Hello to all.

Haven’t seen this discussed here before, so perhaps others will find helpful too.

- There are two biomarkers A and B.
- They are related (one comes from the other) and address the same underlying physiology.
- They are metabolized differently such that patient characteristics (e.g., weight, kidney function) affect the relationship between the concentration of A and concentration of B.
- Studies have been done that show you can convert between A and B using formulas fit with multiple OLS regression where A was regressed on B + covariates.

We want to test one of the formulas in an independent sample and to recalibrate/extend it as necessary.

The issue that seems to have been ignored in numerous studies that have developed and validated these formulas is that there is measurement error in observed A and predicted A (from B + covariates), violating an assumption of OLS. If we evaluate one of these formulas with OLS on our sample I suspect the slope will be underestimated. Methods like Bland-Altman analysis, Deming regression, and Passing-Bablok regression address this.We can use Deming or Passing-Bablok regression to estimate the calibration slope/intercept of observed A vs A predicted from the original formula (based on B + covariates).

To improve the existing formula with additional covariates or updated intercepts on individual covariates is a challenge. Deming and Passing-Bablok regression do not allow for covariates, just a single independent variable. Is there any sense in first fitting the new model with OLS and then calculating a recalibration slope/intercept on the predicted value with Passing-Bablok or Deming? I wonder if could still bootstrap to evaluate optimism-corrected performance.

Alternatively, does anyone have experience with Partial Least Squares or Structural Equation Modelling, which I understand can recover the Deming slope in a multivariable setting?

Thanks very much