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.
- 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.