Bioequivalence and Bioavailability Forum

Dear all,

just put in my two cents.

❝ Deming regression is of limited practical use because it requires a priori knowledge of the ratio of the variances, which is rarely available without replicate measurements by each method.

If one is seriously interested in comparing methods I don’t see why replicates should not be measured. Theoretically the ideal weighting in regression is 1/σ². The commonly applied 1/x, 1/y, are only lousy compromises if replicates are not available.

Panos Macheras told me that he once published a paper about Deming’s regression where the variance-ratio is estimated by the following approach:

• Run Deming’s regressions for an arbitrary – but wide – range of variance-ratios (from very low to very high). The theoretical limits would be OLS y|x and x|y – where the entire error lies either in y or x, respectively.
  
• Calculate the area between the confidence bands around the regressions.
  
• The model with the minimum area gives the ‘best’ estimate of the variance-ratio.

This approach does not require replicates.

❝ Deming regression can be used as a second step in the case where replicate measurements are made. The first step is to use the replicates to estimate the method-specific residual variances, and the second is Deming regression using the mean of replicates to estimate the relationship between methods

I don’t like this idea. Working with means would decrease the degrees of freedom of the model. If one has a priori specifications (e.g., intercept n.s. ≠ 0 and/or slope n.s. ≠ 1) with this approach the chance to pass the method comparison would increase.

❝ As far as I understand Bablok approach is robust (as non-parametric) but sensitive to the non-linearity.

Yes. Although I’m a fan-boy of non-parametrics here I would be conservative. If there are outliers (i.e., methods do not agree at certain values) IMHO, this fact needs to be explored rather than ignored.