Over 10 years ago I submitted a paper critiquing Bland Altman plots. Since the original publication of Bland Altman plots was the most cited paper ever in The Lancet, I submitted my paper with some temerity.

Briefly, the issue is this. When one is comparing two methods, Bland Altman suggest plotting the difference (Y-X) vs. the average of the two methods (Y+X)/2. Bland Altman also stated in a later paper (1) that even if the X method is a reference method (they use the term gold standard) one should still plot the difference against the average and not doing so is misguided and will lead to correlations. They attempted to prove this with formulas.

Not being so great in math, but doubting their premise, I did some simulations. The results are shown in the table below. Basically, this says that when you have two field methods you should plot the difference vs. (Y+X)/2 as Bland Altman suggest. But when you have field and a reference method, you should plot the difference vs. X. The values in the table are the correlation coefficients for Y-X vs. (Y-X)/2 and Y-X vs. X (after repeated simulations where Y is always a field method and X is either a field method or a reference method).

Case | X=X | X=(X+Y)/2 |

X=Reference method | ~0 | ~0.1 |

X=Field method | ~-0.12 | ~0 |

The paranoia

I submitted my paper as a technical brief to Clin Chem and included my simulation program as an appendix. After being told to recast the paper as a Letter, it was rejected. I submitted it to another journal (I think it was Clin Chem Lab Med) and it was also rejected. I then submitted my letter to Statistics in Medicine (2) where it was accepted.

Now in the lab medicine field, I am known by the other statisticians, and sometimes have published papers not to their liking. Regarding Statistics in Medicine, I am an unknown and lab medicine is a small part of Statistics in Medicine. So maybe, my paper was judged solely on merit or maybe I’m just paranoid.

References

- Bland JM, Altman DG. (1995) Comparing methods of measurement – why plotting difference against standard method is misleading. Lancet, 346, 1085-1087.

- Krouwer JS Why Bland-Altman plots should use X, not (Y+X)/2 when X is a reference method. Statistics in Medicine, 2008;27:778-780.