I have multiplex protein levels from patient plasma and would like to compare expression patterns between groups. I plan to perform the following tests: (1) hierarchical clustering of correlation coefficients to identify factors with similar expression patterns, (2) Mann-Whitney tests to identify differences in individual factors, and (3) non-metric multidimensional analysis (NMDS) followed by a permutations test to identify differences in multivariate patterns of expression. I am stuck, however, at the pre-processing step in deciding how to handle values that fell below the limit of detection of my assay. These values fall into three categories: (1) below the published LOD of the kit, (2) below the standard curve but extrapolated by the machine, and (3) reported as undetectable. In essence, I am deciding how to define the LOD of my assay given the discrepancy between published and actual results. My inclination is to use the published LOD, but this eliminates a lot of potential valid low values. Does anyone have experience with this type of analysis?
Thank you in advance for your insights and advice.
The usual logic should be "choose the approach that makes more sense to you". You clearly know what you are talking about, so I'm sure you'll be able to choose a sensible approach.
But I guess my advice would be perhaps to try to run two possible scenarios (more conversative vs. more liberal) and see how different the results are. If the results are robust to your choice of pre-processing, then it probably doesn't matter what you use. If they are quite different, then you might have to re-think the conditions of your experimental approach (since it means you have way too many points below the limit of detection, or your calibration curve is not the best).
Conservative approaches:
- set all points of type 1, 2 and 3 to the LOD;
- set types 1, 2 to the LOD and type 3 to an explicit zero value.
Liberal approaches:
- set points of type 1 and 3 to the LOD, leave points 2 as they are;
- set points of type 1 to the LOD, leave points 2 as they are and assign a literal zero value to points of type 3;
- leave points of type 1 and 2 as they are and assign a literal zero value to points of type 3.
Another possibility (since you have a multivariate dataset) is to set all "dubious" values to NA and use a multiple imputation approach (see attached links). But, again... it's the same situation: the quality/robustness of the results you get from this approach is inversely related to how important those NA values are to define the global structure of the multivariate dataset.
So, anyway, if those types of points you mention are few (e.g. not more than 20% of all the values) and randomly distributed, the results you get should be fairly robust to the type of pre-processing you apply, so you should go with what makes more sense to you. If they are not (i.e. if they affect particularly some samples or some variables), it might makes some sense to trim your dataset (i.e. remove particularly problematic samples/variables) or to simply, as I said before, re-think your strategy (since it means there might be some fundamental problem with your dataset due to the experimental approach).
Good luck.
http://www.stefvanbuuren.nl/mi/MI.html
http://sites.stat.psu.edu/~jls/mifaq.html
I agree with Tome's answer, but would like to add one point.
The NMDS result will depend on the type of similarity/dissimilarity measure you use. Different similarity measures behave very differently when you have zeros in your dataset. If you choose to set your low values to a zero value, consider what this means for your particular application. Bray-Curtis distance, for example, ignores double-zeros, and assumes a zero is essentially an absence of detection, rather than a true measured zero. This may not be the case in your dataset (zeros may be actual zeros). Also, if you have MANY (read, a majority) of zeros, you may find that your objects are very similar, and have difficulty in getting the stress of your NMDS down to an acceptable level.
Good luck!
Daniel brings up an important point. Some analysis methods may have troubles with large quantities of zeros (or, in your case, large quantities of values exactly equal to the LOD). So, whenever you are "forcing" values to be exactly the LOD or zero, you have to make sure your analysis method can handle it.
Using a multiple imputation approach can prevent this mathematical problem from occurring, but, either way, in your particular case, a large number of zeros should not be expected given the nature of the dataset (absolute quantitative measurements, rather than e.g. counts). If you do have a large amount of zeros (or values which are exactly the LOD value), you should probably first try to figure out the underlying reason (e.g. are the plasma samples being diluted? Is the calibration range correct?).
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