LS MAD and LS MaxAD curves don’t have as much information as an error grid

I had seen a paper about LS MAD (locally-smoothed median absolute difference curves) before but it referenced a paper I didn’t have. But now I have come across a paper that is very clear and explains everything (1). The locally-smoothed median absolute difference curves plots the median absolute difference against reference where the median absolute difference is averaged over a small region. Glucose is used as an example and the small region is 30 mg/dL (± 15).

The problem with this approach is simple. Outliers won’t appear on the graph. So if truth is 30 mg/dL and the candidate method reports 300 mg/dL, this life threatening result won’t show up. Hence, the LS MAD curve has lost information contained in the data.

But this paper accounts for that by including a second curve called the LS MaxAD (locally-smoothed maximum absolute difference curves) where the maximum absolute difference is plotted against reference and averaged over a much smaller region of 2 mg/dL (± 1). The region chosen can be changed of course – the ones above are used by these authors.

Now, if truth is 30 mg/dL and the candidate method reports 300 mg/dL, this life threatening result will show up. But there are still problems. If truth is 200 mg/dL, the candidate method might report 50 or 350 – both 150 mg/dL errors but in different directions. But the LS MaxAD curve treats these cases as the same. However, a Parkes error grid would place the -150 error into zone C and the + 150 error into zone B. Zone C is a more serious error than zone B, so the LS MaxAD curve has lost information. And the error grid is one graph whereas LS MAD and LS MaxAD are two.

Reference

  1. Kost GJ, Tran NK and Singh H. Mapping point-of-care performance using locally-smoothed median and maximum absolute difference curves Clin Chem Lab Med 2011;49(10):1637–1646.
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