Detection limit

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How do I deal with values below or above a detection limit?

I have measured the D-dimer value of people a number of times, and the lower limit of what is measurable is 0.17. Because of this, I have <0.17 recorded a number of times in my database. Should I now enter 0, 0.17, or a value in between for the analysis? In addition, we are doing another test: the clot-lysis test. For 3 participants, it turns out that they do not lyse, so the value is effectively infinite (it is a value expressed as the time to lysis). It currently says: 'no lysis'. Can I exclude these participants from the analysis, or should I, for example, enter the upper limit of what is still measurable?

That depends very much on which analyses you want to perform with the data. SPSS will probably not recognize a value of <0.17 as a number, and it might even remove these values in an analysis. If you are going to perform a non-parametric analysis (e.g. Kruskal Wallis or Mann-Whitney U test), then for these 'undetectable' values you can fill in any arbitrary value lower than the first value actually measured. This is because for a non-parametric test it does not matter what the value itself is — only the relative order (ranks) of the values counts. It is therefore important that everyone who scores <0.17 gets the same value.

For the second test, it again depends on the analysis. If you were to analyze the time to lysis as a 'time to event' outcome (e.g. with Kaplan Meier analysis or Cox regression), you would need to give them the last time point at which you were still certain that they had not lysed (the last time you checked this). In a second status variable, you would then enter a 1 for those who did lyse and a 0 for those who did not. If you use a non-parametric test, you can again, as in the first case, fill in an arbitrarily large (but equal) number.

If you exclude these participants from the analysis, your conclusions will only apply to participants in whom lysis occurs / in whom D-dimer is detectable. That may be a shame, since it is not generalizable to all people in whom the test is performed.

How do I deal with it if I have many values below or above a detection limit?

We measured a certain protein in 20 healthy subjects, 60 patients with disease A and 60 patients with disease B. The value of the protein was below the detection limit in 9 (45%) of the healthy subjects, 22 (37%) of the patients with disease A, and 33 (55%) of the patients with disease B. I assigned one value (assigned value) below the detection limit to all participants who were below the detection limit. I then performed a Wilcoxon signed-rank test. Is this a valid method?

If a small number of values (say, up to 5%) fall below the detection limit, you can use an assigned value. However, if the percentage of values below the detection limit increases, it becomes questionable whether your values together are still really continuous. This is because a large number of values have the same value (the 'assigned value'). The data are then no longer really continuous, but a mix of continuous and categorical. In that case, your data no longer satisfy the assumptions of the Wilcoxon signed-rank test. This is certainly the case if 46% (64/140) of your data fall below the detection limit.

One option for easily performing a test on this is to classify the Granzyme B outcome per patient as below (0) or above (1) the detection limit. You can then perform a chi-square test. However, I do wonder whether this is a good marker if almost half of the measurements fall below the detection limit. Furthermore, there is an extensive literature on this topic, including this review.

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