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I want to know if there is a significant difference in a blood biomarker concentration between 2 populations (population 1 = healthy individuals - population 2 = sick individuals). I need to control for the factor 'region'.

My issue is that the distribution of population 2 is not normal (data are censored following the upper detection limit by the lab device) as shown on these plots:

Distribution

With a normal distribution I would use this model in R:

m <- glm(blood.biomarker ~ status + region + status*region, data=f, family="gausian") # status = healthy or sick
summary(m)
emmeans(m, list(pairwise ~ status), adjust = "tukey") 

I am a bit confused regarding the model or the glm family I should use in this case.

I also have a similar situation but with 3 groups (1 group has a normal distribution and 2 groups have a censored distribution). How to deal with this?

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    $\begingroup$ If you have censored data then you need survival analysis. vanilla linear models will not do. $\endgroup$ Commented Feb 16, 2023 at 8:56
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    $\begingroup$ In survival analysis we assume that censoring is independent which is not the case here $\endgroup$
    – Wael
    Commented Feb 17, 2023 at 12:56

2 Answers 2

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The blood biomarker concentration measurements are censored because of the upper detection limit (at 2,500 judging from the plots).

You can use ordinal regression (aka proportional odds regression) to model the data. You can also do a Wilcoxon rank-sum test to compare populations 1 and 2 or the Kruskal-Wallis test to compare more than two populations. But with the tests you cannot include additional covariates (such as region) and in any case ordinal regression generalizes these tests.

Alternatively, you can use tobit regression.

Keep in mind that the censoring implies some loss of information. For example, you can't learn much about the upper quantiles of the blood biomaker in population 2, other than they are ≥ 2,500. Similarly, you cannot do precise inference (say a 95% two-sided confidence interval) for the population 2 mean.

Here are some relevant threads/links:

Or search for censored regression on Cross Validated.

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Possibly you might figure out some distribution and apply some censurized estimation method.

But, in this case, a single regressor (the groups), it might be easier to perform a permutation test.

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