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I have observations taken with different sensitivity thresholds and minimum detection levels, i.e. Lab A is less sensitive and has a minimum detection level of .2 and Lab B is more sensitive and has a minimum detection level of .02.

Edit 2: I have taken $N$ samples and have had them processed by two different labs (for stupid political reasons). Both labs send me the results and I discover that Lab A has a minimum detection level of .2 and Lab B has a minimum detection level of .02. See example:

Each row corresponds to a unique measurement taken by either lab:

Obs | Lab A | Lab B
---------------------
 1  |  .6   |  NA
 2  |  0    |  NA
 3  |  NA   |  .53
 4  |  .2   |  NA
 5  |  NA   |  .07

Edit 2: I would like to be able to use and combine results from both labs, as if they were on the same scale. The problem is that the labs used to process the samples have very different thresholds for detection and have different sensitivity levels.

I think I would like something like:

Obs | LabA  | LabB  | NewLab
----------------------------
 1  |  .6   |  NA   |  .64
 2  |  0    |  NA   |  .13
 3  |  NA   |  .53  |  .53
 4  |  .2   |  NA   |  .21
 5  |  NA   |  .07  |  .07

What techniques are available to standardize the values such that there is not a large loss of information?

  1. Obviously, I could take the values from Lab B and replace anything less than .2 with 0 and then round them, but I want to avoid throwing away information if possible.
  2. One person suggested to add random noise to the values of Lab A, but I'm not sure of the benefit of this vs. simply imputing the missing values from Lab B.

Edit 1: There are no observations for which both Lab A and Lab B values are present, one will always be missing.

Edit 2: What can I do to get results from both labs on a similar scale?

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    $\begingroup$ Your examples all have measurements from one or the other Labs but no samples analyzed by both labs. Is that always the case? The best way to proceed will depend on that. $\endgroup$ – EdM Oct 8 '13 at 15:44
  • $\begingroup$ @EdM yes, that is precisely the problem. I am sorry I was not more clear about this. $\endgroup$ – Ellis Valentiner Oct 8 '13 at 16:24
  • $\begingroup$ Let's assume the sensitivity/detection limit problem was solvable. What is the question of interest? Are you trying to compare means across labs or something? $\endgroup$ – Glen_b Oct 8 '13 at 23:15
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    $\begingroup$ Thanks, @Glen_b. Upon looking back, I can see how unclear my question is. The question is how to combine information from Lab A and Lab B such that they are on the same scale. I've gone back to edit my original post, so hopefully that clears things up. $\endgroup$ – Ellis Valentiner Oct 9 '13 at 13:29
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Unless you have reason to believe that LabA and LabB would systematically provide different results if they ever measured the same set of samples, your data from the 2 Labs "are on the same scale" as far as you can tell from these data. The problem is that the less-sensitive LabA will be unable to report a value for some samples that would have had values reported if LabB had instead done the analysis.

Perhaps the best way to proceed would be to define a class of results called "<0.2", and include in that class all 0 readings from LabA and all readings <0.2 from LabB. How you proceed from there depends on "What is the question of interest?" as @Glen_b put it in a comment.

All will be much more useful and reliable if it is possible to cross-compare a set of samples analyzed by both Labs, because there may be systematic differences between the 2 Labs' results that you don't suspect.

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