Validation and updating of a laboratory conversion formula (OLS, Passing-Bablok, Deming, Bland-Altman)

data analysis model validation
1

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

2

One easy solution is getting a bootstrap confidence interval on the mean absolute discrepency. See Biostatistics for Biomedical Research - 16  Analysis of Observer Variability and Measurement Agreement

3

Great chapter! I worked through the examples.

If there is a proportional bias, say, 20%, then discrepancies between measured and predicted values of the biomarker A will be larger in absolute terms at the higher end of the biomarker than at the lower end. It seems then that to calculate a correction factor I would need a relative measure (like the slope of a regression line). The nice thing about a regression method is the ability to decompose the proportional error (slope) and the constant error (intercept).

I wonder if I first fit via OLS, then use the predictions as the single independent variable in the Passing-Bablok regression, I would get a slope and intercept that I can use to recalibrate the OLS fit so it would generalize better. This I can also do through bootstrapping and use the mean of the bootstrapped slope and intercept. What do you think?

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4

Good question. And there might me some useful thoughts from Eugene Harris’ Clinical Chemistry book.

5

Thank you for referring me to this book. Much related fundamental material but so far nothing in my read of it that informs the issue directly.

Interestingly, I have found nothing in the literature so far that addresses this scenario. The PB-recalibrated OLS idea I think warrants some empiric evaluation.

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