Kruskal-Wallis: how to handle ties that might not be really ties?

Question

I have data from a mass spectrometer that are precise to 6 decimal places and range from 0.1 to 10. However, some items cannot be measured by the mass spectrometer because they are "below the limit of quantitation" (BLQ). Researchers I'm working with say there are trace amounts - somewhere between zero and the limit of quantitation. They suggested imputing zero or 1/2 the limit of quantitation.

Stata has an official command for the Kruskal-Wallis test -kwallis- that lists p-values for both ties and non-ties, regardless if the dataset has ties. In my dataset, the ties come from BLQs. Since these measurements are not really ties - just unmeasurable - should I record the p-value for non-ties? Or should I consider the measurements as effectively zero, and therefore, record the p-value for ties? Or should I impute very small, unique amounts (1 x 10^-6, 2 x 10^-6, etc) that are effectively zero, but not ties?

You may be interested in reading this excellent CV thread: How small a quantity should be added to x to avoid taking the log of zero? — gung - Reinstate Monica, Mar 24 '16 at 21:56
The K-W test often is used precisely because it can handle ties arising from BLQ data: they are considered to be tied with each other and strictly less than all quantified values. Just make sure your software applies the adjustments for ties. The imputation methods mentioned in this post are known to be bad--and the second one, being arbitrary, adds extra risk if the results are to be published or used in a regulated arena (medicine, environment, engineering, etc.). — whuber, Mar 25 '16 at 21:41

score 2 · Answer 1 · answered Mar 25 '16 at 20:58

Welcome to cross validated.

First of all, "below limit of quantitation" does not mean the quantity is unmeasurable, it just means that the relative error at those quantities/concentrations is > 10 % (unless another relative error was specified - but that should then be marked very clearly).

Typically, quantities below the limit of quantitation are measurable. So I'd recommend talking to the lab: ask them to report all measured values together with the limit of quantitation and the calibration range.

The suggested imputations will IMHO not help you at all: regardless of whether those values are 0, 1/2 LOQ, or "BLQ" they are always the same and always the lowest possible value and therefore the same rank.

(As for what those imputations mean, we discussed that in detail in the question @gung linked.)

Kruskal-Wallis: how to handle ties that might not be really ties?

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