method comparison for censored data

[#1]

Hi group,

I would like to compare thow analytical methods that are interval-censored (limit of quantitation - upper limit of quantitation). So I have observations with values of <3 (LOQ) as well as >120 (Upper LOQ). Usually Bland-Altman would do but in this case I am not sure.

Some people suggest for the lowest to substituting BQL observations with LOQ/2. But how about the upper LOQ?

There was discussion in the JMP Discovery Summit 2014 about censored data (https://community.jmp.com/kvoqx44227/attachments/kvoqx44227/discovery-2014-content/53/1/Discovery%20...) but little is explained in this document.

Any suggestions as to how to deal with these data?

Thanks beforehand for any input

Dave

[#2]

Well, to me this is a new field of research and I am learning. But the first thing that came to my mind was about these special observations. Please have a look at the following table, representing concentration measurements in the same units from two different methods. they have different LOQs:

Method A	Method B
6.8	9.8
<0.1	<0.035
1.5	<0.035
5.4	7.2
9.9	9.1
5	6
2	2.9
6.9	13.9
<0.1	<0.035
<0.1	<0.035
<0.1	0.34
<0.1	<0.035
<0.1	<0.035
<0.1	0.49
<0.1	<0.035
<0.1	<0.035
4	1.9
6.7	3
6.8	5.2
0.3	<0.035
6.3	3.5
3.2	3
>10	>15
6.7	1.2
7.8	1.5
6.5	4.1
4	2.5
5.1	1.9
3.6	3.9
1.2	0.8

If I have to discard these observations, that will be ~30% of my dataset because that will have to be pairwise for a comparative analysis. But looking closely one can see that in most of the <LOQ observations, both methods seem to agree that there is a very low concentration. And the only observation that is above the upper LOQ, it is so for both methods. So actually this is very valuable information, qualitatively. 

An initial thought can be, ok, so the observation is above 10 and 15 units respectively, so this observation has at least 10 units for one method and 15 units for the other. This is useful information, isn't it?. On the other hand, <0.035 cannot or should not be replaced by a 0.035, can it? As said before, some authors use LOQ/2 for these values, others, use 0, others discard the information.

Best,

David

[#3 · Accepted solution]

Unfortunately, Generalized Regression cannot deal with errors in both X and Y. Right now, only Bivariate can handle such a case using the Fit Orthogonal command. Method comparison involves a regression analysis of a new assay against a standard assay. Both assays have errors.