How to handle large number of observations below LLOQ

I recently encountered a small cross-sectional retrospective study that was quite interesting.

  • 25 subjects were reported have been exposed to some agent and their serum was collect (in 1999)
  • 13 clinically healthy control subjects had their serum collected (in 2019)

There are two (very) new AKI biomarkers that are being tested on these samples (the PI/ PhD Student hoping this will lead to a publication). The overall hypothesis was to observe if the control group samples are different from the exposed group.

When the serum from the control and the exposed population were run, the control samples had >65% of the samples with values < LLOQ for both serum samples (say 50 ng/dL for AKI marker 1 and 100 ng/dL for AKI marker 2).

You can imagine with such a high number observations below the LLOQ, methods like zero-inflated Poisson, multiple imputation and others do not work very well. In general, imputing values below the LLOQ with the LLOQ value is considered too conservative. But in this case, I feel though as though the claims that can be made with the data is quite limited (small sample size, vastly different collection times between the results, etc…) so being as conservative as possible is justified.

Would be interested to hear other people’s thoughts.

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Here is an entry point …

Otherwise you can have a look at these two papers, which are often used as go-to-references:

  • Beal SL. Ways to fit a PK model with some data below the quantification limit. J Pharmacokinet Pharmacodyn. 2001;28(5):481–504. doi: 10.1023/A:1012299115260
  • Bergstrand M, Karlsson MO. Handling data below limit of quantification in mixed effect models. AAPS J. 2009;11(2):371-380. doi: 10.1208/s12248-009-9112-5

The M3 method is currently the best option for handling BQL data in NONMEM.

Hope that helps,
Best regards

@mgrafit correct me if I am wrong but as the M3 method is a PK method for modelling pharmacokinetic concentrations over time yes?
If so - does this assume a single dose exposure or can it also deal with continuous exposures or repeated exposures? This is important in the context of the OP’s question as a biomarker of kidney injury is unlikely to fit either a single dose exposure assumption or a continuous exposure.

It also occurs that this requires multiple measurements over time per individual - it’s not clear to me that the OP has measurements at more than one time point.

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@mgrafit the techniques you suggested require more data than I have (both in those above the LLOQ and timepoints). This is what makes the questions quite tricky.

Depending on the overall goal of the study (either looking for similarities between groups or differences) you can easily create the “most conservative” method by imputing values that would bring them the closest possible (the LLOQ value) or the farthest possible (zero).

@daszlosek you might find this similar thread interesting which threw up a few options:

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