below LOD's readings - throw away or 0's?

lclance

Does anyone know how iolite treats data points that are below LOD when calculating averages? For instance, if I have 20 data points that make up spot #1 on my sample and some of those data points are below LOD and some are not, does iolite ignore the below LOD spot and calculate the average of spot #1 only using the remaining data points or does it treat the below LOD point as 0 and calculate the average that way? Thanks!

Joe

lclance

Just to be clear: do you mean when calculating group averages or when calculating the average of an individual selection? I think you're asking about individual selections? In either case, I believe the answer is that iolite does not handle data below the LOD any differently (except on export where you can replace those values via the export options). I could be convinced to add options on how to handle below LOD in group averages, but I do not think it makes sense to modify or ignore individual time slices making up a selection. In my view, it is the mean of a selection that is either above or below the LOD. If you modify or ignore the time slices below the LOD then you are changing that mean. I am happy to hear other views though and if someone can give a good reason to modify the data used for a selection's mean, we'll see about adding some options for that.

All the best,

lclance

Joe so what I mean is, if iolite says that the average for spot #1 is 40ppm, and there are 20 data points that are averaged to get to that value, what does iolite software do if one of those points is below LOD? Does it ignore it and only use 19 points for the average, or treat it as a 0?

This also brings up another question... if I have 3 spots for each element for each sample and 1 of those spots is below lod (as exported from iolite) but two are not, when I'm conducting analyses, is the average of all 3 spots only taken with the two spots that did read above lod or does the third spot have to be considered and averaged in by assigning it a value of 0?

amzipkin

How to handle rounded zeroes (below detection limit observations) constitutes a discrete body of literature it turns out; part of the field of compositional data analysis. However, the various strategies for replacing negative or unreportable BDL positive values are typically discussed in the context of interpreting your output data; i.e., the average of an individual Iolite selection that yields one "row" in a data set (for however many columns of analytes were measured). If you have a BDL value for a particular analyte in such a row, then there are multiple ways to deal with it. But I am not familiar with any CoDa literature that deals with replacing or ignoring rounded zeroes at the earlier stage of data reduction. Maybe there is something in the metrology literature specifying how this should be done.

Bence

Hi lclance ,

lclance if iolite says that the average for spot #1 is 40ppm, and there are 20 data points that are averaged to get to that value, what does iolite software do if one of those points is below LOD?

iolite will include those points in the calculation of the mean (unless they are outliers, depending on your stats methods settings). I think this is valid because to determine whether a measurement is below or above LOD, you're looking at the distribution of results to see if that distribution is clearly distinct from the distribution of baseline values. Removing those values from the calculation of the distribution would skew the result and end up with an incorrect distribution.

lclance if I have 3 spots for each element for each sample and 1 of those spots is below lod (as exported from iolite) but two are not, when I'm conducting analyses, is the average of all 3 spots only taken with the two spots that did read above lod or does the third spot have to be considered and averaged in by assigning it a value of 0?

I think whether to exclude results below LOD is a decision that is normally made subsequent to processing in iolite* and perhaps should be done on a study by study basis, depending on what you're trying to achieve (and what proportion of your results are Below LOD) and what effects removing or replacing values below LOD will have. For example, if you have many Below LOD results, and replace these results with the LOD (a common approach) this may skew your statistics towards the LOD value, and give you a non-normal distribution. Similarly, choosing not to replace the values with the LOD, and using the mean and uncertainty even though it is below the LOD has other implications. For example, a very low concentration may have an uncertainty that encompasses negative values (e.g. 1± 2 ppm) and this has other implications (in reality you can't have negative concentrations even if that is implied by your results).

*Whether you include/exclude/replace below LOD values will affect the Group Stats that iolite presents in the Summary Stats tab in the Results View, as well as the stats used in some QAQC modules.

I think this is some of what @amzipkin was referring to: it's pretty involved and does require more than a blanket approach (at least that's my understanding of it).

That said, we're happy to make any changes that the community suggests, whether it be adding options for calculating group means, or something else.

Please let us know what you think.

-Bence

amzipkin

Bence I think adding options for calculating group stats could be a valuable feature, especially if multiple options were made available for the sake of comparison. Some suggestions include:

-Calculate group statistics including positive BDL values but excluding negative values
-Exclude all BDL values and only calculate based on greater than LOD values
-Replace all BDL values with zero before calculating (warning, if you try to log-transform your results later it's not going to work because the log of 0 is undefined)
-Replace all BDL values with the applicable LOD (or ₆₅% of the LOD, which is a popular, if lazy, approach known as simple substitution)

There are waaay more advanced options for rounded zero/BDL replacement that can be implemented after data reduction using CoDaPack: http://www.compositionaldata.com/codapack.php If you are going to use CoDaPack, just reduce your data in Iolite as usual, ignore the group stats. do your BDL replacement in CoDaPack, and then calculate group statistics or run your multivariate analyses afterwards.