In R, how do you impute left-censored data that is below a limit of detection?

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This is probably a simple problem but I just can't work it out. I have a dataframe of biochemistry test results. Some of these tests like base_crp are returning values like <3 because of limits of detection. I need to impute this data before moving forward. I'd like to do this properly, so not just substituting.

I tried multLN from the zCompositions package but it seems to think that all the <3 values are negative (error says X contains negative values). There also doesn't seem to be much documentation out there- is this an obscure package?

I also looked at LODI but it wants me to specify covariates for the imputation model- is there a proper way to select these? Anyway, I picked 3 that would theoretically correlate well and used this code:

clmi.out <- clmi(formula = log(base_crp) ~ base_wcc + base_neut + base_lymph, df = all, lod = crplim, seed = 12345, n.imps = 5)

where base_crp is the variable I'm trying to fix. I replaced all the <3 with NA and inserted a new column all$crplim <- "3". However, this is just returning Error in sprintf("%s must be numeric.") : too few arguments.

Even if I can get LODI working, I'm not sure if it's the right tool. I'm only an undergraduate university student with little statistical background so I don't really understand what I'm doing- I just want something that will populate the column with numbers so I can move forward with Pearson correlations and linear regressions, etc. I would really appreciate some help with this. Thanks in advance.

missing-data correlation statistics r
1 Answers

I've done a bit of statistical modelling of CRP (C reactive protein) levels before - see this peer-reviewed paper as an example. CRP has an approximately log-normal distribution, and the median value in an unselected population across all testing indications is usually around 3.5 mg/l (most healthy people will be in that "<3mg/l" category). You probably don't want to be using an imputation model, because these are for missing data. The low CRP data is not missing. You already know it lies within a certain range, so you are losing information if you do the imputation this way.

It is reasonable to want to replace "<3" with a numeric value for regressions etc, as long as you are using this to correlate CRP with clinical findings etc and not (as Ben Norris points out) for CRP machine calibration.

I can tell you from data of over 10,000 samples of high-sensitvity CRP measurements in the study I linked above that the mean CRP in people with CRP < 3 is about 1.3, and it would be reasonable to substitute all of your "CRP < 3" measurements with 1.3 for most real-world clinical observational studies.

If you really need to have plausible numerical values on the missing CRP, you could impute the bottom half of a lognormal distribution. The following function would give you numbers that would likely be indistinguishable from real-life CRP measurements:

impute_crp <- function(n)
{
   x <- exp(rnorm(10 * n, 1.355, 1.45))
   round(x[x < 3][seq(n)], 1)
}

So you could do

impute_crp(10)
#> [1] 1.5 2.0 1.1 0.4 2.5 0.1 0.7 1.5 1.4 0.4

And

base_crp[base_crp == "<3"] <- impute_crp(length(which(base_crp == "<3"))

However, you will notice that I didn't use imputation at all in my own CRP models. Replacing the lower value with the threshold of detection was good enough for the purposes of modelling - and I'm fairly sure whether you replace the "< 3" with a lognormal tail, or all 1.3, or all 2, it will make no difference to the conclusions you are trying to draw.

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