculated value, y: residual = calculated - measured):

• If residuals are not evenly spread around zero (i.e., you see some kind of curve, or a trend) your model might be wrong -> add or remove terms.
  
• If residuals look like a funnel, the assumption of homoscedasticity (independence of variance from the regressor variable) is not fullfilled. Your data are heteroscedastic -> try another weighting scheme.

See one of my presentations (slides 29-32). In the linear fit (w=1/x) we get a curve of residuals → going to quadratic, residuals are spread around zero – but there's still massive hetero­sce­das­ticity → final model: quadratic, w=1/x².

❝ Is there any statistical test to decide which one is the best fit in all

❝ best fits of the linear and quadratic.

In my example you see that correlation is unsuitable; 0.9995 (w=1/x) seems to be better than 0.9994 (w=1/x²). Decision should be based on residuals and back-calculated x-values. The better model may be chosen based on the minimum AIC (Akaike's Information Criterion) which comes up with 149.5 for w=1/x and with 109.9 for w=1/x². Another possibility would be an F-test.

Remember: According to FDA's guideline you have to justify the chosen model during validation. You may remove calibration points (during validation as well as in the study) only as long as the model will not change.